Answer: (1/2)c
To write an algebraic expression, convert parts of the verbal expression.
What is an expression?An expression is numbers or variables with operations performed between them. It does not have an equal sign.
OperationsOperations are ways we change numbers, usually to make them bigger or smaller. Examples of operations are multiplication, division, subtraction, addition, and square root.
Write an expressionThe question says: "half as big as last night’s crowd"
last night's crowd = c
'half as big' = 1/2
This is a proper fraction with the top number smaller than the bottom number. When we multiply 'c' with a proper fraction, the answer would get smaller.Therefore, we can represent the problem using the expression [tex]\frac{1}{2}c[/tex].
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The flat rate for your service runs $9.50 per hour. To cover costs, you charge the flat rate plus 15% of that rate for the first 8 hours, and 10% of that rate on the second 8 hours. You estimate that a particular job will take 16 hours. Write the equations and the total estimate.
(9.50 + 0.15 x 9.50) x Hours and (9.50 + 0.10 x 9.50) x Hours are the equation to and the total cost estimate is $173.04.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
For the first 8 hours: The flat rate is $9.50 per hour, so 15% of that rate is 0.15 x 9.50 = $1.43.
The cost for the first 8 hours is (9.50 + 1.43) x 8 = $96.64.
For the next 8 hours: The flat rate is still $9.50 per hour, so 10% of that rate is 0.10 x 9.50 = $0.95.
The cost for the next 8 hours is (9.50 + 0.95) x 8 = $76.40.
Total cost estimate = $96.64 + $76.40 = $173.04
We can also write the equations for the costs as follows:
For the first 8 hours: Cost = (9.50 + 0.15 x 9.50) x Hours = 1.15 x 9.50 x Hours
For the next 8 hours: Cost = (9.50 + 0.10 x 9.50) x Hours = 1.10 x 9.50 x Hours
Using these equations, we can calculate the cost for any number of hours up to 16.
Hence, (9.50 + 0.15 x 9.50) x Hours and (9.50 + 0.10 x 9.50) x Hours are the equation to and the total cost estimate is $173.04.
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Answer:
(9.50 + 0.15 x 9.50) x Hours and (9.50 + 0.10 x 9.50) x Hours are the equation to and the total cost estimate is $173.04.
Step-by-step explanation:
Which graph represents the solution -1/2(8x-32)< -4
The solution set for the given inequality is {6, 7, 8, 9, 10,.....}.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -1/2(8x-32)< -4
Multiply by -2 on both the sides of an inequality, we get
(8x-32)>8
Add 32 on both the sides of an inequality, we get
8x>40
Divide 8 on both the sides of an inequality, we get
x>5
So, solution set is {6, 7, 8, 9, 10,.....}
Therefore, the solution set for the given inequality is {6, 7, 8, 9, 10,.....}.
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The area of a square is one third the area of a triangle. If the base of the triangle and a side of the square are equal, what is the ratio of the height of the triangle to the side of the square ?.
The ratio of the height of the triangle to the side of the square is 6.
A triangle is a three-sided polygon with three vertices and three angles. Triangles can have different shapes and sizes, including equilateral, isosceles, and scalene triangles.
Let's call the side of the square x. Since the base of the triangle is equal to the side of the square, we can use x for both. The area of the square can then be found by x² and the area of the triangle can be found by (x)(h)/2, where h is the height of the triangle.
We know that the area of the square is one-third the area of the triangle, so we can set up an equation:
x² = (1/3)(x)(h)/2
Expanding the right side of the equation:
x² = (1/3)(xh)/2
Now we can isolate the height of the triangle by multiplying both sides by 6 and dividing by x:
6x² = (xh)
Finally, we can divide both sides by x to find the ratio of the height of the triangle to the side of the square:
6x = h
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Explain how a shaded line means that fractions, decimals, and numbers not labeled
on a number line can be part of the solution to an inequaliy
Answer:
In a sense, negative numbers could be related to decimals because place values of decimal digits involve taking 10 to negative powers. However, negative numbers do not have to be decimals (for example, -3) and decimals do not have to be negative numbers (for example, 0.2).
Answer:
23456trrytugfygtuh
Step-by-step explanation:
Pleaseee help now please help nowwww
The length of JM is given as follows:
JM = 16.875.
What are similar polygons?Similar polygons are polygons that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.The polygons for this problem are similar, hence the proportional relationship for the segment lengths is given as follows:
16/15 = JM/18
Then the length of JM is obtained applying cross multiplication as follows:
16JM = 15 x 18
JM = 15 x 18/16
JM = 16.875.
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What percent of 72 is 68.4
68.4 is approximately 95% of 72.
Here, we have,
To find out what percent of 72 is 68.4, we can follow these steps:
Step 1: Divide 68.4 by 72.
68.4 / 72 = 0.95
Step 2: Convert the decimal to a percentage by multiplying by 100.
0.95 * 100 = 95
Therefore, 68.4 is approximately 95% of 72.
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Engineers want to measure the distance from P to Q, but the span from P to Q is across the tip of a lake. So they select a point R on land and fine that the distance from R to Q is 100 feet and from R to P is 120 feet. Angle QPR measures 47 degrees. How far is it from P to Q?
The distance of P to Q is given as follows:
89.6 feet.
What is the law of cosines?The law of cosines states that we can find the side c of a triangle as follows:
c² = a² + b² - 2abcos(C)
In which:
C is the angle opposite to side c.a and b are the lengths of the other sides.The parameters for this problem are given as follows:
a = 120, b = 100, C = 47º.
Hence the distance is obtained as follows:
c² = 120² + 100² - 2 x 120 x 100 x cosine of 47 degrees
c² = 8032
c = sqrt(8032)
c = 89.6 feet.
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5. Name the angle that is supplementary to COD.
A
F
OZCOA
O ZBOC
OLCOB
O ZBOA
B
O
۶,
D
(1 point)
Answer: D
Step-by-step explanation:
D. OLCOB. This angle is supplementary to COD because the two angles add up to 180°. OLCOB has a measure of 180° - 90° = 90°, which is supplementary to the 90° measure of COD.
Seven subtracted from fives times a number, and then the difference added to nine times a number.
Step-by-step explanation:
Let n= The first number
Let x= The second number
(5n-7)+9x
This is if the number are different numbers.
If they are the same:
Let n= a number
(5n-7)+9n=
7n-7
The graph shows the amount of a chemical in a patient's body at different times measured in hours since the levels were first checked.
Which equation best represents the graph?
Answer: please look at the image for the answer
Step-by-step explanation:
Aubrey opened a savings account and deposited $100.00. The account earns 2% interest, compounded annually. If she wants to use the money to buy a new bicycle in 3 years, how much will she be able to spend on the bike? nt P(1 + 2)", where A is the balance (final amount), P is the principal Use the formula A = P (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.
In 3 years, Aubrey will be able to spend $106.08 on a new bicycle.
To find out how much Aubrey will be able to spend on the bike in 3 yearsFirst we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A = final amount (balance)
P = principal (starting amount) = $100.00
r = interest rate as a decimal = 2% = 0.02
n = number of times per year that the interest is compounded = 1 (annually)
t = time in years = 3
Plugging in these values, we get:
A = $100.00 * (1 + 0.02/1)^(1 * 3)
A = $100.00 * (1.02)^3
A = $100.00 * 1.0608
A = $106.08
Therefore, in 3 years, Aubrey will be able to spend $106.08 on a new bicycle.
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A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 5 tables is $55. The total cost to rent 6 chairs and 2 tables is $28. What is the cost to rent each chair and each table?
Chair:
Table:
I truly would appreciate if someone could help me understand or solve this quickly :)
The solution is: the cost of renting one chair is $2.25
the cost of renting one table is $8.25.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Let x represent the cost of renting one chair.
Let y represent the cost of renting one table.
The total cost to rent 3 chairs and 5 tables is $48. This means that
3x + 5y = 48 - - - - - - - - - -1
The total cost to rent 6 chairs and 2 tables is $30. This means that
6x + 2y = 30 - - - - - - - - - -2
Multiplying equation 1 by 6 and equation equation 2 by 3, it becomes
18x + 30y = 288
18x + 6y = 90
Subtracting, it becomes
24y = 198
y = 198/24 = 8.25
Substituting y = 8.25 into equation 1, it becomes
3x + 5 × 8.25 = 48
3x + 41.25 = 48
3x = 48 - 41.25
= 6.75
x = 6.75/3
= 2.25
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Describe the problem of acid rain. How can this problem be solved? why does this work?.
Acid rain is the acidic rain that produce due to the mixture of sulhuric and nitric acid with rain water. The problem is solved by using renewable resources that reduces the pollution and the emission of acidic pollutants.
Acid RainAcid rain, or acid deposition, is a broad term that includes any form of precipitation with acidic components, such as sulfuric or nitric acid that fall to the ground from the atmosphere in wet or dry forms. This can include rain, snow, fog, hail or even dust that is acidic.
solution of acid rainA great way to reduce acid rain is to produce energy without using fossil fuels. Instead, people can use renewable energy sources, such as solar and wind power.
Renewable energy sources help reduce acid rain because they produce much less pollution.
Filter and detoxify the water used by the factories before returning it to the rivers.
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OPEN-ENDED Write an algebraic expression using more than one
operation. When you evaluate the expression, how do you know
which operation to perform first?
Answer:
9(4+5)-16=
Explanation:
P (parenthesis) E (exponents) M (multiply) D (divide) A (add) S (subtract)
HOPE THIS HELPS
What is the solution to the inequality 3n-12> 4n-16, using interval notation?
Answer:
the answer is D (4,∞)
Step-by-step explanation:
3n-12>4n-16
C.L.T.
3n-4n>-16+12
-n>-4
n>4
What does Cronbach's alpha calculate?
Cronbach's alpha calculates the internal consistency of a set of variables or items in a questionnaire or test, indicating how reliably they measure the same construct.
Cronbach's alpha is a measure of reliability used in psychometrics to assess the consistency or homogeneity of a set of items in a questionnaire or test designed to measure a specific construct or trait. It calculates the degree of correlation among the items and indicates the extent to which they measure the same underlying concept. A high alpha value (usually ranging from 0 to 1) indicates strong internal consistency and suggests that the items are measuring the same construct in a reliable manner. Researchers use Cronbach's alpha to evaluate the quality of a test or questionnaire and to determine whether it is suitable for the intended purpose.
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What is the probability that the web site has fewer than 5 million visitors in a single day? if needed, round your answer to four decimal digits.
Answer:
Step-by-step explanation: daddy
a)2/5 t=6
t=___
b)-4.5= a-8
a=___
c) 1/2+p=3
p=___
d)-12=-3y
x=___
Solving the equations for each given variables, we have:
a. t = 15
b. a = 12.5
c. p = 5/2
d.
y = 4
How to Find the Value of a Variable in an Equation?Finding the value of a variable in an equation involves solving the equation for that variable. This process typically involves several steps, including isolating the variable on one side of the equation, using inverse operations to simplify the expression, and substituting known values into the equation to find the value of the variable.
Therefore:
a. 2/5t = 6
Multiply both sides by 5/2:
t = 6 * 5/2
t = 15
b. -4.5 = a - 8
Add 8 to both sides:
-4.5 + 8 = a
12.5 = a
a =12.5
c. 1/2 + p = 3
p = 3 - 1/2
p = 5/2
d. -12 = -3y
-12/-3 = y
4 = y
y = 4
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MATHHHHH help plesss
Answer:
c = 13
Step-by-step explanation:
We can solve for c using an equation that models the sum of the interior angles of a triangle.
The interior angles of a triangle add to 180º. Therefore, we can construct the equation:
90 + (3c - 1) + 52 = 180
Then, we can solve for c algebraically.
(3c - 1) = 180 - 90 - 52
3c - 1 = 38
3c = 38 + 1
3c / 3 = 39 / 3
c = 13
Help me please I need someone’s help on this hmh
Note that the area of the smaller square will be depicted by: 20inches.
What is the rationale for the above response?Area of the larger square - Area of the 4 Right Angled Triangles
Since the Area of the larger square = is 36inches; and
Area of the one of the Right Angled Triangles = 4inches
Thus, the Boxes will be completed as follows;
[36in] - (4) [4] or [20in]
Since
36 - 16 = 20 inches.
Note that a square is a closed two-dimensional form having four equal sides and four vertices. Its opposing sides are perpendicular to one other. A square can alternatively be thought of as a rectangle with equal length and width.
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PLEASE HELP
Solve each system of equations algebraically.
The solution to the system of equation y = x + 12 and y = (1/2)x is (-24,-12).
What is the solution to the system of equation?Given the system of equation in the question;
y = x + 12
y = (1/2)x
To solve the system of equation, first plug equation to into equation one and solve for x.
y = x + 12
Plug in y = (1/2)x
(1/2)x = x + 12
Multiply each term by 2
2(1/2)x = 2x + 2(12)
x = 2x + 24
x - 2x = 2x - 2x + 24
x - 2x = 24
-x = 24
x = -24
Now, plug x = -24 into equation two and solve for y.
y = (1/2)x
Plug in x = -24
y = (1/2)( -24 )
y = -24/2
y = -12
Therefore, the value of x is -24 and y is -12.
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How would you solve this problem?
Measure of angle V is 103°.
What is Polygons?Polygons are closed figures which has at least three set of line segments joined together.
The polygon with least number of sides is triangle.
Here is a six sided polygon, which is hexagon.
Sum of interior angles of a polygon = (n - 2) 180, where n is the number of sides of the polygon.
Sum of the interior angles of the given polygon = (6 - 2) 180 = 720
So,
∠S + ∠T + ∠U + ∠V + ∠W + ∠X = 720°
90° + (9x - 19)° + 111° + (5x + 8)° + 128° + (7x + 3)° = 720°
9x + 5x + 7x + 90 - 19 + 111 + 8 + 128 + 3 = 720
21x + 321 = 720
21x = 399
x = 19
∠V = (5 × 19) + 8 = 103°
Hence the angle V is of measure 103°.
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Write the other side of this equation so it has MANY solutions.
6x - 5 =
Answer:
6x - 5 = 6x - 5
Step-by-step explanation:
If we have the same quantity on both sides of the equation, then the equation becomes an identity — an equation that is true for any value of the present variables.
If we set 6x - 5 equal to 6x - 5, then there are infinite solutions.
For example,
when x is 3:
6(3) - 5 = 6(3) - 5
18 - 5 = 18 - 5
13 = 13 ✔
when x is 5:
6(5) - 5 = 6(5) - 5
30 - 5 = 30 - 5
25 = 25 ✔
A restaurant has an aquarium in the shape of a rectangular prism. The base is 6 feet by 2. 5 feet in size. The height is 4 feet. How many square feet of glass was used in making this aquarium? ***hint---where is the glass part of the aquarium?***.
45 square feet of glass was used in making this aquarium.
A region's size on a surface is determined by its area. The term "surface area" refers to the area of an open surface or the perimeter of a three-dimensional object, whereas "plane area" refers to the area of a shape or planar lamina.
The base of the aquarium is 6 feet by 2.5 feet, so its area is 6 x 2.5 = 15 square feet.
Since the aquarium is a rectangular prism, it has three sides that are the same size as the base. So, each of the three sides has an area of 15 square feet.
Therefore, the total area of glass used in making the aquarium is 3 x 15 = 45 square feet.
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Download
Stations - Applicatio....pdf
2.) If you add Ginger and her
grandmother's
ages together it
would be 66. Her grandmouer
is ten times older than Ginger.
What are the ages of each
person?
Answer:
Step-by-step explanation:
Let us consider the Ginger to be x years old.
Therefore, her grandmother will be 10x years old(10 times Ginger's age)
So,
10x+x=66
(adding both Ginger and her grandmother's age)
11x=66
(adding x and 10x)
x=66/11
x=6
Ginger's age is 6.
Her grandmother is 10 times her age.
Therefore she is 60 years old.
7 1/3 divided by 1 2/9
Answer:
6
Step-by-step explanation:
7 1/3 ÷ 1 2/9
7 1/3 = 22/3
1 2/9 = 11/9
22/3 ÷ 11/9
= 22/3 x 9/11
= 198/33
= 66/11
= 6
What is 46 kg in lbs ?
Answer: 101.41 lbs.
Step-by-step explanation:
46 kilograms can be converted to pounds by multiplying the number of kilograms by 2.20462.
So, 46 kg = 46 * 2.20462 = 101.41 lbs.
You invest $500 in an account that has an annual interest rate of 8% compounded weekly for 12 years what is the equivalent interest-rate and how many times will money be compounded how much will you have?
What is the rule for derivative of trigonometric functions?
The derivative of y = sin(x)cos(x) is 2sin(x)cos(x).Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x)
The rule for derivatives of trigonometric functions states that the derivative of a trigonometric function is the product of the coefficient and the derivative of the other function in the product. This rule can be expressed mathematically using the following formula: (f(x)g(x))' = f'(x)g(x) + f(x)g'(x) For example, let's say that we want to calculate the derivative of the function y = sin(x)cos(x). Using the formula above, we can calculate that: (sin(x)cos(x))' = cos(x)sin(x) + sin(x)cos(x) = sin(x)cos(x) + sin(x)cos(x) = 2sin(x)cos(x) Therefore, the derivative of y = sin(x)cos(x) is 2sin(x)cos(x).
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Events A and B are independent, P(A)=P(B) and P(A∪B)=0.63 . Find P(B) .
Answer:
the probability of event B is approximately 0.48.
Step-by-step explanation:
P(A) = P(B) (given)
P(A∪B) = P(A) + P(B) - P(A∩B) (probability rule for the union of two events)
Since events A and B are independent, we know that P(A∩B) = P(A) × P(B).
Substituting the given values, we get:
0.63 = P(A) + P(B) - P(A) × P(B)
Since P(A) = P(B), we can substitute P(B) for P(A):
0.63 = 2P(B) - P(B)^2
Rearranging this equation, we get:
P(B)^2 - 2P(B) + 0.63 = 0
This is a quadratic equation that we can solve using the quadratic formula:
P(B) = [2 ± sqrt(4 - 4×0.63)] / 2
P(B) = [2 ± sqrt(1.48)] / 2
P(B) ≈ 1 or P(B) ≈ 0.48
Since probabilities must be between 0 and 1, we can discard the solution P(B) = 1, and the only possible solution is:
P(B) ≈ 0.48
Therefore, the probability of event B is approximately 0.48.