Kimberley owns 55 pencils.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given: Kimberly owns two less than three times the number of mechanical pencils Jacqueline owns. Julia owns three less mechanical pencils than Jacqueline. Together, the three collectors own a total of 100 mechanical pencils. Let Jacqueline own x pencils then Kimberley owns 3x-2 and Julia owns x-3
Thus 3x-2+ x-3+x=100
5x=95
x=19
Hence, Kimberley owns 55 pencils.
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Complete the following truth table by filling in the blanks with T or F as appropriate.
The required, complete truth table has been shown, where (P→ Q) and (¬Q → ¬P) are logically equivalent.
What is a truth table?A truth table is a table used in logic and mathematics to show the truth or falsehood of propositional statements or logical expressions. It lists all the possible combinations of the truth values of the variables in the expression and the resulting truth value of the entire expression for each combination.
Here,
Using the fact to construct a truth table,
For the implication P → Q only T → F = F or else T,
And ¬T = F, ¬F = T
The complete table has been shown in the image attached below,
In the table column for P → Q and (¬Q → ¬P) have the same truth values.
Thus, (P→ Q) and (¬Q → ¬P) are logically equivalent.
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Alexander is a stockbroker. He earns 11% commission each week. Last week, he sold $7,500 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011?
Answer:
Alexander made $825 in commission last week. If he averaged the same amount each week, he would have made $42,900 in commission in 2011.
Step-by-step explanation:
$7,500 x 0.11 = $825 (Last Week's Commission)
$825 x 52 (weeks in a year) = $42,900 (2011 Commission)
Use the appropriate formula to find the value of the annuity . Find the interest Periodic Deposit 110 at the end of every six months Rate Time 4.5 % compounded semiannually 25 years
The value of the $110 annuity given annual compounding is $9983.338.
What is the value of the annuity?The value of the annuity can be determining using this formula: amount deposited x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
n = number of years
r = interest rate
here, we have,
Periodic Deposit 110 at the end of every six months Rate Time 4.5 % compounded semiannually 25 years
now,
r=4.5%/2
=0.0225
n= 25*2 = 50
using the formula, we get,
the value of the annuity =$9983.338
hence, The value of the $110 annuity given annual compounding is $9983.338.
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Solve the exponential equation for
5^6x+5/125^3x−1=5^−5x+2
The solution of the expression is,
⇒ x = 2
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ [tex]\frac{5^{6x + 5} }{125^{3x - 1} } = 5^{-5x + 2}[/tex]
Now, Solve the equation by rule of exponent as;
⇒ [tex]\frac{5^{6x + 5} }{5^{5 (3x - 1)} } = 5^{-5x + 2}[/tex]
⇒ [tex]\frac{5^{6x + 5} }{5^{15x - 5} } = 5^{-5x + 2}[/tex]
⇒ [tex]{5^{6x + 5} } * {5^{- (15x - 5)} } = 5^{-5x + 2}[/tex]
⇒ [tex]{5^{6x + 5} } * {5^{-15x + 5} } = 5^{-5x + 2}[/tex]
⇒ [tex]{5^{6x + 5- 15 x+ 5} }= 5^{-5x + 2}[/tex]
⇒ [tex]{5^{-9x + 10} } = 5^{-5x + 2}[/tex]
By comparing, we get;
⇒ - 9x + 10 = - 5x + 2
⇒ 10 - 2 = 9x - 5x
⇒ 8 = 4x
⇒ x = 8/4
⇒ x = 2
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if the speed of a boat in still water is 13 mph
A what is the speed going against a current with a rate of x mph ?
B what is it’s speed going with a current with a rate of x mph?
Answer:
A. The speed of the boat going against a current with a rate of x mph is (13 - x) mph.
B. The speed of the boat going with a current with a rate of x mph is (13 + x) mph.
Step-by-step explanation:
What two numbers multiply to 5 and add to -10
Ran ordered 3 large pizzas for a party. At the end of
Answer:
Step-by-step explanation: At the end of what? I need the rest of the question in order to help you.
The problem is I’m the attached image below
Therefore , the solution of the given problem of triangle comes out to be triangle FUN and CAR is congruent thus it is proved that m∠HAT = 50°
Describe the triangle.A triangle is a polygon since it has three parts and three vertices. It is a fundamental geometric figure. A triangle with the corners A, B, & C is referred to as triangle ABC. A single planar and triangle are found in geometric shapes when four elements are not collinear. Due of its three sides and top right corner, triangles are classified as polygons.
Here.
Triangle FUN is congruent with CAR , hence
then,
∠F equals ∠C
∠U is equivalent to ∠A.
∠N equals ∠ R
and,
FN is equivalent to line CR
NU is identical to line RA
UF is equivalent to line AC
Cpct was used to resolve this.
congruent triangle's matching triangle segments
Therefore , the solution of the given problem of triangle comes out to be FUN is congruent with CAR .
For
m∠HAT = 50°
Thus triangle FUN and CAR is congruent thus it is proved that
m∠HAT = 50°
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carly walks 20 ft./s at this rate how many minutes will take Carly to walk a mile if there are 5280 feet in 1 mile
Carly can walk 1 mile in 264 seconds.
What is Unit Rate?Unit rate is the amount of one quantity for a unit amount of the other quantity.
In other words it compares 1 unit of some quantity with different amount of another quantity.
Unit rate of Carly is given.
Unit rate of an object in terms of distance covered and time taken is actually the speed of the object.
The formula for speed is,
Speed = Distance / Time
Speed = 20 feet per second
Distance = 1 mile = 5280 feet
Time taken be t.
20 = 5280 / t
t = 5280 / 20
t = 264 seconds
Hence it will take 264 seconds for Carly to walk a mile.
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what are the coorindates of point A
Point A has coordinates (x1, y1). The x-coordinate, x1, is the horizontal distance from the origin, while the y-coordinate, y1, is the vertical distance from the origin.
What are coordinates?Coordinates in math refer to a pair of numbers that indicate the position of a point on a two-dimensional graph or in a three-dimensional space. The two numbers are usually referred to as the x-coordinate (or abscissa) and the y-coordinate (or ordinate). In three-dimensional space, the third number is referred to as the z-coordinate (or applicate). A point located at (3, 4) on a two-dimensional graph would be located 3 units along the x-axis and 4 units along the y-axis. Similarly, a point located at (3, 4, 5) in three-dimensional space would be located 3 units along the x-axis, 4 units along the y-axis, and 5 units along the z-axis.
Both coordinates indicate the exact location of Point A in a coordinate system. For example, if Point A is located at (2, 4), it means that the x-coordinate of Point A is 2, which is 2 units away from the origin in a horizontal direction, and the y-coordinate of Point A is 4, which is 4 units away from the origin in a vertical direction. The origin is usually located at (0, 0) in a coordinate system.
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For the students collecting the data, it would be [ Select ] ["very difficult", "fairly easy"] to select a random sample from this population.
For the students collecting the data, it would be very difficult to select a random sample from this population.
The term Simple random sample, also known as an SRS, which is also a subset of people chosen at random from a larger group of people, all with the probability which is same. In this method samples are chosen at random. Each and every subset of k people in SRS has the equal opportunity of getting selected for the sample just like some other subset of k people.
An objective sampling strategy is a straightforward random sample. Simple random sampling is the most basic category of sampling that can be used in combination with other, more sophisticated sampling techniques.
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NEED HELP, I HAVE TO GET THESE IN BEFORE TOMORROW
The equation of the circle in the standard form is (x - 2)²+(y + 2)² = 34.
What is standard form?The fundamental form of an equation is the linear equation in standard form. Below is shown the standard form of a linear equation with two variables and more than two variables.
Here, a, b, (A)1, (A)2, (A)3,........ (A)n are referred to as the coefficients, and x, y, or (x)1, (x)2, (x)3,.... represent the variables. Constants are the numbers that appear after the equals to sign.
ax + by = c
A quadratic equation's standard form is a second-degree equation with a variable, coefficients, and constant term. X is a single variable of degree 2 in this situation. A quadratic equation has the following standard form.
ax² + bx + c = 0
We have given that:
[tex]$\left(x-x_0\right)^2+\left(y-y_0\right)^2=r^2$[/tex]
Lets solve
[tex]$P_0(2,-1)$[/tex]
[tex]$d^2=10^2+6^2$[/tex]
[tex]$r=\frac{d}{2}=5.831$[/tex]
[tex]$r^2=34$[/tex]
[tex]$(x-2)^2+(y+1)^2=34$[/tex]
Thus, the equation of the circle in the standard form is (x - 2)²+(y + 2)² = 34.
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the vertical spread of the data points about the regression line is measured by the y-intercept.
The standard error of the estimate measures the vertical spread of the data points around the regression line.
The standard error of the estimate, a measurement of the average deviation of errors, is the difference between the y-values predicted by the multiple regression model and the y-values in the sample. This illustrates the precision of the regression model as well as the range of variation surrounding the estimated regression line.
The standard error of the estimate can be used to produce a confidence interval for the actual regression coefficient. The standard error is calculated by multiplying the standard deviation by the square root of the sample size. The standard deviation of the errors/residuals is the standard error of the estimate for the regression model.
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In the winter the ratio of daylight to darkness on a particular day is 5:7. How many hours of daylight were there?
There were 10 hours of daylight on that particular day
Total number of hours in a day= 24
If the ratio of daylight to darkness is 5:7, the number of hours of daylight is 5x and that of darkness is 7x
Then, 5x + 7x= 24
=> 12x = 24
=> x= 2
Thus, 5x= 5×2= 10
Therefore, there were 10 hours of daylight on that particular day
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1. 14 m find the area of each circle
could some one please answer this for me, thanks
Answer:
x = 2
Step-by-step explanation:
The triangle shown in the image is a right triangle.
The missing side, x, is the leg and its length is equal to other leg because this is also an isosceles triangle. So this triangle is special 45°-45°-90° and the side lengths are represented with a-a-a√2 respectively. The length of hypotenuse is equal to √8 so:a√2 = √8
Divide both sides by √2a = √4
Remember we said a represents legs, in the image x represents the legs so the answer is:
x = √4 and √4 = 2, therefore the answer is 2.
How do you use the distributive property to remove the parentheses. From 5(10+w)
1000
Step-by-step explanation:
5000
uhh can sb help it’s already over due.
The complete statement is ∠M = 40°
Similar triangles:If the only difference between two triangles is their size (and perhaps the need to rotate or flip one), but not their shape, then they are similar.
In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≅"
If ΔABC and ΔXYZ are similar triangles then
∠A = ∠X, ∠B = ∠Y, and ∠C = ∠Z
Here we have
ΔXYZ and ΔLMN are similar triangles
=> ∠X = ∠L, ∠Y = ∠M, and ∠Z = ∠N
From the given figure,
=> ∠X = ∠L = 25°
=> ∠Y = ∠N = 115°
=> ∠Z = ∠M
From ΔLMN
=> ∠L + ∠M + ∠N = 180°
=> 25° + ∠M +115° = 180°
=> ∠M = 180°- 115° - 25°
=> ∠M = 40°
Therefore,
The complete statement is ∠M = 40°
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The coordinates of the vertices of ADOG are D (2,3,), O(2,-2), and G(-3, -2). Determine whether ACAT is a
right triangle and support your decision with evidence. Show all work.
Answer:
Consolidation
Step-by-step explanation:
Maths is a great way to get a job and then you can give it a try for a few days and then again you can give it a try for a few days and then again you can give it a try for a few days
The coordinates of the vertices of quadrilateral LOVE are L (-2, -1), O (2, 1), V (5, 0), and E (-1, -3). Grace
states that quadrilateral LOVE is a parallelogram. Is Grace correct? Support your answer and show all your
work.
Answer:
Corp donates
Step-by-step explanation:
Consolidation is a great way to get a job and then she can u me a little more about it and let me know if
The two polygons are similar?
Answer:
using the knowledge from the chapter similarity we can find how the two triangles are similar
Step-by-step explanation:
Triangle ABC and DEF
A B=DE
AC=DF
BC=EF
AB/DE=AC/DF=BC=EF
2) For which values of S and T does the following equation have infinitely many solutions?
Sx+81-24x+ T
a) S=24 and T=81
b) S = -24 and T = -81.
(c) S = -24 and T=81
d) S=24 and T=-81
The evaluation of the equation in the question for the number of solutions is as follows;
2) The values of S and T for which the equation Sx + 81 = -24x + T have infinitely many solutions is S = 24 and T = -81
c. S = 24 and T = -81
What is an equation?An equation is a statement of equivalence of two expressions.
The specified equation is presented as follows;
S·x + 81 = -24·x + T
The equation will have infinitely many solutions when both sides of the equation refer to the the sam line
The power of x on both sides of the equation is one, therefore, both expressions on the left and right side of the equation refer to linear relationships
The graph of two lines are the same if they have the same slope and the same y-intercept.
The slope of the expression on the left = S
The y-intercept of the expression on the left = 81
The slope of the expression on the right = -24
The y-intercept of the expression on the right = T
When both sides refer to the same line, we get;
S = -24, and T = 81
Therefore, both sides of the equation refers to the same line and therefore have infinitely many solutions when S = -24 and T = 81.
The correct option is option c
(c) S = -24 and T = 81
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Determine whether or not the equation is linear or exponential and explain how you know.
y= 4(5^x)
Last summer, the Abrams family had a 30-gallon baby pool that they could fill in just 2 minutes. This summer, they purchased a larger kiddie pool that holds 150 gallons of water.
If the Abrams fill the larger pool at the same rate, how long will it take to fill it?
The answer is 10 minutes
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Abrams family had a 30-gallon baby pool that they could fill in just 2 minutes. Thus speed = 30/2
=15 gallons per day
Thus to fill 150 gallons the time required is 150/15=10 mins
Hence, The answer is 10 minutes
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NO LINKS!!!!
1. A savings account starts with $720 and earns an annual rate of 4.8%. Write an equation and find the amount of money in the account for 12 years.
Equation:
Solution
2. Bacteria can multiply at an alarming rate when each bacteria splits into two new cells , thus doubling. If we start with only one bacteria, which can double, how many bacteria will we have be the end of 3 days?
Equation:
Solution:
Answer:
[tex]\textsf{1.\;\;Equation:\quad$A=720(1.048)^{t}$}[/tex]
[tex]\textsf{Solution:\quad$\$1263.77$}[/tex]
[tex]\textsf{2.\;\;Equation:\quad$y=2^x$}[/tex]
[tex]\textsf{Solution:\quad$8$}[/tex]
Step-by-step explanation:
Question 1Assuming the account earns annual compound interest.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
P = $720r = 4.8% = 0.048Substitute the given values or P and r into the annual compound interest formula to create an equation for the amount of money in the account after t years:
[tex]\implies A=720(1+0.048)^{t}[/tex]
[tex]\implies A=720(1.048)^{t}[/tex]
To find the amount of money in the account after 12 years, substitute t = 12 into the equation:
[tex]\implies A=720(1.75523549...)[/tex]
[tex]\implies A=1263.76955...[/tex]
[tex]\implies A=1263.77[/tex]
---------------------------------------------------------------------------------
Question 2[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$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]
Given values:
a = 1 (initial number of bacteria)b = 2 (as the bacteria doubles)Substitute the given values or a and b into the exponential function formula to create an equation for the number of bacteria after x days:
[tex]\implies y=1(2)^x[/tex]
[tex]\implies y=2^x[/tex]
To find the number of bacteria after 3 days, substitute x = 3 into the equation:
[tex]\implies y=2^3[/tex]
[tex]\implies y=8[/tex]
Un automóvil tiene una velocidad inicial de 5 m/s, durante 10 segundos , acelera 2m/s2 ¿cuál es su velocidad final en m/s?
The final velocity of the car is given as follows:
25 m/s.
How to model the velocity?The velocity function is a linear function, modeled as follows:
v(t) = v(0) + at.
In which:
v(0) is the initial velocity.a is the acceleration.The parameter values for this problem are given as follows:
v(0) = 5, a = 2.
Hence the velocity function is given as follows:
v(t) = 5 + 2t.
At a time of 10 seconds, the velocity is given as follows:
v(10) = 5 + 2(10)
v(10) = 25 m/s.
TranslationThe car has an initial velocity of 5 m/s, and an acceleration of 2 m/s² during 10 seconds.
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The following scatter plot shows how the cumulative sea level has changed from
1880 to 2015. Which correlation coefficient best represents the scatter plot?
A. r=-0.98
B. r=-0.5
C. r=0.5
D.r=0.98
Based on the scatter plot shown, the correlation coefficient that best represents the scatter plot is r = 0.98.
What is a scatter plot?Several dots are placed on a horizontal and vertical axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the degree of correlation, if any, between the values of observed quantities or occurrences called variables.
The scatter plot shown shows a highly positive correlation between the data. Hence, the value of the correlation coefficient is very nearly 1.
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Find the angle between a diagonal of a cube and one of its faces ?
Answer:
35.26°
Step-by-step explanation:
You have to visualize this or draw a diagram
If a cube has side a, the face diagonal of the cube is √2a . The diagonal of the cube is √3a
One side of length a, another side of length √2a (face diagonal) and the third of √3a form a right triangle with the angle opposite √3a being the 90° angle
Therefore we can find the angle [tex]\theta[/tex] which the cube diagonal makes with the face diagonal using the fact
[tex]\dfrac{a}{\sqrt{2}a} = \tan\theta[/tex]
[tex]\theta = tan^{-1}\left(\dfrac{1}{\sqrt{2}\right)} \\= 35.26^\circ[/tex]
Write a system of linear inequalities represented by the graph.
Inequality 1:
Inequality 2:
A system of linear inequalities represented by the graph are;
Inequality 1: y ≤ 3x - 3
Inequality 2: y ≥ ¹/₂x - 3
How to interpret Inequality Graphs?Inequalities that use < or > symbols are usually plotted with a dashed line that shows us that the line is not included in the region. Meanwhile, Inequalities that use ≤ or ≥ symbols are normally plotted with a solid line that shows us that the line is included in the region.
The general formula of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, the graph that rises to the right side in the first quadrant has;
Slope = (3 - 1)/(3 - 2)
Slope = 3
the y-intercept is at y = -3
Thus, equation is;
y ≤ 3x - 3
Thus, the graph that rises to the left side in the second quadrant has;
Slope = (1 - 0)/(2 - 0)
Slope = 1/2
the y-intercept is at y = 1
Thus, equation is;
y ≥ ¹/₂x - 3
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Evaluate the expression when n=-3. n^2-9n-6
Answer:
30
Step-by-step explanation:
n^2-9n-6
(-3)^2-9(-3)-6
(-3)(-3)+27-6
9+27-6
36-6
30
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{n^2 - 9n - 6}[/tex]
[tex]\mathsf{= -3^2 - 9(-3) - 6}[/tex]
[tex]\mathsf{= -3(-3) - 9(-3) - 6}[/tex]
[tex]\mathsf{= -9 - (-27) - 6}[/tex]
[tex]\mathsf{= -9 + 27 - 6}[/tex]
[tex]\mathsf{= 18 - 6}[/tex]
[tex]\mathsf{= 12}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{12}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]