I don’t know what to do

The area of the shaded region is 15 \(yd^2\).

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Here in the given diagram contains right triangle and rectangle.

We need to find both triangle and rectangle  area in order to find area of shaded region.

Now Base= 3+4 = 7 yd , Height h =6 yd. Then,

Area of triangle A = \(\frac{1}{2}bh\) square unit

=> A = \(\frac{1}{2}\times7\times6\)

=> A = \(7\times3 = 21 yd^2\)

Now breadth b = 3 yd , Width w=2 yd, Then

Area of rectangle = bw square unit.

=> A = 3×2 = 6 \(yd^2\)

Now area of the shaded region = Area of triangle - Area of rectangle

=> Area of shaded region = 21-6 = 15 \(yd^2\).

Hence the area of the shaded region is 15 \(yd^2\).

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Answer:

47.3

Step-by-step explanation:

To find the standard deviation use this example formula

\(a =\sqrt{\frac{(x-u)^{2} }{N} }\)

a = your answer, the standard deviation you are looking for

x = the value of each carrier

u = the carrier numbers mean (such as mean, median, and mode)

N = the overall total of the carriers

If you find this equation still confusing one of my favorite sites to use is Math.way, where you plug in each number with a comma in between and it solves it for you. Other sites work such as Calculatornet, Calculator.Soup, and Math.is.Fun.

Hope this helps :)

Answer:

Step-by-step explanation:why is the trapezoid separated into a triangle and a rectangle

To look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

For a regular polygon with n sides, the sum of its interior angles is given by ((n - 2) × 180) degrees. In the case of a round table seating 6 people, the table can be considered as a hexagon, which has 6 sides. Using the formula, we can calculate the sum of the interior angles:

((6 - 2) × 180) / 6 = (4 × 180) / 6 = 720 / 6 = 120 degrees

Since the table forms a complete circle, the sum of the interior angles is divided equally among the guests. Therefore, each guest sits at an angle of 120 degrees. To look from the guest to their left to the guest to their right, you need to rotate by the angle between adjacent guests, which is half of the angle they sit at:

120 / 2 = 60 degrees

Thus, to look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

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The required specific energy increases with increasing depth and the water surface profile will be rapidly varied.

To determine the type of water surface profile for different depths in the rectangular channel, we can use the concept of specific energy and Manning's equation.

The specific energy (E) is given by the equation:
E = y + (V² / (2g)) + (Sf * x)

Given values:
Width of the rectangular channel (b) = 2.45 m
Discharge (Q) = 2.83 m³/sec
Bed slope (Sf) = 0.003
Manning's roughness factor (n) = 0.015

For each depth, we can calculate the velocity (V) using Manning's equation and then determine the specific energy (E) using the equation mentioned above.

Depth 1 (y₁ = 1.52 m):

First, let's calculate the velocity (V₁) using Manning's equation:\(V_1 = (1/n) * (R_1^{2/3}) * (S_f^{(1/2)})\)

The hydraulic radius (R₁) can be calculated as:
R₁ = (b * y₁) / (b + 2y₁) = (2.45 * 1.52) / (2.45 + 2 * 1.52) ≈ 0.678 m

Substituting the values
\(V_1= (1/0.015) * (0.678 ^{2/3}) * (0.003^{1/2})\) ≈ 2.81 m/s

Now, let's calculate the specific energy (E₁) using the equation:
E₁ = y₁ + (V₁² / (2g)) + (Sf * x)

Substituting the values:
E₁ = 1.52 + (2.976² / (2 * 9.81)) + (0.003 * x)

The above expression shows, the specific energy increases with increasing depth, and the water surface profile will be rapidly varied.

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Given question is incomplete, the complete question is:
2.45-m wide rectangular channel with a discharge of 2.83 m³/sec. has a bed slope of 0.003 and Manning's roughness factor of 0.015. What is the type of water surface profile for depths of 1.52 m, whether it is rapidly varied or not?

Perimeter of one triangle is 20.6 inches.

Perimeter is the length of the boundaries of a closed triangle.

if we add the 3 side lengths of a triangle then the perimeter is determined.

Jane wants to have a rectangular stained glasses that has length 7 inches and width 5 inch.

If she fuses together two triangles of colored glass for obtaining a rectangle, then each triangle will have 3 similar side length.

each triangle has first side length = 5 inches

                              second side length = 7 inches

                   other side length = hypotenuse of right-angled triangle

                       =√(5² + 7²) = √74 inches

A rectangle has four right angles and therefore, the triangles that are developed based on the rectangle must be right-angled.

perimeter of triangle = sum of three side length = (5 + 7+√74) = 20.6 inches

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Answer:

=90\(x^{2}\)+2x+3

Step-by-step explanation:

Let's simplify step-by-step.

2\(x^{2}\) + 82\(x^{2}\) + 8 − ( −6\(x^{2}\) − 2x + 5 )

Distribute the Negative Sign:

= 2\(x^{2}\) + 82\(x^{2}\) + 8 + − 1 ( − 6\(x^{2}\) − 2x + 5 )

= 2\(x^{2}\) + 82\(x^{2}\) + 8 + − 1( − 6\(x^{2}\) ) + − 1 ( −2x ) + ( − 1 ) ( 5 )

= 2\(x^{2}\) + 82\(x^{2}\) + 8 + 6\(x^{2}\) + 2x + − 5

Combine Like Terms:

= 2\(x^{2}\) + 82\(x^{2}\) + 8 + 6\(x^{2}\) + 2x + −5

= ( 2\(x^{2}\) + 82\(x^{2}\) + 6\(x^{2}\) ) + ( 2x ) + ( 8 + − 5 )

= 90\(x^{2}\) + 2x + 3

Hope it helps

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Let's denote the number of sides of the regular polygon as "n".

The number of diagonals in any polygon can be calculated using the formula:

Number of diagonals = (n * (n - 3)) / 2

According to the given information, the number of diagonals is equal to four times the number of sides:

(n * (n - 3)) / 2 = 4n

To solve this equation for "n," we can start by simplifying:

n * (n - 3) = 8n

Expanding the equation:

n^2 - 3n = 8n

Rearranging terms:

n^2 - 11n = 0

Factoring out "n":

n(n - 11) = 0

Setting each factor equal to zero:

n = 0 or n - 11 = 0

Since the number of sides cannot be zero, we discard the solution n = 0.

Therefore, the regular polygon has n = 11 sides.

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Answer:

\(\displaystyle{P(x)=x^3-x^2}\)

Step-by-step explanation:

Given the zeros of 0, 0, 1. We can write the polynomial in form of x-intersects:

\(\displaystyle{P(x) = (x-x_1)(x-x_2)(x-x_3)}\)

Hence:

\(\displaystyle{P(x)=(x-0)(x-0)(x-1)}\)

Which can be simplified to:

\(\displaystyle{P(x)=x\cdot x \cdot (x-1)}\\\\\displaystyle{P(x)=x^2(x-1)}\)

Convert to the standard form by distributing x²:

\(\displaystyle{P(x)=x^2\cdot x - x^2 \cdot 1}\\\\\displaystyle{P(x)=x^3-x^2}\)

Answer:

81 km

Step-by-step explanation:

Speed = distance / time

speed and time are measured in different units, thus, time has to be converted to seconds

60 second = 1 minute

90 x 60 = 5400 seconds

15 m /s = distance / 5400 seconds

distance = 81,000 metre

1000m = 1 km

81000 / 1000 = 81km

A. The maximum mean weight of the passengers cannot exceed 3500 lb if the gondola is filled to its capacity of 25 passengers.

B. To calculate the probability that the mean weight of 25 randomly selected skiers exceeds the maximum weight from part A, we need to use the Central Limit Theorem and standardize the sample mean using z-scores.

C. If the weight assumptions are revised so that the new capacity becomes 20 passengers, the probability that the mean weight of 20 randomly selected skiers exceeds 175 lb can be calculated by standardizing the sample mean using z-scores.

D. To assess the safety of the new capacity of 20 passengers, we need to determine the probability of exceeding the load limit of 3500 lb.

A. Let's denote the mean weight of the passengers as μ and the standard deviation as σ. We know that μ = 180 lb and σ = 38 lb. Since the gondola can carry 25 passengers, the total weight can be calculated as 25 * μ.

To ensure that the total weight does not exceed 3500 lb, we can set up the following inequality:

25 * μ ≤ 3500

Substituting the given values, we have:

25 * 180 ≤ 3500

4500 ≤ 3500

This inequality is not true, which means that the maximum mean weight of the passengers cannot exceed 3500 lb.

B. To determine the probability that the mean weight exceeds the value from part A, we need to calculate the probability distribution of the sample mean.

Now we can calculate the probability that the mean weight exceeds the value from part A, which is the maximum mean weight we found in part A. Let's denote this value as x.

P(x-bar > x) = P(x-bar > 3500 / 25)

To find this probability, we need to standardize the sample mean using z-scores. The formula for the z-score is:

z = (x - μ_x-bar) / σ_x-bar

Substituting the values, we have:

z = (x - 180) / 7.6

We can then look up the corresponding probability in the standard normal distribution table or use statistical software to find the probability.

C. The mean weight of the passengers (μ) remains the same at 180 lb, and the standard deviation (σ) remains at 38 lb. However, since the capacity has changed to 20 passengers, the sample size (n) is now 20.

μ_x-bar = μ = 180 lb

σ_x-bar = σ / √n = 38 lb / √20 ≈ 8.5 lb

Now we can calculate the probability that the mean weight exceeds 175 lb. Let's denote this value as x.

P(x-bar > x) = P(x-bar > 175)

Similarly to part B, we need to standardize the sample mean using z-scores:

z = (x - 180) / 8.5

Then, we can look up the corresponding probability in the standard normal distribution table or use statistical software to find the probability.

D. Is the new capacity of 20 passengers safe? Since the probability of overloading is (under 5%, over 50%), the new capacity (does not appear, appears) to be safe enough.

To calculate this probability, we need to find the probability that the total weight of the 20 randomly selected skiers exceeds 3500 lb. This requires considering the distribution of the sum of 20 normally distributed variables.

The total weight of the 20 skiers can be calculated as 20 * μ, where μ is the mean weight of the passengers (180 lb).

Let's denote the total weight as X. We need to calculate:

P(X > 3500)

To find this probability, we can standardize the variable X using z-scores and then look up the probability in the standard normal distribution table or use statistical software.

If this probability is less than 5%, it indicates that the probability of overloading is under 5%, suggesting that the new capacity of 20 passengers appears to be safe enough. Conversely, if the probability is greater than 50%, it suggests a high risk of overloading.

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Complete Question:

A ski gondola carries skiers to the top if a mountain. assume the weights of skiers are normally distributed with a mean of 180 lb and a standard deviation of 38 lb. the gondola has a stated compacity of 25 passengers, and the gondola is rated fir a load limit of 3500 lb

A. Given that the gondola is rated for a load limit of 3500 lb what is the max mean weight of the passengers if the gondola is filled to the capacity of 25 passengers?

B. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part A.

C. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the max weight hat does not cause the total load to exceed 3500lb

D. Is the new capacity of 20 passengers safe? Since the probability of overloading is (under 5%, over 50%) the new capacity (does not appear, appears) to be safe enough.

Answer:

x<3

Step-by-step explanation:

-4x>12

-x>3

x<3

Given the trigonometry equation expressed as;

We are to simplify for the value(s) of 'x"

Recall from trigonometry identity that:

Substitute the result into the original equation to have:

Solve for the value of "x"

The general solution to the given trigonometry function is:

The population size of mantis shrimp will be approximately 266 individuals after 5 years.

The intrinsic rate of increase is an essential concept in population biology. It is the rate at which a population is growing at a particular moment in time. The population size after a particular period can be calculated using the intrinsic rate of increase with the help of this formula:

Nt = N0e^(rt)

where Nt is the future population size, N0 is the initial population size, r is the intrinsic rate of increase, and t is the time in years.

The population size of mantis shrimp is 475 individuals and the intrinsic rate of increase is -0.10.

We can calculate the population size after 5 years using the above formula as follows:

Nt = N0e^(rt)

Nt = 475 * e^(-0.10 * 5)

Nt = 475 * e^(-0.50)

Nt ≈ 266

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The volume of the box is 72 cubic feet.

We have,

To find the volume of the box, we need to multiply its length, width, and height.

Given:

Length = 4 ft

Breadth = 6 ft

Height = 3 ft

The volume of the box is:

Volume = Length x Breadth x Height

Volume = 4 ft x 6 ft x 3 ft

Volume = 72 cubic feet

Therefore,

The volume of the box is 72 cubic feet.

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Answer:

w

Step-by-step explanation:

The amount of water they need to bring depends on how long they will be hiking.

In ΔQRS, if sin R = cos S, we can conclude that ∠R and ∠S are complementary angles.

In a right triangle, the sine of an angle is equal to the cosine of its complement. By the given equation sin R = cos S, it implies that R and S are complementary angles that add up to 90 degrees.

To understand this concept, we can consider the unit circle. The sine of an angle represents the y-coordinate on the unit circle, while the cosine represents the x-coordinate. When sin R = cos S, it means that the y-coordinate of angle R is equal to the x-coordinate of angle S. This suggests that angle R and angle S are complementary angles, as they share the same relationship between their trigonometric ratios.

Therefore, we can conclude that in ΔQRS, ∠R and ∠S are complementary angles, with their measures adding up to 90 degrees.

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The complete question is:

In ΔQRS, sin R= cos S. What can you conclude about ∠R and ∠S?

Both are supplementary angles.

Both are complementary angles.

Both are obtuse angles.

Both are right angles.

Answer:

5

Step-by-step explanation:

Answer:

If there's a common factor, divide both sides of the equation by that number to simplify the situation. If b = 0 (no bx term), go to the square root method. (if c is positive, there are no solutions). If c = 0, then one of your solutions is x = 0

Step-by-step explanation:

hope this helps!!!!

Answer:

(a-5) / 6 = -4

or

-19

Step-by-step explanation:

(a-5) / 6 = -4

multiply by 6

a - 5 = -24

+5       +5

a = -19

Given: Surya Steel kadai costs Rs 235Trish Non-stick kadai costs Rs 372Shalini visits this shop and buys the steel kadai. She changes her mind the next day and comes to take the non-stick one instead. She pays for the excess amount with a 500 rupee note. The amount that should be returned to her is Rs. 363.

The amount of Trish Non-stick kadai =Rs.372.00The amount of Surya Steel kadai=Rs.235.00 Amount paid by Shalini for Trish Non-stick kadai=Rs.372.00 . Amount paid by Shalini initially=Rs.235.00 . Amount she should get back= 500 - (372 - 235) = 500 - 137= Rs. 363. Hence, the amount that should be returned to her is Rs. 363.

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(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R'  is 1/2

(B) Coordinates of Δ P"Q"R"

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) Triangles PQR and P"Q"R" are not congruent.

Given

ΔPQR is transformed into ΔP'Q'R'

Coordinates of P, Q, R are

P (8,0),

Q(6,2)

R(-2,-4)

Coordinates of P'Q'R' are

P′(4, 0)

Q′(3, 1)

R′(−1, −2)

(A) By Distance formula we can find the distance between P Q and P'Q'

Distance formula = \(D = \sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

Where D = Distance between two points

from distance formula we can write that

PQ = \(\sqrt{(6-8)^{2} +(2-0)^{2} } = \sqrt{4+4} =2 \sqrt{2}\)

Similarly

P'Q'= √2

PQ /P'Q' = 2

hence the scale factor of dilation is 1/2 (Compression)

(B )The Coordinates of Reflection about y axis can be written for a point

(x,y) as (-x,y)

So the Coordinated of Δ P"Q"R" can be written as

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) ΔPQR  and ΔP"Q"R" are similar triangles but they are not  congruent because their sides  are not equal in size.

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The rank of a matrix is the number of linearly independent columns or rows in the matrix.

If the columns of an n × n matrix A are linearly independent as vectors in ℝn, then the rank of A is n. This is because linearly independent vectors are not multiples of each other, and therefore do not reduce to a smaller set of linearly independent vectors when the matrix is put in reduced row echelon form. As a result, the rank of the matrix is equal to the number of columns, which is n. Therefore, the rank of A is n.

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Answer:

13 and 15

Step-by-step explanation:

x + (x+1) + (x+2) > 40

3x + 3 > 40

3x > 37

x > 12.34

Therfore x= 13,15 satisfy the equation

Answer:

Step-by-step explanation:

Given

\(2r + 4 = y + 2\)

\(2-r = y\)

\(y=-22 + 16 +34\)

\(r- y = 13\)

Required

Determine which is not a function

A [linear] function is always in the form:

\(y = mx + b\)

Checking each of the given options:

A.

\(2r + 4 = y + 2\)

Subtract 2 from both sides

\(2r + 4 - 2= y + 2 - 2\)

\(2r + 2= y\)

Reorder

\(y = 2r + 2\)

B.

\(2 - r = y\)

Reorder

\(y = 2 - r\)

C.

\(y=-22 + 16 +34\)

\(y=28\)

D.

\(r- y = 13\)

Subtract r from both sides

\(r - r - y = 13 - r\)

\(- y = 13 - r\)

Multiply both sides by -1

\(y = -13 + r\)

\(y = r - 13\)

Only option C does not conform with the general form \(y = mx + b\)

Hence;

Option C answers the question

The estimated winners' prize in 2040, assuming the same rate of increase per year, is approximately $54,680,580,063,400.

The initial value is $150, and the final value is $1,163,000. The number of years between 1895 and 2007 is 2007 - 1895 = 112 years.

Using the formula for percentage increase:
Percentage Increase = [(Final Value - Initial Value) / Initial Value] * 100
= [(1,163,000 - 150) / 150] * 100
= (1,162,850 / 150) * 100
= 775,233.33%

Therefore, the winners' check increased by approximately 775,233.33% over the period from 1895 to 2007.

To estimate the winners' prize in 2040, we assume the same rate of increase per year. We can use the formula:
Future Value = Initial Value * (1 + Percentage Increase)^Number of Years

Since the initial value is $1,163,000, the percentage increase per year is 775,233.33%, and the number of years is 2040 - 2007 = 33 years, we can calculate the future value:

Calculating this expression:
Future Value = 1,163,000 * (1 + 775,233.33%)^33

Using a calculator or computer software, we can evaluate this expression to find the future value. Here's the result:

Future Value ≈ $1,163,000 * (1 + 77.523333)^33 ≈ $1,163,000 * 47,051,979.42 ≈ $54,680,580,063,400

Therefore, based on the assumed rate of increase per year, the estimated winners' prize in 2040 would be approximately $54,680,580,063,400.

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Answer:

21x

Step-by-step explanation:

i think the expression should be x ×21 =21x

The volume of the figure is approximately 1591.63 cm³.

We have,

To find the volume of the figure with a semicircle on top of a cone, we can break it down into two parts: the volume of the cone and the volume of the semicircle.

The volume of the Cone:

The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.

Given that the diameter of the cone is 14 cm, the radius (r) is half of the diameter, which is 7 cm.

The height (h) of the cone is 17 cm.

Plugging the values into the formula, we have:

V_cone = (1/3)π(7 cm)²(17 cm)

V_cone = (1/3)π(49 cm²)(17 cm)

V_cone = (1/3)π(833 cm³)

V_cone ≈ 872.67 cm³ (rounded to two decimal places)

The volume of the Semicircle:

The formula for the volume of a sphere is V = (2/3)πr³, where r is the radius of the sphere. In this case, since we have a semicircle, the radius is half of the diameter of the base.

Given that the diameter of the cone is 14 cm, the radius (r) of the semicircle is half of that, which is 7 cm.

Plugging the value into the formula, we have:

V_semicircle = (2/3)π(7 cm)³

V_semicircle = (2/3)π(343 cm³)

V_semicircle ≈ 718.96 cm³ (rounded to two decimal places)

Total Volume:

To find the total volume, we add the volume of the cone and the volume of the semicircle:

V_total = V_cone + V_semicircle

V_total ≈ 872.67 cm³ + 718.96 cm³

V_total ≈ 1591.63 cm³ (rounded to two decimal places)

Therefore,

The volume of the figure is approximately 1591.63 cm³.

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Answer: 1/2

Step-by-step explanation:

The probabilities must add to 1, so:

\(P(x < 9) +P(X=9)+P(X > 9)=1\\\\\frac{1}{6}+P(X=9)+\frac{1}{3}=1\\\\P(X=9)=\boxed{\frac{1}{2}}\)