Aliyah either takes a bus or Uber to get to work and has a
$240 monthly budget for her round trip weekday
commute. A bus ride costs $3, and an average Uber costs
$12.
a Create an equation that represents the

Answer:

Zeros → (-2, 0) and (4, 0)

Step-by-step explanation:

Equation of the graph has been given as,

y = \(\frac{1}{2}x^{2} -x-4\)

For zeros of the function,

y = 0

Therefore, \(\frac{1}{2}x^{2} -x-4=0\)

By solving the equation algebraically,

x² - 2x - 8 = 0

x² - 4x + 2x - 8 = 0

x(x - 4) + 2(x - 4) = 0

(x + 2)(x - 4) = 0

x = -2, 4

Therefore, coordinates of the zeros will be (-2, 0) and (4, 0).

Let's confirm the zeros (x-intercepts) from the graph attached,

Coordinates of the x-intercepts are,

(-2, 0) and (4, 0)

Answer:2x-1=0

Step-by-step explanation:

x=1/2

Cross multiply

2x=1

Subtract 1 from both sides

2x-1=1-1

2x-1=0

The equation below has a solution of x= 1/2 will be 2x-1=0.Option A is correct.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

Given expression;

x=1/2

2x=1

Take 1 away from both sides.

2x-1=1-1

2x-1=0

The equation below has a solution of x= 1/2 will be 2x-1=0.

Hence, option A is correct.

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This question is Incomplete

Complete Question

What sample size is needed to give a margin of error within ± 13 in estimating a population mean with 99% confidence, assuming a previous sample had s=116

Answer:

The sample size n = 530 samples

Step-by-step explanation:

Margin of Error formula = z × standard deviation/√n

Margin of Error = ± 13

Standard deviation = 116

z = z score of 99% = 2.58

±13 = 2.58 × 116/√n

Cross Multiply

±13 × √n = 2.58× 116

±13 × √n = 299.28

√n = 299.28/±13

√n = ± 23.0215384615

Square both sides

(√n)² = (±23.0215384615)²

n = 529.991233134

Approximately , n = 530 samples

The equivalent expressions are given below;

a) x²+3x+5

b) x²-3x+5

c) 3x³+15x

d)  x²+5/3x

Given the following function

f(x)=x²+5 and;

g(x)=3x

a) (f + g)(x) = f(x) + g(x)

(f + g)(x) = x²+5 + 3x

(f + g)(x) = x²+3x+5

b)  (f - g)(x) = f(x) - g(x)

(f - g)(x) = x²+5 - 3x

(f - g)(x) = x²-3x+5

c) (f * g)(x) = f(x) * g(x)

(f * g)(x) = 3x(x²+5)

(f * g)(x) = 3x³+15x

d) (f/g)(x) = f(x)/g(x)

(f/g)(x) = x²+5/3x

This expressions gives the equivalent answer.

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Answer:

81

Step-by-step explanation:

9x9 = 81

Answer:

\(2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25\)

Answer:

15

Step-by-step explanation:

The thermometer reading would be 73.48°C.

The boiling point of water is generally considered to be 100°C. According to the given information, the temperature of the liquid in the thermometer is 26.52°C lower than the boiling point of water. Therefore, to find the thermometer reading, we subtract 26.52 from 100.

100 - 26.52 = 73.48

Hence, the thermometer reading would be 73.48°C.

In this scenario, we are assuming that the thermometer is calibrated to measure temperature in Celsius. The boiling point of water at standard atmospheric pressure is 100°C, and the given information states that the liquid in the thermometer is 26.52°C lower than the boiling point.

By subtracting 26.52 from 100, we obtain a reading of 73.48°C.

Thermometers work by utilizing the principle that certain substances, such as mercury or alcohol, expand or contract with changes in temperature. The expansion or contraction is measured using a scale, which is marked with various temperature values.

In this case, the thermometer is calibrated in Celsius, so we refer to the Celsius scale. By subtracting 26.52 from 100, we find the temperature at which the liquid in the thermometer is settled, which is 73.48°C.

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Answer:

5.164×10^-5

Step-by-step explanation:

\(5.164 \times {10}^{ - 5} \)

Answer:

What is the minimum:

What is the maximum:

What is the range:

How many data are displayed in the table?

Answer:

There are 32 ferrets, 112 rabbits and 16 dogs at the shelter.

Step-by-step explanation:

There are 160 animals at the shelter. You know that of this amount of animals,\(\frac{1}{5}\) are ferrets. So, the number of ferrets can be calculated by:

\(\frac{1}{5}*160\)

To multiply a fraction by a whole number, any integer n can be written as the fraction \(\frac{n}{1}\). Then you multiply the numerators and denominators. In this case:

\(\frac{1}{5}*160=\frac{1}{5}*\frac{160}{1} =\frac{1*160}{5*1} =\frac{160}{5}\)

Now you must reduce to the simplest form. To get a simplified result, divide the numerator by the denominator. In this case:

\(\frac{160}{5}\) = 160 ÷ 5= 32

So, there are 32 ferrets at the shelter. Then, the number of animals remaining is calculated by the difference:

160 animals - 32 ferrets= 128 animals

\(\frac{7}{8}\) of the remaining animals are rabbits. Then:

\(\frac{7}{8}*128\)

Solving in the same way as in the previous case:

\(\frac{7}{8}*128=\frac{7}{8}*\frac{128}{1} =\frac{7*128}{8*1} =\frac{896}{8}\)

\(\frac{896}{8}\)= 896 ÷8= 112

So, there are 112 rabbits at the shelter.  Then the remaining animals will be dogs, which will be calculated by the difference:

128 animals - 112 rabbits= 16

Finally, there are 16 dogs at the shelter.

Answer:

3 7/12

Step-by-step explanation:

Answer: 168

Step-by-step explanation: 70/5=14. 14x7=98.  70+98=168.

The 95 percent confidence interval is (0.20, 0.32).

a. We can construct a 95% confidence interval to estimate the percentage of yellow peas as follows:

Let p = proportion of yellow peas = 155/595 = 0.26

Sample size = n = 595

Standard error = SE = √(p × (1-p) / n) = √(0.26 × (1-0.26) / 595) = 0.03

95% confidence interval = p ± 1.96 × SE

= 0.26 ± 1.96 × 0.03

= 0.26 ± 0.06

So, the 95% confidence interval is (0.20, 0.32).

b. Yes, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow, as the 95% confidence interval does not include the expected value of 0.25.

Therefore, the 95 percent confidence interval is (0.20, 0.32).

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Answer:

For 6, iT would be 26

Step-by-step explanation:

Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

One - way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

Step-by-step explanation:

ANOVA is a statistical technique designed to test mean of one or more quantitative populations.  In two-way ANOVA it equals the block mean. Column block means square is three-way ANOVA. It is a statistical technique designed to test mean of one or more quantitative populations. In two-way ANOVA it equals the block mean. Column block means square is three-way ANOVA.

One-way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

It should be the statistical technique that are made for testing the mean for one or more than one quantitative population. In two-way ANOVA it should be equivalent to the block mean. Here the column block represent the square be the three-way ANOVA.

Therefore, One-way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

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Answer:

\(f(300)=906\)

Step-by-step explanation:

\(f(x)=3x+6\\\\f(300)=3(300)+6\\\\f(300)=900+6\\\\\boxed{f(300)=906}\)

Hope this helps.

The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

The Mean is defined as the ratio of sum of numbers present in the data to the total numbers present in the data. Median is defined as the ratio of sum of middle numbers present in the data. Mode is defined as the most recurring number present in the data. Midrange is the ratio of the largest and smallest number in the data to 2.

Let's see how to calculate Mean, Median, Mode and Midrange.

Mean = 13 + 15 + 18 + 18 + 21 / 5

Mean = 85 / 5

Mean = 17

Median = 18 (as it is the middle term of the data)

Mode = 18 (as it is most recurring number)

Midrange = 21 + 13 / 2

Midrange = 34 / 2

Midrange = 17

Therefore, The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

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Answer:

\( = 367 \div 5 = 73 \: rem5 \\ = 73 \div 5 = 14 \: rem6 \\ = 14 \div 5 = 2 \: rem8 \\ = > 2865 _{five}\)

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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The period of the function is 1/60 minutes

As a result, blood pressure changes between each heartbeat as a consequence of these oscilllations happening every second.

Max value = 110 mmHg

the minimum = 50 mmHg.

This suggests that systolic pressure remains at 110 mmHg and diastolic pressure is still maintained at 50 mmHg.

blood pressure peaks occur at times t = (1/2 + 2 * k) / 120 seconds.

(a) The given function is:

p(t) = 80 + 30 * sin(120 * pi * t)

This is equivalent to sinusoidal function in the form of:

p(t) = A + B * sin(C * t)

Where:

A is the baseline value,

B is the amplitude, and

C determines the frequency of the function.

Information given in the problem

A = 80, B = 30, and C = 120 * pi.

The period of a sinusoidal function is given by:

Period = 2 * pi / C

Period = 2 * pi / (120 * pi) = 1/60 minutes

The period of the function is 1/60 minutes, which means that the blood pressure oscillates every 1/60 minutes or 1 second. As a result, blood pressure changes between each heartbeat as a consequence of these oscilllations happening every second.

(b) maximum and minimum values of a sinusoidal function

Max value = A + B

Min value = A - B

Substituting the values of A and B:

Max value = 80 + 30 = 110 mmHg

Min value = 80 - 30 = 50 mmHg

Max value = A + B giving values of 110 mmHg

the minimum is A - B delivering 50 mmHg.

This suggests that systolic pressure remains at 110 mmHg and diastolic pressure is still maintained at 50 mmHg.

(c)  the time at which the blood pressure is at its maximum, we solve for t when the sinusoidal function is at its peak.

sin(120 * pi * t) = 1

Taking the inverse sine of both sides:

120 * pi * t = pi/2 + 2 * pi * k (where k is an integer)

Solving for t:

t = (1/2 + 2 x k)/120 (for k = 0, 1, 2, ......)

implying that blood pressure peaks occur at times t = (1/2 + 2 * k) / 120 seconds.

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Answer:

The p-value is 0.1228.

Step-by-step explanation:

Before testing the hypothesis, we need to find the sample mean and the standard deviation.

Sample of 13:

The sample mean is the sum of all values divided by 13. Using a calculator, it is: X = 28.15.

The sample standard deviation is the square root of the division of the sum of the differences squared between each value and the mean, by the number of values. Using a calculator, we get s = 4.0162.

A researcher wants to test whether the average gas mileage of this type of car is different from 30 mpg.

At the null hypothesis, we test if the average gas mileage is of 30 mpg, that is:

\(H_0: \mu = 30\)

At the alternate hypothesis, we test if the average is different from 30, that is:

\(H_1: \mu \neq 30\)

The test statistic is:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

30 is tested at the null hypothesis:

This means that \(\mu = 30\)

From the sample:

\(X = 28.15, s = 4.0162\).

Value of the test-statistic:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{28.15 - 30}{\frac{4.0162}{\sqrt{13}}}\)

\(t = -1.66\)

P-value of the test:

The p-value of the test is the probability that the sample mean differs from 30 by at least |28.15 - 30| = 1.75, which is a two-tailed test with t = -1.66 and 13 - 1 = 12 df.

Using a t-distribution calculator, this p-value is 0.1228.

Answer:

The car turns right because the person driving hit the right blinkers and wants to go right.

Step-by-step explanation:

common sense

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

From the question, we have the following ordered pairs

x intercepts = (6,0) and (18, 0)

Vertex = (12, -36)

Points (21, 41.25)

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is the calculated using

m = [f(21) - f(18)]/[21 - 18]

This becomes

m = [f(21) - f(18)]/3

Substitute the known values in the above equation

m = [41.25 - 0]/3

Evaluate the difference

m = 41.25/3

Evaluate the quotient

m = 13.75

Approximate

m=14

Hence, the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

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Complete question

The graph below shows the value of Edna's profits f(t), in dollars, after t months:

What is the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month?

See attachment for graph

Answer:

15/20 inches

Step-by-step explanation: