April spent $10.25 on supplies to make lemonade. At least how many glasses of lemonade must she sell at $0.35 per glass to make a profit?
At most 29.29 glasses
At most 3.59 glasses
At least 30 glasses
At least 4 glasses

Answer:

Interest = $112

Step-by-step explanation:

From the question, we know that the amount deposited (principal amount) is $700, and the interest rate is 4%. We are asked to calculate the interest amount.

In order to calculate the interest amount, we have to use the following formula:

\(\boxed{I = \frac{PRT}{100}}\),

where:

• I = simple interest

• P = principal amount

• R = simple interest rate

• T = time

Using the above formula and the given information, we can calculate the simple interest:

I = \(\frac{700 \times 4 \times \ 4}{100}\)

 = $112

Therefore, she will be paid $112 interest in 4 years.

The given statement, "We can use the normal distribution to approximate the sampling distribution of the average (\(\bar X\)) for a small sample (n<30) even if our sample has clear outliers." is false.

Several random samples of a predetermined size are taken from the same population to generate a sampling distribution, which is a sort of probability distribution. You can better understand how a sample statistic fluctuates from sample to sample by using these distributions.

The given statement is false because when the sample size is small (n < 30) and the data have clear outliers, the normal distribution may not be a suitable approximation for the sampling distribution of the average (\(\bar X\)). In such cases, the presence of outliers can significantly affect the distribution, causing it to deviate from a normal distribution.

For small samples with outliers, it is generally recommended to use alternative methods or non-parametric tests that do not assume a specific distribution. These methods take into account the non-normal nature of the data and provide more robust and reliable results.

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Let's denote this probability as p, where p represents the probability of a single calculator failing. Therefore, the probability of both calculators failing is given by \(p^2\).

If the failure rate of the second calculator is the same and independent of the first, we can assume that the probability of failure for each calculator remains constant. To determine the probability of both calculators failing, we need to multiply the probabilities of each calculator failing independently. Since the events are independent, we can multiply the individual probabilities together.

Probability of both calculators failing = Probability of first calculator failing * Probability of second calculator failing

= p * p

= \(p^2\)

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Answer; the  Negative of 12 is -12

Step-by-step explanation: first of all the reciprocal of 12 is 1 over 12. so that's not it. The absolute value of 12 is still 12 so that's not it. So the only thing that it can be is the Negative of 12 is -12  

The answers to each part is mentioned above.

Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.

Equation for tank {1} -

y = 175 - 25x

Equation for tank {2} -

y = 200 - 30x

For the solution we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5

and

y = 200 - 150

y = 50

For the same amount of water we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5 hours

In tank (1), there is : 175 - 25 x 5 = 50 gallons

In tank (2), there is : 200 - 30 x 5 = 50 gallons

Therefore, the answers to each part is mentioned above.

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The correct choice to the question "Which of these statements is true about adding a number to the list?" is D: 11 would be added after 7.

A sequence is a list of items that follows a particular order

The given sequence of numbers is:

-9, -3, 7

This sequence is in increasing order from the least to the greatest

Note that:

-6  >  -9.

-6 should be added after -9 and not before it because the sequence is in ascending order. Therefore, option A is wrong

-2 >  -9.

-2 should be added after -9 and not before it because the sequence is in ascending order. Therefore, option B is wrong

5 < 7

5 should be added before 7 and not after it because the sequence is in ascending order. Therefore, option C is wrong

11 > 7

11 would be added to the sequence after 7 because the sequence is in ascending order. Option D is the correct choice

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Therefore, the standard deviation for the number of people with the genetic mutation in groups of 500 is approximately 6.726.

To find the standard deviation for the number of people with the genetic mutation in groups of 500, we can use the binomial distribution formula.

Given:

Probability of having the genetic mutation (p) = 0.09

Sample size (n) = 500

The standard deviation (σ) of a binomial distribution is calculated using the formula:

σ = √(n * p * (1 - p))

Substituting the given values:

σ = √(500 * 0.09 * (1 - 0.09))

Calculating the standard deviation:

σ ≈ 6.726 (rounded to three decimal places)

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If the allowable increase for a constraint is 100 units and we add 110 units of the resource, the impact on the objective function value depends on the specific problem and its constraints.

In general, adding more units of a resource beyond the allowable increase can lead to different outcomes:

Feasible Solution: If adding the additional 110 units of the resource still allows the problem to satisfy all constraints and remain feasible, the objective function value may improve or remain the same. This is because the extra resources can be utilized to optimize the objective function further.

Infeasible Solution: If adding the extra 110 units violates any of the problem's constraints, the solution becomes infeasible. In this case, the objective function value may become undefined or have no meaning since the problem cannot be solved within the given constraints.

It's important to note that the specific impact on the objective function value will depend on the nature of the problem, the objective function itself, and the constraints involved. Each problem may have its own unique behavior when additional resources are added beyond the allowable increase.

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The amount of wrapping paper used by Gavin to wrap a triangular prism box is 647.75 m².

What is a prism?

A prism is a polyhedron in geometry made up of an n-sided polygon basis, a second base that is a rigidly translated copy of the first base, and n additional faces that must all be parallelograms and connect the corresponding sides of the two bases.

The formula for area of rectangle is -

Area = length × breadth

The area of rectangle ABFG is -

Area = AB × BF

The value for line segment AB = 15 m

The value for line segment BF is -

BF = BC + CE + EF

BF = 14 + 7 + 15.65

BF = 36.65 m

So, the area of rectangle ABFG is -

Area = 15 × 36.65

Area = 549.75 m²

Now, the triangular prism has triangle part left.

The formula for area of triangle is -

Area = 1/2 × base × height

So, the area of triangle IJH is -

Area = 1/2 × IJ × JH

The value for line segment IJ = 14 m

The value for line segment JH = 7 m

So, the area of triangle IJH is -

Area = 1/2 × 14 × 7

Area = 49 m²

Since, there are two triangles (Δ IJH = Δ CDE ) so the area of total shape is -

Total area = Area of ABFG + 2(Area of Δ IJH)

Total area = 549.75 + 2(49)

Total area = 647.75 m²

Therefore, the area of triangular prism box is 647.75 m².

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Answer:

The total length of the fox is 30 3/5 inches

Step-by-step explanation:

Here, we are interested in calculating the total length of a fox, given the length of its head and body and also the length of its tail.

Mathematically, the total length of the fox = length of its head and body + length of its tail

length of the head and body = 19 4/5

length of its tail = 10 4/5

Plugging these values into the equation, we have;

19 4/5 + 10 4/5

99/5 + 54/5 = (99 + 54)/5 = 153/5 = 30 3/5 inches

Answer:

12

2

answer

hope it helps

The labor productivity of this manufacturing process in terms of dollars per labor hour is $73.47.

To find the labor productivity of this manufacturing process in terms of dollars per labor hour, we need to calculate the total revenue from the tuxedos and divide it by the total number of labor hours.

Total revenue from tuxedos = 96 tuxedos * $225 per tuxedo

                                               = $21,600

Total number of labor hours = 7 employees * 42 hours per employee

                                               = 294 labor hours

Labor productivity = Total revenue / Total number of labor hours

                               = $21,600 / 294 labor hours

                               = $73.47 per labor hour

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The domain of the function shown in the graph is the one in option A:

6 ≤ k ≤ 11

The domain of a function y = f(x) is the set of the inputs of the function. To identify the domain in a graph, we need to look at the horizontal axis (also called the x-axis).

On the graph we can see that it starts at x = 6 with a closed dot, and it ends at x = 11 also with a closed dot.

That means that these values belong to the domain, so we can write the domain as follows:

Domain = 6 ≤ k ≤ 11

(notice that the variable in the horizontal axis is k).

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Answer:

16.5 centimeters

I hope it will help you

Therefore , the solution of the given problem of percentage comes out to be $239.6 price he will pay on first store and $419.3 on second store.

In mathematics, a percentage is any value that can be written as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," or "pc." However, it is commonly indicated by the "%" mark. The proportional amount is flat and lacks any dimensions. Since percentages have a numerator of 100, they can be thought of as fractions. The percent symbol (%) must come after a number to denote that it is a percentage.

Here,
Given :

Price of television is $599

a)

First store is :

=> 50/100 * 599

=> 299.5

and

additional 20% discount :

=> 20/100 * 299.5

=> 59.9

current price =299.5 -59.9 =  $239.6

b)

=> 30/100 * 599

=> 179.7

=> 599 - 179.7

=> $419.3

Therefore , the solution of the given problem of percentage comes out to be $239.6 price he will pay on first store and $419.3 on second store.

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Answer:

y= -a/bx +c/b

m= -a/b

b= c/b

Step-by-step explanation:

Hope this helps

The given function f does not have a one-to-one correspondence between its domain and the range.

Set A, B, and C, prove that the given function f is not one-to-one: Let F(IR, R) be the set of all functions from I. We have to prove that FR, 2¹ > 2¹⁰¹. Here, I = {A, B, C}, i.e. the set of elements is {A, B, C}.To prove the function f is not one-to-one, consider the following steps:Step 1: Consider a function f ∈ F(2, 1) defined as: $f(A) = x$ and $f(B) = y$, where $x, y \in \{0, 1\}$.Step 2: Also, consider A, B $\in$ 2¹ such that A = $\{x, y\}$ and B = $\{y, z\}$. Here, x $\ne$ y, y $\ne$ z, and x $\ne$ z. Thus, we have A $\ne$ B.Step 3: Now, assume that f(A) = f(B). Hence, we have: $f(A) = f(B) \Rightarrow x = y$ and $y = z \Rightarrow x = z$Step 4: This contradicts the assumption that x $\ne$ z. Hence, the given function f is not one-to-one, i.e. it is many-to-one.Inference: Thus, the given function f does not have a one-to-one correspondence between its domain and the range.

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According to the question we have the radius of the sphere is 5 inches.

To find the radius of a sphere given its volume, we can use the formula:

V = (4/3)πr³

where V is the volume of the sphere and r is its radius. We are given that the volume of the sphere is:

V = 500π/3 cubic inches

Substituting this value into the formula, we get:

500π/3 = (4/3)πr³

Multiplying both sides by 3/4π, we get:

r³ = (500/4)

Simplifying, we get:

r³ = 125

Taking the cube root of both sides, we get:

r = 5

1. Divide both sides by π:
(500/3) = (4/3)r³

2. Multiply both sides by 3 to remove the fraction:
500 = 4r³

3. Divide both sides by 4:
125 = r³

4. Take the cube root of both sides:
r = 5

Therefore, the radius of the sphere is 5 inches.

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Answer:

mAB = 49°

mABC = 253°

mBAC = 156°

mACB = 311°

Step-by-step explanation:

You need to find the degree measures for these, which are said below:

mAB = 49°

mABC = 253°

mBAC = 156°

mACB = 311°

The length of the arcs are given as follows -

L{AB} = 0.854r

L{ABC} = 4.42r

L{BAC} = 2.8r

L{ACB} = 5.45r

The formula to calculate the arc length is -

L{arc} = (θ/360°) x 2πr

Given is a circle as shown in the image.

We can write the measure of arcs as -

{ 1 } -

L{AB} = (49°/360°) x 2πr

L{AB} = 307.72/360

L{AB} = 0.854r

{ 2 } -

L{ABC} = {(360 - 107)°/360°) x 2πr

L{ABC} = (253/360) x 2πr

L{ABC} = (1588.84/360)r

L{ABC} = 4.42r

{ 3 } -

L{BAC} = {(107 + 49)°/360°) x 2πr

L{BAC} = (156/360) x 2πr

L{BAC} = (979.68/360)r

L{BAC} = 2.8r

{ 4 } -

L{ACB} = {(311)°/360°) x 2πr

L{ACB} = (311/360) x 2πr

L{ACB} = (1953.08/360)r

L{ACB} = 5.45r

Therefore, the length of the arcs are given as follows -

L{AB} = 0.854r

L{ABC} = 4.42r

L{BAC} = 2.8r

L{ACB} = 5.45r

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To solve for x in the equation 6x + 5 = 7 + 2x, you want to isolate the variable on one side of the equation. First, you can subtract 2x from both sides to get 4x + 5 = 7.

Then, you can subtract 5 from both sides to get 4x = 2. Finally, you can divide both sides by 4 to get x = 1/2. Therefore, the solution is x = 1/2.
To solve the equation "6x + 5 = 7 + 2x" and find the value of x, follow these steps:
Step 1: Isolate the x terms on one side of the equation by subtracting 2x from both sides.
6x - 2x + 5 = 7 + 2x - 2x
Step 2: Simplify the equation.
4x + 5 = 7
Step 3: Isolate the x term by subtracting 5 from both sides.
4x + 5 - 5 = 7 - 5
Step 4: Simplify the equation.
4x = 2
Step 5: Solve for x by dividing both sides by 4.
4x / 4 = 2 / 4
Step 6: Simplify to find the value of x.
x = 1/2
So, the solution to the equation "6x + 5 = 7 + 2x" is x = 1/2.

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\((\stackrel{x_1}{-9}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{(-9)}}} \implies \cfrac{-1 +4}{-5 +9} \implies \cfrac{ 3 }{ 4 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{ 3 }{ 4 }}(x-\stackrel{x_1}{(-9)}) \implies {\large \begin{array}{llll} y +4= \cfrac{ 3 }{ 4 } (x +9) \end{array}}\)

Answer:

the correct answer is : option c)infinitely many

EXPLANATION:

infinite lines pass through a point . so, infinite solution is the correct answer

The temperature (t) needs to be greater than 60

So you would have t > 60

Answer:

t > 60

Explanation:

In order to answer this question we must determine two things: what two terms will be compared in the inequality and what symbol we will use to compare them. Let's start by finding, 'what two terms will be compared.'

Read the following quote from the problem...

"Forest fires are most likely to occur when the air temperature (t) is greater than 60°F."

Since the temperature (t) must be greater than sixty degrees to start a forest fire, these are the two terms that we will be comparing in the inequality.

Now, let's find out what symbol we will use to compare the terms.

Because the problem uses the phrase "greater than" to represent the comparison between the temperature of the air and an average of sixty degrees, the symbol we will be using in the inequality is the greater than sign, >.

Finally, use all the facts we have established to write the inequality.

· t = air temperature

· > = greater than

· 60 = max temp. before forest fire occurs

Therefore, the inequality for the solution is t > 60.

Answer:

$870.00 is the motorcycle price after a 40% discount

Step-by-step explanation:

discount = original price x discount % / 100

discount = 1450 x 40 / 100

discount = 1450 x 0.4

discount = $580.00

Final Price = Original Price - Discount

Final Price = 1450 - 580

Final Price = $870

Answer:

Step-by-step explanation:

a. (I) x = 65

(ii) vertically opposite angles are equal.

b. (i) 71 degrees

(ii) alternate interior angles are equal

c. (i) z = 180 - 71 = 109 degrees

(ii) angles on a line add up to 180 degrees

Answer:

x = 65°, y = 71°, z = 44°

Step-by-step explanation:

x and 65 are vertical angles and congruent, thus

x = 65°

y and 71 are alternate angles and congruent, thus

y = 71°

The sum of the 3 angles in a triangle = 180°, thus

z = 180° - (65 + 71)° = 180° - 136° = 44°

Hence

x = 65°, y = 71° and z = 44°

Angles π/2 and 3π/2 and for  0 and π are not in domain of secant function and cosecant function on given interval [0, 2).

The secant function is defined as the reciprocal of the cosine function, which means it is not defined when the cosine function is equal to zero.

In the interval [0, 2), the cosine function is equal to zero at π/2 and 3π/2.

The angles π/2 and 3π/2 are not in the domain of the secant function on the given interval [0, 2).

The cosecant function is defined as the reciprocal of the sine function, which means it is not defined when the sine function is equal to zero.

In the interval [0, 2), the sine function is equal to zero at 0 and π.

The angles 0 and π are not in the domain of the cosecant function on the given interval [0, 2).

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Answer:

36 ft

Step-by-step explanation:

If a 3-foot stick makes a 2-foot shadow that means the shadow is 2/3 the height. If the tree makes a 24-foot shadow, the equation to find the height is 24/(2/3).

x = 24/(2/3)

x = 24/.66666

x = 36

Answer:

The answer is y = 7/x -6.

Step-by-step explanation:

A linear function is one where x and y are both to the first power.  Using this knowledge, let's look at the options that we are given.

y = 4x + 9

In the above equation, both x and y are raised to the first power, so we know that this equation is linear.

y = 7/x - 6

In the above equation, y is raised to the first power, but x is not.  Since x is in the denominator of a fraction, it actually has a power of -1, which makes this equation nonlinear.

y = x - 6/7

In the above equation, both x and y are raised to the first power, making the equation linear.

Therefore, the correct choice is y =7/x - 6.

Hope this helps!