Sophie is selling cups of yellow lemonade and pink lemonade at her lemonade stand. She made 25 cups of yellow lemonade. She made 3 times as many cups of pink lemonade as yellow lemonade. Sophie has only sold 18 cups of pink lemonade. How many cups of pink lemonade does Sophie have left for sale?

Step-by-step explanation:

Force= mass× acceleration

acceleration = Force/mass = 4/800 = 0.005 m/s²

The answer is C. Ability to rust. This is because rusting is a chemical property of a substance, which is caused by environmental factors causing said substance to tarnish.

The image vertices for a dilation with center (0,0) and a scale factor of 4 are given as follows:

A'(-12, 4), B'(16, -12), C'(8, 12) and D'(-4,16).

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The vertices of the original figure are given as follows:

A(-3,1), B(4,-3), C(2,3) and D(-1, 4).

The scale factor of the dilation is given as follows:

k = 4.

Hence the vertices of the dilated figure are the vertices of the original figure multiplied by 4, as follows:

A'(-12, 4), B'(16, -12), C'(8, 12) and D'(-4,16).

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Answer:

2/3

Step-by-step explanation:

Simplify the following:

(8/27)^(1/3)

Hint: | For all n>=0, (m/n)^(1/3) = (m^(1/3))/(n^(1/3)).

(8/27)^(1/3) = (8^(1/3))/(27^(1/3)):

(8^(1/3))/(27^(1/3))

Hint: | Simplify radicals.

27^(1/3) = (3^3)^(1/3) = 3:

(8^(1/3))/3

Hint: | Simplify radicals.

8^(1/3) = (2^3)^(1/3) = 2:

Answer: 2/3

Answer:

slope: 0

Step-by-step explanation:

You are solving for the slope. To solve, use the slope-intercept form:

slope (m) = \(\frac{y_2 - y_1}{x_2 - x_1}\)

Choose two points to use. Let:

\((x_1 , y_1) = (2 , 3)\\(x_2 , y_2) = (5 , 3)\)

Plug in the corresponding numbers to the corresponding variables:

slope (m) = \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 3}{5 - 2}\)

Simplify. Combine like terms:

m = \(\frac{3-3}{5-2} = \frac{0}{3} = 0\)

This means that the slope is 0. Plot the points on a graph.

~

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at the point where y is changing at the same rate as the distance from the origin (2), the derivative of y with respect to time (dy/dt) is equal to 8.
 

To find the point on the trajectory where the height (y) is changing at the same rate as the distance (2) from the projectile's point of origin, we need to calculate the derivative of both variables with respect to time and set them equal to each other.

Differentiating the equation 2(y + 2) = (x + 2)^2 with respect to time, we get:
2(dy/dt) = 2(x + 2)(dx/dt)

Since the distance from the origin is given as 2, we have:
dx/dt = 2

Substituting this value into the equation, we have:
2(dy/dt) = 2(2 + 2)(2)
dy/dt = 8

Therefore, atat the point where y is changing at the same rate as the distance from the origin (2), the derivative of y with respect to time (dy/dt) is equal to 8.

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The most common error when entering a formula is to reference the wrong cell in the formula.

This error occurs when the cell references within a formula do not match the intended cells. It can lead to incorrect calculations and produce unexpected results. For example, if a formula is supposed to use data from cell A1 but mistakenly refers to cell B1, the calculation will be based on the wrong data. It is important to double-check and ensure that the cell references in a formula accurately reflect the intended data sources to avoid this common mistake.

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Answer:

Step-by-step explanation:

The the terms be x and y

The sum of the terms = x+y

Difference of terms = x-y

Product of the sun and differences will be expressed as:

(x-y)(x+y) = x²-xy+xy-y²

(x-y)(x+y) = x²-y²

Hence the product of the terms is equivalent to the difference of two squares of the terms

Answer:

$93.75

Step-by-step explanation:

The computation of the total cost of order is shown below:

The Cost of 8 pounds of Pepperoni is

=  8 × $3.15

= 25.2

The Cost of 15 pounds of cheese is

= 15 × $1.85

= $27.75

The Cost of 12 pounds of sausage is

= 12 × $3.40

= $40.8

So, The total cost is

= $25.2 + 27.75 + $40.80

= $93.75

Answer:

a

Step-by-step explanation:

The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

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Both the expressions from parts are correct.

In calculus, integration by substitution, also known as μ substitution, inverse chain rule, or change of variables , is a method of evaluating integrals and antiderivatives. This is the counterpart of the chain rule for differentiation and can loosely be thought of as using the chain rule backwards.

In first option we integrate the equation

Consider the integral

∫7x(x²+1) dx

A. First, rewrite the integral by multiplying out the integrand:

∫7 x (x² + 1) dx = ∫(7x^3)+(7x)

Then evaluate the resulting integral term-by-term:

∫7x(x²+1)dx = 7(x^4/4+x^2/2)+C

B. Next, rewrite the integral using the substitution w =(x² + 1):

∫7 x (x² + 1) dx= ∫1/(2sqrt(w-1))

Evaluate this integral (and back-substitute for w) to find the value of the original integral:

∫7x(x²+ 1) dx = 7x^4/4+7x^2/2+7/4+C

C. How are your expressions from parts (A) and (B) different? What is the difference between the two? (Ignore the constant of integration.)

(answer from B)-(answer from A) = 7/4

And in second way we used substitution so both the methods are correct.

Therefore both the Answers are correct .

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SOLUTION:

Case: Shifting a graph

The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input. Adding to the output of a function moves the graph up. Subtracting from the output of a function moves the graph down. Here are the graphs of y = f (x), y = f (x) + 2, and y = f (x) - 2

Given:

Required:

To show how the function changes

Method:

Step 1:

The original function

At the original function, the graph cuts through (0,0).

Step 2:

When it is shifted 8 units up, the graph will now cut through (0,8).

The function will now be:

Final answer:

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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Answer:

The generalization will be biased because they are not surveying people from the other regions.

Step-by-step explanation:

Note that the very first step in verifying a statement about a product is represented by the acronym C.L.A.I.M. The first letter "C" stands for Claim.  

L - Logic: Examining the logic of the claim to see if it is reasonable and if the evidence offered supports the assertion.

A - Attribution: Identifying the source of the assertion and assessing its reliability.

I - Investigation: Research and evidence collecting to support or reject the allegation.

M - Measurement: Evaluating the quality and quantity of evidence obtained and assessing whether or not it supports the claim being made.

Following the CLAIM technique allows one to assess the correctness and validity of a claim and make an educated judgment about the product or service in issue.

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P-value is0.1558 and the z- value is 1.012 when a random sample of 40 drivers was questioned to determine whether the commute time differs in the winter.

Given that,

The Census Bureau informs us that Cleveland, Ohio residents commute on average for 33 minutes. A random sample of 40 drivers was questioned to determine whether the commute time differs in the winter.

The standard deviation of the population is estimated to be 7.5 minutes, and the average commute time for the month of January was calculated to be 34.2 minutes.

Let = μ average commute time in winter.

So, Null Hypothesis, H₀ : μ = 33 minutes      {means that the commuting times are same in the winter}

Alternate Hypothesis, H₁ : μ≠  33 minutes      {means that the commuting times are different in the winter}

The test results that would be utilised in this z test statistics for one sample given our understanding of population standard deviation;

T.S. = ((X bar-mean)/ standard deviation)/root n   ~ N(0,1)

Here, X bar = sample mean commute time for the month of January = 34.2

Standard deviation = population standard deviation = 7.5 minutes

n = sample of drivers = 40

The value of z test statistics is 1.012.

Also,

P-value of the test statistics is given by;

P-value = P(Z > 1.012) = 1 - P(Z  1.012)

= 1 - 0.84423

= 0.1558

Therefore, P-value is0.1558 and the z- value is 1.012 when a random sample of 40 drivers was questioned to determine whether the commute time differs in the winter.

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390 senior citizen tickets were sold. The total receipts from ticket sales are given as $6540, so we have the equation: 22A + 10S = 6540.

Let's assume the number of adult tickets sold is A and the number of senior citizen tickets sold is S.

According to the given information, the total number of tickets sold is 510. So we have the equation: A + S = 510 ...(1)

The cost of each adult ticket is $22, so the total revenue from adult tickets can be calculated as 22A. The cost of each senior citizen ticket is $10, so the total revenue from senior citizen tickets can be calculated as 10S.

The total receipts from ticket sales are given as $6540, so we have the equation: 22A + 10S = 6540 ...(2)

Now we can solve these two equations simultaneously to find the values of A and S. From equation (1), we can express A in terms of S as A = 510 - S. Substituting this into equation (2), we get: 22(510 - S) + 10S = 6540

Simplifying the equation: 11220 - 22S + 10S = 6540

-12S = 6540 - 11220

-12S = -4680

Dividing both sides by -12: S = -4680 / -12

S = 390. Therefore, 390 senior citizen tickets were sold.

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Answer:

28.1%

Step-by-step explanation:

A town's population in 2019 was 438,000. The town's current population is 561,000. What is the percent of change?

The formula for Percent change =

Final value - Initial value/Initial value × 100

= 561000 - 438000/438000 × 100

= 123000/438000 × 100

= 28.082191781%

Approximately = 28.1%

Therefore, percent change = 28.1%

To determine whether the actual fit is an interference fit or a clearance fit, you need to measure the actual sizes of the shaft and hole and compare them to the tolerance limits specified by the H8 and p7 designations.

In a transition fit, such as φ50 H8/p7, the fit allows for both interference and clearance depending on the actual sizes of the shaft and hole.

To determine whether the actual fit formed by the actual shaft and hole is an interference fit or a clearance fit, we need to compare the actual sizes of the shaft and hole with the tolerance limits specified by the H8 and p7 designations.

In this case, the H8 tolerance for the hole indicates a basic hole size with a relatively tight tolerance, while the p7 tolerance for the shaft indicates a basic shaft size with a looser tolerance. The "φ50" specification specifies the nominal size of the fit as 50 mm.

If the actual shaft size falls within the upper limit of the p7 tolerance and the actual hole size falls within the lower limit of the H8 tolerance, the fit will be a clearance fit. This means that there will be a gap or clearance between the shaft and the hole, allowing for easy assembly and potential movement or play between the parts.

On the other hand, if the actual shaft size falls within the lower limit of the p7 tolerance and the actual hole size falls within the upper limit of the H8 tolerance, the fit will be an interference fit. This means that the shaft will be larger than the hole, resulting in a tight fit where the parts are pressed or forced together. This can create friction and require more force for assembly.

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The distance from the gazebo to the dock is approximately 120.45 meters.

The given problem can be solved using the concept of trigonometry.

let the distance from the gazebo to the dock be "d".

According to the question it is known that the bearing from the gazebo to the dock is S 41° W which means that the angle between the line from the gazebo to the dock and due south is 41°.

Hence the angle between the line from the gazebo to the tree and due south is =(74°-41°) =33°

Similarly, the angle between the line from the dock to the tree and due south is = 28°-x =28°-41°= -13°(As it is to the west of south).

Using the trigonometry law of sines we can write,

d/ sin(41°) = 100/ sin(33°)

d=(100/sin(33°))*sin(41°)

d= 120.45 meters

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Answer:

i dont eather i need to know the ?

Step-by-step explanation:

To represent decimal values ranging from 0 to 12,500, we need 14 bits.

To determine the number of bits needed to represent decimal values ranging from 0 to 12,500, we need to find the smallest number of bits that can represent the largest value in this range, which is 12,500.

The binary representation of a decimal number requires log base 2 of the decimal number of bits. In this case, we can calculate log base 2 of 12,500 to find the minimum number of bits needed.

log2(12,500) ≈ 13.60

Since we can't have a fraction of a bit, we round up to the nearest whole number. Therefore, we need at least 14 bits to represent values ranging from 0 to 12,500.

Using 14 bits, we can represent decimal values from 0 to (2^14 - 1), which is 0 to 16,383. This range covers the values 0 to 12,500, fulfilling the requirement.

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Answer:

the answer is A

Step-by-step explanation:

this is because √83 equals 9.11043357

… which would make it closest to 9.1

Answer:

1.5 or 3/2

Step-by-step explanation:

The representation of D in the form D_x, D_y, where the x and y components are separated by a comma will be D[6.08,7.27]

Any vector oriented in two dimensions can be understood to have an impact in both directions. This implies that it may be divided into two halves. A component is a portion of a two-dimensional vector. The components of a vector assist to represent the vector's effect in a certain direction. The total impact of these two components is equivalent to the influence of the separate two-dimensional vectors. The two vector components can substitute the single two-dimensional vector.

Determine the x and y components for each vector A & B for vector A

Ax=sin (15) * 2=0.5176

Ay=cos (15) * 2=1.9318

for Vector B

Bx=cos (15) * 4=3.8637

By=sin (15)* 4=1.0352

The vector addition and scalar multiplication for x and y individually D=4.3 * A+B

Dx=4.3 *(sin (15) * 2)+cos (15) * 4

Dx=4.3 * 0.5176+3.8637

Dx=6.0893

Dy=4.3 *(cos (15) * 2)-sin (15) * 4

Dy=4.3 * 1.9318-1.0352

Dy=7.2715

D[6.08,7.27]

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The actual question may be:

Express D in the form D_x, D_y, where the x and y components are separated by a comma using two significant figures.

Answer:

about =502.65

Step-by-step explanation: