Answer:
C = 1.
Step-by-step explanation:
A: 4/5 x 3/3 (1) = 4/5, Incase you didn't know, 3/3 means 1 whole because it is full. We can tell by just looking that this doesn't represent a value greater than 4/5, In fact, it's equal to 4/5.
B: 4/5 x 1/2 = 2/5 <--- By not using any calculator or math, we already know that 4/5 is greater than 2/5 and that 2/5 is less than 4/5. This is not the correct answer because it's less than 4/5.
C: 4/5 x 5/4 = 1. This could be a correct answer choice because one is greater than 4/5. If your confused, think of it like this, 5/5 is equal to one and then there's 4/5. Then you compare and contrast and see that 5/5 is greater than 4/5 so this is a correct answer choice.
D: 4/5 x 4/5 is equal to 16/25. In my opinion, I wouldn't choose this answer choice because though the numbers are bigger than 4/5, 4/5 IS equal to 16/25, so it wouldn't really be a correct answer choice.
Hope this helped!
Select the correct answer from each drop-down menu. A triangle ABC with base AC is shown. A line DE, parallel to line AC, passes through vertex B. Interior angle at vertex A is labeled 1, at vertex C is labeled 3, and at vertex B is labeled 2. The exterior opposite angles at vertex B are 4 and 5. Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°. Statement Reason Points A, B, and C form a triangle. given Let be a line passing through B and parallel to . definition of parallel lines ∠3 ≅ ∠5 and ∠1 ≅ ∠4 m∠1 = m∠4 and m∠3 = m∠5 m∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight line m∠1 + m∠2 + m∠3 = 180° substitution
The statement to prove that the sum of the interior angles of ΔABC is 180° should be completed as follows;
Statements Reasons
Points A, B, and C form a triangle. ⇒ Given
Let DE be a line passing through B and parallel to AC. ⇒ definition of parallel lines
∠3 ≅ ∠5 and ∠1 ≅ ∠4 ⇒ alternate interior angle theorem.
m∠1 = m∠4 and m∠3 = m∠5 ⇒ congruent angles have equal measures.
m∠4 + m∠2 + m∠5 = 180° ⇒ angle addition and definition of a straight line
m∠1 + m∠2 + m∠3 = 180° ⇒ substitution
What is the congruence of angles?In Mathematics, congruence of angles can be defined as a theorem which states that two (2) angles are congruent when the measure of their angles are equal.
This ultimately implies that, two (2) congruent angles would always have equal measures as depicted in triangle ABC with line DE;
m∠1 = m∠4 and m∠3 = m∠5
By applying the Alternate Interior Angles Theorem to triangle ABC and line DE, we have the following:
∠3 ≅ ∠5 and ∠1 ≅ ∠4
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NO LINKS!!
Write an equation to represent the following graphs:
a. passes through (-2, 18.75 and (1, 1, 1.2)
a-value:___________ b-value:____________
Equation: _____________________
b. passes through (0, 6) and (2, 8.64)
a-value:_____________ b-value:_____________
Equation:________________________
Answer:
[tex]\textsf{a)\;\;passes\;through\;$(-2, 18.75)$\;and\;$(1, 1.2)$}[/tex]
[tex]\textsf{$a$-value:\;\;3 \quad $b$-value: \;\;0.4}[/tex]
[tex]\textsf{Equation: \quad $y=3 (0.4)^x$}[/tex]
[tex]\textsf{b)\;\;passes\;through\;$(0, 6)$\;and\;$(2, 8.64)$}[/tex]
[tex]\textsf{$a$-value:\;\;6 \quad $b$-value: \;\;1.2}[/tex]
[tex]\textsf{Equation: \quad $y=6 (1.2)^x$}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Part (a)Given points:
(-2, 18.75)(1, 1.2)Substitute both points into the exponential function formula to create two equations:
[tex]\textsf{Equation\;1}: \quad 18.75=ab^{-2}[/tex][tex]\textsf{Equation\;2}: \quad 1.2=ab[/tex]Divide the equations to eliminate a, then solve for b:
[tex]\implies \dfrac{18.75}{1.2}=\dfrac{ab^{-2}}{ab}[/tex]
[tex]\implies15.625=\dfrac{b^{-2}}{b}[/tex]
[tex]\implies15.625=b^{-2}b^{-1}[/tex]
[tex]\implies15.625=b^{-3}[/tex]
[tex]\implies15.625=\dfrac{1}{b^{3}}[/tex]
[tex]\implies b^{3}=\dfrac{1}{15.625}[/tex]
[tex]\implies b=0.4[/tex]
Substitute the found value of b into the second equation and solve for b:
[tex]\implies 1.2=0.4a[/tex]
[tex]\implies a=3[/tex]
Therefore, the exponential equation is:
[tex]y=3 (0.4)^x[/tex]
-------------------------------------------------------------------------------------------
Part (b)Given points:
(0, 6)(2, 8.64)Substitute point (0, 6) into the exponential function formula and solve for a:
[tex]\implies 6=ab^0[/tex]
[tex]\implies 6=a(1)[/tex]
[tex]\implies a=6[/tex]
Substitute the found value of a and point (2, 8.64) into the exponential function formula and solve for b:
[tex]\implies 8.64=6b^2[/tex]
[tex]\implies b^2=\dfrac{8.64}{6}[/tex]
[tex]\implies b^2=1.44[/tex]
[tex]\implies b=\sqrt{1.44}[/tex]
[tex]\implies b=1.2[/tex]
Therefore, the exponential equation is:
[tex]y=6 (1.2)^x[/tex]
A quadrilateral with vertices (2, 5) and (-3, -4) has point symmetry about the origin.
a. What transformation maps the quadrilateral onto itself?
b. What are the other two vertices of the quadrilateral?
The transformation that maps the quadrilateral into itself is [-1 0] and [ 0 -1] and the vertices of the quadrilateral is (-3,-4),(2,5),(-2,-5),(3,4)
What is Transformation of the Quadrilaterala. A point symmetry about the origin is a transformation that maps a figure onto itself by reflecting it across the origin. This transformation is known as a central reflection or an isometry, and it is represented by the matrix (with respect to the standard basis)
[-1 0]
[ 0 -1]
b. To find the other two vertices of the quadrilateral, we can apply the transformation to the given vertices.
The transformation maps (2,5) to (-2,-5) and (-3,-4) to (3,4).
So, the other two vertices of the quadrilateral are (-2,-5) and (3,4)
So the quadrilateral will be (-3,-4),(2,5),(-2,-5),(3,4)
Note that a quadrilateral with point symmetry about the origin is called a kite.
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Dan is mailing packages. Each small package costs him $2.30 to send. Each large package costs him $3.90. How much will it cost him to send 4 small packages and 6 large packages?
Answer: $32.60
Step-by-step explanation:
(4)(2.30) + (6)(3.90)
= 32.60
Answer:
for him it send 4 small packages it will cost 9.20
For him to send 6 large packages it will cost 23.40
23.40 + 9.20 = 32.60
Step-by-step explanation:
Formula: Quanity x Cost = Total
After Totals + Costs = Exact Total
PLEASE HELP
The graph for the equation y = 2 x minus 2 is shown below.
On a coordinate plane, a line goes through points (0, negative 2) and (1, 0).
If another equation is graphed so that the system has one solution, which equation could that be?
y = 2 (x + 1)
y = 2 (x minus 1)
y = 2 (x minus 2)
y = negative 2 (x + 1)
From the graph solution of system of equations is (0, -2). Therefore, option D is the correct answer.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given equation is y=2x-2.
Graph the line using the slope and y-intercept, or two points.
Slope: 2
y-intercept: (0, -2)
Now,
A) y=2(x+1)
2x-2=2(x+1)
No solution
B) y=2(x-1)
2x-2=2(x-1)
No solution
C) y=2(x-2)
2x-2=2(x-2)
No solution
D) y=-2(x+1)
2x-2=-2(x+1)
2x-2=-2x-2
4x=0
x=0
Substitute x=0 in y=-2(x+1), we get y=-2
Therefore, option D is the correct answer.
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What is the value of mm in the equation m+6=43m+6=43?
The value of m from the given equation is 37.
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The given equation is m+6=43
We need to find the value of m from the given equation.
The group of values used to replace the unknowns in an equation to make it true is known as the solution.
To solve given equation:
Transpose 6 to RHS of the equation, we get
m=43-6
Subtract 43 and 6 we get 37
So, m=37
Therefore, the value of m from the given equation is 37.
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The APR on your credit card is current 31.2%. What is your monthly periodic rate?
If the APR on your credit card is current 31.2%. your monthly periodic rate is: 2.6%.
How to find the monthly periodic rate?Using this formula to determine the monthly periodic rate
Monthly periodic rate = APR / 12 months
Where:
APR = Annual percentage rate = 31.2% or 0.312
Let plug in the formula
Monthly periodic rate = 0.312/12
Monthly periodic rate = 0.026 or 2.6%
Therefore we can conclude that the monthly periodic rate is 2.6%.
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2. Solve for BC using Law of Sines. Round to the nearest tenth when necessary
Answer:
the answer to the question is 9.9 in the nearest tenth
A farmer has several packages of fertilizer for his new grain crop. The old packages contain 60 pounds of
long-term-growth supplement and 50 pounds of weed killer. The new packages contain 65 pounds of
long-term-growth supplement and 45 pounds of weed killer. Using past experience, the farmer estimates that he
needs 1550 pounds of long-term-growth supplement and 1200 pounds of weed killer for the fields. How many old
packages of fertilizer and how many new packages of fertilizer should he use?
Answer: This is a linear equation problem. The farmer needs 1550 pounds of long-term-growth supplement and 1200 pounds of weed killer. We can create two equations to represent this information:
Let x be the number of old packages
x(60) + y(65) = 1550 (long-term-growth supplement)
x(50) + y(45) = 1200 (weed killer)
Now we can use the system of equation to find the number of old and new packages:
x(60) + y(65) = 1550
x(50) + y(45) = 1200
We can use any method of solving system of equations like substitution, elimination or graphing to find the solution.
Example using substitution method:
x(50) + y(45) = 1200
x = (1200 - y(45)) / 50
x(60) + y(65) = 1550
(1200 - y(45)) / 50 * 60 + y(65) = 1550
We can then solve for y and then x by substituting the value of y back into the first equation
y = (1550- (1200 - y(45)) / 50 * 60 ) / 65
Finally, the number of old packages is x and the number of new packages is y.
Step-by-step explanation:
The number of old packages and the number of new packages is 15 and 10 respectively.
What are linear equations?Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true.
Given that, the farmer needs 1550 pounds of long-term-growth supplement and 1200 pounds of weed killer.
We can create two equations to represent this information:
Let,
x = the number of old packages
y = the number of new packages
The system of equations that describes the situation is:
60x + 65y = 1550
12x+13y = 310......(i)
50x + 45y = 1200
10x+9y = 240......(ii)
Solving the equations,
Multiply the eq(i) by 10 and the eq(ii) by 12, and then subtract,
22y = 220
y = 10
Put y = 10 in eq(ii)
10x+90 = 240
10x = 150
x = 15
Hence, the number of old packages and the number of new packages is 15 and 10 respectively.
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Explain in your own words:
What is a linear function?
You deposit $120 in an investment account that earns 6.4% annual interest compounded quarterly write a function that represents the balance y (in dollars) of the investment account after t years y= ? What is the balance of the account after 6 years
Answer:1200
Step-by-step explanation:
Answer:
[tex]\textsf{Function:} \quad y=120\left(1.016\right)^{4t}[/tex]
The balance of the account after 6 years is $175.64 (nearest cent).
Step-by-step explanation:
To write a function that represents the balance y (in dollars) of the investment account after t years, substitute the given values into the compound interest formula.
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
A = yP = $120r = 6.4% = 0.064n = 4 (quarterly)t = t yearsSubstitute these values into the formula:
[tex]\implies y=120\left(1+\dfrac{0.064}{4}\right)^{4t}[/tex]
[tex]\implies y=120\left(1+0.016\right)^{4t}[/tex]
[tex]\implies y=120\left(1.016\right)^{4t}[/tex]
To calculate the balance of the account after 6 years, substitute t = 6 into the function:
[tex]\implies y=120\left(1.016\right)^{4 \cdot 6}[/tex]
[tex]\implies y=120\left(1.016\right)^{24}[/tex]
[tex]\implies y=120\left(1.46368961...\right)^{24}[/tex]
[tex]\implies y=175.642753...[/tex]
Therefore, the balance of the account after 6 years is $175.64 (nearest cent).
Juan has a blueprint of a professional basketball court. The scale is 1 inch to 4 feet. If the
professional basketball court is 50 feet wide, how wide is the drawing of the court on the blueprint?
Use the questions below to help you solve.
a. Write the scale as a ratio.
b. Use your answer from part (a) and the information in the problem to write a scale
proportion.
c. Solve the scale proportion you wrote in part (b) to determine the width of the
professional basketball court in the blueprint. Show all your work.
Answer:
a. The scale is 1 inch to 4 feet. This can be written as a ratio: 1:4
b. Using the ratio from part a, the scale proportion is: 1/4 = width of the drawing/50 feet
c. To find the width of the drawing, we will use cross multiplication and solving for the width, we have 1/4 * 50 feet = width of the drawing/50 feet = 1* 50/4 =12.5 inches.
The width of the drawing on the blueprint is 12.5 inches.
Step-by-step explanation:
The answer to each part is mentioned below.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Juan has a blueprint of a professional basketball court. The scale is 1 inch to 4 feet and the professional basketball court is 50 feet wide.
After the dilation, the relation between final and initial dimensions of the image is -
y = Kx
where -
{K} is a dimensionless quantity called scale factor.
{a} -
the scale as a ratio can be written as -
K = (1 inch/4 feet) = (1/12 feet/4 feet) = (1/48) = 1 : 48
K = 1 : 48
{b} -
We can write the scale proportion as -
(1/48) = (x/50)
{c} -
The width of the professional basketball court in the blueprint is -
x = 50/48
x = 1.05 feet
Therefore, the answer to each part is mentioned above.
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QUIZ:
Composite Figures
What is the area of this polygon
Area of given polygon is 39 unit².
In arithmetic, what is a polygon?As seen above, a polygon is a geometric shape that is described as "consisting of a number of points (called vertices) and an equal number of line segments (called sides), namely a cyclically ordered set of points in a plane, with no three successive points collinear, as well as the line segments joining the points."
A polygon has flat surfaces throughout. A polygon must have three sides at a minimum. Only at its terminal must each side of a line segment cross another line segment. We can quickly determine the geometry of a polygon based on how many sides it has.
For the given polygon,
Below is the given image of partition,
We will calculate the area by dividing the figure in different portions,
triangle and rectangle,
Area of triangle = 1/2 × Base × Height
Base = 6 units
Height = 3 units
= 1/2 × 6 × 3 = 9 unit²
Area of rectangle = length × breadth
length = 5 units
breadth = 6 units
Area = 5 × 6 = 30 unit²
Total area = area of triangle + area of rectangle = 9 + 30 = 39 unit²
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a warehouse 40 yards long, and 25 yards wide, and it is piled with cartons to a height of 3 yards. what is the area of the warehouse floor? what is the total volume of the cartons? (assume there is no space between cartons.)
The area of the warehouse floor is 1000 square yards. This can be calculated using the formula A = lw, where A is the area, l is the length, and w is the width. Therefore, in this case A = 40 x 25 = 1000.
What is the calculated ?The calculated answer is the result of a mathematical equation or calculation. Calculations can range from simple addition and subtraction to complex integrations and derivatives. By using mathematical formulas, equations, and algorithms, the calculated answer can be used to solve problems and make predictions. Calculated answers can be used in fields such as science, engineering, economics, and finance. Calculated answers can also be used to make decisions about investments, projects, and other business decisions. In addition, calculated answers can be used to analyze data and make decisions based on the results.
The area of the warehouse floor is 1000 square yards. This can be calculated using the formula A = lw, where A is the area, l is the length, and w is the width. Therefore, in this case A = 40 x 25 = 1000.
The total volume of the cartons is 12500 cubic yards. This can be calculated using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height. Therefore, in this case V = 40 x 25 x 3 = 12500.
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Round the answer to the correct number of significant figures.
28.23
3.49
+ 5.3 = 13.389
Answer:
13.389 = 13.4
Which linear equation represents the graph? Responses A y = 9x − 9y = 9x − 9 B y = −9x + 9y = −9x + 9 C y = 9x + 9y = 9x + 9 D y = −9x − 9
The linear equation y = -9x + 9 represents the line given in the graph. Thus, option D is correct.
What is linear equation?Linearity is a property of equations with highest degree of 1. There isn't a single variable in it with an exponent greater than 1. The name "linear equation" comes from the fact that a linear equation always results in a straight line on a graph.
Linear equations in one variable and two variables are common in mathematics.
Two of lines' points on the plane are (1, 0)and (0, 9)
Lets put the value in the slope formula
y₂ - y₁ = m(x₂ - x₁)
9 - 0 = m(0 - 1)
9 = -m
m = -9
As we have the slope of the line lets put one of the values to get slope intercept form
y - y₁ = m(x - x₁)
y - 9 = -9(x - 0)
y = -9x + 9
Thus, The linear equation y = -9x + 9 represents the line given in the graph. Thus, option D is correct.
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For a goodness-of-fit test, the frequencies obtained from the performance of an experiment are the:
i) subjective frequencies
ii) observed frequencies
iii) expected frequencies
iv) objective frequencies
Option B : observed frequencies are the frequencies obtained from the performance of an experiment for a goodness-of-fit test .
The frequency, or outcomes, that are gathered during an experiment are known as observed frequencies. This is frequently the collection of data that is documented in mathematics. The distinction between an observed frequency and an expected frequency is described on the display poster. Counts derived from experimental data are known as observed frequencies. In other words, you really take measurements when the data is being collected. For instance, you might roll a die ten times and then tally the number of times each number appears. Following the experiment, the count is made. The observed frequencies are these numbers, and the sign for an observed frequency is O. There are k entries in the table. There are n total observed frequencies. Calculating predicted frequencies involves multiplying the probability.
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Gary found 72 shells and 40 coins at the beach. he wants to give them to some of his friends. Each friend will receive the same number of shells and the same number of coins. What is the greatest number of friends Gary can give shells and coins to? How many shells will each friend receive? How many coins? Select your answers from the drop-down lists.
The greatest number of friends Gary can give shells and coins to is ___
friends. Each friend will receive ___
shells and ___
coins.
The greatest number of friends Gary can give shells and coins to is 8
friends. Each friend will receive 9 shells and 5 coins.
How to solve for the number of friendsWe have to find the factors of 72
72/ 2 = 36 / 2 = 18/ 2 = 9/ 3 = 3
72 = 2 * 2* 2 * 3
We would find the factors of 40
40 / 2 = 20 / 2 = 10 / 2 = 5
40 = 2 * 2 * 2 * 5
Then we would find the common factors they have
2 * 2 * 2 = 8
This is the number of friends that Gary can have
Then 72 / 8 = 9
40 / 8 = 5
The greatest number of friends Gary can give shells and coins to is 8
friends. Each friend will receive 9 shells and 5 coins.
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Find the measures of all of the angles.
The measure of all the angles are given as follows;
<XVR = 125° [Sum of angle on a straight line]
<RVS = 55° [Angle on a straight line or Opposite Angles]
< WVS = 125° [Opposite Angles]
< RST = 125° [Angle on a straight line] Note that ΔRVS is an equilateral
< RSV = 55° [Equilateral Triangle]
<VSU = 125° [VSU and RST are Opposite angles]
<UST = 55° [Opposite Angles]
<TUS = 54° [Sum of angles in a Triangle.
What is the sum of Angles on a Straight Line?A straight line's angles add up to 180°. Angles may also be calculated using this information.
Opposite angles are non-adjacent angles created by two intersecting lines, which is also a mathematical truth.
Angles that are opposite each other are congruent (equal in measure). They are also known as vertically opposing angles and are occasionally referred to as vertical ones. Because they are vertically opposing' at the same vertex, the two angles labeled 'a' are equal.
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describe three different methods that you could use to prove that quadrilateral abcd is a parallelogram.
Quadrilateral ABCD is a Parallelogram can be proved by many postulates. The most important three Postulates are:-
1. The two opposite side pairs are parallel.
2. The two opposing side pairs are both congruent.
3. One set of opposite sides is parallel and congruent.
In geometry, you'll frequently be required to provide evidence that a particular shape actually exists. For instance, you can be asked to demonstrate that a quadrilateral is a parallelogram after being shown it. Do not forget that a quadrilateral is a flat, four-sided shape. A quadrilateral with two sets of opposing, parallel sides is referred to as a parallelogram.
A quadrilateral ABCD is a Parallelogram
The five approaches to demonstrate that a quadrilateral is a parallelogram will be discussed first, though. You'll employ one of these five methods, depending on the data you've got to work with.
1. Establish the parallelism of the two pairs of opposite sides.
This one is just the opposite of what a parallelogram is. If you can demonstrate that the quadrilateral satisfies the requirements for a parallelogram, then it is one.
2. Establish the congruence of both pairs of opposite sides.
There will always be two opposite pairs of parallel sides in a quadrilateral if both pairs of opposite sides are congruent. They measure similarly when objects are congruent.
3. Establish that one pair of opposing sides is parallel and congruent.
The previous procedure and this one are quite comparable. It simply presents the evidence in a different manner. Actually, four toothpicks will work for this experiment. Try it by aligning two toothpicks in a parallel but opposing direction. Now join these two toothpicks to the other two toothpicks at both ends. You'll see that your second pair of toothpicks will always be parallel, regardless of how you arrange your first set.
Hence, Quadrilateral establish parallelogram.
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A ball is dropped from the top of a building 74 ft tall, How long will it take to fall to ground level?
To determine how long it will take for a ball to fall from the top of a building 74 ft tall to ground level, we can use the formula:
t = √(2*d/g)
where t is the time in seconds, d is the distance in feet, and g is the acceleration due to gravity (approximately 32.2 ft/s^2 on Earth).
Plugging in the values:
t = √(2*74 / 32.2)
t ≈ 3.63 seconds
So the ball will take approximately 3.63 seconds to fall to the ground level.
It's important to note that this calculation assumes that there's no air resistance and the ball is dropped vertically. In reality, air resistance and the ball's trajectory would affect the time it takes to fall.
Fuel consumption is commonly measured in miles per gallon (mi/gal). An agency designed new fuel consumption tests to be used starting with 2008 car models. Listed below are randomly selected amounts by which the measured MPG ratings decreased because of the new 2008 standards. Find the range, variance, and standard deviation for the sample data. Is the decrease of 4 mi/gal unusual? Why or why not? 2 1 2 1 3 3 4 2 2 2 2 2 2 2 2 3 2 2 2 2 2 The range of the sample data is mi/gal. (Type an integer or a decimal.) The variance of the sample data is . (Round to one decimal place as needed.) mi/gal. The standard deviation of the sample data is mi/gal.
(Round to one decimal place as needed.) Is the largest decrease, 4 mi/gal, unusual? Why or why not? O A. The decrease of 4 mi/gal is unusual because the smallest value in a data set is usually an outlier. O B. The decrease of 4 mi/gal is unusual because it is more than two standard deviations from the mean. O C. The decrease of 4 mi/gal is not unusual because the sample is a simple random sample, in which no values are considered unusual. O D. The decrease of 4 mi/gal is not unusual because it is within two standard deviations of the mean.
A. The range of the sample data is 4 mi/gal.
B. The variance of the sample data is 0.98 mi/gal.
C. The standard deviation of the sample data is 0.99 mi/gal.
D. The decrease of 4 mi/gal is not unusual because it is within two standard deviations of the mean (4 mi/gal is less than 2*0.99 mi/gal).
A. To find the range of the sample data, we need to find the difference between the largest and smallest values in the sample. In this case, the largest value is 4 mi/gal and the smallest value is 1 mi/gal. The range is the difference between these two values, which is 4 mi/gal - 1 mi/gal = 3 mi/gal.
B. To find the variance of the sample data, we first need to find the mean of the sample. The mean is calculated by summing all the values in the sample and dividing by the number of values in the sample. In this case, the mean is [tex]\frac{(2+1+2+1+3+3+4+2+2+2+2+2+2+2+2+3+2+2+2+2+2)}{20} = 2.05[/tex].
Next, we need to subtract the mean from each value in the sample, square the result, and divide it by the number of values in the sample. The variance is
[tex][(2-2.05)^2 + (1-2.05)^2 + (2-2.05)^2 + (1-2.05)^2 + (3-2.05)^2 + (3-2.05)^2 + (4-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (3-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2 + (2-2.05)^2] = 19.6[/tex]
[tex]\frac{19.6}{20} = 0.98 mi/gal.[/tex]
C. To find the standard deviation, we take the square root of the variance. The standard deviation is [tex]\sqrt{0.98} = 0.99 mi/gal[/tex]
D. The standard deviation measures the amount of variation or dispersion in the data. The standard deviation is used to determine how much the values in a sample differ from the mean. If a value is more than two standard deviations away from the mean, it is considered unusual. In this case, the value of 4 mi/gal is less than 2*0.99 mi/gal = 1.98 mi/gal away from the mean, so it is not considered unusual.
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Improper fraction 2x2/3
You want to calculate the height of a tree in your yard. You stand 25 feet from the base of the tree and with a special instrument, you measure the angle of elevation from where you are on the ground to the top of the tree. You find that the angle of elevation is about 52°. What is the approximate height of the tree?
Between the horizontal line and the line of sight, an angle called the angle of elevation is created. When the line of sight is upward from the horizontal line, an angle of elevation is created.
What is angle of elevation?The angle of elevation is defined in mathematics as "the angle created between the horizontal line and the line of sight when an observer looks upwards." It's always higher than the spectator, usually at a greater height. Angles of depression are created when a person looks downward, and they are the polar opposite of angles of elevation. While studying heights and distances in trigonometry, it is crucial to understand the angle of elevation and depression. Angle, horizontal line, and line of sight are the three general terms used to describe the angle of elevation.
To calculate the height of a tree using trigonometry, you would use the tangent function. Specifically, you would use the tangent of the angle of elevation (52° in this case) and the distance from the base of the tree to where you are standing (25 feet in this case).
The formula is:
height = distance * tangent(angle of elevation)
So, the height of the tree is approximately:
25 * tangent(52) = 25 * 1.19 = 29.75 feet
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which equations are equivalent to -2y+3/2x+7/4
a) -1/2xy+7/4
b) 3/2x-2(y+7/2)
c) -1/4y+3/2 (y+x)
d-2y+1/2(3x+7/2)
e) 1/4 (-8y+6x+7)
The equations equivalent to the given equation are -2y+1/2(3x+7/2) and 1/4(-8y+6x+7). The solution has been obtained by using the simplification method.
What is simplification?
Simplifying in mathematics refers to the process of working with and understanding an equation in a way that makes it more understandable or transparent. The process of grouping similar terms together so that the problem can no longer be solved further is known as simplification.
We are given -2y + 3/2x + 7/4
In order to find which expression is equivalent to the given, we need to simplify the expressions.
a. -1/2xy+7/4
This is not the same expression as given.
b. 3/2x-2(y+7/2)
⇒ 3/2x - 2y - 7
This is not the same expression as given.
c. -1/4y+3/2 (y+x)
⇒ -1/4y + 3y/2 + 3x/2
This is not the same expression as given.
d. -2y+1/2(3x+7/2)
⇒ -2y + 3x/2 + 7/4
This is the same expression as given.
e. 1/4 (-8y+6x+7)
⇒-2y + 3x/2 + 7/4
This is the same expression as given.
Hence, the equations equivalent to the given equation are -2y+1/2(3x+7/2) and 1/4(-8y+6x+7).
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LESSON 7 SESSION 2
Develop Using the Standard Algorithm
to Add and Subtract Decimals
Read and try to solve the problem below.
How much greater is the mass of a dollar coin than the combined
masses of a dime and a quarter?
TRY
IT
put
Math Toolkit base-ten blocks, base-ten grid paper,
grid paper, number lines, place-value charts
Mass of U.S. Coins
Periny: 2.5 g
Dime: 2.268 g
Nicket: 5. g
Quarter: 5.67 g
Half-Dollar: 11.34 g Dollar 8.1 g
Exploring Base Ten Blocks : Measure 1 x 1 x 1 cm with units of "ones."
Measure 1 cm by 1 cm by 10 cm for each rod, where tens are the unit of length.
Hundred times flats Count 1 cm by 10 cm by 10 cm.
Cubes are thousands; the dimensions are 10 cm x 10 cm x 10 cm.
How do you solve a base ten block?Our base ten number system is spatially represented by Base Ten Blocks. The four separate concrete representations known as "Base Ten Blocks" are generally used in middle school arithmetic after being introduced in elementary school.
Measure 1 x 1 x 1 cm with units of "ones."
Measure 1 cm by 1 cm by 10 cm for each rod, where tens are the unit of length.
Hundred times flats Count 1 cm by 10 cm by 10 cm.
Cubes are thousands; the dimensions are 10 cm x 10 cm x 10 cm.
When names are given based on shape rather than value, it is possible to rename the pieces as needed. For instance, a class learning decimals can use the flat to represent a unit and then determine the value of the other components.
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serious reply for finding the function to f(x+1)=3x squared +4x-2
The numeric value of the function f(x) = 3x² + 4x - 2 at x = x + 1 is obtained as follows:
f(x + 1) = 3x² + 10x + 3.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
f(x) = 3x² + 4x - 2
The numeric value at x = x + 1 is found replacing both instances of x by x + 1, hence:
f(x + 1) = 3(x + 1)² + 4(x + 1) - 2
f(x + 1) = 3(x² + 2x + 1) + 4x + 4 - 4
f(x + 1) = 3x² + 6x + 3 + 4x
f(x + 1) = 3x² + 10x + 3.
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1.On the accompanying grid, sketch the graphs of y = 2^x and 3y = 7x + 3 over the interval
-3 ≤ x ≤ 4. Identify and state the coordinates of all points of intersection.
As a result, the coordinates of the equations y = 2x and 3y = 7x + 3 throughout the range of -3 ≤ x ≤ 4 are (-3,-6) and (-3,8), respectively.
what are coordinates ?When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a two-dimensional plane requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact locations. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the distance from top to bottom. In (12.5), for example, there are 12 units below and 5 above.
given
y = 2^x and 3y = 7x + 3 over the interval -3 ≤ x ≤ 4.
as x = -3
y = 2^x= 2^-3 = -8
y = 8
3y = 7x+3
3y= 7*-3 +3
3y = -21 + 3
y = -6
As a result, the coordinates of the equations y = 2x and 3y = 7x + 3 throughout the range of -3 ≤ x ≤ 4 are (-3,-6) and (-3,8), respectively.
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Please help I’m struggling
Answer:
B
Step-by-step explanation:
Each floor, the rent is 3% more than the previous floor, so we multiply by 1.03.
Since we do this 17 times, the answer is [tex]1420 \cdot 1.03^{17}[/tex].
Answer: B
Step-by-step explanation:
You just need to find the formula, replace 17 with variable x and $2347.04 with y and graph. It will give you the right answer.
i need help with this