Answer:
3
Step-by-step explanation:
1 foot = 12 inches
Jana can jump 36 inches!
Divide this by 12 to get the feet:
36 / 12 = 3
Check: 12 + 12 = 24 + 12 = 36
so, Jana can jump 3 feet above the ground
A student believes there is a correlation between the number of texts sent during class and GPA. The student collected data and found that the line of fit can be modeled by the equation ŷ = 3.9 − 0.1x.
Identify and interpret the slope in this scenario.
The slope is 3.9. Starting at 0.1, the GPA will increase by 3.9 for every text sent in class.
The slope is 3.9. Starting at 0.1, the GP will decrease by 3.9 for every text sent in class.
The slope is −0.1. Starting at 3.9, the GPA will increase by 0.1 for every text sent in class.
The slope is −0.1. Starting at 3.9, the GPA will decrease by 0.1 for every text sent in class.
An identification and interpretation of the slope in this scenario is: The slope is −0.1. Starting at 3.9, the GPA will decrease by 0.1 for every text sent in class.
How to identify and interpret the slope?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c .......equation 1.
Where:
m represents the slope.x represents the number of texts.y represents the GPA.c represents the y-intercept.From the information provided, we have the following equation:
y = 3.9 - 0.1x
Rewriting the equation in slope-intercept form, we have:
y = -0.1x + 3.9 .......equation 2.
Comparing equation 1 and equation 2, we have:
Slope, m = -0.1
y-intercept, c = 3.9, which also represents the initial value.
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what is the equation for the line in slope-intercept form that passes through points (4,-4) and (8,4)?
Answer:
y = 2x - 12
Step-by-step explanation:
(y-4)/(-4-4) = (x-8)/(4-8)
(y-4)/-8 = (x-8)/-4
y-4 = 2x - 16
y = 2x - 16 + 4
y = 2x - 12
what us f(x)= -1/3 + 13 when the value is f(-3)
Answer:
14, or f(-3)= 14
Step-by-step explanation:
Input the -3, so you will get f(-3)= -1/3(-3) + 13.
Do -1/3 x -3, which will get you 1.
Do 1 + 13, which will get you 14.
So, the answer will be 14, or f(-3)= 14.
Is it possible to form a triangle with side lengths 3. 5, 3. 5, and 9? if so, will it be scalene, isosceles, or equilateral?.
Triangles with the provided side lengths of 3.5, 3.5, and 9 cannot be formed.
According to the Properties of triangle, the length of the third side of a triangle must be greater than the sum of any two of a triangle's sides.
Given the side lengths are 3.5, 3.5 and 9;
Sum of two sides = 3.5 + 3.5 = 7 cannot exceed 9
Thus, it is clear that a triangle cannot be formed using the specified side lengths of 3.5, 3.5, and 9.
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the length of time it takes to find a parking space at 9 a.m. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. seventy percent of the time, it takes more than how many minutes to find a parking space?
Seventy percent of the time, the length of time to find a parking space takes more than 4 minutes.
For a normally distributed set of data, given the mean and standard deviation, the probability of having the data less than a value can be determined by solving the z-score and using the z-table.
If the probability is 70%, then, using the z-table, the z-score would be -0.52485.
at p = 1 - 0.70 = 0.30 z = -0.52485
Using the formula for finding the z-score, solve for the data value, x.
z-score = (x – μ) / σ
where x = individual data value
μ = mean = 5
σ = standard deviation = 2
z-score = (x – μ) / σ
-0.52485 = (x - 5) / 2
x - 5 = -1.0497
x = 3.9503
Round off to the nearest whole number.
x = 4
Hence, 70% of the time, it takes more than 4 minutes to find a parking space.
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The linear function f(x) is represented in the graph, and the linear function g(x) is represented in the table. Graph of linear function f of x going through negative 4 comma negative 1, negative 2 comma 0, 0 comma 1, and 4 comma 3. x g(x) −4 3 0 1 2 0 4 −1 Which of the following best compares the slopes and y-intercepts of the two functions? (1 point) The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
The correct option regarding the slope and the intercept of the linear functions is given as follows:
The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
What is the definition of a linear function?The definition of a linear function is presented as follows:
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope of the function, which is the rate of change of the output variable y relative to the input variable x.b is the y-intercept of the function, which is the value of y when the function crosses the y-axis, that is, when x = 0.The points that compose function f(x) are given as follows:
(0,1) and (4,3).
Hence:
The slope is of 0.5, as when x increases by 4, y increases by 2.The intercept is of 1, as when x = 0, y = 1.The points that compose function g(x) are given as follows:
(0,1) and (4,-1).
Hence the coefficients are as follows:
The slope is of -0.5, as when x increases by 4, y decreases by 2.The intercept is of 1, as when x = 0, y = 1.Hence the correct option is:
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The ages of Michael, Flo, Ella and Arlo add
up to 60 years.
The ratio of Michael's age to Flo's age to
Ella's age to Arlo's age is 3:7:6:4.
How many years old is Flo?
PLEASE HELP ASAP
The age of Flo based on the ratio is 21 years.
How to calculate Flo's age?From the information illustrated, the ages of Michael, Flo, Ella and Arlo add up to 60 years and the ratio of Michael's age to Flo's age to 3:7:6:4.
In this case, Flo is represented as 7 and the total ratio is (3+7+6+4) = 20
Therefore the age will be:
= 7/20 × Total age
= 7/20 × 60.
= 21
Flo is 21 years
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Each week Martin revived 8$ allowance. He pent five dollar. How much money did Martin have left to put in aving
Answer:
3
Step-by-step explanation:
suppose that 11% of people are left-handed. if 5 people are selected at random, find the probability that exactly 2 are left- handed.
The probability that exactly 2 people are left handed if 11% people are left handed and 5 are selected at random is 100.
Probability is a method with the help of which we chose a particular object on random from many given objects.
P(E) = no of favorable outcomes/total number of outcomes
Let there are 100 people
11% are left handed = 11% of 100 = 11
5 are selected randomly.
No of favorable outcomes = 5
Total no of outcomes = 11
Hence, the probability that people selected are left handed is 5/11
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From the given percent of people are left handed and probability of exactly 2 of them are left handed from 5 selected at random is equal to 0.0853.
As given in the question,
Number of people selected at random 'n' = 5
Percent of people are left handed = 11%
Probability of success 'p' = 0.11
Probability of failure 'q' = 1- p
= 1-0.11
= 0.89
Exact number of left handed people 'x' = 2
Probability of people that are exactly left handed
= ⁿCₓ (p)ˣ(q)ⁿ⁻ˣ
=⁵C₂(0.11)²(0.89)⁵⁻²
= (5!/ (5-2)!2!) × (0.0121) × (0.704969)
= 10 × (0.0121) × (0.704969)
= 0.0853
Therefore, from the given percent of people are left handed and probability of exactly 2 of them are left handed from 5 selected at random is equal to 0.0853.
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Which calculation can be used to find the value of y in the equation y3 = 27?
Answer:3 and multiplication
Step-by-step explanation: 3 times 9 equals 27.
15. Evie added 4 stamps to her collection and then lost 9 stamps when she brought her stamp book outside. Write an equation that shows Evie's net gain or loss.
The linear equation y = x - 5 show's Evie's net loss or gain
Linear EquationLinear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.
In solving this problem, we have to write the problem in a form of linear equation.
Let;
y = The number of stamps available nowx = number of stamps she originally hady = x + 4 - 9
y = x - 5
The equation to show Evie's net gain or loss is y = x - 5
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Amar owes $2,000 on his credit card with a minimum percentage of 4% or $60, whichever is higher. How much is the minimum payment due?.
Amar owes $2,000 on his credit card with a minimum percentage of 4% or $60, whichever is higher.
The Minimum Payment due is $ 80 as it is higher from the minimum payment of $60.
Given :
Credit Card amount = $2000
Minimum Percentage = 4%
By using the below formula we can find the minimum balance
Minimum Balance = Credit Card Amount * Minimum Percentage
Minimum Balance = $2000 * 4%
= $80
So According to the question Amar owes $2000 on his credit card with a minimum percentage of 4% or a minimum payment of $60, whichever is higher.
So the minimum percentage of 4% or minimum balance is higher than $60.
So that’s why the minimum payment due is $80.
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a 70% cu-30% zn brass sheet is 0.09675 cm thick and is 40% cold-rolled. what must be the final thickness of the sheet? (1 point)
The final thickness of the sheet is = 0.0669 cm
brasses are copper zinc alloys. In general, they have good strength and corrosion resistance, although their structure and properties are a function of zinc content , Alloys containing up to approximately 35% zinc are single phase alloys, consisting of a solid solution of zinc and alpha copper
% cold reduction = (initial thickness - final thickness ) × 100
initial thickness
0.30% = (0.0955cm - final thickness ) × 100
0.0955cm
final thickness = 0.0669cm
Brass in an alloy of copper and zinc, bonze is an alloy containing 80% of cropper. A fuses mass of brass and bronze is found to contain 74% . Brass, alloy of copper and zinc, of historical and enduring importance because of its hardness and workability
Hence the final thickness of sheet is 0.0669 cm
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We are evaluating a project that costs $786,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 65,000 units per year. Price per unit is $48, variable cost per unit is $25, and fixed costs are $725,000 per year. The tax rate is 22 percent, and we require a return of 10 percent on this project.
We are evaluating a project that costs $786,000, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 65,000 units per year. Price per unit is $48, variable cost per unit is $25, and fixed costs are $725,000 per year. The tax rate is 22 percent, and we require a return of 10 percent on this project
The tax rate for 10% is IRR = 78%.
The Initial evaluating cost is $786000 and the
Depreciation expense per year will be = $786,000 / 8 = $98,250.
and the contribution margin per unit = $48 - $25 = $23
total units sold Projected per year = 65,000
fixed costs will be per year = $725,000
At Present the tax rate = 22%
Net cost fixed per year = -$786,000
Net Cost Fixed year 1-8 = {[($23 x 65,000) - $98,250 - $725,000] x 0.78} + $98,250 = $622,215
Net Per Variable = $2,533,471.10
Hence the answer is, The tax rate for 10% is IRR = 78%.
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11. Trey drained 12 quarts of water from a cooler after a camping trip. The graph shows the remaining quarts of water as a linear function of x, the time in minutes. Which best represents the domain and range of the function?
Answer:
The domain is the time, in minutes from 0 to however long it takes to drain the cooler.
The range is from 12 quarts water to empty.
Step-by-step explanation:
I don't see a graph, but will use the given information to identify a domain and range for the information provided.
The domain is the range of values that are possible for the x axis. In this case, the x axis it time, in minutes. If we set x as the time, in minutes, that the water has been draining, time = 0, is the start of the process.
The y axis, the range, starts at 12 quarts at time = 0. It then decreases with time until the cooler is empty. The range of the function is thus 12 quarts to 0 quarts: Full to empty.
If we knew the actual rate that the cooler drains (e.g., quarts/minute), we could estabish an upper limit to the domain. If a graph were shown of the data, this rate could be calculated and an upper end to the domain could be set. If the rate were 2 quarts/minute, the upper end of the domain would be (12 quarts/2 quarts/minute) = 6 minutes. The domain would be 0 - 6 minutes.
You earn $10.00/hour. You invest $4,000.00 at an interest rate of 5% APR for a year. How much interest did that savings earn in a year in terms of hours of work?
-100 hours
-20 hours
-40 hours
-400 hours
The interest that the savings earned in a year in terms of hours of work is B. 20 hours.
What is the interest?Interest is the additional earning obtained from an investment.
It is computed as the principal multiplied by the annual percentage rate (APR) and the period.
Earnings per hour = $10
Investment = $4,000
APR = 5%
Period of investment = 1 year
Interest earned = $200 ($4,000 x 5% x 1)
Interest earned expressed as hours = 20 hours ($200/$10)
Thus, the investor, who earns $10 per hour, earns 20 hours in interest by investing $4,000 at 5% in a year.
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The sampling distribution of the sample mean will always have the same _________ as the original distribution.
The sampling distribution of the sample mean will always have the same the mean of the original non-normal distribution, as the original distribution.
What is distribution?
Each of these samples contains a mean, and if we add up all of the means, we can construct a probability distribution that explains the distribution of the means. As long as we have sufficient samples, as will be discussed later, this distribution is always normal and is referred to as the sampling distribution of the sample mean.
Since the sample mean's sampling distribution is normal, we can naturally calculate the distribution's mean and standard deviation and utilise that information to analyse probability questions.
Here, The sample variance is equal to the population variance divided by the sample size if the population is infinite and the sampling is random, or if the population is finite but we are sampling with replacement.
So we need to use the mean of non-normal distribution.
Hence the answer will be the mean of the original non-normal distribution.
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11
How much money is pictured below?
LIBERTY
LEEE
¢
SEPERTY
15
16
Answer:
Step-by-step explanation:
Ok:
1. The first one seems to be a quarter which is 25 cents
2. The next two are dimes which are 10 cents each
3. Caculate
25+10+10= 45 cents in total!
4. Answer: 45 cents
Identify the maximum value of extreme values possible for each polynomial f(x)=5x^2-8x+12
[tex](\frac{4}{5}, \frac{44}{5})[/tex] is the maximum value of extreme values for the given polynomial.
What is extreme value?
According to the Extreme Value Theorem, if a function is continuous on the interval [a, b], it must have a maximum and a minimum on that range.
Consider, the given function
f(x) = 5x^2 - 8x + 12 ..(1)
Since, if y = f(x) is a function, then the value of x where f'(x) is zero is called extreme value.
Differentiate equation (1) with respect to x.
10x - 8 = 0
10x = 8
x = 8/10
x = 4/5
Plug x = 4/5 in equation (1),
[tex]f(\frac{4}{5}) = 5(\frac{4}{5})^2 -8(\frac{4}{5})+12\\ = \frac{16}{5} -\frac{32}{5} + 12\\ = \frac{44}{5}[/tex]
Therefore, [tex](\frac{4}{5}, \frac{44}{5})[/tex] is the maximum value of extreme values for the given polynomial.
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Answer:
Answer
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author link
tutorconsortium344
is the maximum value of extreme values for the given polynomial.
What is extreme value?
According to the Extreme Value Theorem, if a function is continuous on the interval [a, b], it must have a maximum and a minimum on that range.
Consider, the given function
f(x) = 5x^2 - 8x + 12 ..(1)
Since, if y = f(x) is a function, then the value of x where f'(x) is zero is called extreme value.
Differentiate equation (1) with respect to x.
10x - 8 = 0
10x = 8
x = 8/10
x = 4/5
Plug x = 4/5 in equation (1),
Therefore, is the maximum value of extreme values for the given polynomial.
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Be wise think wise. YES PLEASE BRAINILESTor sum
Step-by-step explanation:
I thought of a 3 digit number. Each digit i the quare of the digit to the right. What i my number?
The answer to the given question is 111.
The complete question might be as follows:
I thought of a 3 digit number. Each digit is the square of the digit to the right. What is my number?
= x*100 + y*10 + z.
Requirements:
y = z^2
x = y^2.
Now we shall start to give values to z. Let us start with zero.
If z = 0, then: y = 0^2 = 0, then: x = 0^2 = 0. Then the number would be 0*100 + 0*10 + 0 = 0. This is not a 3 digit number.If z = 1, then: y = 1^2 = 1, then: x = 1^2 = 1. Then the number would be 1*100 + 1*10 + 1 = 111. This is a 3 digit number.If z = 2, then: y = 2^2 = 4, then: x = 4^2 = 16. Then the number would be 16*100 + 4*10 + 2 = 1642. This is not a 3 digit number. This happened because the first digit (x) is not a single digit number.So, values of z which are equal or larger than 2 can be eliminated.Hence, for the question: I thought of a 3 digit number. Each digit is the square of the digit to the right. What is my number? The answer is 111, because the 3 digit number that would fit the requirements mentioned is only 111.
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Solve the following multi-step equations and write the answers on the solutions column. If the answer is correct, it will turn green and part of the picture will appear
Answer: for the first question it is 4
Step-by-step explanation:
5x -3x= 15-7
2x=8
2x/2x 8/2
x=4
Answer:
[tex]10x + 17 - 5x = 27 \\ 10x - 5x = 27 - 17 \\ 5x = 10 \\ x = \frac{10}{5} \\ x = 2 [/tex]
Solve this.
15 = x/6 - 1
A) x=96
B) x=90
C) x=84
D) x=80
The value of x in the algebraic expression is option A 96.
Given,
The algebraic expression; 15 = x/6 - 1
We have to solve the expression and find the value of x.
Here,
15 = x/6 - 1
First solve the right hand side
x/6 - 1 = (x - 6) / 6
Now,
15 = (x - 6) / 6
Multiply both sides with 6.
15 × 6 = (x - 6) × 6 / 6
90 = x - 6
Now add 6 to both sides
90 + 6 = x - 6 + 6
x = 96
That is,
The value of x in the algebraic expression is option A 96.
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Write 0.0401907 correct to
3 significant figures.
Answer:
0.0401907 = 0.040 (to 3dp)
Tell whether (1, 0) is a solution of y = 3x − 3.
O yes
O no
(1, 0) is the solution of the line y = 3x - 3
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
The given line is
y = 3x - 3
To test whether (1, 0) is a solution of the line y = 3x - 3
Putting x = 1
y = 3[tex]\times[/tex] 1 - 3 =
y = 3 - 3
y = 0
(1, 0) is the solution of the line y = 3x - 3
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Please help me on imagine math please
Can anyone solve this for me?
Answer:
21.17 to 2d.p.
Step-by-step explanation:
Using Pythagoras rearrage to find b c^2-a^2 = b^2
c= hypothenuse
32^2 = 1024 and 24^2 = 576
1024 -576 = 448
[tex]\sqrt{448}[/tex] = 21.1660105
21.17 to 2d.p.
Commute times in the U.S are heavily skewed to the right We select random sample of 500 people from the 2000 U.S, Census who reported a non-zero commute time: In this sample the mean commute time is 27.6 minutes with standard deviation of 19.6 minutes: Are researchers able to conclude from this data that the mean commute time in the U.S.is less than half an hour? Conduct a hypothesis test at the 5% level of significance using an online applet (directions) or calculating and using the T-Distribution Calculator above. Based on your hypothesis test; what can we conclude? Nothing: The distribution of the variable in the population is heavily skewcd, s0 the conditions for use of t-model are not met We cannot trust that the p-value accurate for this reason: With mean ol 27.6 minutes, the data supports the clalm that the average commute time Is less than 30 minutes, but the difference is not statistically significant We fail to reject the null hypothesis that the mean commute time in the U.S, in the year 2000 was 30 minutes: With a mean of 27.6 minutes the data supports the claim that the average commute time is significantly less than 30 minutes We reject the null hypothesis that the mean commute time in the U.S.in the year 2000 was 30 minutes
We conclude that the mean commute time in the U.S. is less than half an hour.
We are given that a random sample of 500 people from the 2000 U.S. Census is selected who reported a non-zero commute time.
In this sample the mean commute time is 27.6 minutes with a standard deviation of 19.6 minutes.
Let = mean commute time in the U.S..
So, Null Hypothesis, : [tex]H_0:[/tex] μ ≥ 30 minutes {means that the mean commute time in the U.S. is more than or equal to half an hour}
Alternate Hypothesis, : [tex]H_A[/tex]: μ < 30 minutes {means that the mean commute time in the U.S. is less than half an hour}
The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;
T.S. = (X -μ)/[tex]{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, X = sample mean commute time = 27.6 minutes
s = sample standard deviation = 19.6 minutes
n = sample of people from the 2000 U.S. Census = 500
So, the test statistics = (27.6 - 30)/[tex]\frac{19.6}{\sqrt{500} }[/tex] ~ [tex]t_4_9_9[/tex]
= -2.738
The value of t test statistic is -2.738.
Also, P-value of test statistics is given by the following formula;
P-value = P( [tex]t_4_9_9[/tex] < -1.645)
Since, we know that at large sample size, the t distribution follows like normal distribution, that means;
P( [tex]t_4_9_9[/tex] < -1.645) = P(Z < -1.645) = 1 - P(Z ≤ 1.645)
= 1 - 0.95002 = 0.04998
Now, at 5% significance level the t table gives critical values of -1.645 at 499 degree of freedom for left-tailed test.
Since our test statistic is less than the critical value of t as -2.378 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean commute time in the U.S. is less than half an hour.
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0.60 gal to 0.12 gal as a fraction
Answer:
0.60 gal to 0.12 gal can be rewritten as:
[tex]\frac{0.60}{0.12} =\frac{0.6}{0.6(0.2)} =\frac{1}{0.2}[/tex]
[tex]\frac{1}{0.2}*1=\frac{1}{0.2}*\frac{10}{10} =\frac{10}{2} =5[/tex]
(e) what is the probability that the actual weight differs from the prescribed weight by more than 0.45 g? (round your answer to four decimal places.)
Determine the probability that actual weight is within 0.45 g of the prescribed weight we need to integrate with 2.55 to 3.45
we have to integrate with : 2.55 to 3.45
p(3-0.45<X<3+0.45)
P( 2.55<X<3.45)
= [2.7-24.47-24.3+48.609/3]
=0.6325
What is probability:
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
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The question was incomplete. Check below the complete question.
The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf. f(x) = k 1 ? (x ? 3)2 2 ? x ? 4 0 otherwise.
Johan starts a new job. His salary when hired is $31,000.
He receives a raise of 2.5% every year. Write an equation to model Johan’s salary after
x years. After how many years will Johan’s salary be greater than $45,000?
The exponential growth from the exponential function shows it will take approximately 15.09 years for his salary to reach $45000
Exponential FunctionAn exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x. This could also be an exponential growth or exponential decay which depends on the situation.
The exponential function is an important mathematical function which is of the form f(x) = ax
Data;
Principal (p) = $31000rate = 2.5%final amount = $45000time = ?The exponential function to represent this will be
45000 = 31000(1 + 0.025)ˣ
x = 15.09 years
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