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The calculated value of x from the special triangle is 17.0

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

The right triangle

The right triangle is a special triangle that has a measure of 45 degrees

For a triangle that has a measure of 45 degrees, we have

Hypotenuse = Legs√2

In this case, we have

Leg = x

Hypotenuse = 24

So, we have

x√2 = 24

Divide by √2

x = 24/√2

Evaluate

x = 17.0

Hence, the calculated value of x is 17.0

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7. The exact values of x is 17.

8. The exact values of x is 12.

9. The exact values of x is 10.9.

10. The exact values of y is 15.

11. The exact values of y is 15.

12. The exact values of y is 6.

The exact values of x and y is calculated by applying Pythagoras theorem as follows;

7.

x² = 8² + 15²

x² = 289

x = √289

x = 17

8.

x² = 15² - 9²

x² = 144

x = √144

x = 12

9.

x² = 12² - 5²

x² = 119

x = √119

x = 10.9

The value of y is calculated as follows;

10.

y² = 12² + 9²

y² = 225

y = √(225)

y = 15

11.

y² = 17² - 8²

y² = 225

y = √(225)

y = 15

12.

y/10 = 6/10

y = 6

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this will be the square -

[tex]2 \times \sqrt[5]{4} [/tex]

or 2,63902

The average speed of the bike is calculated as: 15.67 mph

The formula for the average speed is:

Average speed = Distance/Speed

We are given the parameters as:

Time = 180 minutes = 3 hours

Distance = 47 miles

The average speed is defined as the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction.

Thus:

Average speed = 47/3

= 15.67 mph

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If points A, B, and C are not three nonadjacent vertices of the cube or three adjacent vertices of the cube, then the cross-section will be a polygon with more than four sides, and its shape will depend on the location of the points A, B, and C on the cube.

What is meant by cross section?

The form we obtain by cutting a straight through an object is called a cross-section.

The shape of the cross section of a cube that is cut into two pieces by a single slice that passes through point A, B, and C depends on the location of these points on the cube.

If points A, B, and C are three nonadjacent vertices of the cube, then the cross section will be a triangle. Specifically, it will be an isosceles triangle with base equal to the length of the edge of the cube and legs equal to the distances between point A and the other two points B and C.

If points A, B, and C are three adjacent vertices of the cube, then the cross section will be a square. Specifically, it will be a square with side length equal to the length of the edge of the cube.

If points A, B, and C are not three nonadjacent vertices of the cube or three adjacent vertices of the cube, then the cross section will be a polygon with more than four sides, and its shape will depend on the location of the points A, B, and C on the cube.

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Answer:

vertical because they are right across from each with the same degrees

The ages of people who can get a driver's license can be represented in three forms as follows;

x ≥ 16

x ≤ 85

16 ≤ x ≤ 85

The ages of people who cannot get a driver's license can be represented in three forms as follows;

x ≤ 16

x ≥ 85

16 ≥ x ≥ 85

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Assuming the variable x denotes the ages of people who wishes to obtain a driver's license, a set of inequality which can be used to represent those who are eligible in three forms include;

x ≥ 16

x ≤ 85

16 ≤ x ≤ 85

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Answer:

We should use 30 pints of the first drink and 120 pints of the second drink

Step-by-step explanation:

Let x represent the number of pints of the first drink used
Volume of fruit juice in x pints = 35% of x = 0.35x

Let y represent the number of pints of the second drink used
Volume of fruit juice in y pints = 85% of y= 0.85y

Since the final mixture volume is 150 pints we get
x + y = 150  ..... [1]

If the final mixture has to contain 75% pure fruit juice, the volume of fruit juice in the mixture = 0.75 x 150 = 112.5 pints

Therefore
0.35x + 0.85y = 112.5  ...[2]

We will solve this set of simultaneous equations by making the coefficients of one of the variables equal and then subtracting to eliminate that variable

Multiply equation [1] by 0.35 to get the x coefficients equal

0.35 x [1]
=>  0.35(x + y) = 0.35(150)

=> 0.35x + 035y = 52.5  ... [3]

Subtract [3] from [2]:

[3] - [2] =>

0.35x + 0.85y - (0.35x + 035y) = 112.5 - 52.5

0.35x + 0.85y - 0.35x - 0.35y = 60

0x + 0.5y = 60

0.5y = 60

y = 60/0.5

y = 120

Therefore x = 150 - 120 = 30

Therefore we should use 30 pints of the first drink and 120 pints of the second drink

Working out the expression 320.041 - 47.96 gives 272.081

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

320.041 - 47.96

The above expression is a difference or subtraction expression that can be done using a calculator

Using the above as a guide, we have the following:

320.041 - 47.96

Evaluate using a calculator

So, we have

320.041 - 47.96 = 272.081

Hence, teh solution of 320.041 - 47.96 is 272.081

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We can rewrite 3^6 as the product of two whole-number powers of 3 as: [tex]3^4 . 3^2.[/tex]

To rewrite 3^6 as the product of two whole-number powers of 3, we need to find two exponents that add up to 6.

A way to do this is to use the fact that 3^4 = 81, which is close to 3^6.

Specifically, we have:

3^6 = 3^4 * 3^2

We can check that this is true by using the rule for multiplying exponents that states that a^m * a^n = a^(m+n).

Applying this rule, we get:

= 3^4 * 3^2

= 3^(4+2)

= 3^6.

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Our calculated t-value of [tex]4.22[/tex] is greater than the critical t-value of 1.684, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean starting salary for college graduates who major in Statistics has increased.

We can use a one-sample t-test to test the claim that the mean starting salary for college graduates who major in Statistics has increased.

The null hypothesis is that the mean starting salary is still $[tex]54000[/tex], while the alternative hypothesis is that the mean starting salary is greater than $[tex]54000[/tex].

We can calculate the t-statistic as:

t = (sample mean - null hypothesis value) / (standard error of the mean)

= [tex](63500-54000)/(10540/\sqrt{40}[/tex]

= [tex]4.22[/tex]

where [tex]\sqrt{40}[/tex] is the sample size.

The degrees of freedom for the t-test is [tex](n-1) = 39[/tex], where n is the sample size.

Using a t-table or calculator with [tex]39[/tex] degrees of freedom, a one-tailed test, and a significance level of [tex]0.05[/tex], we find the critical t-value to be [tex]1.684[/tex]

Since our calculated t-value of [tex]4.22[/tex] is greater than the critical t-value of [tex]1.684[/tex], we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean starting salary for college graduates who major in Statistics has increased.

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question 9.

Based on a cubic modeling equation, the  prediction about this data that is  most reliable is a $70k house would have 1,354 square ft.

Option A is correct.

Question 10.

The second coordinate in a scatterplot of the linearized data and  rounding the answer to the tenth place is 0.8

Option A is correct.

Question 11.

The approximate value when x=4 and rounding the answer to the nearest whole number is 1,168

Option C is correct.

The equation is given as

Log y= 0.75821x+0.03442

We substitute x = 4 into the given equation and solve for y:

log y = 0.75821(4) + 0.03442

log y = 3.07286 + 0.03442

log y = 3.10728

We take the antilogarithm of both sides,

y = 10^(3.10728)

y = 1,168.66

Rounding off, the closest answer is option  (c) 1,168.

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The sample mean for the number of years worked is 12.9, and 35% of the employees in the sample worked for the company for at least 10 years.

To find the sample mean, we need to add up all the years worked and divide by the total number of employees:

8 + 13 + 15 + 3 + 13 + 28 + 4 + 12 + 4 + 26 + 29 + 3 + 10 + 3 + 17 + 13 + 15 + 15 + 23 + 13 = 258

So, the sample mean is 258/20 = 12.9 (rounded to the nearest tenth).

To find the percentage of employees who worked for at least 10 years, we need to count the number of employees who worked for 10 years or more.

From the data, we see that 7 employees worked for at least 10 years (Employee Number: 2, 3, 5, 10, 11, 15, and 19). So, 7 out of 20 employees worked for at least 10 years, which is 35%. Therefore, the answer is 35% (rounded to the nearest integer).

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The centerline=  459.9

The upper control limit=  852.55.

The lower control limit = 67.25.

We determine the mean to set up the standard limits:

Mean is gotten as :

(465 + 502 + 395 + 488 + 472 + 462 + 524 + 434 + 481 + 386) / 10

mean = 459.9

we then find the Standard Deviation:

Standard Deviation = √variance

variance = ((465-459.9)^2 + (502-459.9)^2 + (395-459.9)^2 + (488-459.9)^2 + (472-459.9)^2 + (462-459.9)^2 + (524-459.9)^2 + (434-459.9)^2 + (481-459.9)^2 + (386-459.9)^2) / 9

variance = 17119.1

Standard Deviation = √(17119.1)

Standard Deviation= 130.88

Hence

Centerline = 459.9

upper control limit  = 459.9 + 3 x (130.88) = 852.55

lower control limit. = 459.9 - 3 x (130.88) = 67.25

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The probability of correctly guessing which pies were sold on the first day is  near to 2/3.

The Fundamental Counting Principle states that if there are m number of ways to do an activity and n number of ways for a second activity, then there are m x n ways to do the two activities together.

In this case, there are 7 pies and 4 of them were sold on the first day. Therefore, the probability of correctly guessing which pies were sold on the first day is 4/7.

This can be written in simplest form as 2/3.

In conclusion, the probability of correctly guessing which pies were sold on the first day is 2/3.

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If in sample of 210 students from district and finds 35 have submitted "box-tops" this year, then

(a) Yes, data provide enough evidence regarding contest which has increased participation in "box-tops" for "education-program",

(b) the p-value is 0.0187.

Part(a) : To find if contest has increased the participation in "box-tops" for "education-program", we conduct a "hypothesis-test".

We use a "significance-level" of 0.05, which means we will accept a 5% chance of making a "Type I Error",

Let Null Hypothesis ⇒ The proportion of students submitting "box-tops" is = 12%,

Let Alternative Hypothesis ⇒ The proportion of students submitting "box-tops" for education is increased after contest,

To test above hypothesis, we use "one-sample" proportion-test.

We will use the sample proportion (p') = 35/210 = 0.1667, as estimate of  population proportion (p).

So, "test-statistic" (z) is ⇒ z = (p' - p₀)/√(p₀ × (1-p₀)/n),

where n = sample size,

In "Null-Hypothesis", the "expected-value" of the test statistic is 0, and  "standard-deviation" of the "test-statistic" is √(p₀×(1-p₀)/n),

Substituting, p₀ = 0.12 and n = 210,

We get,

⇒ z = (0.1667 - 0.12)/√(0.12 x 0.88/210) ≈ 2.08,

Now, we know that "right-tailed" critical value at 0.05 level is = 1.645,

Since, z (2.08) > 1.645, the Null-Hypothesis is Rejected.

So, above data provides enough evidence regarding contest has increased the participation in "box-tops" for "education-program".

Part(b) : We need to find the "p-value" for the test-statistic that we found in part(a),

So, p-value = P(z>2.08),

⇒ 1 - P(z ≤ 2.08),

⇒ 1 - 0.9813,

⇒ 0.0187,

Therefore, the required "p-value" is 0.0187.

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Answer:

Step-by-step explanation:

Given you have collected 70 coins and stamps, and your friend has collected 1/5 as many coins and twice as many stamps, for a total of 95 coins and stamps, you want the numbers of each.

We can let x represent the number of coins you have collected. Then 70 -x is the number of stamps you have collected. The corresponding numbers for your friend are x/5 coins and 2(70-x) stamps. Your friend's collection is ...

  x/5 +2(70 -x) = 95

  -9/5x +140 = 95 . . . . . . . . simplify

  45 = 9/5x . . . . . . . . . . . . . add 9/5x -95

  25 = x . . . . . . . . . . . . . . . . multiply by 5/9

  70 -x = 45

  1/5x = 5

  2(70 -x) = 90

You collect 25 coins and 45 stamps; your friend collects 5 coins and 90 stamps.

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The correct answer is option B. That is the amount of plastic needed for making one plastic cylinder is 57 cm²

A cylinder is a three-dimensional geometric shape that has two congruent circular bases that lie parallel to each other and are connected by a curved surface. It can be thought of as a stack of circles or as a prism with a curved surface. Some common examples of cylinders include soda cans, water bottles, and pipes.

Given that the individual container of bubbles will be a plastic cylindrical tube with a diameter 2 cm and a height of 8 cm.

So radius = diameter/2 = 2/2 = 1 cm.

The surface area of the cylinder = 2πrh + 2πr²

SA = 2π × 1 ×8 + 2π × 1²

SA = 2π + 16π

SA = 18π

Substituting the value of π = [tex]\frac{22}{7}[/tex]

Hence, SA = 18π = 18 × [tex]\frac{22}{7}[/tex] ≈ 56.57

Rounding to the nearest integer, we get:

Answer: B. 57 cm^2.

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Step-by-step explanation:

See image

a) The number of weeks that she has been saving when she needs $277 is given as follows: 17 weeks.

b) The amount she will need after 5 weeks is given as follows: $505.

The function for this problem is defined as follows:

A(w) = 600 - 19w.

The output of the function is the amount remaining after w weeks.

Hence the number of weeks that she has been saving when she needs $277 is obtained as follows:

277 = 600 - 19w

19w = 600 - 277

w = (600 - 277)/19

w = 17 weeks.

The amount that she needs after 5 weeks is given as follows:

A(5) = 600 - 19 x 5

A(5) = $505.

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Answer:

Maliks fruit salad will taste more melony

Step-by-step explanation:

To determine whose fruit salad will taste more "melony," we can calculate the percentage of melon in each fruit salad for Aisha and Malik.

For Aisha's fruit salad:

Total cups of fruit = 4 cups of melon + 1 cup of apple = 5 cups

Percentage of melon = (4 cups of melon / 5 cups of total fruit) x 100%

For Malik's fruit salad:

Total cups of fruit = 13 cups of melon + 3 cups of apple = 16 cups

Percentage of melon = (13 cups of melon / 16 cups of total fruit) x 100%

Now we can calculate the percentages:

Aisha's percentage of melon:

(4 cups of melon / 5 cups of total fruit) x 100% = 80%

Malik's percentage of melon:

(13 cups of melon / 16 cups of total fruit) x 100% ≈ 81.25%

Based on the calculations, Malik's fruit salad has a higher percentage of melon (81.25%) compared to Aisha's fruit salad (80%). Therefore, Malik's fruit salad is likely to taste more "melony" compared to Aisha's fruit salad.

The height of the building , given the shadow that it casts would be 93 meters tall .

Utilizing proportions can be an effective method to tackle this issue. By defining ' h ' as the height of the building responsible for casting a 39.75 meter shadow, we may establish the ensuing proportion :

h / 39. 75 = 3. 2 / 1. 37

Solving for h gives us :

h / 39. 75 = 2. 336

h = 2. 336 x 39. 75

h = 92. 8 56

h = 93 meters tall

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Answer:

we have to first start converting the given volume to liters, since the answer is expected in hectoliters.

36 liters + 4,000 milliliters = 36 liters + 4 liters = 40 liters

1 hectoliter = 100 liters

Therefore, we have:

40 liters = 0.4 hectoliters

So, we have 0.4 hectoliters of fuel.

Answer:

0.4 hectoliters of fuel

Step-by-step explanation:

We Know

You have 36 liters of fuel and just added 4,000 milliliters more.

How many hectoliters of fuel do you have?

1000 milliliters = 1 liters

4000 milliliters = 4 liters

We Take

36 + 4 = 40 liters of fuel

We Convert 40 liters to hectoliters

1 liter = 0.01 hectoliters

40 liters = 40 x 0.01 = 0.4 hectoliters

So, you have 0.4 hectoliters of fuel.

The required, we can put 125 bottles of water or 8 cans of food in each box, and each box will contain the same number of items.

To find the largest number of relief supplies that can be put in each box, we need to find the greatest common factor (GCF) of 2250 and 144. We can do this by listing the prime factors of each number:

2250 = 2 * 3 * 3 * 5 * 5 * 5 * 2

144 = 2 * 2 * 2 * 2 * 3 * 3

To find the GCF, we need to find the highest power of each common prime factor that appears in both numbers. In this case, the common prime factors are 2 and 3, so we take the highest power of each:

2 * 3 * 3 = 18

So the largest number of relief supplies that can be put in each box is 18. We can check that this works by dividing each quantity by 18:

2250/18 = 125

144/18 = 8

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After 16 minutes of decay, approximately 182.3 grams of the element remains.

To calculate how much of the element remains after 16 minutes of decay, we can use the formula for exponential decay:

A = A₀ * [tex]e^{(-kt)[/tex]

where A is the amount of the element remaining after time t, A₀ is the initial amount of the element, k is the decay constant, and t is the elapsed time.

In this case, we have A₀ = 420 grams, k = 0.118 (since the element decays by 11.8% per minute), and t = 16 minutes. Plugging these values into the formula, we get:

A = 420 * [tex]e^{(-0.118*16)[/tex]

A = 182.3 grams

We round our answer to the nearest 10th of a gram, as requested in the problem.

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The coordinate of points K, L and M is the location of the points on a coordinate plane

Here, we have,

to determine the missing coordinates:

The given parameters are:

K = (10, )

L = ( ,10)

M = (30, )

The question has missing parameters.

So, I will assume that the line is a perfectly horizontal line.

This means that the y-coordinates of points K, L and M are equal.

The y-coordinate of point L is 10.

So, we have:

K = (10, 10)

L = ( ,10)

M = (30, 10)

Assume that point L is halfway points K and M, then we have:

K = (10, 10)

L = (20, 10)

M = (30, 10)

See attachment for the diagram of the coordinate plane showing the line

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Answer:

3 divide 2/5 is 7.5 since 2/5 is 0.4

Answer:

To calculate the monthly payments for each option, we can use the PMT function in Excel or a financial calculator.

For the new car option:

Loan amount = $31,000

Interest rate (annual) = 7.19%

Loan term = 3 years

Number of payments = 3 x 12 = 36

Using the PMT function in Excel, we get:

PMT(7.19%/12, 36, -$31,000) = $966.59

For the used car option:

Loan amount = $16,000

Interest rate (annual) = 5.89%

Loan term = 4 years

Number of payments = 4 x 12 = 48

Using the PMT function in Excel, we get:

PMT(5.89%/12, 48, -$16,000) = $385.36

The difference in monthly payments between the two options is:

$966.59 - $385.36 = $581.23

Therefore, the difference in monthly payments between financing the new car and financing the used car is $581.23.

Step-by-step explanation:

Using the quadratic equation, the solution is x = -8 and x = -17.

A second-order equation of the form ax2 + bx + c = 0 denotes a quadratic equation, where a, b, and c are real number coefficients and a 0.

The equation is x²+25x+136=0

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

For the given equation x² + 25x + 136 = 0, we can identify a = 1, b = 25, and c = 136.

Substituting these values in the quadratic formula, we get:

x = (-25 ± √(25² - 4(1)(136))) / 2(1)

x = (-25 ± √(625 - 544)) / 2

x = (-25 ± √(81)) / 2

imply them

x = (-25 + 9) / 2 or x = (-25 - 9) / 2

x = -8 or x = -17

Therefore, the solutions to the quadratic equation x^2 + 25x + 136 = 0 are x = -8 and x = -17.

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