The angle measures of a triangle are shown in the diagram below.
What is the value of x?

Record your answer in the grid. Be sure to use the correct place value.

8 points total

7 points correct answer

1 point correct bubbling on grid

The surface area of the rectangular prism is (26/3) times larger than the surface area of the cube.

Given data ,

Let the surface area of the cube be S₁

Let the surface area of the rectangular prism be S₂

Let the volume of the cube be V₁

Let the volume of the prism be V₂

On simplifying , we get

The side length of cube = x

So , surface area of cube = 6x²

The volume of cube = x³

And , the surface area of prism = 2 ( 12x² + 8x² + 6x² )

S₂ = 52x²

And , volume of prism = l x w x h

V₂ = ( 2x ) ( 3x ) ( 4x ) = 24x²

So , S₂ = ( 26/3 ) S₁

52x² = ( 26/3 ) ( 6x² )

52x² = 52x²

Hence , The rectangular prism's surface area is (26/3) times greater than the cube's surface area.

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The complete question is attached below :

The dimensions of a cube and a rectangular prism are shown below.

Which statement is true?

A The surface area of the rectangular prism is 24 times larger than the surface area of the cube.

The surface area of the rectangular prism is times larger than the surface area of the cube.

C The volume of the rectangular prism is 48 times larger than the volume of the cube.

D The volume of the rectangular prism is 3 times larger than the volume of the cube.

The claims are this year some of their clients will have a starting salary of at least $38,500 and last year at least one of their clients had a starting salary of exactly $38,500. Correct options are A and B.

Based on the given information, option A can be true. This is because the average starting salary of the job placement agency's clients was $38,500 last year, which means some clients had a starting salary equal to or greater than that amount.

Option B is also true because the mean includes all values, including the value of $38,500, so it is likely that at least one client had that starting salary.

Option C cannot be determined from the given information as it is unclear what percentage of clients had a starting salary above $38,500. Option D is not necessarily true as there is no information on the starting salary of any client exceeding $42,000.

Option E is also not true as the average salary of $38,500 does not guarantee that all clients had that same starting salary. Therefore, the correct answer is A and B, and the rest cannot be determined from the given information.

Correct options are A and B.

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The correct option is D, the parent quadratic function is:

f(x) = x²

First, we define the parent functions as the simplest function for each type.

For example, the parent linear function is.

y = x

The parent square root function is:

y = √x

The parent absolute value function is:

y = |x|

And so on.

So the parent quadratic function is a polynomial of degree 2 where we only have the quadratic term (and no coefficient).

Thus, the correct option is D; f(x) = x²

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Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

Answer:

x+3x-4=2x+x+5

Step-by-step explanation:

=4x-4= 3x+5

=4x-3x=5+4

= x=9. Done

The measure of the angle 4, m∠4, obtained from the measure formed by the diagonals of a rhombus is; m∠4 = 38°

The diagonals of a rhombus bisect the angles at the vertices of the rhombus

The diagonals of a rhombus are perpendicular bisectors of each other, therefore;

The measure of the angle m∠2 = 90°

Therefore; m∠1 = 90° - 52° = 38°

The triangle with base angles ∠1, and ∠4, is an isosceles triangle, with the base angles ∠1, and ∠4

The base angles of an isosceles triangle are congruent, therefore;

∠1 ≅ ∠4

m∠1 = m∠4

m∠4 = m∠1 = 38°

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Answer:

1 1/6 metre

Step-by-step explanation:

1/3 pink + 5/6 purple

To add, we need to get a common denominator

1/3 *2/2 = 2/6

2/6 + 5/6

7/6

Change from an improper fraction to a mixed number

1 1/6 metre

The exponential function that model this situation is [tex]A(t) = 2500(1 + 0.035)^t.[/tex]

The account will have $5000 in 20 years.

Let A be the amount in the account after t years.

Then, we can model this situation with the function A(t) = 2500(1 + 0.035)^t with the use of compound intererst formula which is [tex]P = A*(1+r)^t[/tex]

To find when the account will have $5000, we can set A(t) = 5000 and solve:

5000 = 2500(1 + 0.035)^t

2 = (1.035)^t

Taking the natural logarithm:

ln(2) = t ln(1.035)

t = ln(2)/ln(1.035)

t = 20.148791684

t = 20 years.

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Answer:

1)  21 years

2) 26 years

Step-by-step explanation:

To model the account balance of Vanessa's account at t years, we can use an exponential function in the form:

[tex]\large\boxed{A(t) = A_0(1 + r)^t}[/tex]

where:

Given Vanessa invested $2500 into the account and it will increase in value by 3.5% each year:

Substitute these values into the formula to create an equation for A in terms of t:

[tex]A(t) = 2500(1 + 0.035)^t[/tex]

[tex]A(t) = 2500(1.035)^t[/tex]

To find when the account balance will be $5000, set A(t) equal to $5000 and solve for t:

[tex]A(t)=5000[/tex]

[tex]2500(1.035)^t=5000[/tex]

[tex](1.035)^t=\dfrac{5000}{2500}[/tex]

[tex](1.035)^t=2[/tex]

[tex]\ln (1.035)^t=\ln 2[/tex]

[tex]t \ln 1.035=\ln 2[/tex]

[tex]t=\dfrac{\ln 2}{ \ln 1.035}[/tex]

[tex]t=20.1487916...[/tex]

[tex]t=20.15\; \sf years\;(2\;d.p.)[/tex]

Therefore, it will take approximately 20.15 years for Vanessa's account to reach a value of $5000.

Since the interest rate is an annual rate of 3.5%, it means that the interest is applied once per year, at the end of the year. Therefore, we need to round up the number of years to the next whole number.

So Vanessa's account will have $5,000 after 21 years.

Note: After 20 years, the account balance will be $4,974.47. After 21 years, the account balance will be $5,148.58.

[tex]\hrulefill[/tex]

To model the increase in movie ticket prices over time, we can use an exponential function in the form:

[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]

where:

Given the initial price of the ticket was $4.22 and the price has increased by 3.1% each year:

Substitute these values into the formula to create an equation for P in terms of t:

[tex]P(t) = 4.22(1 + 0.031)^t[/tex]

[tex]P(t) = 4.22(1.031)^t[/tex]

To find how many years until tickets cost $9.33, we can set P(t) equal to $9.33 and solve for t:

[tex]P(t)=9.33[/tex]

[tex]4.22(1.031)^t=9.33[/tex]

[tex](1.031)^t=\dfrac{9.33}{4.22}[/tex]

[tex]\ln (1.031)^t=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]

[tex]t \ln (1.031)=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]

[tex]t =\dfrac{\ln \left(\dfrac{9.33}{4.22}\right)}{\ln (1.031)}[/tex]

[tex]t=25.9882262...[/tex]

Therefore, it will take approximately 26 years for movie ticket prices to reach $9.33, assuming the annual growth rate remains constant at 3.1%.

In a case whereby A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position the degrees north of west it turned is 72°

From trigonometry, the law of cosines states  the side c of a triangle can be found as

c² = a² + b² - 2abcos(C)

where

C = angle opposite to side c.

a and = lengths of the other sides.

a = 94, b = 119, c = 173.

c² = a² + b² - 2abcos(C)

173² = 94² + 119² - 2 x 94 x 119cos(C)

22327cos(C) = -6932

cos(C) = -6932/22327

C = arccos(-6932/22327)

C = 108º.

Then,

T = 180 - C

= 180 - 108 = 72º.

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Based on the information, we can infer that the correct answer is 90° clockwise (option A).

To identify the correct rotation of this figure we must perform the following procedure:

1. We must identify the reference figure.

2. We must identify the figure that expresses the rotation.

3. We must identify the angle of rotation of the figure.

4. Select the option that correctly expresses the sense of rotation.

Based on the above, we can infer that the correct answer is A. 90° Clockwise because the rotation is to the right.

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The coordinates in the solution to the systems of inequalities is (12, 1)

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

y > -4x + 6

y > 1/3x - 7

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (12, 1)

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a) The correct option is C. Construct a 99% confidence interval for μ in order to see the magnitude of the difference between 115 and your sample results.

b) The correct option is B. Use a very small level of significance.

c) The correct option is B. The sample size is small.

d) The lack of statistical significance at the 0.10 significance level suggests that the observed doubling of survival time may not be practically significant as the actual increase is only two years.

(a) To assess the practical significance of the results, the most helpful approach would be to construct a 99% confidence interval for the population mean, μ. This would provide a range of values within which the true population mean is likely to fall. By comparing this interval to the hypothesized value of 115, you can evaluate the magnitude of the difference and determine if it is practically significant.

Therefore, the correct option is C. Construct a 99% confidence interval for μ in order to see the magnitude of the difference between 115 and your sample results.

(b) When the consequences of rejecting the null hypothesis are very serious, it is important to be cautious and use a very small level of significance. The level of significance determines the threshold for rejecting the null hypothesis. By using a very small level of significance, you are setting a higher standard for rejecting the null hypothesis, reducing the likelihood of making a Type I error (false positive). This ensures that strong evidence is required to support rejecting the null hypothesis when the consequences are significant.

Therefore, the correct option is B. Use a very small level of significance.

(c) In this scenario, the explanation for the lack of statistical significance at the 0.10 significance level, despite the survival time doubling, is likely due to the small sample size. With only three subjects, the sample may not provide enough statistical power to detect a significant difference. The variability in survival times within the sample might also influence the lack of significance. A larger sample size would provide more reliable and statistically significant results.

Therefore, the correct option is B. The sample size is small.

d) The explanation for the lack of statistical significance in this scenario is that although the survival time has doubled from two years to four years, the actual increase is still only two years. This means that the difference between the standard treatment and the new treatment is not as substantial as it may initially seem.

When conducting statistical tests, it is important to consider both statistical significance and practical significance. While the survival time doubling may be a positive outcome, if the actual increase is only two years, it may not be considered practically significant in the context of cancer treatment.

Statistical significance is determined by conducting hypothesis tests and examining the p-value. In this case, even at the 0.10 significance level, the results are not statistically significant, indicating that the observed difference in survival times could likely be due to chance.

It is important to interpret the results in the context of the specific situation and consider factors such as sample size, variability, and clinical significance. In this case, the small sample size of three subjects may limit the statistical power to detect a significant difference. Additionally, the placebo effect or other factors may also play a role in limiting the statistical significance of the results.

In summary, the lack of statistical significance at the 0.10 significance level suggests that the observed doubling of survival time may not be practically significant as the actual increase is only two years.

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Answer:

Step-by-step explanation:

Make a plan:

Solve the problem:

Draw the conclusion:

Hope this helps!

The result of the expression (A ∩ B) - C is [-2, 5] U [13, 18] is [-2,5,13,18].

To find the result of the expression (A ∩ B) - C, where A, B, and C are sets, we need to perform the following steps:

Given the sets:

A = < - 7, 5 ] U [10, 18 >

B = [ - 2, 8 > U < 13, 23 >

C = < 1, 15 >

1.Find the intersection of sets A and B (A ∩ B):

2. Subtract set C from the intersection (A ∩ B):

Subtracting set C = <1, 15> from the intersection [-2, 5] U [13, 18] means removing any elements that are present in set C from the intersection.

Since set C = <1, 15> does not overlap with either [-2, 5] or [13, 18], the subtraction (A ∩ B) - C results in the same set as the intersection:

(A ∩ B) - C = [-2, 5] U [13, 18].

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Volume of the cylinder =  6838.92 cubic inches

We have to given that;

Sam needs to fill a cylindrical container with punch.

And, The container has a radius of 11 inches and a height of 18 inches.

Since, To determine the amount of cat litter the cylinder can hold, we need to calculate the volume of the cylinder.

Volume of a cylinder = πr²h

Where,

r=radius

h= height

Then,

π=22/7 or 3.14 (constant value)

r=11 inches

h=18 inches

Volume of a cylinder is,

= 3.14 × (11)² × 18

= 6838.92 cubic inches

Hence, Volume of the cylinder =  6838.92 cubic inches

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Answer:

Step-by-step explanation:

To estimate the original volume of the pyramid in Figure 15.28, we can use the formula for the volume of a frustum of a pyramid. The frustum is the portion of the pyramid between the top and bottom, created by removing the top section.

The formula for the volume of a frustum of a pyramid is:

V = (1/3) * h * (A + sqrt(A * B) + B)

Where:

V = Volume of the frustum

h = Height of the frustum (vertical distance between the top and bottom)

A = Area of the top base

B = Area of the bottom base

Given the dimensions provided, we can calculate the areas of the bases:

Area of the top base (A) = 4 m * 4 m = 16 m²

Area of the bottom base (B) = 20 m * 20 m = 400 m²

The height of the frustum (h) is given as 12 m.

Now we can plug these values into the formula:

V = (1/3) * 12 m * (16 m² + sqrt(16 m² * 400 m²) + 400 m²)

Calculating the square root and simplifying:

V = (1/3) * 12 m * (16 m² + 20 m² + 400 m²)

V = (1/3) * 12 m * (436 m²)

V = 1744 m³

Therefore, the estimated original volume of the pyramid in Figure 15.28 is approximately 1744 cubic meters.

The length of a side of the square garden is 5.75 feet.

(x+10)(x+5) - x² + (x+13)(x+8) - x² = 700

Simplifying and solving for x, we get:

2x^2 + 46x - 177 = 0

Using the quadratic formula, we can solve for x:

x = (-46 ± ✓46² - 4(2)(-177))) / (2(2))

x = (-46 ± 26) / 4

x = 5.75

The length of a side of the square garden is 5.75 feet.

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1. The proportion is; x/4 = 12/18

2. The height of the mailbox is 2.7 feet

In mathematics, a proportion is an equation that states that two ratios are equal. It expresses the relationship between the quantities in terms of their relative sizes or magnitudes. Proportions are used in various areas of mathematics and real-life applications, such as ratios

We have;

Length of the mail box shadow = 4 feet

Length of the tree shadow = 18 feet

Height of the mail box = x

Height of the tree = 12 feet

Thus;

x/4 = 12/18

x = 4 * 12/18

x = 2.7 feet

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a. The value of sin θ = 13/18

b. The size of sin θ is 46.2 degrees

First, we need to know the different trigonometric identities.

These trigonometric identities are listed thus;

From trigonometric relations, we have that the ratio for sine identity is represented as;

sin θ = opposite/hypotenuse

Then, we have from the information given that;

Hypotenuse side = 18cm

Opposite side = 13cm

Substitute the values, we have;

sin θ = 13/18

Divide the values

sin θ = 0. 7222

Find the sine inverse value, we have;

so, θ = sin⁻¹(13/18) = 46. 2 degrees

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a) The area of the rectangular shaped bathroom floor is A = 30.375 feet²

b) The number of boxes of tiles = 25 boxes

Given data ,

Jordan is putting new tile on the bathroom floor. The width of the floor is 4 2/4 feet and the length is 6 3/4 feet

Now , Area of Rectangle = Length x Width

On simplifying , we get

Width = 4 2/4 feet = (4 x 4 + 2)/4 = 18/4 feet

Length = 6 3/4 feet = (6 x 4 + 3)/4 = 27/4 feet

Area = (18/4) x (27/4) = (18 x 27)/(4 x 4) = 30.375 feet²

Therefore , the area of bathroom floor is A = 30.375 feet²

Now , the number of boxes is given by

Number of boxes of tiles = Total area of bathroom floor / Area covered by each box of tiles

B = 30.375 / 5

B = 6.075

B = 6 tiles

Hence , the area of bathroom floor is A = 30.375 feet²

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Donald traveled approximately 100 kilometers on each of his trips to the amusement park.

Now, the distance Donald traveled on each of his trips to the amusement park.

If he drove a total of 399 kilometers over the course of four trips, we can find the average distance he traveled per trip by dividing the total distance by the number of trips.

So, We get;

= 399 divided by 4

= 399 / 4

= 99.75 kilometers per trip

≈ 100 kilometers per trip.

Therefore, Donald traveled approximately 100 kilometers on each of his trips to the amusement park.

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Band B-1 is a band of the electromagnetic spectrum that is used for cellular communications. It is located in the 2100 MHz frequency range.

Band B-2 is also a band of the electromagnetic spectrum that is used for cellular communications. It is located in the 1900 MHz frequency range.

The main difference between band B-1 and band B-2 is their range. Band B-1 has a longer range than band B-2. This is because it is located in a higher frequency range. Higher frequency ranges have shorter wavelengths, which means that they can travel through objects more easily. This makes them better for use in areas where there are a lot of obstacles, such as buildings and trees.

Band B-2 has a shorter range than band B-1, but it is better for use in areas where there are a lot of people. This is because it is located in a lower frequency range

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A z-score of 0 indicates that the person's score is equal to the mean, so they are right at the Average Performance level.the z-score of a person who scored 300 on the exam is 0.

The z-score of a person who scored 300 on the exam, we can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

In this case, the person scored 300 on the exam, which is equal to the mean (μ). Therefore, we can substitute these values into the formula:

z = (300 - 300) / 40

Simplifying the equation, we have:

z = 0 / 40

Since any number divided by zero is undefined, we can conclude that the z-score of a person who scored 300 on the exam is 0.

The z-score measures the number of standard deviations a data point is away from the mean. In this case, a z-score of 0 indicates that the person's score is equal to the mean, so they are right at the average performance level.

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We are 98% confident that the true mean amount of money spent per month on home maintenance by all homeowners is between $70.19 and $75.81.

A confidence interval is a range of values that is likely to contain the true value of the population parameter with a given level of confidence. A confidence interval for the population mean μ can be constructed as follows:

μ = sample mean ± margin of error where the margin of error is given by:margin of error = (critical value) x (standard error)

Here, we want to construct a 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners. We are given that a survey of 81 randomly selected homeowners finds that they spend a mean of $73 per month on home maintenance.

The population standard deviation is assumed to be $10 per month.

Therefore, the standard error of the mean is given by:standard error = σ / sqrt(n) = 10 / sqrt(81) = 10 / 9 = 1.11

where σ is the population standard deviation and n is the sample size.To find the critical value, we need to look up the t-distribution table with 80 degrees of freedom and a significance level of 0.01 (since we want a 98% confidence interval).

The corresponding value is 2.527.

Therefore, the margin of error is:margin of error = (critical value) x (standard error) = 2.527 x 1.11 = 2.81

Finally, we can construct the confidence interval as follows:73 ± 2.81 = (70.19, 75.81)The confidence interval is rounded to the nearest cent.

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The quadrilateral given on the image can be said to be a parallelogram because the diagonals bisect each other.

An effective way to check if a four-sided figure is a parallelogram is through the diagonal test, which involves inspecting its diagonals. According to the examination, if the two diagonals of a four-sided shape intersect at their midpoint, the shape is classified as a parallelogram.

The two diagonals in a parallelogram intersect at their midpoint, although they may not have the same length. This implies that the intersection point of every diagonal bisects the diagonal into two identical parts. Despite the unequal length of its diagonals, the parallelogram is still considered as such due to the bisecting property.

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The quadratic equation with the given roots is:

y = 0.5x² + 1.5x - 5

For a quadratic equation with a leading coefficient a, and roots:

x = h and x = k, we will get general formula:

y = a*(x - h)*(x - k)

Here we know that the roots are x = 2 and x = -5, replacing that we will get:

y = a*(x - 2)*(x + 5)

And we know that this quadratic passes through (1, -3), replacing these values:

-3 = a*(1 - 2)*(1 + 5)

-3 = a*(-1)*(6)

-3 = -6a

-3/-6 = a

0.5 = a

Replacing that:

y = 0.5*(x - 2)*(x + 5)

Expanding the quadratic we will get:

y = 0.5x² + 1.5x - 5

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Answer:

47703169206

Step-by-step explanation:

7 x 787 x 9999 x 866 = 47703169206 via the process of multiplication

Answer:

8,9740 that is your answer and then I hope you have a good day and hope this helps

Answer:

hey it is

Step-by-step explanation:

22 × 18 or 12 into 18

An equation that satisfies all three pairs of a and b values listed in the table include the following: C. 3a - b = 10.

In order to determine an equation that satisfies all three pairs of a and b values listed in the table, we would substitute each of the numerical values corresponding to each variable into the given equations and then evaluate as follows;

a - 3b = 10

0 - 3(-10) = 30 (False).

3a + b = 10

3(0) - 10 = -10 (False).

3a - b = 10

3(0) - (-10)

0 + 10 = 10 (True).

3a - b = 10

3(1) - (-7)

3 + 7 = 10 (True).

3a - b = 10

3(2) - (-4)

6 + 4 = 10 (True)

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Complete Question:

Which equation satisfies all three pairs of a and b values listed in the table?

a b

0 -10

1 -7

2 -4

The equation is?

A.) a-3b=10

B.) 3a+b=10

C.) 3a-b=10

D.) a+3b=10

The probability that a randomly chosen person would score less than 86 is 0.8643, and the probability that a randomly chosen person would score more than 86 is 0.1357.

We consider X to be a random variable that represents the score of a person. So according to the question, X follows the given normal distribution and the given curve represents its distribution.

Now from the curve, we can see that the proportion of observation under the score 86 is 0.8643.

So we have,

P[X < 86] = 0.8643

A) We have to find the probability that a randomly chosen person would score less than 86. i.e, we have to find P[X < 86]

It is clearly given from the curve that, P[X < 86] = 0.8643

B) Now it is required to find the probability that a person chosen at random would score higher than 86 on this test. i.e P[X > 86]

P[X > 86] = 1 - P[X < 86]

= 0.1357

Therefore, the probability that a randomly chosen person would score less than 86 is 0.8643, and the probability that a randomly chosen person would score more than 86 is 0.1357.

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