50 POINTS FOR ANSWER AND BRAINLIEST

mukti step equation​

Answer:

[tex]\dfrac{7}{9}[/tex]

Step-by-step explanation:

Let x be the denominator.

If the numerator is 2 less than the denominator, then the expression for the numerator is (x - 2):

[tex]\dfrac{x-2}{x}[/tex]

If 3 is added to both the numerator and the denominator, and the answer is 5/6, then:

[tex]\dfrac{x-2+3}{x+3}=\dfrac{5}{6}[/tex]

Now we can solve the equation for x.

Simplify the numerator in the fraction on the left of the equation:

[tex]\dfrac{x+1}{x+3}=\dfrac{5}{6}[/tex]

Cross mutliply:

[tex]6(x+1)=5(x+3)[/tex]

Expand the brackets:

[tex]6 \cdot x +6 \cdot 1 = 5 \cdot x + 5 \cdot 3[/tex]

[tex]6x+6=5x+15[/tex]

Subtract 5x from both sides of the equation:

[tex]6x+6-5x=5x+15-5x[/tex]

[tex]x+6=15[/tex]

Subtract 6 from both sides of the equation:

[tex]x+6-6=15-6[/tex]

[tex]x=9[/tex]

Therefore, the value of x is 9.

Now substitute the found value of x into the original rational expression:

[tex]\dfrac{x-2}{x}=\dfrac{9-2}{9}=\dfrac{7}{9}[/tex]

Therefore, the original fraction is:

[tex]\boxed{\dfrac{7}{9}}[/tex]

The data set is not approximately periodic. The correct option is A.

The values do not repeat after a certain interval. For example, the value of 36 is not repeated after 6 days, 12 days, or any other interval. Therefore, the data set is not periodic.

A periodic function is a function that repeats its values after a certain interval. For example, the function f(x) = sin(x) is periodic with a period of 2π. This means that the values of f(x) repeat every 2π units of x.

The data set in the question does not repeat its values after a certain interval. Therefore, the data set is not periodic.

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Answer:

m∠1 = 111°: m∠4 = 61°; m∠6 = 141°; m∠7 = 47°

m∠2 = 69°; m∠3 = 119°; m∠5 = 39°; m∠8 = 133°

Step-by-step explanation:

The Polygon Exterior Angle Sum Theorem states the sum of the measures of the exterior angles of a polygon always equals 360°.  

Step 1:  Find x by setting sum of exterior angles equal to 360:

m∠1 + m∠4 + m∠6 + m∠7 = 360

(5x + 11) + (3x + 1) + (8x - 19) + (3x - 13) = 360

(5x + 3x + 8x + 3x) + (11 + 1 - 19 - 13) = 350

19x - 20 = 360

19x = 380

x = 20

Step 2:  Check validity of answer by plugging in 20 for x in the equations representing the measures of angles 1, 4, 6, and 7 and checking that we get 360:

(5(20) + 11) + (3(20) + 1) + (8(20) - 19) + (3(20) - 13) = 360

(100 + 11) + (60 + 1) + (160 - 19) + (60 - 13) = 360

(111 + 61) + (141 + 47) = 360

172 + 188 = 360

360 = 360

Thus, x is indeed 20.

Step 3:  Find the measures of angles 1, 4, 6, and 7 by plugging in 20 for x in the equations representing the measures of the angles.

Plugging in 20 for x in (5x + 11) to find m∠1:

m∠1 = 5(20) + 11

m∠1 = 100 + 11

m∠1 = 111°

Plugging in 20 for x in (3x + 1) to find m∠4:

m∠4 = 3(20) + 1

m∠4 = 60 + 1

m∠4 = 61°

Plugging in 20 for x in (8x - 19) to find m∠6:

m∠6 = 8(20) - 19

m∠6 = 160 - 19

m∠6 = 141°

Plugging in 20 for x in (3x - 13) to find m∠7:

m∠7 = 3(20) - 13

m∠7 = 60 - 13

m∠7 = 47°

In polygons, an interior angle and its corresponding exterior angle are always supplementary and thus the sum of their measures always equals 180°.

Step 4:  Identify the interior angles and their corresponding exterior angles:

∠2 is the interior angle, and its corresponding exterior angle is ∠1.

∠3 is the interior angle, and its corresponding exterior angle is ∠4.

∠5 is the interior angle, and its corresponding exterior angle is ∠6.

∠8 is the interior angle, and its corresponding exterior angle is ∠7.

Step 3:  Find the measures of angles 2, 3, 5, and 8 by subtracting the measures of angles 1, 4, 6, and 7 from 180:

Finding the measure of ∠2:

m∠1 + m∠2 = 180

m∠2 = 180 - m∠1

m∠2 = 180 - 111

m∠2 = 69°

Finding the measure of ∠3:

m∠4 + m∠3 = 180

m∠3 = 180 - m∠4

m∠3 = 180 - 61

m∠3 = 119°

Finding the measure of m∠5:

m∠6 + m∠5 = 180

m∠5 = 180 - m∠6

m∠5 = 180 - 141

m∠5 = 39°

Finding the measure of m∠8:

m∠7 + m∠8 = 180

m∠8 = 180 - m∠7

m∠8 = 180 - 47

m∠8 = 133°

Step 5:  Check validity of answer.

We can find the sum of all the interior angles of a polygon using the formula 180(n-2), where

Since there are 4 sides, the sum of the interior angles of this polygon equals 180 as 180(4-2) = 360

We can check the validity of our answers for Step 3 by seeing if their sum is 360:

m∠2 + m∠3 + m∠5 + m∠8 = 360

(69 + 119) + (39 + 133) = 360

188 + 172 = 360

360 = 360

Thus, we've correctly found the measures of the interior angles.

In this context, "surplus" refers to the excess or additional amount beyond the ideal diameter of 24 inches that the actual diameter of the cake possesses.

It represents the difference between the actual diameter and the desired or expected diameter, taking into consideration the specified margin of error.

When a chef aims to purchase a cake with a margin of error of 3 inches, the surplus indicates the extent to which the cake's diameter surpasses the desired size.

It is a measure of how much larger the cake is compared to the ideal diameter, considering the acceptable range within the margin of error.

The surplus can be positive or negative, depending on whether the actual diameter is larger or smaller than the ideal diameter.

If the actual diameter is greater than 24 inches, the surplus will be a positive value, indicating the excess size of the cake.

Conversely, if the actual diameter is smaller than 24 inches, the surplus will be a negative value, representing the shortfall in size.

By quantifying the surplus, the chef can assess the degree to which the actual cake deviates from the ideal size and make an informed decision based on their specific requirements and preferences.

The surplus helps ensure that the cake's dimensions align with the desired specifications and meets the chef's expectations within the specified margin of error.

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Answer:

66 inches²

Step-by-step explanation:

Area of 1 triangle = ½ × base × height = ½ × 7 × 4 = 14 in²

Area of 2 triangles = 14 × 2 = 28 in²

Area of outer rectangles = (6 × 2) × 2 = 24 in²

Area of inner rectangle = 2 × 7 = 14 in²

Total surface area = 28+24+14 = 66 in²

The regression equation that correctly models the data is B. y = 2.87x + 11.85

The regression equation is calculated using the following formula:

y = a + bx

where:

y is the dependent variable (daily food costs)

x is the independent variable (number of children in attendance)

a is the y-intercept

b is the slope of the line

The slope of the line is calculated using the following formula:

b = (∑xy - ∑x ∑y / n) / (∑x2 - (∑x)² / n)

Using the data from the table, we can calculate the y-intercept and slope of the line as follows:

a = 411 / 5 = 82.2

b = (13,393 - (143)(411) / 5) / (4,573 - (143)² / 5) = 2.87

Substituting the y-intercept and slope into the regression equation, we get the following equation:

y = 11.85 + 2.87x

Simplifying, we get the following equation:

y = 2.87x + 11.85

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a. The two-digit number  is 19

b. The number is 22

C. The number is 44

(a) To solve this problem, we are looking for a two-digit number less than 20, odd  and with a sum of digits equal to 10.

the only number that satisfies these conditions is 19.

(b) We need to find a two-digit even number

the only number that meets these criteria is 22.

(c) We are searching for a two-digit number less than 80, even, with identical digits and a multiple of 4.

the only number that satisfies all these conditions is 44

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Answer:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

Step-by-step explanation:

Total expenses for this year: $214.00

The child fee will be: $x

and the adult fee will be $(x+2)

Last year the number of children was 44

and the number of adults was 33

this year also has the same number of children and adults.

which means the entrance fee total for children will be $44x and for adults will be $33(x+2).

44x + 33(x+2) = 214

--> 44x + 33x + 66 = 214

--> 77x = 214 - 66 = 148

--> x = 148/77 = 1.92

So children's price is $1.92 and adults price is $1.92 + 2

hence:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

Answer:

shaded area ≈ 69.53 cm²

Step-by-step explanation:

the shaded area (A) is calculated as

A = area of square - area of circle

area of square = 18² = 324

area of circle = πr² ( r is the radius )

the diameter of the circle = 18 , so r = 18 ÷ 2 = 9

area of circle = π × 9² = 81π

then

A = 324 - 81π ≈ 69.53 cm² ( to 2 decimal places )

Answer:

The distance from each chord to the center of the circle is approximately 12.09 inches.

Step-by-step explanation:

To find the distance from each chord to the center of the circle, we can use the following formula:

[tex]d = \sqrt{r^2-(l/2)^2}[/tex]

Where:

- "d" is the distance from the chord to the center of the circle,

- "r" is the radius of the circle, and

- "l" is the length of the chord.

Given that the diameter of the circle is 29 inches, we can find the radius by dividing the diameter by 2:

[tex]r = 29/2 = 14.5[/tex] Inches

Now, let's calculate the distance from each chord to the center of the circle:

For the first chord with a length of 16 inches:

[tex]d_{1} =\sqrt{14.5^2-(16/2)^2} = \sqrt{210.25-64} = \sqrt{146.25} = 12.09[/tex] Inches

For the second chord with a length of 16 inches:

[tex]d_{2} = \sqrt{14.5^2-(16/2)^2} = \sqrt{210.25-64} = \sqrt{146.25} = 12.09[/tex] Inches

Therefore, the distance from each chord to the center of the circle is approximately 12.09 inches.

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{14.5}\\ a=\stackrel{adjacent}{8}\\ o=\stackrel{opposite}{x} \end{cases} \\\\\\ x=\sqrt{ 14.5^2 - 8^2}\implies x=\sqrt{ 210.25 - 64 } \implies x=\sqrt{ 146.25 }\implies x\approx 12.09[/tex]

The exact value of cos(2θ) given the information and using trigonometric identity is 1519.

To find the exact value of cos(2θ), we can use the double-angle formula for cosine:

cos(2θ) = cos²(θ) - sin²(θ)

First, let's find the values of sin(θ) and cos(θ) using the given information about θ:

Given:

tan(θ) = 9/40

θ : lies in the fourth quadrant (3π/2 < θ < 2π).

In the fourth quadrant, both sin(θ) and cos(θ) are negative.

Since:

tan(θ) = sin(θ)/cos(θ),

we can write:

9/40 = sin(θ)/cos(θ)

Using the properties of trigonometric functions, we can rewrite this as:

sin(θ) = -9

cos(θ) = -40

Now, let's calculate cos²(θ) and sin²(θ):

cos²(θ) = (-40)² = 1600

sin²(θ) = (-9)² = 81

Finally, we can substitute these values into the double-angle formula for cosine:

cos(2θ) = cos²(θ) - sin²(θ)

        = 1600 - 81

        = 1519

Therefore, the exact value of cos(2θ) is 1519.

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Answer:

Step-by-step explanation:

3.14 . 11= 150/360

The probability that either event A or B will occur is equal to 0.89 to the nearest hundredth

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 20 + 12 + 4 = 36

probability of A = P(A) = 20/36

probability of B = P(B) = 12/36

probability that either event A or B will occur = 20/36 + 12/36

probability that either event A or B will occur = (20 + 12)/36

probability that either event A or B will occur = 32/36

probability that either event A or B will occur = 0.89

Therefore, the probability that either event A or B will occur is equal to 0.89 to the nearest hundredth

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The shepherd could put 7 sheep in the second pen and 49 sheep in the third pen.

We have,

Let's solve the problem step by step.

-Let's assume that the number of sheep in the second pen is 7x, where x is a positive integer representing the number of multiples of 7.

Similarly, let's assume that the number of sheep in the third pen is 7y, where y is a positive integer representing the number of multiples of 7.

According to the given information, the shepherd placed a total of 63 sheep in the pens:

7 + 7x + 7y = 63

We can simplify this equation by dividing both sides by 7:

1 + x + y = 9

Now we need to find positive integer values for x and y that satisfy this equation.

Since we know that there were more sheep in the third pen, y should be greater than x.

Let's try different values for x and y:

If x = 1, then y = 9 - (1 + 1) = 7

If x = 2, then y = 9 - (2 + 1) = 6

If x = 3, then y = 9 - (3 + 1) = 5

If x = 4, then y = 9 - (4 + 1) = 4

We can see that when x = 1, y = 7, which satisfies the condition that there were more sheep in the third pen.

Therefore, the number of sheep in the second pen (7x) is 7 x 1 = 7, and the number of sheep in the third pen (7y) is 7 x 7 = 49.

Thus,

The shepherd could put 7 sheep in the second pen and 49 sheep in the third pen.

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The complete question:

A shepherd put sheep in pens. In a corral he placed 7 sheep, in the

second and in the third pen he placed multiples of 7. If in total he placed 63

sheep, knowing that where more sheep, was in the third corral.

How many sheep could he put in pens 2 and 3?

Answer:

goat= 45 birr

sheep = 50 birr

Answer:

Goats =45

sheep =50

Step-by-step explanation:

3 sheep ÷375=7

looking to open the Naeem:

looking to open the Naeem

looking to open the Naeem:

how ❓️ ❓️,

In "f(3)", we are told to use an x-value of 3.

Looking at the function, we can either pick a formula that is used when x≤0 or x>0.

Since 3 > 0, we need to use the formula paired with x > 0:

    f(x) = x + 1  if  x>0

So f(3) = 3 + 1 = 4.

Julia's total cost for the car purchase, including the negotiated price, rebate coupon deduction, optional stereo and accessories, and financing, amounts to $16,531.05 + $380 = $16,911.05 (excluding title fees, license plate charges, and sales taxes).

Let's break down the information given and calculate the various costs and payments involved in Julia's car purchase:

1. Dealer's Cost:

The dealer's cost is 11.7% lower than the sticker price of $17,350.

Dealer's Cost = $17,350 - (11.7% * $17,350) = $15,320.95

2. Negotiated Price:

Julia negotiated a price that left the dealer with a 9.5% profit margin over the invoice price.

Negotiated Price = Dealer's Cost + (9.5% * Dealer's Cost) = $15,320.95 + (9.5% * $15,320.95) = $16,781.05

3. Rebate Coupon:

Julia has a rebate coupon of $250, which will be deducted from the negotiated price.

Negotiated Price after Rebate = Negotiated Price - $250 = $16,781.05 - $250 = $16,531.05

4. Optional Stereo and Accessories:

Julia ordered a $300 stereo unit and other accessories costing $80.

Total Additional Cost = $300 + $80 = $380

5. Financing:

Julia will finance 83% of the total cost at an APR of 9 ¼ % over 4 years.

Loan Amount = 83% * Negotiated Price after Rebate = 83% * $16,531.05 = $13,711.48

APR = 9.25%

Loan Term = 4 years

6. Title Fees, License Plate Charges, and Sales Taxes:

The costs for title fees, license plate charges, and sales taxes will be paid later at the Registry of Motor Vehicles and are not included in the calculations above.

In summary, Julia's total cost for the car purchase, including the negotiated price, rebate coupon deduction, optional stereo and accessories, and financing, amounts to $16,531.05 + $380 = $16,911.05 (excluding title fees, license plate charges, and sales taxes).

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Answer:

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

using any of the tangent, sine, cosine ratios in the right triangle.

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{7}{6}[/tex] , then

Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{7}{6}[/tex] ) ≈ 49.40° ( to 2 decimal places )

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

sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2}{6.32}[/tex]

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{6.32}[/tex]

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{2}{6}[/tex]

the measure of the angle within the 10 degrees rotation is determined as 170 degrees.

The measure of the angle within the 10 degrees rotation is calculated by applying sum of circle theorem as shown  below.

The sum of angles in the straight line 180 degrees, and we can apply this principle in calculating the expected angle within the 10 degrees rotation as follows;

Let the expected measure of the angle = θ

θ + 10 = 180 ( sum of angles in a straight line )

θ = 180 - 10

θ = 170

Thus, the measure of the angle within the 10 degrees rotation is determined as 170 degrees.

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The number of boxes of lawn seed that will be needed will be 4.

From the information, an area is formed by a square, ABCB, and a semi circle. BD is the diameter of the semi circle.The radius of the semi circle is 4m. The area is going to be covered completely with lawn seed.

The area of the square is s²

= 4²

= 16 m²

The area of the semi-circle is (πr²)/2:

= (π*4²)/2

= 8π m²

The total area is 16 + 8π m²

The number of boxes of lawn seed needed is (16 + 8π)/25 = (8 + 4π)/25

≈ 3.44 boxes

≈ 4 boxes

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To find the previous population, we need to determine the population before the 27% decrease. Here's how we can calculate it:

Let's assume the previous population is P.

According to the problem, the current population is 7300, which represents 100% - 27% of the previous population:

(100% - 27%) * P = 7300

To simplify the equation, convert 27% to decimal form:

(100% - 0.27) * P = 7300

Simplifying further:

0.73P = 7300

Divide both sides of the equation by 0.73:

P = 7300 / 0.73

P ≈ 10000

Therefore, the previous population was approximately 10,000.

~~~Harsha~~~

The experimental probability of not spinning a 1 is 21/25.

To find the experimental probability of not spinning a 1, we need to calculate the ratio of the total number of times a number other than 1 was spun to the total number of spins.

From the bar graph, we can see that the number 1 was spun 8 times. Therefore, the total number of spins is the sum of the frequencies for all the bars:

8 + 6 + 9 + 11 + 9 + 7 = 50.

To find the total number of times a number other than 1 was spun, we need to subtract the frequency of 1 from the total number of spins: 50 - 8 = 42.

The experimental probability of not spinning a 1 is given by:

Probability(not spinning a 1) = (Number of times not spinning a 1) / (Total number of spins)

Probability(not spinning a 1) = 42 / 50

Simplifying the fraction, we get:

Probability(not spinning a 1) = 21 / 25

Therefore, the experimental probability of not spinning a 1 is 21/25.

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Answer:

a) .12 × $2,400 = $288

b) $2,400 + $288 = $2,688

Answer:

5446cm²

Step-by-step explanation:

the surface area = the 2 isosceles triangles + the 2 sides + the base

= 2 (24/2 X 35) + 2(37 X 47) + (47 X 24)

= 5446cm²

Answer: 5,446 cm²

Step-by-step explanation:

First, we will find the area of the two triangle sides.

       A = 2 * ([tex]\frac{bh}{2}[/tex])

       A = bh

       A = (35 cm)(24 cm)

       A = 840 cm²

Next, we will find the area of the three rectangular sides. We have two that are congruent and a third that is not.

       A = 2 * (LW)

       A = 2 * ((47 cm)(37 cm))

       A = 2 * 1,739 cm²

       A = 3,478 cm²

       A = LW

       A = (24 cm)(47 cm)

       A = 1,128 cm²

Lastly, we will add all of these faces together.

       840 cm² + 3,478 cm² + 1,128 cm² = 5,446 cm²

Answer:

Step-by-step explanation:

The length and width of the wall of the barn are 2 feet and 12 feet

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

The area of a rectangle is calculated as

Area  = Length * Width

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

x * (2x + 8) = 24

Express 24 as 2 * 12

So, we have

x * (2x + 8) = 2 * 12

This means that

x = 2 and 2x + 8 = 12

Evaluate

x = 2

Hence, the length of the rectangle is 2 feet

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Vector g is from the red jet ski to the green boat. The magnitude is √26 and the direction angle is 248.7°, the component form of vector g is approximately (-3.8, -1.4).

To write the component form of vector g, we need to determine the horizontal and vertical components of the vector.

Given:

Magnitude of g = √26

Direction angle = 248.7°

To find the horizontal component (g_x) and vertical component (g_y) of vector g, we can use the following trigonometric formulas:

g_x = magnitude * cos(angle)

g_y = magnitude * sin(angle)

Substituting the given values:

g_x = √26 * cos(248.7°)

g_y = √26 * sin(248.7°)

Now, let's calculate the values:

g_x = √26 * cos(248.7°) ≈ -3.8

g_y = √26 * sin(248.7°) ≈ -1.4

Therefore, the component form of vector g is approximately (-3.8, -1.4).

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Answer:

  {3, 4, 5}

Step-by-step explanation:

You want the integer values that satisfy the inequality 3 ≤ x < 6.

The interval of interest has an open circle at 6, which means x=6 is not included in the solution set. (The "or equal to" condition is missing there.) The integers that are included are shown in the attachment.

  {3, 4, 5} . . . . possible integer values of x

<95141404393>