Find the tangent of ∠R.

Answer:

The population of this city in 13 years is 440,550.

Step-by-step explanation:

Given:

Suppose a city with population 300, 000 has been growing at a rate of 3​% per year.

Now, to find the population of this city in 13 years.

Let the population of this city in 13 years be [tex]A.[/tex]

Population ([tex]P[/tex]) = 300,000.

Rate per year ([tex]r[/tex]) = 3%.

Time ([tex]t[/tex]) = 13 years.

Now, we put formula to get the population of the city in 13 years:

[tex]A=P(1+r)^t\\\\A=300,000(1+3\%)^{13}\\\\A=300,000(1+0.03)^{13}\\\\A=300,000(1.03)^{13}\\\\A=300,000\times 1.4685\\\\A=440,550.[/tex]

Therefore, the population of this city in 13 years is 440,550.

Answer:

27 triangles

Step-by-step explanation:

triangle given by [tex]\frac{n(n+2)(2n+1)}{8}[/tex], where n is the amount of triangles on the base

4(6)(9)/8 = 216/8 = 27

Answer:

1

Step-by-step explanation:

9-8=1

since it is on the same y coordinate it doesn't move much

Answer:

The probability that a student pick from this group at random either has blue or brown eyes is

P = 40/65 = 0.6154

P = 61.54%

Corrected question;

In a group of 65 students 10 have brown eyes and 30 have blue eyes. Find the Probability that a student pick from this group at random either has blue or brown eyes

Step-by-step explanation:

Given;

Total number of students = 65

Number of students with either blue or brown eyes;

= 10+30 = 40

The probability that a student pick from this group at random either has blue or brown eyes is

P = 40/65 = 0.6154

P = 61.54%

Probability is the likelihood of an event happening. In this case, the probability of picking a student with blue or brown eyes is 19/13.

Probability is the likelihood of an event happening, calculated by dividing the number of favorable outcomes by the total number of outcomes.

In this case, the total number of students is 65. The probability of picking a student with brown eyes is 65/65 = 1, and the probability of picking a student with blue eyes is 30/65. To find the probability of picking a student with either blue or brown eyes, you add the probabilities, getting 1 + 30/65 = 95/65, which simplifies to 19/13.

The question keeps telling me to STOP!  Never mind.

The octagon is 8 isosceles triangles.  Each has common side r and base 10.  The central angle is 360/8 = 45°.  By the Law of cosines,

10² = r² + r² - 2 r² cos 45° = 2r²(1 - √2/2) = r²(2-√2)

r² = 100/(2-√2)

The area of a triangle with sides a,b and included angle C is (1/2)ab sin C. Our 8 octagon isosceles triangles each have sides r and r and included angle 45° so our total area, 8 triangles, is

A = 8(1/2) r² sin 45° = (400/(2-√2)) (√2/2) × (2+√2)/(2+√2) = 200(1+√2)

A ≈482.84271

Answer: 482.8 sq cm

Final answer:

To find the area of a regular octagon with a side length of 10 cm, use the formula: Area = 2 * (1 + √2) * side length². Substitute the given side length and round the answer to the nearest tenth.

Explanation:

To find the area of a regular octagon with a side length of 10 cm, we can use the formula:

Area = 2 * (1 + √2) * side length²

Substituting the given side length into the formula:

Area = 2 * (1 + √2) * (10)²

Area = 2 * (1 + √2) * 100

Area ≈ 414.2 cm² (rounded to the nearest tenth)

After further computation, the area approximates 414.2 cm², rounded to the nearest tenth. This formula captures the geometric intricacies of a regular octagon, demonstrating a concise method to calculate its area based on the given side length. This formula encapsulates the unique characteristics of a regular octagon, providing a streamlined approach to computing its area and showcasing the elegant relationship between side length and the polygon's spatial coverage.

Answer: If you round it, should be about 5 hours.

The actual distance from Sandpoint to Grangeville would be 248 miles. If Joaquin's mother drives an average of 50 miles per hour, the trip will take almost 5 hours without any stops.

To solve this problem, we need to calculate the actual distance and then the time it will take. As it is mentioned that 1 inch on the map represents 62 miles in reality, if Joaquin measures the distance on the map to be 4 inches, then the actual distance will be 4 inches * 62 miles per inch = 248 miles. Then, if Joaquin's mother drives at a speed of 50 miles per hour, the time it will take to travel that distance can be calculated by dividing the total distance by the speed. So, 248 miles / 50 mph = 4.96 hours. It means that their trip will take almost 5 hours without any stops.

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Answer:

Yes if [3,5] is a set of integers then it contains elements 3,4,5

As Closed bracket denotes that extreme points are also included and 4 is mid element in between 3 and 5

Step-by-step explanation:

let the blank be x

[tex] \frac{3}{4} = \frac{x}{24} [/tex]

[tex]x = \frac{24 \times 3}{4} = 6 \times 3 = 18[/tex]

therefore,

[tex] \frac{3}{4} = \frac{18}{24} [/tex]

Answer:

The answer can be 18/24

Step-by-step explanation:

Divide 18/24 by 6

You get 3/4

Then you divide to get 0.75

Answer:

Interquartile Range

Step-by-step explanation:

In a box-and-whisker plot, the interquartile range is a measure of the spread of the middle half of the data.

Answer:

Median

Step-by-step explanation:

Median is the middle number in a data set, or the middle value in a list of numbers.

I tried.

Answer:

42

Step-by-step explanation:

have a wonderful day

Answer:

42

Step-by-step explanation:

To find the area of a rectangular prism, you do height*width*base.

5 1/4 also known as 5.25 is the area of the width and hieght multiplied together. So then we would just multiply 5.25 by the base (8) to get 42.

Answer:

x = 52

y = 38

Step-by-step explanation:

Angle x is supplementary to a 128º angle.

Supplementary angles add to 180

x+128 = 180

Subtract 128 from each side

x+128-128 = 180-128

x =52

Angle x and y are complementary.  

Complementary angles add to 90

x+y =90

52+y =90

Subtract 52 from each side

52-52 +y = 90-52

y = 38

Answer:

x = 52°

y = 38°

Step-by-step explanation:

x = 180 - 128

x = 52

y = 90 - 52 = 38

Answer:

SE=$128.13

Step-by-step explanation:

-Given the sample mean is $34,250 and standard deviation is $2,050 with n=256:

-Standard error is calculated using the formula:

[tex]SE=\frac{s}{\sqrt{n}}[/tex]

Where s is the sample standard deviation.

#We substitute our values to solve for SE:

[tex]SE=\frac{s}{\sqrt{n}}\\\\=\frac{2050}{\sqrt{256}}\\\\=128.125\approx128.13[/tex]

Hence, the standard error is $128.13

Answer:

40

Step-by-step explanation:

Step-by-step explanation:

RAGL is a rhombus.

[tex] \therefore RA = AG..

(sides\: of\: rhombus) \\

\therefore m\angle ARG = m\angle AGR... (1)[/tex]

(Angles opposite to equal sides are equal)

[tex] In\:\triangle RAG, \\

m\angle ARG +\bold{ m\angle AGR} + {m\angle RAG} = 180°\\

m\angle ARG +\bold {m\angle ARG} + 58° = 180°\\

[From\:equation \: (1)]\\

2m\angle ARG = 180°-58° \\

2m\angle ARG = 122° \\

m\angle ARG =\frac{122°}{2} \\

\huge \red {\boxed {m\angle ARG = 61°}} [/tex]

Hence, option A is the correct answer.

Answer:

None of the given points lies on the circle.

Step-by-step explanation:

The circle is represented by the following formula:

(x - xc)² + (y - yc)² = r²

Where (xc,yc) are the coordinates of the center and r is the radius of the circle. In the case we have:

(x+5)² + (y-9)² = 82

If a point belongs to this circumference, then the results of applying the points to the equation should be valid. To test all the points we are going to apply each to the equation as shown below:

A.

(0 + 5)² + (8-9)² = 82

5² + (-1)² = 82

25 + 1 = 82

26 = 82 (invalid)

The point does not lies on the circle.

B.

(13 + 5)² + (-9-9)² = 82

(18)² + (-18)² = 82

324 + 324 = 82

648 = 82 (invalid)

The point does not lies on the circle.

C.

(-5 + 5)² + (1 - 9)² = 82

0² + (-8)² = 82

64 = 82 (invalid)

The point does not lies on the circle.

D.

(3 + 5)² + (17-9)² = 82

8² + 8² = 82

64 + 64 = 82

128 = 82 (invalid)

The point does not lies on the circle.

Answer:

c

Step-by-step explanation:

Answer:

The value of printer will $23,219.72 after 8 years.

Step-by-step explanation:

Given that, Daniels print shop purchases a new printer for $35,000.

Each year it depreciates at a rate 5%.

Exponential function:

[tex]P(t)=P_0(1-r)^t[/tex]

P(t)= Price of printer after t years

[tex]P_0[/tex]= Initial price of printer

r= rate of depreciate.

t=Time

Here, [tex]P_0[/tex] = $35,000,r=5%=0.05, t=8 years

[tex]P(8)= 35000(1-0.05)^8[/tex]

      =$23,219.72

The value of printer will $23,219.72 after 8 years.

The exponential equation is solved and the cost of printer is A = $ 23219.71

Given data:

To find the approximate value of the printer after 8 years, considering a depreciation rate of 5% per year, we can use the formula for exponential decay:

V = P * (1 - r)^t

Where:

V = Value after t years

P = Initial value (purchase price)

r = Depreciation rate (as a decimal)

t = Number of years

In this case, the initial value (P) is $35,000, the depreciation rate (r) is 5% or 0.05, and the number of years (t) is 8.

Plugging in these values into the formula:

V = 35,000 * (1 - 0.05)⁸

V = 35,000 * (0.95)⁸

On simplifying the equation , we get

V ≈ 35,000 * 0.6634

V ≈ $ 23219.71

Hence, the approximate value of the printer after 8 years, considering a 5% depreciation rate per year, is $ 23219.71

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Answer:

1. Compliment: 30 degrees. Supplement: 120 degrees.

2. Compliment: 42 degrees. Supplement: 132 degrees.

3. Compliment: None. Supplement: 83 degrees.

Answer:

2

Step-by-step explanation:

|a+x|/2 − |a−x|/2 , if a=−2; x=−6

Evaluate this expression

Simply plug in the numbers

| -2 + -6 | /2   -   |-2 - -6|/2

|-8| /2  -   |4|/2

4 - 2

2

Answer:

2

Step-by-step explanation:

So you're dealing with absolute value which means that whatever is inside these symbols |  | will be positive after all the calculations inside are done.

Plug in your values

|(-2) + (-6)|/2

-2 - 6 = -8

absolute value of -8 is 8

8/2 = 4

First part is 4

|(-2) - (-6)|/2

-2 + 6 = 4

4/2 = 2

Second part is 2

Put the two values back into your original equation

4-2 = 2

Answer:

The probability that the customer is charged incorrectly on at least 3 items is 88.11%

Step-by-step explanation:

For each item, there are only two possible outcomes. Either they are charged correctly, or they are not. The probability of an item being charged incorrectly is independent of other items. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A survey finds customers are charged incorrectly for 4 out of every 10 items.

This means that [tex]p = \frac{4}{10} = 0.4[/tex]

Suppose a customer purchases 11 items.

This means that [tex]n = 11[/tex]

Find the probability that the customer is charged incorrectly on at least 3 items.

Either he is charged incorrectly on less than 3 items, or at least 3. The sum of the probabilities of these events is decimal 1. So

[tex]P(X < 3) + P(X \geq 3) = 1[/tex]

We want [tex]P(X \geq 3)[/tex]. So

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{11,0}.(0.4)^{0}.(0.6)^{11} = 0.0036[/tex]

[tex]P(X = 1) = C_{11,1}.(0.4)^{1}.(0.6)^{10} = 0.0266[/tex]

[tex]P(X = 2) = C_{11,2}.(0.4)^{2}.(0.6)^{9} = 0.0887[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0036 + 0.0266 + 0.0887 = 0.1189[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.1189 = 0.8811[/tex]

88.11% probability that the customer is charged incorrectly on at least 3 items

Final answer:

To determine the probability that a customer is charged incorrectly on at least three items out of 11, we use the binomial probability formula, summing up probabilities from 3 to 11 incorrect charges.

Explanation:

Probability of Being Charged Incorrectly on At Least 3 Items

To solve the problem of finding the probability that a customer is charged incorrectly on at least three items when they purchase 11 items, we use the binomial probability formula. Given that the probability of being charged incorrectly for one item is 0.4 (4 out of 10), we denote this as p=0.4. The probability of being charged correctly is q=1-p=0.6. The total number of items, n, is 11.

The binomial probability P(X ≥ k) for at least k successes out of n trials is calculated by summing up the probabilities of having k, k+1,..., n successes.

To find P(X ≥ 3) we calculate:

This calculation involves using the binomial formula which is:

P(X=k) = C(n,k) × p^k × q^(n-k)

Where C(n,k) is the combination of n items taken k at a time.

Once each individual probability is calculated, add them up to find the total probability of being charged incorrectly on at least 3 items. Remember, it is not possible to have a probability greater than 1, as this would imply certainty beyond the maximum possible (100%).

The total shaded area is four times the area of the inner shaded square. If the side length of the inner square is [tex]\(a\) units, the total shaded area is \(4a^2\)[/tex]square units. This is derived by adding the area of the inner square to the outer shaded region's area.

To find the total area shaded, we need to calculate the combined area of the inner shaded square and the outer shaded region.

Let's denote the side length of the inner square as a units and the side length of the outer square as b units. Since the design consists only of squares, the outer square will have sides twice as long as the inner square, so [tex]\(b = 2a\).[/tex]

The area of the inner shaded square is [tex]\(a^2\)[/tex] square units, and the area of the outer shaded region is the difference between the area of the outer square and the area of the inner square, which is[tex]\(b^2 - a^2\).[/tex]

Substituting [tex]\(b = 2a\), we get the area of the outer shaded region as \((2a)^2 - a^2 = 4a^2 - a^2 = 3a^2\)[/tex] square units.

Therefore, the total shaded area is the sum of the area of the inner square and the area of the outer shaded region: [tex]\(a^2 + 3a^2 = 4a^2\).[/tex]

So, the total area shaded is [tex]\(4a^2\) square units, where \(a\)[/tex] is the side length of the inner shaded square.

complete question

Diane made a design using only squares she shaded the inner square and outer region find the total area that is shaded explain how you found your answer.

Answer: the sale price of one hammer is $6.8

the sale price of one nail is $0.16

Step-by-step explanation:

Let x represent the sale price of one hammer.

Let y represent the sale price of one nail.

His first customer bought 3 hammers and 16 nails for $22.96. It means that

3x + 16y = 22.96- - - - - - - - -1

His last customer bought 2 hammers and 20 nails for $16.80. It means that

2x + 20y = 16.8- - - - - - - - - 2

Multiplying equation 1 by 2 and equation 2 by 3, it becomes

6x + 32y = 45.92

6x + 60y = 50.4

Subtracting, it becomes

- 28y = - 4.48

y = - 4.48/- 28

y = 0.16

Substituting y = 0.16 into equation 2, it becomes

2x + 20 × 0.16 = 16.8

2x + 3.2 = 16.8

2x = 16.8 - 3.2

2x = 13.6

x = 13.6/2

x = 6.8

Answer:

1. 70% of 7 = 4.9

2. 30% of 134 =  40.2

3. 100% of 109 =  109

4. 60% of 112 =  67.2

5. 40% of 142 =  56.8

6. 20% of 89 =  17.8

7. 10% of 127 =  12.7

8. 80% of 7 =  5.6

9. 90% of 95 =  85.5

10. 90% of 7 =  6.3

11. 80% of 154 =  123.2

12. 10% of 2 =  0.2

13. 100% of 2 =  2

14. 30% of 76 =  22.8

15. 70% of 43 =  30.1

Step-by-step explanation:

1. I

2. USED

3. GOOGLE

You're welcome! <3

Answer: [tex]x=-3\\y=8[/tex]

Step-by-step explanation:

[tex]3x+y=-1\\2x+3y=18[/tex]

Multiply by -3 the upper equation to make y equal in value but with opposite signs.

[tex](-3)(3x+y=-1)\\-9x-3y=3[/tex]

Now add equation 1 and 2.

[tex]-9x-3y=3\\2x+3y=18[/tex]

--------------------------

[tex]-7x=21[/tex]

Solve for x;

To isolate x, divide by -7

[tex]\frac{-7x}{-7}=\frac{21}{-7}[/tex]

[tex]x=-3[/tex]

Now use one of the equations above and replace the value of x.

[tex]3x+y=-1\\3(-3)+y=-1\\-9+y=-1\\y=-1+9\\y=8[/tex]

To prove if it's correct, take either equation and replace both x and y values, if the results are equal to each other, it is correct.

[tex]2x+3y=18\\2(-3)+3(8)=18\\-6+24=18\\18=18[/tex]

Answer:

The area of the surface that needs to be iced is 480 m².

Step-by-step explanation:

A cake has the same shape as a rectangular prism. A rectangular prism has six faces. The first one is formed by the length and the width, the second is formed by the length and the height and the third is formed by the width and the height, each of these faces is mirrored, so the surface area for the cake is:

surface area = 2*width*height + 2*width*length + 2*length*height

surface area = 2*12*4 + 2*12*12 + 2*12*4

surface area = 96 + 288 + 96 = 480 m²

The area of the surface that needs to be iced is 480 m².

Answer:

480 m².

Step-by-step explanation:

A cake will be similar to rectangular prism i.e a solid (3-dimensional) object which has six faces that are rectangle.

Finding surface area for all rectangular prisms involves both addition and multiplication. so the surface area for the cake is given by:

surface area = 2(widthxheight) + 2(widthxlength) + 2(lengthxheight)

surface area = 2(12 x 4) + 2(12 x 12) + 2(12 x 4)

surface area = 96 + 288 + 96 = 480 m²

Therefore, the cake will need the surface area of  480 m² to be iced.

Answer:

No solution

Step-by-step explaination

i got it right have a great day  

There is no solution because the variables level out to zero. Option D

A simultaneous equation, also known as a system of equations, refers to a set of two or more equations with multiple variables that are solved together. To find a solution to the system, we are looking for values of x and y that make both Equation 1 and Equation 2 true at the same time.

We have the equation as;

5x – 4y = 6  ---(1)

–5x + 4y = –10 ---- (2)

Add (1) and (2)

When we add the both equations, we would arrive at no possible solution because the variables would be levelled out to zero.

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Answer:(-4,-9)

Step-by-step explanation:

Final answer:

After rotating the point (4,9) 180° about the origin, the new coordinates would be (-4, -9).

Explanation:

To determine the new coordinates of a point after a 180° rotation about the origin, you can apply the rules of rotation in a coordinate plane.

For a 180° rotation, each coordinate (x, y) becomes (-x, -y).

Therefore, if we rotate the point (4,9) 180° about the origin, we change the sign of both coordinates.

The new point after rotation would be (-4, -9).

Answer:

Darnell will do 75 knee lifts

Step-by-step explanation:

in two minutes he did 50. So that means that in one minute he did 25. add 50 and 25 together and you get 75 for your answer

Answer:75 knee lifts

Step-by-step explanation:2 mins       50 knee lifts

                                            1 min          25 knee lifts

Answer:

    2          |   1 |     3  8

  3 0         |  2 |     5

9  8   2     |  3 |    6

3   3  1       | 4  |     1  5  5  

9  5 2   1   |  5 |     0  3  7  9  

                | 6  |    2  2

Step-by-step explanation:

Answer: A. Experimental Study