Use the test for primality to determine whether the following numbers are prime or not. Test for Primality Given an integer n > 1, to test whether n is prime check to see if it is divisible by a prime number less than or equal to its square root. If it is not divisible by any of these numbers, then it is prime. (a) Let n = 323. How many prime numbers are less than or equal to the square root of n? Let n = 421. How many prime numbers are less than or equal to the square root of n?

The proportion of identity theft complaints in the state is significantly higher than 23%.

The random variable for this scenario is the proportion of identity theft complaints out of the total number of complaints received by the state. The population parameter is the true proportion of identity theft complaints in the entire population of complaints in the state.

The null hypothesis (H0) is that the proportion of identity theft complaints in the state is equal to or less than 23%. The alternative hypothesis (Ha) is that the proportion of identity theft complaints in the state is greater than 23%.

To test this hypothesis, the state needs to conduct a one-tailed hypothesis test with a significance level (alpha) of 0.05. They can use the z-test statistic to compare the sample proportion with the population proportion. If the test statistic is greater than the critical value, they can reject the null hypothesis.

It is important to note that this test assumes that the sample of 1245 complaints is randomly selected and representative of the entire population of complaints in the state. If there is any bias or non-representativeness in the sample, the results of the test may not be accurate.

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To solve the equation 135°·(7x-10)=(11x+10)·(7x) is x ≈ -0.203 or x ≈ 1.567.

To solve the equation 135°·(7x-10)=(11x+10)·(7x), we can use the distributive property to expand the right side of the equation and then simplify.

First, convert the angle measure of 135 degrees to radians:

135° = 135/180π = 3π/4

Then substitute and simplify;

3π/4(7x - 10) = (11x + 10)(7x)

21πx/4 - 15π/4 = 77x² + 70x

Move all the terms to one side:

77x² + 70x - 21πx/4 + 15π/4 = 0

Next, we can solve for x using the quadratic formula;

x = (-b ± √(b² - 4ac))/2a

where a = 77, b = 70 - 21π/4, and c = 15π/4.

Plugging in these values, we get;

x = (-[70 - 21π/4] ± √[(70 - 21π/4)² - 4(77)(15π/4)])/(2(77))

Simplifying this expression gives two possible solutions for x;

x ≈ -0.203 or x ≈ 1.567

Therefore, the solution to the equation 135°·(7x-10)=(11x+10)·(7x) is x ≈ -0.203 or x ≈ 1.567.

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The equation of line passes through the points (-2, 1) and (0, 5). will be;

⇒ y = 2x + 5

And, Slope = 2

And, Y - intercept  = 5

Given that;

Two points on the line are (-2, 1) and (0, 5).

Now,

Since, The equation of line passes through the points (-2, 1) and (0, 5).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5 - 1) / (0 - (-2))

m = 4 / 2

m = 2

Thus, The equation of line with slope 2 is,

⇒ y - 1 = 2 (x - (-2))

⇒ y - 1 = 2 (x + 2)

⇒ y - 1 = 2x + 4

⇒ y = 2x + 5

Therefore, The equation of line passes through the points (-2, 1) and (0, 5). will be;

⇒ y = 2x + 5

And, Slope = 2

And, Y - intercept  = 5

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The area of the composite figure by adding the areas of the rectangle and the triangle is 375 cm, option (C) is correct.

Let the height of the rectangle and the triangle be 'h', and let the base of the triangle be 'b'. Then, the base of the rectangle is '2b' since it is twice the base of the triangle.

Area of the rectangle = base x height

A₁ = 2b x h

A₁ = 2bh

Area of the triangle = (1/2) x base x height

A₂ = (1/2) x b x h

A₂ = (b/2) x h

Total area of the composite figure = A₁ + A₂

Aₙ = 2bh + (b/2)h

Aₙ = (5/2)bh

Substituting the given values, we get:

A(total) = (5/2)(b x h)

A(total) = (5/2)(15 x 10) [given values: b=15, h=10]

A(total) = 375 cm

Hence, option (C) is correct.

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Answer:

The given function is:

f(x) = -3x^2 + 12

To find the interval over which the function is increasing, we need to find the critical points of the function.

f'(x) = -6x

The critical point is where f'(x) = 0

-6x = 0

x = 0

Now, we need to check the sign of f'(x) on either side of the critical point to determine whether the function is increasing or decreasing.

If x < 0, then f'(x) < 0, so the function is decreasing.

If x > 0, then f'(x) > 0, so the function is increasing.

Therefore, the interval over which the function is increasing is:

(0, infinity)

Step-by-step explanation:

gg

The scale factor of the dilation is 1/3.

Scale factor is a numerical scale that represents the ratio of the dimensions of two similar geometric figures. It is used in geometry to compare the size of two similar figures.

To determine whether the dilation is an enlargement or a reduction, we need to compare the size of the solid and dashed triangles.

We can calculate the lengths of the sides of the solid triangle using the distance formula:

[tex]Side 1: \sqrt{[(6 - (-6))^2 + (3 - 0)^2]} = \sqrt{(12^2 + 3^2)} = \sqrt{(144 + 9)} = \sqrt153\\\\Side 2: \sqrt{[(6 - (-6))^2 + ((-6) - 0)^2]} = \sqrt{(12^2 + 6^2)} = \sqrt{(144 + 36)} = \sqrt{180}\\\\Side 3: \sqrt{[(6 - 6)^2 + ((-6) - 3)^2]} = \sqrt{(0 + 81)} = \sqrt81 = 9[/tex]

So, the solid triangle has side lengths of √153, √180, and 9.

We can also calculate the lengths of the sides of the dashed triangle using the distance formula:

[tex]Side 1: \sqrt{[(2 - (-2))^2 + (1 - 0)^2]} = \sqrt{(4^2 + 1^2)} = \sqrt17\\\\Side 2: \sqrt{[(2 - (-2))^2 + ((-2) - 0)^2]} = \sqrt{(4^2 + 2^2)} = \sqrt20\\\\Side 3: \sqrt{[(2 - 2)^2 + ((-2) - 0)^2]} = \sqrt{(0 + 4)} = 2[/tex]

So, the dashed triangle has side lengths of √17, √20, and 2.

Comparing the side lengths, we can see that the dashed triangle is smaller than the solid triangle. Therefore, the dilation is a reduction.

To find the scale factor of the dilation, we can choose any corresponding side lengths from the solid and dashed triangles and divide them. For example, we can choose side 1:

Scale factor = (length of corresponding side in dashed triangle) / (length of corresponding side in solid triangle)

= √17 / √153

= √(17/153)

= (√17) / (3√17)

= 1/3

Therefore, the scale factor of the dilation is 1/3.

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Answer:

We know that the number of scoops of powder varies directly with the number of cups of milk. This means that there is a constant ratio between the two quantities.

Let's call this constant ratio k. Then, we can set up a proportion:

scoops of powder / cups of milk = k

We also know that 3 scoops of powder are needed for 5 cups of milk. We can use this information to find k:

3 / 5 = k

Simplifying this gives us:

k = 0.6

Now that we know k, we can use the proportion we set up earlier to find the formula for the number of scoops of powder, p, as a function of the number of cups of milk, m:

p / m = k

Multiplying both sides by m gives us:

p = km

Substituting the value of k we found earlier gives us:

p = 0.6m

Therefore, the formula for the number of scoops of powder, p, as a function of the number of cups of milk, m, is:

p = 0.6m

Answer:

28/45[tex]a^{2}[/tex]

Step-by-step explanation:

Helping in the name of Jesus.

Answer:

The simplified expression is 28/45a².

Step-by-step explanation:

To simplify (7/9a)(4/5a), we can multiply the numerators together and the denominators together, which gives:

(7/9a)(4/5a) = (7 x 4) / (9a x 5a) = 28 / 45a²

Therefore, the simplified expression is 28/45a².

The product of (x+7)(x-7) is x²-49

A product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.

For example, the product of 5 and 4 is 20. i.e 5×4 is 20. And this also implies that 5 and 4 are part of the factors of 20.

Solving (x+7)(x-7), we can use distributive method,

x( x-7) + 7(x-7)

= x²-7x+7x-49

= x²-49

therefore we can say the product of (x+7)(x-7) is x²-49

Using thesame method,

(27)(13) = 20(13) + 7(13)

= 260+91

= 351

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The statement which is true about the function of the temperature of the soup over time is D. As time increases, the temperature of the soup approaches 72 °F.

Given a table of values which shows the temperature of a bowl of soup left out on the kitchen counter with the time.

Here the time shown are ranged from 5, 10, 20, 30, 45, 60, 80.

Corresponding temperature of the soup left ranges from 139.503, 109.047, 83.158, 75.361, 72.556, 72.092, 72.008 respectively.

It is clear that as the time increases, the temperature of the soup is decreasing and at last approaches to 72 °F.

Hence the correct statement is D.

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Answer:

x= 21

Step-by-step explanation:

(x+6)^1/3-5=-2

Solve for x

Add 5 to each side

(x+6)^1/3-5+5=-2+5

(x+6)^1/3=3

Cube each side.

((x+6)^1/3)^3=3^3

x+6 = 27

Subtract 6 from each side

x+6-6 = 27-6

x= 21

Answer:

x = 21

Step-by-step explanation:

[tex]\sf(x+6)^\frac{1}{3} -5=-2[/tex]

First, add 5 to both sides.

[tex]\sf(x+6)^\frac{1}{3} =-2+5\\\\\sf(x+6)^\frac{1}{3} =3\\\\\sqrt[3]{(x+6)} =3[/tex]

Cube both sides.

[tex]\sqrt[3]{(x+6)} =3\\\\x+6=3^3\\\\x+6=27[/tex]

Subtract 6 from both sides.

[tex]x+6=27\\\\x=27-6\\\\x=21[/tex]

Answer:

rail, lap, pal, pail

Step-by-step explanation:

Answer: $1040

Step-by-step explanation:

There are 52 weeks in a year so they will get 26 haircuts in the year at every 2 weeks.

26x$40 =$1040

The product of the zeros in the given polynomial is 5.

Given is a polynomial p(x) = (a+1)x² + (2a+3)x + (3a+4), the sum of zeros is -1,

We need to find the product of its zeros,

So,

We know that in the polynomial ax²+bx+c = 0,

the sum of the roots = -b/a

Product of the roots = c/a

Therefore,

Here a = a+1, b = 2a+3 and c = 3a+4

So,

-(2a+3)/a+1 = -1

-2a-3 = -a-1

-a = 2

a = 2

Put a = 2 in value of c,

c = 3(2)+4 = 10

So, the product of the zeros is = 10/2 = 5

Hence the product of the zeros in the given polynomial is 5.

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Answer: 24 clothing items

Step-by-step explanation:

The total is 120.

1/5 of 120 is the same as saying 120 divided by 5.

120 divided by 5 is 24.

Answer : 24

Longwei should first recognize that implementing goals, policies, and structure is only one aspect of effective leadership. A leader's ability to motivate and inspire their employees is just as important. Therefore, Longwei should use the principles of organizational behavior (OB) to better understand his employees and their motivations.

Additionally, Longwei should take a personality assessment to become more self-aware of his own leadership style and how it may be impacting the employees. He should examine his perceptions and biases to ensure that he is making fair and objective judgments and decisions. This may involve seeking feedback from other leaders or mentors, participating in leadership development programs, or engaging in self-reflection and mindfulness practices.

By taking these steps, Longwei can better understand and address the unmotivated employees in his company. He can then develop strategies to engage and inspire them, such as offering incentives, providing opportunities for professional development, or creating a more positive and inclusive work environment. Ultimately, Longwei's success as a leader will depend not only on his ability to set and implement goals but also on his ability to motivate and engage his employees.

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Answer:

Set your calculator to degree mode.

The measure of angle Q is

[tex] {cos}^{ - 1} \frac{29}{63} = 62.6 \: degrees[/tex]

Angle Q measures 62.6°.

Answer:

x^2 - 4x + 24 cannot be factored.

Answer:

[tex]3k = 36[/tex]

[tex]k = 12[/tex]

Answer:

12

Step-by-step explanation:

If y = 36 and X = 3 then K would = (y divided by x) so it would be 36 divide 3

that being 12 so, therefore, the answer is 12.

K= 12

The number of smaller boxes that would be needed to fill a large box is given as follows:

250 smaller boxes.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

Hence the volume of the large box is given as follows:

V = 50 x 20 x 30

V = 30000 cm³.

The volume of the smaller box is given as follows:

V = 10 x 4 x 3

V = 120 cm³.

Then the number of the smaller boxes needed to fill the large box is given as follows:

30000/120 = 250 smaller boxes.

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Answer:

To find n if the mean of 30n, 12, 40, and 10 is n, we can use the formula for the mean of a set of numbers:

mean

=

sumofnumbers

numberofnumbers

mean=

numberofnumbers

sumofnumbers

​

In this case, we have four numbers: 30n, 12, 40, and 10. The mean is n. So we can write:

�

=

30

�

+

12

+

40

+

10

4

n=

4

30n+12+40+10

​

Simplifying the right-hand side:

�

=

30

�

+

62

4

n=

4

30n+62

​

Multiplying both sides by 4:

4

�

=

30

�

+

62

4n=30n+62

Subtracting 30n from both sides:

−

26

�

=

62

−26n=62

Dividing both sides by -26:

�

=

−

31

13

n=−

13

31

​

Therefore, if the mean of 30n, 12, 40, and 10 is n, then n is approximately -2.381.

Using the definition of supplementary angles, we can see that x = 60

Im just answering the first question.

We know that two angles A and B are supplementary if the sum of their measures is equal to 180°.

Then:

A + B = 180°

In this case, we know taht:

m∠A = (3x + 21)° and m∠B = (6x − 21)°

We can replace that in the equation to get:

3x + 21 + 6x - 21 = 180

Now solve that for x:

9x =180

x = 180/9

x = 60

That is the value of x.

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Answer:

Let us now solve the inequality:

5 + 8x < 3(2x + 4)

To begin, we will simplify the right side:

5 + 8x < 6x + 12

The variable on one side will then be isolated by subtracting 6x from both sides:

5 + 2x < 12

Then we'll take 5 off each sides:

2x < 7

Finally, split both sides by two:

x < 3.5

As a result, the solution to the inequality is x 3.5.

Thus, the probability that two people picked at random both own a dog is 0.1296 or 1296/10000.

To solve this problem, we need to use the formula for calculating the probability of independent events: P(A and B) = P(A) x P(B).

In this case, let A be the event that the first person owns a dog and B be the event that the second person owns a dog.

We know that P(A) = 0.36, or 36% chance that the first person owns a dog. Since the events are independent, P(B) is also 0.36.

So, the probability of both events occurring (both people owning dogs) is:

P(A and B) = P(A) x P(B)
= 0.36 x 0.36
= 0.1296

This can also be expressed as a fraction:

P(A and B) = 36/100 x 36/100
= 1296/10000

Therefore, the probability that two people picked at random both own a dog is 0.1296 or 1296/10000.

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As per the unitary method, the duration of the movie is 1 hour and 10 minutes.

To solve this problem, we can use a mathematical concept called the "unitary method."

Now, let's take a closer look at the information given in the problem. We have two analog clocks: one labeled "start" and the other labeled "end." The hour and minute hands on each clock provide information about the time.

Since the minute hand has moved halfway between the 6 and 7 marks, we can say that it has moved 30 minutes (since each mark represents 5 minutes). Therefore, the time on the start clock is 11:30 + 30 minutes = 12:00.

To determine the duration of the movie, we can subtract the start time from the end time.

End time - start time = 1:10 - 12:00

First, we need to convert the end time to 24-hour format for easier calculation. Since the hour hand is between 1 and 2, we know that the time is in the afternoon or evening. Therefore, we can add 12 to the hour value to convert it to 24-hour format.

1:10 + 12 hours = 13:10 (in 24-hour format)

Now, we can subtract the start time from the end time:

13:10 - 12:00 = 1 hour and 10 minutes

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The appropriate measure of variability depends on the characteristics of the data and the research question being addressed and the IQR is a more robust measure than the range if the data is skewed, and a large IQR indicates a wide range of expenses, requiring more funds. (option c)

Firstly, the IQR of 10 is the most accurate to use if the data is skewed. IQR is a measure of variability that measures the spread of the middle 50% of the data, thus, reducing the influence of outliers. Therefore, if the data is skewed, the IQR provides a more robust measure of variability than the range. The range is the difference between the largest and smallest value in a dataset and is sensitive to extreme values, which can distort the results.

Secondly, the IQR of 45 is the most accurate to use if the charity wants to show that they need more money. If the IQR is large, it means that there is a large variation in the data, and the spread is significant. Therefore, in this scenario, a large IQR indicates that the charity has a wide range of expenditures, and some expenses are significantly higher than others. Thus, the charity needs more funds to cover these expenses adequately.

Finally, the range of 45 is the most accurate to use if the charity wants to show that they have plenty of money. A large range indicates that the data points are spread out, and there is a significant variation in the expenses.

Therefore, in this scenario, a large range indicates that the charity has a wide range of expenses, and some expenses are higher than others, but overall, they have enough money to cover these expenses.

Hence the correct option is (c).

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The expression uses to find the product 6300, are 7×900, 700×9, 70×90.

Given is a number 6300, we need to write it as a product of numbers,

So, the factors of 6300 = 2, 2, 3, 3, 7, 5, 5

We cannot write the, (7 × 9) + (10 × 10), (63) + (100) as a product of 6300,

(7× 9) + (10 × 10) = 63 + 100 = 163

(63) + (100) = 163

But,

7×900 = 6300

700×9 = 6300

70×90 = 6300

Hence, the expression uses to find the product 6300, are 7×900, 700×9, 70×90.

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The total weight of seafood at the boil is 16 15/24 pounds.

Hence the correct option is C.

To find the total weight of seafood at the boil, we need to add up the weights of shrimp, crawfish, and crab.

First, we can convert the mixed numbers to improper fractions for easier calculations

Shrimp: 5 4/6 pounds = 5 × 6/6 + 4/6 = 30/6 + 4/6 = 34/6 pounds

Crawfish: 4 1/2 pounds = 4 × 2/2 + 1/2 = 8/2 + 1/2 = 9/2 pounds

Crab: 6 5/8 pounds = 6 × 8/8 + 5/8 = 48/8 + 5/8 = 53/8 pounds

Now we can add these fractions

34/6 + 9/2 + 53/8

We need a common denominator to add these fractions, which is the least common multiple of 6, 2, and 8, which is 24. So we can convert each fraction to have a denominator of 24

(34/6) × (4/4) = 136/24

(9/2) × (12/12) = 108/24

(53/8) × (3/3) = 159/24

Now we can add these fractions

136/24 + 108/24 + 159/24 = 403/24

This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1

403/24 = 16 15/24

Therefore, the total weight of seafood at the boil is 16 15/24 pounds.

Hence the correct option is C.

The given question is incomplete and the complete question is '' Shanti brought 5 4/6 pounds of shrimp to the seafood boil. James brought 4 1/2 pounds of crawfish. Roberto brought 6 5/8 pounds of crab. How many pounds of seafood were at the boil? 15 10/24 pounds 15 10/12 pounds 16 15/24 pounds 7 6 19/24 pounds''.

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The measure of angle C is 37°.

Given is a triangle, ABC, where ∠B = 70°, AC = 14, AB = 9, we need to find the measure of angle C,

Using the sine law for the triangles,

AC / Sin B = BC / Sin A = AB / Sin C

Therefore,

AC / Sin B = AB / Sin C

14 / Sin 70° = 9 / Sin C

Sin C = 9/14.9

C = sin⁻¹(9/14.9)

C = 37°

Hence, the measure of angle C is 37°.

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Answer:

approximately 5.9 meters.

Step-by-step explanation:

sin(42°) = r/9

r = 9 * sin(42°)

r ≈ 5.9 m

Therefore, the length of side r is approximately 5.9 meters.