Answer:
C
Step-by-step explanation:
9
7. The ratio of blue cars to red cars in the parking lot is 3 to 5. If there are 60 red cars, how many
blue cars would there Be
The number of blue cars is 375.
What is a ratio?
Ratio is a relationship between two values, represented by numbers or percentage Which expresses which of the two value are bigger. And to find that we cancel the common factor between them.
We are given that the ratio of blue cars to red cars is 3:5
Also there are 600 cars in the parking lot
Now, Let the common factor between them be 'x'
Hence the number of red cars is 3x and number of blue cars is 5x
Hence the equation can be given as
3x+5x = 600
8x = 600
Dividing both sides by 8 we get
x= 75
Hence the number of blue cars is 5(75)= 375
The number of blue cars is 375
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Assume that a constant rate of change exists for the model formed. The table lists data regarding the average salaries of
several professional athletes in the years 1991 and 2001.
a) Use the two data points to find a linear function that fits the data. Let x = the number of years after 1990 and S(x) = the
average salary.
b) Use the function of part (a) to estimate the average salary in 2005. Predict the average salary in 2010.
The average salary is s(x) = 117400 x + 138600
The average salary in 2005 is $1899600
The average salary in 2010 is $2486600
What is average salary ?
The mean wage earned by a country's working population is known as the national average salary (or national average wage). It is computed by adding together the yearly wages of everyone who is employed and dividing the total by the number of employees.
Let s(x) = mx + b →Linear model in slope-intercept form
at s(1) = $256,000
s(11) = $1430000
slope [tex]m = \frac{s(11) - s(1)}{11-1}[/tex]
= (1430000-256000) / 10
= 117400
To find b we can write
s(1) = 117400 (1) +b
256000 = 117400 + b
b = 256000 - 117400
= 138600
s(x) = 117400 x + 138600
(b) s(15) = 117400 (15) + 138600
= $1899600
(c) s(20) = 117400 (20) + 138600
= $2486600
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if f(x) =-2^2+6 find f(2)
The value of f(2) when f(x) = [tex]-x^{2} +6[/tex] will be 2.
According to the question,
We have the following expression:
f(x) = [tex]-x^{2} +6[/tex]
Now, we can easily find the value of f(2) by putting the value of x in the given expression as 2.
So, we will have the following expression:
f(2) = [tex]-(2)^{2} +6[/tex]
f(2) = -4+6
(More to know: the two integers with different signs are subtracted but the sign in the final result remains that of the larger integer. So, in this case, the sign will be positive in the final result.)
f(2) = 2
Hence, the value of f(2) when f(x) = [tex]-x^{2} +6[/tex] will be 2.
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A parking lot has a length of 32 meters and a width of 24 meters. Madison made a scale drawing of the parking lot using a scale of
2
1
inch = 4 meters.
Label the dimensions of the scale drawing.
The dimensions of the scale drawing is length = 168 inches and width = 126 inches
How useful is a scale drawing?Scale drawing helps to represent surfaces on earth in a paper by either enlarging its dimension, reducing its dimension by a constant factor called the scale factor.
The conversion or scale factor is 21 inches = 4 meters
If 21 inches = 4 meters,
then 1 meter = 21/4 inches
32 meters inches = 32 x 21/4 = 168 inches
24 meters = 24 x 21/4 = 126 inches.
In conclusion, length of the scale drawing is 168 inches and width of the scale drawing iss 126 inches
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Factor Completely
6p² +90p + 300
Answer:
6(p + 5)(p + 10)
Step-by-step explanation:
6p² + 90p + 300 ← factor out 6 from each term
= 6(p² + 15p + 50) ← factor the quadratic
consider the factors of the constant term (+ 50) which sum to give the coefficient of the p- term (+ 15)
the factors are + 5 and + 10 , then
p² + 15p + 50 = (p + 5)(p + 10)
and
6p² + 90p + 300
= 6(p + 5)(p + 10)
Last year, Alonzo had 30,00 to invest. He invested some of it in an account that pain 7% simple interest per year, and he invested the rest in an account that paid 5% simple interest per year. After one year, he revived a total of 1680 in interest. How much did he invest in each account?
Alonzo invests 76,500 in each account.
What is simple interest?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
Here, we
Let x and y be the amounts invested at 7% and 5% respectively.
then,
x + y = 30,00 for the parts of the Principal
0.07x + 0.05y = 1680 For the rates and total Earnings
x + y = 30,00
y = 30,00 - x
y can be rewritten as 30,00 - x
Using the rates to total earnings we have
0.07x + 0.05(30,00 - x) = 1680
0.07x - 0.05x + 150 = 1680
0.02x = 1680 - 150
0.02x = 1530
x = 76,500
Hence, Alonzo invests 76,500 in each account.
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5(m - 6) = 10 - 4[2(m - 7) - 5m]
Answer:
m = -96/7
Step-by-step explanation:
5(m - 6) = 10 - 4[2(m - 7) - 5m]
5m - 30 = 10 - 4[2m - 14 - 5m]
5m - 30 = 10 - 4(-3m - 14)
5m - 30 = 10 + 12m + 56
-7m = 96
m = -96/7
Identify the domain of the function shown in the graph -6 < x < 6
The domain of the function shown on the graph is given by the following option:
B. All real numbers.
What is the domain of a function?The domain of a function is the set composed by all the input values that are assumed by the function.
On a graph, the meaning of each variable is given as follows:
Values of x -> horizontal axis -> input values.Values of y -> vertical axis -> output values.Hence, considering the graph of the function, the domain of the function is the set that contains all the values of x of the function.
From the image given at the end of the answer, the line continues to left and to right, meaning that it has no spaces in it's definition, and thus the function is defined for all real values and the correct option is given by option b.
Missing InformationThe problem containing the graph of the function and the options is given by the image presented at the end of the answer.
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After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?.
After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large, the best recommendation is c. Increase the sample size.
What is a confidence interval?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specific confidence level; the 95% confidence level is the most commonly used, but other levels, such as 90% or 99%, are also used.
Confidence intervals are used by statisticians to quantify uncertainty in a sample variable. A researcher, for example, may randomly select different samples from the same population and compute a confidence interval for each sample to determine how well it may represent the true value of the population variable. The resulting datasets are all unique, with some intervals containing the true population parameter and others not.
In this case, the sample size should be increased when the results are meaningless because the width of the interval is too large.
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Complete questions
After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?
a. Increase the level of confidence for the interval
b. Decrease the sample size
c. Increase the sample size
d. Reduce the population variance
Thaddeus wants to attend a sports camp this spring that costs $170.00 for the week. He rakes leaves during the fall and earns $58.35 . He shovels snow during the winter and earns $58.35 . How much more money does Thaddeus need to earn to pay for the sports camp? Write your answer as a decimal.
Thaddeus needs to earn $blank.
Cost of Thaddeus camp is $170.00 and total money earned by Thaddeus in raking leaves and shovels snow is $58.35 each then total amount of money Thaddeus required to earn to pay sports camp fee is equal to $53.3.
As given in the question,
Cost of Thaddeus sports camp is equal to $170.00
Money earned by Thaddeus while raking leaves = $58.35
Money earned by Thaddeus while shovels snow = $58.35
Total amount of money Thaddeus required to earn to pay sports camp fee
= $170 - $(58.35 + 58.35)
= $(170 - 116.7)
= $53.3
Therefore, cost of Thaddeus camp is $170.00 and total money earned by Thaddeus in raking leaves and shovels snow is $58.35 each then total amount of money Thaddeus required to earn to pay sports camp fee is equal to $53.3.
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(8x-12)=64
Solve for x
Answer:
-4
Step-by-step explanation:
Simplifying
8(x + 12) = 64
Reorder the terms:
8(12 + x) = 64 (12 * 8 + x * 8) = 64 (96 + 8x) = 64
Solving
96 + 8x = 64
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-96' to each side of the equation.
96 + -96 + 8x = 64 + -96
Combine like terms: 96 + -96 = 0
0 + 8x = 64 + -96
8x = 64 + -96
Combine like terms:
64 + -96 = -32
8x = -32
Divide each side by '8'.
x = -4
Simplifying
x = -4
Answer:
x = 19/2 (or) 9.5
Step-by-step explanation:
The equation is,
→ (8x - 12) = 64
Now the value of x will be,
→ (8x - 12) = 64
→ 8x = 64 + 12
→ x = 76/8
→ x = 19/2
→ [ x = 9.5 ]
Hence, the value of x is 9.5.
A furniture store sells 16 tables for every 96 chairs in a given week. What is the unit rate of chairs to tables?
Answer: For every 6 chairs sold they sell 1 table
Step-by-step explanation:
After some work this is my answer
Hope this helps :)
What amount is 20 more than 70?.
The amount is 20 more than 70 that will be 90.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
We have been given that the statement is "20 more than 70"
WE are asked to find the amount of the given statement.
More means addition therefore,
20 more than 70 = 20 + 70
= 90
Therefore, the amount is 20 more than 70 that will be 90.
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A piece of notebook paper measures 8 1/2 inches by 11 inches. Which of the following metric approximations is the same?
2 m x 2.8 m
3 cm x 4 cm
22 cm x 28 cm
30 m x 40 m
ade's gem shop is having its annual spring sale, when every item in the store gets marked down. during the sale, charm bracelets sell for $4 less than full price. kristen purchases 5 identical charm bracelets: one for each of her friends. she pays a total of $45. which equation can kristen use to find how much money, c, each charm bracelet costs at full price?
Based on the information provided, the equation that can be used to find how much money, c, each charm bracelet cost at full price is 5(c – 4) = 45.
An equation is its simplest form in algebra, refers to a mathematical statement that represents that two mathematical expressions are equal. For example, 2x + 6 = 14 is an equation, where 2x + 6 and 14 are two expressions that are separated by an equal sign. In the given case, as each bracelet cost is reduced by $4 from the full price, and the total cost of 5 identical charm bracelets is $45, the equation that can be used is given by:
5(c – 4) = 45
Solving the equation,
5(c – 4) = 45
c – 4 = 9
c = 9 + 4 = $13
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−50÷(−10)
solve and show how you solved
13. list all the steps used to search for 9 in the sequence 1, 3, 4, 5, 6, 8, 9, 11 using a) a linear search. b) a binary searc
By linear search, We discovered that element 9 is the seventh in the sequence, meaning that number 9 appears on the list in the sequence 1, 3, 4, 5, 6, 8, 9, 11.
Define sequence.A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.
Given,
Sequence = 1, 3, 4, 5, 6, 8, 9, 11
By linear search,
The first element is compared to 9 first. If the element's value is less than nine, we compare the subsequent element with nine, and so on.
Step 1: 9 is not the same as 1.
Step 2: 9 is not the same as 3.
Step 3: 9 is not the same as 4
Step 4: 9 is not the same as 5
Step 5: 9 is not the same as 6
Step 6: 8 and 9 are not the same.
Step 7: 9 equals 9.
We discovered that element 9 is the seventh in the sequence, meaning that number 9 appears on the list.
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procedures that allow researchers to rule out certain explanations for results other than the hypotheses they wish to test are referred to as
Control procedures are those that enable researchers to rule out specific causes for results other than the hypotheses they intend to test.
In a controlled experiment, every factor besides the independent variable is kept under control or constant to ensure that it has no impact on the dependent variable.
This experiment involves the systematic manipulation of an independent variable (the cause) and the measurement of the dependent variable (the effect). This ensures that any extraneous variables are controlled.
This experiment aids the researcher in determining whether the experimental group and control group differ from one another.
For example, during the medication effect test, the group that receives the medication is referred to as the experiment group. Those who don't get any medication are referred to as the control group.
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given m n, find the value of x and y
x = 24
y = 58
Step-by-step explanation:
5x+20 = 6x-4 ( vertically opposite angles)
20+4 = 6x-5x(collect like terms)
x = 24
(y-18)+(5x+20) = 180 (sum of angles on a straight line)
(y-18)+(5×24+20) = 180
(y-18)+140 = 180
y-18 = 180-140(collect like terms)
y-18 = 40
y = 40+18
y=58
f ( x) = 4/x - 5
plss helppp
The coordinates of a point are given. What is its line of reflection?
(7,−7)⟶(7,7)
Answer:
reflection over the y-axis
Step-by-step explanation:
formula for reflection over y is (x,y) -> (x,-y)
Write the equation of the line in fully simplified slope-intercept form. HELPPP PLS
Answer:
The equation of the line in fully simplified slope-intercept form is [tex]y=\frac{2}{3}x-6[/tex]
Step-by-step explanation:
The equation of the line in fully simplified slope-intercept form can be calculated as follows
The first step is to calculate the slope [tex]m[/tex] of the given line using the slope formula as follows
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Take two coordinates on the given line
[tex](9, 0)~\text{and}~ (0, -6)[/tex]
Substitute [tex]-6[/tex] for [tex]y_{2}[/tex], [tex]0[/tex] for [tex]x_{2}[/tex] , [tex]0[/tex] for [tex]y_{1}[/tex], [tex]9[/tex] for [tex]x_{1}[/tex] in the slope formula
[tex]m=\frac{-6-0}{0-9}[/tex]
Simplify the numerator and the denominator at the right side of the equation
[tex]m=\frac{-6}{-9}[/tex]
Simplify the equation
[tex]m=\frac{2}{3}[/tex]
The second step is to find the slope-intercept form of the given line by the point-slope form formula as follows
[tex]y-y_{1}=m(x-x_{1})[/tex]
Take any coordinates on the given line, take [tex](9,0)[/tex]
Substitute [tex]0[/tex] for [tex]y_{1}[/tex], [tex]9[/tex] for [tex]x_{1}[/tex], [tex]\frac{2}{3}[/tex] for [tex]m[/tex]
[tex]y-0=\frac{2}{3}(x-9)[/tex]
Simplify the left side of the equation
[tex]y=\frac{2}{3}(x-9)[/tex]
Expand the right side of the equation
[tex]y=\frac{2}{3}x-\frac{2\times 9}{3}[/tex]
Simplify the right side of the equation
[tex]y=\frac{2}{3}x-6[/tex]
Hence the equation of the line in fully simplified slope-intercept form is
[tex]y=\frac{2}{3}x-6[/tex]
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Is 13 72/99 rational or irrational
13 72/99 is rational number.
A rational number is a number that can represented in the form p/q where p, q are integers and q ≠ 0. E.g. 3/1, 5/12.
An irrational number is the opposite of a rational number that cannot be represented in the form p/q where p, q are integers and q ≠ 0. E.g. √2
Given, number = 13 72/99
It is a mixed fraction. It can be converted into proper fraction :
(13×99 + 72)/99 = 1359/99
1359/99 is a rational number since numerator and the denominator are both integers.
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The distribution of heights in a population of women is approximately normal. Sixteen percent of the women have heights less than 62 inches. About 97.5% of the women have heights less than 71 inches. Use the empirical rule to estimate the mean and standard deviation of the heights in this population. Mean: K inches Standard Deviation: inches
The mean is 65 inches and the standard deviation is 3 inches.
Given,
In a group of women, the distribution of heights is roughly normal. Women who are shorter than 62 inches in height make up 16% of the population.
The empirical rule, less than μ - σ of 16% of the data is accurate.
P (x < μ - σ) = 16%
μ - σ = 62 → (I)
Approximately 97.5% of the women are under 71 inches in height,
P (x < μ + 2σ) = 97.5%
μ + 2σ = 71 → (II)
By solving (I) & (II);
μ - σ = 62
μ + 2σ = 71
3σ = 9
σ = 3
From (I);
μ - σ = 62
μ - 3 = 62
μ = 65
Hence, Mean = 65 inches
Standard deviation = 3 inches
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Find the measure of the marked angles.
(11x + 17) = ____.
(13x - 1) = ____.
Answer:
(11x + 17) = 116°
(13x - 1) = 116°
Step-by-step explanation:
(11x + 17) and (13x - 1) are equal because they are vertically opposite angles.
11x + 17 = 13x - 1
2x = 18
x = 9
Substitute x = 9 into angle measures.
11(9) + 17 = 116°
Since both angles are equal, (13x - 1) is also 116°.
Can someone help me really quick
(Please Explain how you know this is correct.)
The price per gallon will be 2.4 at Miguel's gasoline center.
What is the slope of the line?The slope of the line is represented as the rise of the line.
Here the price per gallon is equal to the slope of the given points
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
we take the two points (4, 10) and (9, 22)
Let
x₁ = 4, y₁ = 10
x₂ = 9, y₂ = 22
∵ Slope m = (y₂ - y₁)/(x₂ -x₁ )
Substitute values in the formula
m = (22 - 10) / (9 - 4)
m = (12)/(5)
m = 2.4
Thus, the price per gallon will be 2.4 at Miguel's gasoline center.
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A roofer charges $60 for the first hour of a service call and $20 per hour for each additional hour, as shown on the graph below.
Look at the above Roofer’s Prices graph and then answer the following questions.
Part A What is the slope of a line joining the points on this graph? Show your work or explain your answer.
Part B What does the slope represent?
Slope of line will be 2 and both the variable quantity charge and time are positively related that means if time will increase cost will also increases.
Slope for two points:
P(x1,y1) and Q(x2,y2)
slope of line PQ,
[tex]m_{pq}[/tex] = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
while calculating the slope it may comes positive or negative,
A positive slope means that two variables are positively related to each other.
while,
A negative slope means that two variables are negatively related.
from the given graph,
Part A :
we have two points
A(1 , 60)
B(3,100)
slope of AB will be,
[tex]m_{AB}[/tex] = [tex]\frac{100 - 60 }{3 - 1}[/tex]
= 40 / 2
= 2
slope of line in graph will be 2
Part B:
Here slope of line is 2 which is positive, means both the variables charges and hours are positively related.
that means, if time will increase the cost will also increases.
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Can you factor [tex]12x^{2} -8x+1=0[/tex]?
Answer:
Yes
Step-by-step explanation:
You must use the quadratic formula
-b√b^2 -4ac/2a --> -8√-(-8)^2 -4(12)(1)/2(12)
8 +/- 4/24
(1/2, 1/6)
Yes, we can factor 12x²-8x+1=0 and the factors are x=1/6 and x= 1/2.
What is factor?
A factor in maths is one of two or more numbers that divides into a number without a remainder, making it a whole number.
In other words, a factor is a number that divides another number evenly.
12x² -8x +1=0
⇒ 12x² -2x- 6x+1=0
⇒ 2x (6x-1) -1 (6x-1)=0
⇒ (2x-1) (6x-1)=0
⇒ 2x-1 = 0, 6x-1 = 0
⇒ x=1/2, x=1/6
Therefore, the factors of 12x²-8x+1=0 are 1/2, 1/6.
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Explain how to make a standard form parabola equation into vertex form
We can convert a parabola equation from standard form to vertex form. This is in the vertex form and has the formula y = a (x - h)2 + k. The vertex, in this case, is (h, k)=(-1,-6)
Standard Form
A parabola's standard form is: y = ax2 + bx + c
Here, a, b, and c are real numbers (constants), with a = 0. x and y are variables, with (x, y) representing a parabola point.
Vertex Form
A parabola's vertex form is: y = a (x - h)2 + k
Here, a, h, and k are real numbers, with a = 0. x and y are variables, with (x, y) representing a parabola point.
There is a "whole square" in the vertex form, y = a (x - h)2 + k. To convert from standard to vertex form, we simply need to complete the square. Aside from that, we have a formula method for doing this. Let us investigate both methods.
By Finishing the Square
Consider the following standard-form parabola: y = -3x2 - 6x - 9 and complete the square to get the vertex form. First, we must ensure that the x2 coefficient is 1. If the coefficient of x2 is NOT 1, the number will be placed outside as a common factor. We'll get: y = 3x2 6x 9 = 3 (x2 + 2x + 3).
Now, the coefficient of x2 is 1. Here are the steps to convert the above expression into the vertex form.
Determine the x coefficient. 3 (x2 + 2x + 3)
Divide it in half and square the result.
(2/2)^2 = 1^2 = 1
Y= -3(x2+2x+1-1 +3)
Using the appropriate identity, factor the perfect square trinomial formed by the first three terms.
We can use x2 + 2xy + y2 = (x + y) in this case.
x2 + 2x + 1 = (x + 1) in this case.
The preceding expression becomes:
Y= -3 (x2 + 2x + 1-1 +3)
Y= -3(x+1)^2 – 1 +3
The last two numbers should be simplified, and the outside number should be distributed.
Here, -1 + 3 = 2. As a result, the preceding expression becomes:
Y= -3(x+1)^2 + 2
Y = -3(x+1)^2 - 6
This is in the vertex form and has the formula y = a (x - h)2 + k. The vertex, in this case, is (h, k)=(-1,-6)
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Express 2x² + 12x + 8 in the form a(a + b)² + c, where a, b and c are
numbers.
What are the values of a, b and c ?
We can write given quadratic expression 2x² + 12x + 8 as 2(x + 3)² - 10
And a = 2, b = 3, c = -10
We have been given an expression 2x² + 12x + 8
We need to write given expression in the form a(a + b)² + c, where a, b and c are numbers.
2x² + 12x + 8
= 2x² + 12x + 18 - 18 + 8
= (√2x + 3√2)² - 10
= (√2)² (x + 3)² - 10
= 2(x + 3)² - 10
Comparing with a(a + b)² + c, where a, b and c are numbers.
a = 2, b = 3 and c = -10
Therefore, we can write given quadratic expression 2x² + 12x + 8 as 2(x + 3)² - 10
And a = 2, b = 3, c = -10
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