..............................

The length of curve DE is equal to 26.25 units.

In Mathematics and Geometry, Pythagorean's theorem is modeled by the following mathematical expression:

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

In order to determine the length of the hypotenuse in this right-angled triangle, we would have to apply Pythagorean's theorem as follows;

AC² + BC² = AB²

20² + 15² = AB²

AB² = 400 + 225

AB = √625

AB = 25 units.

For the length of curve DE, we have:

DE = 105% of AB

DE = 1.05 × 25

DE = 26.25 units.

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The amount of money earned over six weekends is best described as decreasing. The Option A.

Decreasing income refers to a situation in which an individual or household experiences a reduction in the amount of money earned over a certain period of time.

This can be caused by a variety of factors, such as job loss, reduction in work hours, or a decrease in wages. When income decreases, individuals may find it more difficult to meet their financial obligations, such as paying bills, making rent or mortgage payments, and purchasing basic necessities like food and clothing.

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Answer:

it's 17.04 as u showed in the answer

Step-by-step explanation:

1st u change the mixed no. to improper fraction

2nd u will multiply it by it's resprocal then u will get 17.04

Answer:

x = 3.5 pages per minute

Step-by-step explanation:

We make the relationship

21 pages ------ 6 min

x pages -------- 1 min

So x= (21x1)/(6)

x = 3.5 pages per minute

Answer:

b. 8/17

Step-by-step explanation:

hope this helps ;)

Answer:

Θ ≈ 28.07°

Step-by-step explanation:

using the sine ratio in the right triangle

sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{17}[/tex] , then

Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{8}{17}[/tex] ) ≈ 28.07° ( to the nearest hundredth )

Box plot, as the median can be easily ascertained from the substantial amount of data. The answer is option (a).

The middle value in a given set of figures or statistics is referred to as the median. The average value for a given collection of integers can be calculated using one of three main methods in mathematics. The mean, the median, and the mode are the three. Central tendency measurements refer to these three factors. The average value of the supplied data is calculated using mean. The midpoint value of the given data is defined by a median. The input data's repeating value is defined by the mode.

A box plot is a very visual way to show a brief summary of one or more sets of data. It is particularly useful for quickly comparing and summing multiple sets of findings from distinct trials. A box plot provides a visual picture of the distribution of results as well as clues regarding data symmetry at a look.

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If your friend in college decides to purchase textbooks using his credit card. The number of  year his credit card balance be $1360 is 8 years.

We can use the continuous compounding formula to solve this problem:

A = Pe^(rt)

where A is the ending balance, P is the initial balance, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.

In this case, we want to solve for t when P = 500 and A = 1360. The interest rate is given as 12.5% compounded continuously, which means r = 0.125. Substituting these values into the formula, we get:

1360 = 500e^(0.125t)

Dividing both sides by 500, we get:

e^(0.125t) = 2.72

Taking the natural logarithm of both sides, we get:

0.125t = ln(2.72)

Solving for t, we get:

t = ln(2.72)/0.125 ≈ 8

Rounding to the nearest year, we get that it will take 8 years for the credit card balance to reach $1360 without making any payments.

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From the given information about the vertices of the quadrilateral, the point at which the PQRS quadrilateral will be made a rectangle is S(17/14, -1/7).

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The answer is option c.) S(-8,2).

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

For PQRS to be a rectangle, its opposite sides must be parallel and have equal length. We can find the length of PQ and RS using the distance formula:

PQ = √[(Qx - Px)² + (Qy - Py)²]

  = √[(-3 - (-5))² + (6 - 7)²]

  = √[4 + 1]

  = √[5]

RS = √[(Sx - Rx)² + (Sy - Ry)²]

  = √[(-8 - (-6))² + (2 - 0)²]

  = √[4 + 4]

  = √[8]

Since PQ and RS are not equal, we need to find a point S such that PQRS has equal sides. Moreover, the diagonals of a rectangle bisect each other. Hence, we can use the midpoint formula to find a point that bisects PR:

M = [(-5 - 6)/2, (7 + 0)/2]

 = (-11/2, 7/2)

Let's consider each option:

a.) S(-4,-1)

The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-8 + 6) = 1, so S(-4, -1) cannot be a point of RS.

b.) S(-7,2)

The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-7 + 6) = -2, so S(-7, 2) cannot be a point of RS.

c.) S(-8,2)

The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (2 - 0)/(-8 + 6) = 1, so S(-8, 2) could be a point of RS. Moreover, the distance from S to the midpoint of PR is:

√[(-11/2 - (-8))² + (7/2 - 2)²]

= √[25/4 + 9/4]

= √[34]/2

This is equal to the length of PQ, so PQRS could be a rectangle with S(-8, 2).

d.) S(-8,1)

The slope of PQ is (6 - 7)/(-3 + 5) = -1/2, so the slope of RS must be -1/2 as well. The slope of RS is (1 - 0)/(-8 + 6) = -1, so S(-8, 1) cannot be a point of RS.

Therefore, the answer is option c.) S(-8,2).

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By using slope intercept , These were the two points on the line: (0,-2) and (7,2).

A line is defined by the equation y = mx + b, which is also known as the slope-intercept form. When the line is graphed, m represents the slope and b the point at which the line intersects the y-axis.

We may use the slope-intercept form of a line, which is y=mx+b where m is the slope and b is the y-intercept, to graph the line y=4/7x-2. Therefore, m=4/7 and b=-2.

These variables allow us to plot two spots along the line. Since the line crosses the y-axis at (0,-2) (the y-intercept), that location will be one of the points.

We can utilize the slope of 4/7 to locate a different point along the line. This indicates that we advance up 4 units in the y direction for every 7 units we move to the right (in the x direction). We can therefore move 7 units to the right and then 4 units up, starting at (0,-2), to reach (7,2).

So now we have two points on the line: (0,-2) and (7,2). These points can be plotted on a coordinate plane, and then a straight line can be drawn through them to create the graph.

Graph given below:

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The sum of the NPV and false omission rate for any test will always be 100%.

The NPV (Negative Predictive Value) is the proportion of people who test negative for a condition and actually do not have it, while the false omission rate is the proportion of people who have the condition but test negative for it.

When we add together the NPV and the false omission rate for any test, we are essentially considering all the cases where the test result is negative.

The NPV represents the proportion of people who truly do not have the condition and test negative for it, while the false omission rate represents the proportion of people who actually have the condition but test negative for it.

Together, these two values cover all possible cases where the test result is negative, which means that they represent the entirety of the negative results for the test.

Since the sum of all probabilities for an event must always equal 100%, the sum of the NPV and false omission rate must also equal 100%.

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Answer:

Step-by-step explanation:

Average rate of change = (Ending value - Beginning value) / Time elapsed

Using the formula for the average rate of change, we get:

(1824 - 1140) / 1095 = $0.55 per day

(1824 - 1140) / 36 = $19 per month

(1824 - 1140) / 12 = $54 per quarter

(1824 - 1140) / 3 = $228 per year

Therefore, the average rate of change for Tony's investment was $19 per month.

The polar form of the rectangular coordinates (-3√3, 0) is r = 3√3 and θ = 0

To convert the rectangular coordinates (-3√3, 0) into polar form, we can use the following equations:

r = √(x² + y²)

θ = tan⁻¹(y/x)

In this case, x = -3√3 and y = 0, so we have:

r = √((-3√3)² + 0²) = 3√3

θ = tan⁻¹(0/(-3√3)) = tan⁻¹(0) = 0

Since the angle is given in radians over the interval 0 ≤ θ < 2π (which is equivalent to 0 ≤ θ < 6.28318), we need to add 2π to θ if it is negative, to ensure that θ is in the specified interval.

However, in this case, θ is already equal to 0, which is within the specified interval.

Therefore, the polar form of the rectangular coordinates (-3√3, 0) is:

r = 3√3

θ = 0 (in radians, over the interval 0 ≤ θ < 2π)

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Null hypothesis: The mean height of top-rated roller coasters is 160 feet (H0: u = 160).

1) Null hypothesis: The mean height of top-rated roller coasters is 160 feet (H0: u = 160). Alternative hypothesis: The mean height of top-rated roller coasters is not 160 feet (Ha: u ≠ 160). The claim is the null hypothesis.

2) Sample mean = (325+188+306+107+208+167+105+78+140+232+230+170+170+205+305+135+200+200+100+223+135+195+80+90+120+210+82+161+245+88+70+116+121+146+149+124)/36 = 164.97 feet. The test statistic z = (x - μ) / (σ / √n) = (164.97 - 160) / (71.6 / √36) = 1.21.

3) The p-value is the probability of observing a test statistic as extreme as the one computed from the sample, assuming the null hypothesis is true. Using a standard normal distribution table, the p-value is 0.1131.

4) At α = 0.05, the p-value (0.1131) is greater than a. Therefore, we fail to reject the null hypothesis.

5) Based on the statistical analysis, we do not have sufficient evidence to reject the claim that the mean height of top-rated roller coasters is 160 feet.

6) Hypothesis testing is a statistical method used to make decisions based on the analysis of sample data. It is used to determine whether a claim or hypothesis about a population is supported by the evidence provided by the sample data.

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We need to integrate the function

y = 2x - x² with respect to x, from x = 0 to x = 2.

The graph of the function intersects the x-axis at x = 0 and x = 2.

So,

Area of region R = ∫[0,2] (2x - x²) dx

= [x² - (1/3)x³] from 0 to 2

= [2² - (1/3)(2)³] - [0² - (1/3)(0)³]

= 4/3

Now, let's find the equation of the line y = cx. Since the line passes through the origin (0,0), we have y = cx.

To find the value of c that divides the region R into two equal subregions, we need to find the value of x where the

area under the curve y = 2x - x² is equal to the area under the line y = cx.

∫[0,a] (2x - x²) dx = ∫[0,a] cx dx

[2x²/2 - x³/3] from 0 to a = [c/2 x²] from 0 to a

2a²/2 - a³/3 = c/2 a²

We multiply both sides by 6, we get:

12a² - 2a³ = 3ac

2a² - (1/3)a³ = (1/2)ac

2a - (1/3)a² = (1/2)c

c = (4a - (2/3)a²)/2

We know that the area under the line is equal to the area under the curve up to the point of intersection, we have:

∫[0,a] (2x - x²) dx = ∫[0,a] (cx) dx - ∫[a,2] (2x - x²) dx

2a²/2 - a³/3 = c/2 a² - 2a² + (8/3)a³ - 4a + (4/3)a²

10a³/3 - 7a² + 4a = 0

a = 0, 1.4105, -0.6172

The only value of a that is within the range 0 to 2 is a = 1.4105. Substituting this value into the equation for c, we get:

c = (4a - (2/3)a²)/2 = 1.636

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Answer:

If there are 15 boys in Mr. Day’s class and the girl to boy ratio is 3 to 5, then there are 9 girls in Mr. Day’s class. To find out how many more boys there are than girls, you can subtract the number of girls from the number of boys:

15 boys - 9 girls = 6 more boys than girls.

Step-by-step explanation:

The area of the given circle is 616 sq.cm.

The volume of rectangular prism is 416 mm³

A circle is a particular type of ellipse when the eccentricity is zero and both foci are present. The locus of points drawn equally apart from the centre is also referred to as a circle. The radius of a circle is the separation between its centre and its periphery. The circle's diameter, which is equal to twice its radius, is the line that splits the circle into two equal pieces.

Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle. The unit of area is the square unit, such as m², cm², etc.

Area of Circle = πr² or πd²/4, square units

where π = 22/7 or 3.14

according to question,

Area = pi times the radius squared

A = pi * r²

A = 22/7 * 14²

A = 22/7 * 196

A = 4,312 / 7

A = 616 sq. cm.

V = l*w*h

To determine the volume, multiply all three dimensions together.

For Connexus users Rectangular prisms and volume quiz part 2:

l * w * h = 8 * 5 * 10.4 = 416

the volume of rectangular prism is 416 mm³

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Answer:

To determine which equation represents how much the worker earns in x hours, we can use the table to find the rate of pay per hour, which is the change in wages divided by the change in hours:

Change in wages = $105.50 - $25.50 = $80

Change in hours = 6 - 2 = 4

Rate of pay per hour = Change in wages / Change in hours

= $80 / 4

= $20

Therefore, the worker earns $20 per hour. To find the total earnings, we can multiply the hourly rate by the number of hours worked:

y = $20x

Therefore, the correct equation is D) y = 10x, which represents how much the worker earns in x hours.

Step-by-step explanation:

       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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Answer:

a. $58.57

Step-by-step explanation:

Billy is in a pickle. He has a credit card debt of $3500 with a 16% annual interest rate, and he wants to pay it off in a year. He also wants to ask his boss for a raise, but he doesn't know how much to ask for. Luckily, he has a friend who is good at math and can help him out.

The friend tells Billy that we need to use the formula for the monthly payment of a credit card debt, which is:

P = (r / 12) * B / (1 - (1 + r / 12)^(-n))

where P is the monthly payment, r is the annual interest rate, B is the current balance, and n is the number of months to pay off the debt.

Using this formula, the friend calculates how much Billy is currently paying and how much he would need to pay to clear his debt in 12 months. The friend also finds the difference between these two payments, which is the amount of extra income Billy would need from his raise.

The friend shows Billy the calculations and says:

"Here you go, Billy. You are currently paying $280.42 per month to pay off your debt in 15 months. If you want to pay it off in 12 months, you would need to pay $331.79 per month. That means you would need an additional monthly income of $51.37 from your raise. The closest answer choice to this amount is a. $58.57, so this is the best option."

Billy thanks his friend and says:

"Wow, you are amazing! Thank you so much for helping me out. I'm going to ask my boss for a raise right now. Wish me luck!"

The friend wishes Billy good luck and hopes that he will get his raise and pay off his debt soon.

The total rations will be: 0.75 times the number of meals.

A ration refers to the fixed portion of food or other goods allowed to each person in times of shortages.

In this context, If you decide to eat only 75% of each meal, that means you will consume 0.75 times the number of meals.

For example, if you originally had 100 meals, you will now have:

= 0.75 x 100

= 75 rations in total.

This approach allows to stretch your meals and make them last longer by rationing your food intake.

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The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. The test score esteem that isolates the beat 2.5% of normal distribution from the rest of the understudies is roughly 83.72.

To discover the test score esteem that isolates the best 2.5% of the understudies, we got to discover the z-score comparing to that rate utilizing the standard ordinary conveyance table.

z = (x - μ) / σ

To discover the z-score compared to the best 2.5%, we see up the region of the right-hand tail of the standard normal distribution table, which is 0.025. This compares to a z-score of roughly 1.96.

Presently ready to utilize the z-score equation to unravel for x:

1.96 = (x - 70) / 7 Increasing both sides by 7, we get:

x - 70 = 13.72

Including 70 to both sides, we get:

x = 83.72

Hence, the test score esteem that isolates the beat 2.5% of the understudies from the rest of the understudies is roughly 83.72.

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Applying the Angles of Intersecting Chords Theorem, the value of x in the circle is: x = 69 degrees.

The Angles of Intersecting Chords Theorem if two chords intersect inside a circle, then the size of the angle formed by the intersection is equal to half the sum of the sizes of the intercepted arcs, along with the size of its vertical angle.

Apply the theorem to find the value of x by creating the equation below:

x = 1/2 * (86 + 52)

x = 1/2 * (138)

x = 69 degrees.

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If a taxi company charges ​f(x)=2. 20+0. 6[4x] dollars, the cost of a 2.7-mile trip is $8.68.

To find the cost of a 2.7-mile trip using the given function f(x) = 2.20 + 0.6[4x], we substitute x = 2.7 in the function.

f(2.7) = 2.20 + 0.6[4(2.7)]

f(2.7) = 2.20 + 0.6[10.8]

f(2.7) = 2.20 + 6.48

f(2.7) = 8.68

The function f(x) = 2.20 + 0.6[4x] represents the cost of a taxi ride based on the distance traveled. The first term 2.20 represents the base fare, which is added to the cost regardless of the distance.

The second term 0.6[4x] represents the variable cost, which is calculated by multiplying the distance traveled by 4 and then by 0.6. This function helps the customers to calculate their fare in advance and plan their expenses accordingly.

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The value of k is approximately 0.034. The projected Hispanic resident population in 2015 is approximately 73.9 million. The Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.

To find k, we can use the fact that A = 35.3 million when t = 0 (i.e., in 2000), and A = 50.5 million when t = 10 (i.e., in 2010). Substituting these values into the exponential growth function, we get

35.3 = 35.3e^0k

50.5 = 35.3e^(10k)

Dividing the second equation by the first equation, we get

50.5/35.3 = e^(10k)

Taking the natural logarithm of both sides, we get

ln(50.5/35.3) = 10k

Solving for k, we get

k ≈ 0.034

Therefore, the exponential growth function is A = 35.3e^(0.034t).

To project the Hispanic resident population in 2015, we need to find A when t = 15 (i.e., 15 years after 2000). Substituting t = 15 into the exponential growth function, we get

A = 35.3e^(0.034*15) ≈ 73.9 million

Therefore, the projected Hispanic resident population in 2015 is approximately 73.9 million.

To find the year in which the Hispanic resident population reaches 70 million, we need to solve the exponential growth function for t when A = 70. Substituting A = 70 into the exponential growth function, we get

70 = 35.3e^(0.034t)

Dividing both sides by 35.3, we get

e^(0.034t) = 70/35.3

Taking the natural logarithm of both sides, we get

0.034t = ln(70/35.3)

Solving for t, we get

t ≈ 24.7

Therefore, the Hispanic resident population will reach 70 million in approximately 24.7 years after 2000, which corresponds to the year 2024.

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Answer: We can use the properties of the normal distribution to solve both parts of this problem.

a) The number of months with sales greater than 100 is a binomial random variable with parameters n = the number of months and p = the probability of a single month having sales greater than 100. Since each month is an independent normal random variable, we can use the standard normal distribution to find this probability. Let X be the number of months with sales greater than 100. Then:

X ~ Binomial(n, p)

where n is the number of months and p is given by:

p = P(X_i > 100) = P(Z > (100 - a) / a)

where Z is a standard normal random variable.

Using the binomial probability formula, the probability of exactly k months having sales greater than 100 is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

So the probability of exactly 3 months having sales greater than 100 is:

P(X = 3) = (n choose 3) * p^3 * (1 - p)^(n - 3)

= (12 choose 3) * P(Z > (100 - a) / a)^3 * [1 - P(Z > (100 - a) / a)]^(12 - 3)

b) The total sales in the next 12 months is a normal random variable with mean 12a and standard deviation sqrt(12)a. Let Y be the total sales in the next 12 months. Then:

Y ~ Normal(12a, sqrt(12)a)

The probability of the total sales being greater than some value x can be found by standardizing Y and using the standard normal distribution:

P(Y > x) = P((Y - 12a) / (sqrt(12)a) > (x - 12a) / (sqrt(12)a))

= P(Z > (x - 12a) / (sqrt(12)a))

where Z is a standard normal random variable. So the probability of the total sales in the next 12 months being greater than 1500 is:

P(Y > 1500) = P(Z > (1500 - 12a) / (sqrt(12)a))

Step-by-step explanation:

Answer:

42 degrees

Step-by-step explanation:

So, first to find <QUT, which is a vertical angle, we have to figure out either QUR or TUS.  So:

9x+3=11x-27

solve for x:

x=15

Then, plug it into one of the equations.  Let's use 9x+3.

9(15)+3=138

So, we know that QUR is 138 degrees.

That means that TUS is ALSO 138.

138x2=276

Now we know that QUT and RUS have to equal whatever 360-276 is:

360-276=84

QUT and RUS have to equal 84 degrees, so we DIVIDE by 2.

84/2=42

So, QUT=42 degrees

Answer:

42 Degrees

Step-by-step explanation

Becuase (11x-27) and (9x+3) are vertical angles that means they are equal to each other

(11x - 27) = (9x + 3)

First you will add 27 to both sides

11x -27 = 9x +3

     +27         +27

Making it to:

11x = 9x + 30

Now you need to subtract 9x from both sides

11x = 9x +30

-9x   -9x

Turning it into this

2x= 30

Now Lastly, divide both sides by 2

2x = 30

2x     2x

And the answer is...... X=15

Now that you have the x value, we go back to the 11x-27 and replace the X with 15

11(15) -27 = 138 degress

Now because angle QUT and 138 degrees make a straight line that means together they will be 180 degress so you will subtract 180 by 138

Giving you the final answer of

42 Degrees