A rectangular photograph is 8 inches by 10 inches. It will be put into a rectangular frame that is 2 inches wide on all sides. What is the area of the photograph when it is put into the
frame?

A sample size of at least 61 should be taken to obtain a margin of error of 0.04 for the estimation of a population proportion at a 95% confidence level.

Given data:

To determine the sample size required for estimating a population proportion with a given margin of error at a 95% confidence level, you can use the following formula:

[tex]n=\frac{Z^2 \cdot p(1-p)}{E^2}[/tex]

n is the required sample size.

Z is the Z-score corresponding to the desired confidence level. For a 95% confidence level, the Z-score is approximately 1.96.

p is an estimate of the population proportion (since you don't have prior data, you can use p =0.5  for maximum variability, which results in the largest sample size requirement).

E is the desired margin of error, which is 0.04 in this case.

Substitute the values into the formula:

[tex]n=\frac{1.96^2*0.5^2}{0.04^2}[/tex]

The value of n = 60.26

Since the sample size is a whole number, n = 61

Hence, a sample size of at least 61 should be taken for the estimation of a population proportion at a 95% confidence level.

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If the objective function coefficient for variable 1 decreases by 20, the solution will shift in the direction of the decrease in the objective function coefficient. It means that the optimal solution that was obtained previously will no longer remain optimal, and the new optimal solution will be found with the new objective function coefficient.

In linear programming, the objective function determines the maximum or minimum value that can be attained in the solution, subject to the constraints. The constraints in the problem can be either equalities or inequalities, which limit the range of values that the decision variables can take on.

The change in the objective function coefficient will change the direction of the optimal solution, and it may affect the feasibility of the solution. It means that some constraints may no longer be satisfied, or some variables may become infeasible.

In such cases, it will be necessary to revise the constraints or the variables to ensure the feasibility of the solution.

The solution can also be affected if the constraints of the problem change. The new constraints may limit the range of values that the variables can take on, or they may add new variables to the problem. These changes can affect the feasibility of the solution, and it may require the problem to be solved again to obtain the new optimal solution.


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[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{k=0}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 0 )}{3} \right)\right][/tex]

[tex]\sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o }{3} \right) +i \sin\left( \cfrac{ 219^o }{3} \right)\right]\implies \boxed{4[\cos(73^o)+i\sin(73^o)]} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=1}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 1 )}{3} \right)\right][/tex]

[tex]\sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 579^o }{3} \right) +i \sin\left( \cfrac{ 579^o }{3} \right)\right]\implies \boxed{4[\cos(193^o)+i\sin(193^o)]} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=2}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 939^o }{3} \right) +i \sin\left( \cfrac{ 939^o }{3} \right)\right]\implies \boxed{4[\cos(313^o)+i\sin(313^o)]}[/tex]

Therefore, approximately 68.26% of people are expected to score higher than 2.5 but lower than 3.5.

Based on the information provided, the mean (X) is 3.00 and the standard deviation (SD) is 0.50. To find the percentage of people expected to score higher than 2.5 but lower than 3.5, we will use the standard normal distribution (z-score) table.

First, we need to calculate the z-scores for both 2.5 and 3.5:
z1 =[tex] (2.5 - 3.00) / 0.50 = -1.0[/tex]
z2 = [tex](3.5 - 3.00) / 0.50 = 1.0[/tex]

Now, we can use the standard normal distribution table to find the probability of the z-scores. For z1 = -1.0, the probability is 0.1587 (15.87%). For z2 = 1.0, the probability is 0.8413 (84.13%).

To find the percentage of people expected to score between 2.5 and 3.5, subtract the probability of z1 from the probability of z2:

Percentage = [tex](0.8413 - 0.1587) x 100 = 68.26%[/tex]

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The correct answer to the question, "Which of the following is equivalent to the probability of getting less than 50% democrats in a random sample of size 100?" is: B. P( z < 50 — 55/ √55(45)/100).

To find the probability, we first calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value (50%), μ is the mean (55%), and σ is the standard deviation.

The standard deviation can be calculated as:

σ = √(np(1-p))

where n is the sample size (100) and p is the proportion of democrats (0.55).

Now, plug in the values into the z-score formula:

z = (50 - 55) / √(100 * 0.55 * 0.45)

The probability is then found as P(z < z-score), which is represented by the option B.

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Answer:

Step-by-step explanation:

Standard: 2x^3 - 7x^2 -x-2

Quotient: 2x^3- 7x^2 -x-2

remainder: 0

We can say with 95% confidence interval that the true mean lifetime of the tires is between 49,020 and 50,980 miles.

To calculate the confidence interval, we use the formula:

CI = x-bar ± z* (σ/√n)

where x-bar is the sample mean (50,000 miles), z is the z-score associated with the desired confidence level (in this case, 1.96 for 95% confidence level), σ is the standard deviation (5,000 miles), and n is the sample size (100).

Plugging in the values, we get:

CI = 50,000 ± 1.96*(5,000/√100)

Simplifying the expression, we get:

CI = 50,000 ± 980.

Therefore, we can say with 95% confidence that the true mean lifetime of the tires is between 49,020 and 50,980 miles.

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The mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability.

Standard deviation of the given data is 20 grams. The mean weight of the cauliflower is 400 grams. Now, for calculating the probability, we need to standardize the given mean weight of cauliflower. It will be as follows. Z-score for the mean weight of cauliflower is given as:

z = (X - μ) / σwhere X = 400 grams (mean weight of cauliflower)

μ = 400 grams (mean weight of the population)

σ = 20 grams (standard deviation)z = (400 - 400) / 20 = 0

Now, the probability of the mean weight of an individual cauliflower being between 400 and 409 grams is as follows:

P(400 < X < 409) = P(0 < Z < 0.45)

Using the standard normal distribution table, the probability is 0.1745.

The mean weight of a random sample of 36 of the cauliflowers is between 400 and 409 grams. The mean weight of a random sample of 36 of the cauliflowers is given by:

(X-μ)/ (σ/√n)where μ = 400 grams (mean weight of cauliflower)

σ = 20 grams (standard deviation)

n = 36 (number of samples)

Now, we need to standardize the sample mean. It will be as follows:

z = (X - μ) / (σ/√n)z = (400 - 400) / (20 / √36)

z = 0

As the z-score is zero, the probability will be equal to 0.5. Hence, the mean weight of an individual cauliflower being between 400 and 409 grams has a greater probability than the mean weight of a random sample of 36 of the cauliflowers being between 400 and 409 grams.

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Photosynthesis is maximum in red light because chlorophyll, the primary pigment responsible for capturing light energy in plants, absorbs red light most efficiently.

What is red light in Photosynthesis?

Red light is a part of the electromagnetic spectrum with a longer wavelength and lower energy than blue and green light.

Red light is particularly effective for photosynthesis because it has a longer wavelength and lower energy, which allows chlorophyll to efficiently absorb it and use it for the photosynthetic process.

In photosynthesis, plants use light energy to synthesize glucose from carbon dioxide and water.

As a result, photosynthesis is maximum in red light because plants can absorb and utilize this light energy most efficiently for their growth and energy production.

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Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.

To represent the problem as an equation, we first need to define some variables. Let's let "f" represent the number of fiction books, and "n" represent the number of nonfiction books. We know from the problem that there are 2 times as many nonfiction books as fiction books, so we can write:

n = 2f

We also know that they put the same number of books on each of the 7 bookshelves and put as many as they can on each shelf. Let's call this number "s". We can then write an equation for the total number of books that can fit on the bookshelves:

7s = f + n

Since n = 2f, we can substitute 2f for n in the equation:

7s = f + 2f

Simplifying, we get:

7s = 3f

Finally, we know that any remaining books are put on Ms. Krebs's desk. Let's call this number "r". We can write an equation for the total number of books:

f + n = 7s + r

Substituting 2f for n, we get:

f + 2f = 7s + r

Simplifying, we get:

3f = 7s + r

Now we can solve for "f":

3f = 7s + r

f = (7s + r) / 3

We don't have enough information to solve for "s" or "r", but we can use this equation to find the number of fiction books. For example, if we know that there are a total of 70 books, we can write:

f + n = 70

f + 2f = 70

3f = 70

f = 23.33

Since we can't have a fractional number of books, we would round down to the nearest whole number and get:

f = 23

We could then use the equation f = (7s + r) / 3 to find the number of books on each shelf, assuming there are no books left over:

23 = (7s + 0) / 3

69 = 7s

s = 9.86

Since we can't have a fractional number of books on a shelf, we would round down to the nearest whole number and get:

s = 9

So Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.

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Answer:

no

Step-by-step explanation:

using Pythagorean theorem:

[tex]26^{2} +42^{2}=50^{2}[/tex]

676+1764=2500

2440=2500

2440<2500

Answer:no

Answer:

Area: 81*pi

Circumference: 18*pi

Step-by-step explanation:

Area: 9^2= 81

So it would be 81*pi

Circumference: 9*2= 18

So it would be 18*pi

If you want the full area then it's 81*pi= 254.34

If you want the full circumference it's 18*pi= 56.55

The amount of the mark up is $66 and the selling price is $286.

The amount by which a product's cost is raised to determine its selling price is known as the markup percentage. Usually, it is represented as a percentage of the item's price. Markup percentage is determined by the following equation:

Markup percentage = (Selling price - Cost price) / Cost price x 100%

Given that, the mark up is 30%.

Thus,

Mark up = 0.3 x $220 = $66

The selling price is:

Selling price = $220 + $66 = $286

Hence, the amount of the mark up is $66 and the selling price is $286.

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Answer:Hence, Nathan rode 2 miles

Step-by-step explanation:ask if you need any questions

The point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.

Let P = (x, y) be the point that partitions segment AB in a 1:4 ratio, where AP:PB = 1:4. Then, we have:

[tex]$\frac{AP}{AB} = \frac{1}{1+4} = \frac{1}{5}$$[/tex]

and

[tex]$\frac{PB}{AB} = \frac{4}{1+4} = \frac{4}{5}$$[/tex]

Using the distance formula, we can find the lengths of AP, PB, and AB:

[tex]AP &= \sqrt{(x+3)^2 + (y-2)^2} \\PB &= \sqrt{(x-7)^2 + (y+10)^2} \\\ AB &= \sqrt{(7+3)^2 + (-10-2)^2} = \sqrt{244}[/tex]

Substituting these into the section formula, we have:

[tex]$\begin{aligned}x &= \frac{4\cdot(-3) + 1\cdot(7)}{1+4} = -1 \ y &= \frac{4\cdot2 + 1\cdot(-10)}{1+4} = -\frac{2}{5}\end{aligned}$$[/tex]

Therefore, the point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

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the decay constant for this material is approximately 0.0445.when t = 8 years, the amount of the material remaining is 550 grams.

The formula for radioactive decay is given by:

a = [tex]e^(-kt)\\[/tex] * A

where a is the final amount,A is the initial amount, t is the time in years, and k is the decay constant.

We can use the given information to solve for k as follows:

When t = 0, a = A. So, we have:

A = [tex]e^(0 * k)[/tex] * A

Simplifying this gives:

1 = e^0

Therefore, we can see that k = 0 at the start of the decay process.

Now, when t = 8 years, the amount of the material remaining is 550 grams. Therefore, we have:

550 = [tex]e^(-8k)[/tex] * 700

Dividing both sides by 700 and taking the natural logarithm of both sides, we get:

ln(550/700) = -8k

Simplifying this gives:

k = ln(700/550)/8

Using a calculator, we can evaluate this expression to get:

k ≈ 0.0445

Therefore, the decay constant for this material is approximately 0.0445.

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The graph for the linear equation y=24x, will be a straight line having coordinate (1,24) i.e. B.

What is a linear equation, exactly?

A linear equation is a first-degree algebraic equation in which each term is either a constant or the product of a constant and a single variable (degree 1). A linear equation is stated as y = mx + b, where y is the dependent variable, x is the independent variable, m is the line's slope, and b= y-intercept .

A linear equation's graph is a straight line. The line's slope decides how steep it is, and the y-intercept indicates where the line crosses the y-axis. Linear equations are used to model relationships between variables that are directly proportional to each other, such as distance and time, or cost and quantity.

Now,

Given equation is y=24x

then for  x,    y is

              1,    24

              2,   48

              3,    72

              4,     96

Hence, the graph will be as represented in option 2.

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Answer: the team amassed 88i points total, by shooting t two-point baskets and u 1-point free throws.

t+u = 53

total is:  2t + u = 88.

Step-by-step explanation:

hope i makes sense

Answer:

x = 26.

Step-by-step explanation:

Given: 2x + 3x + 50 = 180

First, write it down:

2x + 3x + 50 = 180

Then, collect like terms:

2x + 3x = 180 - 50

Then calculate:

5x = 130  (Divide both sides by 5)

x = 26

Using expressions,

4a. x= 0 is not possible.

4b. x= 1 is not possible.

5a. (9x-5)(9x+5)

5b. (x-3)(2x+1)

6. 1/(3x-7)

7a. x = (-5,∞)

7b. x = (∞,2]

7c. x = (-3,7]

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Let's examine the writing of expressions.

The other number is x, and a number is 6 greater than half of it.

As a mathematical expression, this proposition is denoted by the expression x/2 + 6.

Here the values of x has to be such that the denominator is not equal to zero.

So, x cannot be zero and x cannot be 1 as these two values in the respective questions will make the denominator zero.

a. 81x²-25

= 81x² + 45x-45x-25

=9x(9x+5)-5(9x+5)

= (9x-5)(9x+5)

b. 2x²-5x-3

= 2x² + x - 6x -3

= x(2x+1)-3(2x+1)

=(x-3)(2x+1)

Next, the intervals for x are as follows:

x = (-5,∞)

x = (∞,2]

x = (-3,7]

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to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.

To find 7/8 of 3.5, we can simply multiply 7/8 and 3.5 together.

7/8 x 3.5 = (7/8) x (7/2) = 49/16

So, the answer is 49/16. However, we need to write the answer as a mixed number in the simplest form.

To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. In this case, 49 divided by 16 is 3 with a remainder of 1.

So, the mixed number is 3 1/16.

To simplify the mixed number, we need to check if we can reduce the fraction part (1/16) further. 1 is not divisible by any number other than 1 itself, so it is already in its simplest form.

Therefore, the final answer is 3 1/16.

In summary, to find 7/8 of 3.5, we multiplied 7/8 and 3.5 together to get 49/16, which we then converted to a mixed number in the simplest form, giving us the answer of 3 1/16.

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Answer: multiplied by 5 or squared

Step-by-step explanation:

If the number 5 goes in and 25 is the result, the rule could be multiplying by 5 or squaring the number that goes in (input).

5 x 5 = 25

5^2 = 25.

Answer: D = 3c-5

Step-by-step explanation:

The first shape shows the input, C, the second one multiplies it by 3, next, it subtracts C by 5, leaving you with D equaling C times three, minus five.
You can simplify this equation into this:

D=3C (multiplied by 3)

Then subtract by 5
D=3C-5

Answer:

-10

Step-by-step explanation:

I added a photo of my solution

Answer:

Answer is -10

Step-by-step explanation:

The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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Answer:

See below!

Step-by-step explanation:

a) 1, 2, 3, 4, 5

The possible outcomes are all the options that there are on the spinner

b) 2

There are only 2 even numbers!

c) [tex]\frac{2}{5}[/tex] or 0.4

There are 2 out of 5 numbers are even on the spinner so that must be the solution!

d) 1

The spinner has only one multiple of 3, so the possible outcome should also be 1.

e) [tex]\frac{1}{5}[/tex] or 0.2

There are only 1 out of 5 options which are multiples of 3, so that would be our solution

f) 4

There are 4 prime numbers in the spinner (1, 2, 3, 5), so that would be a possible outcome.

g) [tex]\frac{4}{5}[/tex] or 0.8

The spinner has 4 out of 5 prime numbers, so our answer would be that!

Hope this helps, have a lovely day! :)

Answer:

Y = 4x

Step-by-step explanation:

In this equation, x represents the input value, and Y represents the output value. Coefficient 4 illustrates the rate of change or slope of the function, indicating that for every unit increase in x, the value of Y increases by four units. When x is 0, Y is also 0, consistent with the given data. Similarly, when x is 1, 2, and 3, Y is 4, 8, and 12, respectively, matching the provided output values.

the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:

To find the interval where both functions F(x) and g(x) are increasing, we need to determine where the derivative of each function is positive. A function is increasing when its derivative is positive, which means that the function is becoming larger as x increases.

The derivative of F(x) can be found by applying the derivative rules for absolute value and addition, which gives us:

F'(x) = 3x/|x|

Now, we need to determine where F'(x) is positive. This occurs when either 3x is positive and |x| is positive, or when 3x is negative and |x| is negative. Therefore, F'(x) is positive for x > 0 and x < 0.

Next, we need to find the derivative of g(x) by applying the derivative rules for subtraction and multiplication, which gives us:

g'(x) = -1 + 8

Simplifying the expression, we get:

g'(x) = 7

Since g'(x) is a constant, it is always positive, which means that g(x) is increasing for all values of x.

To find the interval where both F(x) and g(x) are increasing, we need to identify where both F'(x) and g'(x) are positive. This occurs when x < 0, as this satisfies the condition for F'(x) being positive, and g'(x) is always positive.

Therefore, the interval where both F(x) and g(x) are increasing is x < 0, which can be represented on the number line as follows:

     <=====o------------------------>

         x<0                    x>0

In this interval, both functions are increasing as x becomes more negative.

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