Sarah is training for a bike race. She rides her bike 5 3/4 miles in 1/3 hour. What is Sarah’s rate in miles per hour. Express your answer as a mixed number

Answer:

B. 80

Step-by-step explanation:

(I used a calculator, but I shall explain better for ya :)

Make 32% a fraction:

32/100

Finding the fraction of a number is the same as multiplying the fraction with the number:

32/100 x 250

Just divide and multiply since a fraction is the same thing as dividing

your answer = 80

using a calculator simply enter 32 ÷ 100 x 250 which will give you 80 as the answer.

Answer:

She paid $10.36

Step-by-step explanation:

Answer:

10.36

Step-by-step explanation:

4 x 2.59 = 10.36

Answer:

9x + 4y < 110

Step-by-step explanation:

This inequality works because its the cost of hammers ($9) multiplied by how many hammers are bought (x) plus the cost of wrenches ($4) multiplied by how many wrenches are bought (y). The total cost has to be less than 110.

Answer:

Step-by-step explanation:

A transformation that changes the orientation of a figure but not the orientation of the vertices is called a "reflection."

A reflection is a transformation that flips a figure over a line, called the "line of reflection." The line of reflection can be a line on a coordinate plane, or it can be a line in the space of the figure. The transformed figure, or the image, is a mirror image of the original figure, with respect to the line of reflection. The line of reflection is the perpendicular bisector of the line connecting any two non-adjacent vertices of the figure, then the figure's orientation remains unchanged but it's flipped over that line.

For example, if you reflect a square over its diagonal line, the square will be flipped but its vertices will still be in the same order, so the orientation won't change.

The power of 0.95 shows that there is a 95% chance of rejecting the alternative hypothesis of p = 0.16 where the true proportion is actually 0.08. That is if the proportion of users who experience abdominal pain is actually 0.08, then there is a 8% chance of supporting the claim that the proportion of users who experience abdominal pain is more than 0.08.

Given that the alternative value of p is 0.16, it means that the power of the test is 0.95.

This means that if the true proportion of drug users experiencing abdominal pain is indeed 0.16, then by conducting the hypothesis test with a significance level of 0.05, we will correctly reject the null hypothesis and support the claim that more than 8% (0.08) of the drug's users experience abdominal pain with a probability of 0.95.

In other words, the power of 0.95 indicates that the test has a high chance (95%) of correctly detecting a true difference and correctly concluding that the proportion of drug users experiencing abdominal pain is greater than 8% when the true proportion is actually 16%. It demonstrates the test's ability to identify and support the alternative hypothesis when it is true.

It's important to note that the power of the test is influenced by factors such as sample size, significance level, effect size, and variability. In this case, with a power of 0.95, there is a high probability of detecting the claimed difference if it truly exists.

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The end-points of the line segment will be negative 1.25 and 0.25.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,

⇒ - 0.50 ± (1.50) / 2

Simplify the expression, then we have

⇒ - 0.50 ± (1.50) / 2

⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2

⇒ - 0.50 - 0.75, - 0.50 + 0.75

⇒ - 1.25, 0.25

The end-points of the line fragment will be negative 1.25 and 0.25.

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Answer:

y = 27

Step-by-step explanation:

line segment BA and CD are congruent, turn them into an equation

3y - 59 = y - 5

subtract 1y from both sides, you get 2y - 59 = -5

then, add 59 to both sides and the equation is now 2y = 54

divide each side by 2 and you get the value of y (y = 27)

The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)

From the question, we have the following function definition that can be used in our computation:

cos(xº)

Changing the degree into radian, we have

cos(xπ/180)

Express as a function

So, we have

y = cos(xπ/180)

When the cosine function is differentiated, we have

y' = -sin(xπ/180)

Hence, the differentiated function is y' = -sin(xπ/180)

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Given statement solution is :- The manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.

To determine if the manager will have enough funds to cover the nightly payroll for the next four weeks, we need to calculate the total cost for four weeks and compare it to the amount set aside.

The nightly payroll has a mean of $2200 and a standard deviation of $300. Since there are seven nights in a week, the weekly payroll can be calculated as:

Weekly Payroll = Nightly Payroll * Number of Nights in a Week

= $2200 * 7

= $15,400

To calculate the total cost for four weeks, we multiply the weekly payroll by four:

Total Cost for Four Weeks = Weekly Payroll * Number of Weeks

= $15,400 * 4

= $61,600

Now, let's calculate the z-score using the formula:

z = (X - μ) / σ

Where:

X = Total Cost for Four Weeks

μ = Mean of the distribution

σ = Standard deviation of the distribution

z = ($61,600 - $2200) / $300

z = $59,400 / $300

z ≈ 198

To determine if the manager will have enough funds to cover the payroll, we need to find the proportion of the distribution that is less than or equal to the z-score. This can be done by consulting a standard normal distribution table or using statistical software.

For a z-score of 198, the proportion in the tail of the distribution is essentially 1 (or 100%). This means that the manager is virtually guaranteed to have enough funds to cover the payroll for the next four weeks.

Since the manager has set aside $10,000, which is less than the calculated total cost of $61,600, he will indeed have enough funds to cover the payroll.

Therefore, the manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.

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Answer:

Option A.

Step-by-step explanation:

The parent function is the quadratic function, that is:

\(f(x) = x^2\)

Function g:

The function g is the function f concave down, that is, -f.

Also, for the parent function, we have that y = 1 when x = 1. On the function g, otherwise, we have that when x = 1, y = -1/3. So:

\(g(x) = -\frac{1}{3}f(x) = -\frac{1}{3}x^2\)

The correct answer is given by option A.

-3x^2

just did it and it’s correct. Your welcome <3

The probability distribution of the number of customers that enter the store on a given day is described as follows:

Poisson with a mean of 70 customers.

In a Poisson distribution, the mass function probability that X represents the number of successes of a random variable is given by the equation presented as follows:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

A combination of Poisson variables is a Poisson variable, hence the daily distribution is a Poisson variable with mean given by the sum of these following observations:

Hence the mean is of:

8 + 16 + 18 + 28 = 70 customers.

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Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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The expression (-3)0 has a value of 0 when evaluated because a number multiplied by 0 gives 0

From the question, we have the following parameters that can be used in our computation:

(-3)0

The above statement is a product expression that multiplies the values of -3 and 0

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

(-3)0 = 0

This means that the value of the expression is 0 i.e a number multiplied by 0 gives 0

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The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.

To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.

Given the table:

X: 2 0 4

Y: -4 3 1

We can plot these points on a graph and see that they form a straight line.

Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.

Based on the given options, we can now evaluate each equation to see which one represents the line:

Y = 1/2x + 5

When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.

Y = -1/2x + 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.

Y = 2x - 3

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.

Y = -4x + 2

When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.

In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.

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Answer:

\(f(126) \approx 5.01333\)

Step-by-step explanation:

Given

\(\sqrt[3]{126}\)

Required

Solve using differentials

In differentiation:

\(f(x+\triangle x) \approx f(x) + \triangle x \cdot f'(x)\)

Express 126 as 125 + 1;

i.e.

\(x = 125; \triangle x = 1\)

So, we have:

\(f(125+1) \approx f(125) + 1 \cdot f'(125)\)

\(f(126) \approx f(125) + 1 \cdot f'(125)\)

To calculate f(125), we have:

\(f(x) = \sqrt[3]{x}\)

\(f(125) = \sqrt[3]{125}\)

\(f(125) = 5\)

So:

\(f(126) \approx f(125) + 1 \cdot f'(125)\)

\(f(126) \approx 5 + 1 \cdot f'(125)\)

\(f(126) \approx 5 + f'(125)\)

Also:

\(f(x) = \sqrt[3]{x}\)

Rewrite as:

\(f(x) = x^\frac{1}{3}\)

Differentiate

\(f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}\\\)

Using law of indices, we have:

\(f'(x) = \frac{x^\frac{1}{3}}{3x}\)

So:

\(f'(125) = \frac{125^\frac{1}{3}}{3*125}\)

\(f'(125) = \frac{5}{375}\)

\(f'(125) = \frac{1}{75}\)

So, we have:

\(f(126) \approx 5 + f'(125)\)

\(f(126) \approx 5 + \frac{1}{75}\)

\(f(126) \approx 5 + 0.01333\)

\(f(126) \approx 5.01333\)

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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The height of the stump is 3 ft.

The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.

In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:

h(0) = -16(0)² + 64(0) + 3

Since any term multiplied by zero is zero, we can simplify further:

h(0) = 0 + 0 + 3

Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.

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3x-1=4x+8-x

3x -4x +x = 8+1

4x -4x = 9

0x =9

x= 9/0 which is undefined .

Answer:

yes u would be on track.

Step-by-step explanation:

yes; 10 miles in 12 days is equivalent to 10 ÷ 2 = 5 miles in 12 ÷ 2 = 6 days.

:o)

The transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

A Transformation in Math is a process of moving an object (two-dimensional shape) from its original position to a new position.

Given that, a function f(x) undergo some transformations to become f(x+9)-1,

We know that,

Vertical Shifting:

Adding a constant to a function will shift its graph vertically (i.e. y = f (x) + c). Adding a positive constant c will shift the graph upward c units, while adding a negative constant c will shift it downward c units.

Horizontal Shifting:

Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right. Combining the two types of shifts will cause the graph of a function to shift up or down and right or left.

Therefore, there is transformation of a horizontal and vertical shift.

Hence, the transformations taking place in the given function is a horizontal left ward shift of 9 units and 1 unit upward vertical shift.

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Answer:

Mason is left with 54.7 pounds of apples

Answer:

2x + 1

Step-by-step explanation:

\(y = {x}^{2} + x - 1 \\ \\ differentiating \: w.r.t.x \: on \: both \\ sides \\ \\ \frac{dy}{dx} = \frac{d}{dx} ({x}^{2} + x - 1) \\ \\\frac{dy}{dx} = 2x + 1 - 0\\ \\ \frac{dy}{dx} = 2x + 1 \\ \\\)

60 is thaks for points

Step-by-step explanation:

I think

Answer:

2

Step-by-step explanation:

2 + 6 - 6

8 - 6

2

2 would be the answer

Answer:

z = -11, z = -2

Step-by-step explanation:

Given that, (\(f(z)=\sqrt{z+27} -z\)) and (\(f(z)=7\)), set up an equation that puts the first value of (\(f(z)\)) equal to the other given value of the function.

\(f(z)=\sqrt{z+27}-z=7\)

Use inverse operations to solve,

\(\sqrt{z+27}-z=7\\\\\sqrt{z-27}=7+z\\\\z+27 = (7+z)^2\\\\z + 27 = 49+14z+z^2\\ -(27+z)\\\\0 = z^2+13z+22\)

Factor,

\(0=(z+11)(z+2)\)

Solve using the zero product property, the zero product property states that any number times zero equals zero;

\(z=-11,z=-2\)

Answer:

Then solve the rest using the quadratic formula

Answer:

bxjfjxucjkkdndjkjhkjjnn

Answer:

Step-by-step explanation:

slope intercept form  =>   Y = mx + b  

find m... the slope by using any two points on the line

p1 = (0,5)  by inspection

p2=(4,6)  by inspection

find m  = y2-y1 / x2-x1

      m   = 6 - 5 / 4 - 0  

      m    =1 / 4

then use the slope intercept formula

y = 1/4x + 5      for your answer.  we know b = 5 b/c thats where the line crosses the y axis.

y = \(\frac{1}{4}\)x + 5    is the answer