ACB radio is rated at 7.5 watts, and actual measurements show that it delivers 5.1 watts to its antenna. What is its
efficiency?

(Type a whole number or decimal rounded to two decimal places as needed)

The value of the integral ∫(1+3x) dx is equal to 14.

Integration is a process of adding up small elemental volumes to find the larger volume.

Given is to find the integral -

∫(1+3x)

We can find the equivalent values as -

∫(1+3x) dx = ∫1 dx + ∫3x dx

∫(1+3x) dx = x + 3x²/2

For the limit x = 1 to x = 3, we can write -

∫(1+3x) dx = (3 + 27/2) - (1 + 3/2)

∫(1+3x) dx = 33/2 - 5/2 = 14

Therefore, the value of the integral ∫(1+3x) dx is equal to 14.

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The equations that determine the cost of each hamburger and each fries is 4x + 5y = 20 and 10x + 7y = 41.20

An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents

Let x represent the cost of each hamburger and y represent the cost of each fries.

She purchased 4 hamburgers and 5 fries for $20.00, hence:

4x + 5y = 20    (1)

She purchased 10 hamburgers and 7 fries for $41.20, hence:

10x + 7y = 41.20   (2)

From both equations, solving simultaneously:

x = 3; y = 1.6

The cost of each hamburger is $3 while the cost of each fries is $1.6

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The new account balance at the end of 2 years is $517.

Simple interest

5 yearsUsing this formula I= (P+r×t)

Where: I=Interest=?

P=Principal=$400

r=Interest rate=3.5%

t=Time=5 years

Hence: I= ($400×0.035 x 5) which makes I= $70

2 years

I=Interest=?

P=Principal=$470

r=Interest rate=5%

t=Time=2 years

I=($470+0.05×2) which makes I=$47

New balance:

New balance=$400+$70+$47

New balance=$517

Inconclusion the new account balance at the end of 2 years is $517.

Answer:

A right triangle is a type of triangle that has one angle measuring 90 degrees and two acute angles. It has a hypotenuse and two legs, and it is the only type of triangle that the Pythagorean theorem can be applied to. There are different types of right triangles, including isosceles right triangles, 45-45-90 triangles, and 30-60-90 triangles, each with its own unique properties.

Step-by-step explanation:

A right triangle is a type of triangle that has one angle which measures exactly 90 degrees, which we call the right angle. The other two angles are called acute angles and they are always less than 90 degrees.

A right triangle has a special property: the side opposite the right angle is called the hypotenuse. This is the longest side of the triangle and it is always opposite to the right angle. The other two sides are called legs.

One important thing to note is that the Pythagorean theorem only works for right triangles. This theorem tells us that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. This formula is often written as a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse.

There are actually several different types of right triangles. For example, if the two legs have the same length, we call it an isosceles right triangle. If one of the acute angles measures exactly 45 degrees, we call it a 45-45-90 triangle, and if one of the acute angles measures exactly 30 degrees and the other measures 60 degrees, we call it a 30-60-90 triangle. These triangles have special properties that make them useful in many different areas of math and science.

In summary, a right triangle is a type of triangle that has one angle measuring 90 degrees and two acute angles. It has a hypotenuse and two legs, and it is the only type of triangle that the Pythagorean theorem can be applied to. There are different types of right triangles, including isosceles right triangles, 45-45-90 triangles, and 30-60-90 triangles, each with its own unique properties.

The solution is, x = 39. Since we have a 102 degree angle it is a obtuse triangle.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

given that,

its angles , x, 102, x

now, we know,

The sum of the angles in a triangle add to 180

i.e.

x+ 102+x = 180

Combine like terms

so, we get,

102 + 2x = 180

Subtract 102 from each side

2x = 78

divide by 2, both sides,

x =39

Since we have a 102 degree angle it is a obtuse triangle.

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Answer:

can you explain a bit better what the problem is?

The correct statements are -

In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set.

Given is to identify which of the following statements is most accurate with respect to outliers in this example.

The correct statements are -

Therefore, the correct statements are -

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The fraction of the teams which walked as part of the fundraiser for the library, that raised extra money, is D. 1 / 3.

You must count the number of teams that were able to walk more than 50 laps in order to determine the percentage of teams that raised the additional funds. The distance walked by teams more than 50 laps were :

There are 12 teams overall, which is equal to the number of leaves.

The fraction of teams that raised additional funds is:

= 4 teams / 12 total teams

= ( 4 ÷ 4 ) / ( 12 ÷ 4 )

= 1 / 3

In conclusion, the fraction of teams which raised extra money was 1 / 3.

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Answer:

Step-by-step explanation:

2X3x2Xx

The total monthly payment of Ricky with an APR of 3.84 % is given by the equation M = $ 1,208.0523

The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. An APR is a number that represents the total yearly cost of borrowing money, expressed as a percentage of the principal loan amount.

The monthly payment [tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1][/tex]

where

M = Total monthly payment

P = The total amount of your loan

I = Your interest rate, as a monthly percentage

N = number of months for paying off your mortgage

Given data ,

Let the monthly payment be represented as M

Now , the number of years n = 20 years

The annual interest rate i = 3.84 %

The total loan amount P = $ 258,000

Now , the monthly payment [tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1][/tex]

On simplifying , we get

[tex]M = 258,000 [ ( \frac{ 0.0384}{12} ) ( 1 + \frac{ 0.0384}{12} )^{12*30} ] / [ ( 1 + \frac{ 0.0384}{12} )^{12*30} - 1 ][/tex]

[tex]M = 258,000 [ (0.0032 ) ( 1.0032 )^{360} ] / [ ( 1.0032 )^{360} - 1 ][/tex]

On further simplification , we get

M = 258,000 [ 0.0101078417 ] / [ 2.158700543922579 ]

M = 258,000 ( 0.00468237327729 )

M = $ 1,208.0523

Hence , the monthly payment of Ricky is $ 1,208.0523

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Answer:based on the student's work?A Each side of the equation, in one variable, can be found by isolating the x-variable of each equationin the s

Step-by-step explanation:

Chart that arranges all of the known elements in a particular order.

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

Rearrange unknown terms to the left side of the equation: [tex]x-2x = -4 - 3[/tex]

Combine like terms: [tex]-x = -4-3[/tex]

Calculate the sum or difference: [tex]-x = -7[/tex]

Divide both sides of the equation by the coefficient of variable: [tex]x = 7[/tex]

The number of hamburgers sold in the winter is 57 million.

What is percentage ?

Percentage is a way of expressing a fraction or ratio as a portion of 100. It is denoted by the symbol "%".

For example, if there are 10 green balls in a bag of 20 balls, we can say that the percentage of green balls is:

(10/20) x 100% = 50%

This means that 50% of the balls in the bag are green.

Percentages are often used to represent proportions or amounts in many contexts, such as finance, statistics, and everyday life. They can be used to express changes, comparisons, and relationships between different quantities.

In addition, percentages are commonly used in calculations involving tax, interest rates, discounts, and other types of financial transactions. It is important to have a good understanding of percentages in order to manage personal finances, make informed business decisions, and interpret data accurately.

Let's suppose that the total number of hamburgers sold by the fast food chain in a year is represented by the height of the bars in the bar graph. We know that 25% of the hamburgers are sold in the fall, which means that the bar representing the fall sales must be 25% of the total height of the bars.

Since there are four seasons in a year, each season must represent 25% / 4 = 6.25% of the total height of the bars. Therefore, the height of each bar is 6.25% of the total number of hamburgers sold.

Let's denote the number of hamburgers sold in the winter by x. Then, the height of the winter bar is also x/100 of the total height of the bars.

We know that the winter bar is covered by a smudge, but we can still use the information we have to set up an equation. Since the heights of the bars must add up to the total height, we can write:

25% + 6.25% + 6.25% + 6.25% + x/100 = 100%

Simplifying the left-hand side, we get:

43% + x/100 = 100%

Subtracting 43% from both sides, we get:

x/100 = 57%

Multiplying both sides by 100, we get:

x = 57 million hamburgers.

Therefore, the number of hamburgers sold in the winter is 57 million.

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Answer:

Please Mark Brainlaiest Answer

Step-by-step explanation:

The best linear approximation for f(x) = cos(x) near x = pi/2 is given by the equation:

y = -(x - pi/2) + 1

This is because the linear approximation should have the same value and slope as the original function at x = pi/2.

At x = pi/2, the value of f(x) = cos(pi/2) = 0. The value of the linear approximation at x = pi/2 is:

y = -(pi/2 - pi/2) + 1 = 1

So, the value of the linear approximation matches the value of the original function at x = pi/2.

The slope of the original function at x = pi/2 is -sin(pi/2) = -1. The slope of the linear approximation is:

y' = -1

So, the slope of the linear approximation also matches the slope of the original function at x = pi/2.

Therefore, the best linear approximation for f(x) = cos(x) near x = pi/2 is:

y = -(x - pi/2) + 1

Hence, the correct option is "y equals negative x plus pi over 2 plus 1".

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Verified Answer ✅

Answer:

Step-by-step explanation:

rational

Intersection points for the lines are,

⇒ (3, 5) (1, 7) and (1, 5)

Line segment is the part of line which have two endpoint and bounded by two distinct end points and it contain every point on the line which is between its endpoint.

Given that;

The equation of lines are,

x + y = 8  .. (i)

y = 5 .. (ii)

x = 1  .. (iii)

Now, Intersect point for equation (i) and (ii);

x + y = 8  .. (i)

y = 5 .. (ii)

⇒ x + 5 = 8

⇒ x = 3

Hence, The intersection point = (3, 5)

And, Intersect point for equation (i) and (iii);

x + y = 8  .. (i)

x = 1  .. (iii)

⇒ x + y = 8

⇒ y = 8 - 1

⇒ y = 7

Hence, The intersection point = (1, 7)

And, Intersect point for equation (ii) and (iii);

⇒ (1, 5)

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The values of x and y are x = 6 and y = 3√5

Triangle 1

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

The right triangle where one of the angles is 45 degree

This is a special triangle such that

Hypotenuse = Legs * √2

So, we have

x = 3√2 * √2

Evaluate

x = 6

Triangle 2

Here, we have:

The right triangle where one of the angles is 60 degrees

So, we have

cos(60) = y/6√5

This gives

y = 6√5 * cos(60)

Evaluate

y = 3√5

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Answer:t= 1/4

Step-by-step explanation:

Divide both sides by -2/3, and simplify which would leave u with 1/4.

The probability that the sum of numbers we will get will be 6 is 7/27.

Probability is simply the possibility that something will happen.

Since we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.

The study of events that fit into a probability distribution is known as statistics.

Probability, or the likelihood that an event will occur, is calculated by dividing the number of favorable outcomes by the total number of potential possibilities.

A coin toss serves as the most simple illustration.

When you flip a coin, there are only two possible outcomes: heads or tails.

So, the probability formula:

P(E) = Favourable events/Total events

We need to get the probability of getting the sum of 6.

Then, calculate as follows:

P(E) = Favourable events/Total events

P(E) = 7/27

Therefore, the probability that the sum of numbers we will get will be 6 is 7/27.

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Correct question:
3 three-sided dice (with sides labeled 1, 2, and 3) are rolled and their sum is recorded. What is the probability of rolling a sum of 6?

The rock has an instantaneous velocity of 16 meters per second.

In this problem we need to determine the average velocity of the rock, represented by a secant line, and estimate its instantaneous velocity, represented by a tangent line. The average speed is defined by the following expression:

u = [y(t + Δt) - y(t)] / Δt

Where:

The instantaneous speed is the average speed when Δt ⇒ 0.

Part A

Case I

y(1) = 20 · 1 - 1.87 · 1²

y(1) = 20 - 1.87

y(1) = 18.13 m

y(2) = 20 · 2 - 1.87 · 2²

y(2) = 40 - 7.48

y(2) = 32.52 m

u = (32.52 m - 18.13 m) / 1 s

u = 14.39 m / s

Case II

y(1.1) = 20 · 1.1 - 1.87 · 1.1²

y(1.1) = 19.737 m

u = (19.737 m - 18.13 m) / 0.1 s

u = 16.07 m / s

Case III

y(1.01) = 20 · 1.01 - 1.87 · 1.01²

y(1.01) = 18.292 m

u = (18.292 m - 18.13 m) / 0.01 s

u = 16.2 m / s

Case IV

y(1.001) = 20 · 1.001 - 1.87 · 1.001²

y(1.001) = 18.146 m

u = (18.146 m - 18.13 m) / 0.001 s

u = 16 m / s

And the instantaneous velocity of the rock is approximately 16 meters per second.

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Answer:

it depends on how many students?

Step-by-step explanation:

To find the perimeter of the triangle, we need to calculate the length of each of its sides and then add them up.

Let's start by finding the length of the side between (-1, -14) and (7, 1). We can use the distance formula for this:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates, we get:

distance = sqrt((7 - (-1))^2 + (1 - (-14))^2)

= sqrt(8^2 + 15^2)

= sqrt(289)

= 17

So the length of the first side is 17.

Now let's find the length of the side between (-1, -14) and (-1, 7):

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates, we get:

distance = sqrt((-1 - (-1))^2 + (7 - (-14))^2)

= sqrt(0^2 + 21^2)

= 21

So the length of the second side is 21.

Finally, let's find the length of the side between (7, 1) and (-1, 7):

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates, we get:

distance = sqrt((-1 - 7)^2 + (7 - 1)^2)

= sqrt((-8)^2 + 6^2)

= sqrt(100)

= 10

So the length of the third side is 10.

Now we can add up the lengths of all three sides to get the perimeter:

perimeter = 17 + 21 + 10

= 48

Therefore, the perimeter of the triangle is 48.

The solution to the equation 17(4 + 15) is 323

An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents

Given the equation:

17(4 + 15)

= 17(19)

= 323

OR

17(4 + 15)

= 17(4) + 17(15)

= 68 + 255

= 323

The solution to 17(4 + 15) can be gotten by determining the product of 17 and 19; or adding the product of 17 and 4 to the product of 17 and 15

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Answer:

The investment in the fund was $19000 x 0.12 = $2280

The investment in the stock was $19000 - $2280 = $16720

The net profit was $520, so the amount of the profit from the fund was $520 x (2280/16720) = $136

The amount of the loss from the stock was $520 - $136 = $384

Answer:

(2x-1)(3x-4)

Step-by-step explanation:

6x²-11x+4

Now we will split the middle term so when we add the digits it will give the original number back but when we multiply them, it will give the sum of the first and the last digit

6x²-11x+4

6x²-3x-8x+4

Now you can that if we add -3 and -8, we get -11 back but if we multiple them, we get the sum of 6 and 4 (the first and the last digits), which is 24

Now we will simplify the values

3x(2x-1) - 4(2x-1)

Simplifying further, we get

(2x-1) (3x-4) which is the answer

Answer:

C

The value of the variables in answer C satisfies both of the equations

The height of the balloon is 1.3 miles above the ground.

Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. For example, a person's height is typically measured using a stadiometer and is recorded in centimeters or feet and inches. The height of a mountain is usually measured in meters or feet. In aviation, height is measured from the surface of the earth, either above ground level (AGL) or above mean sea level (AMSL).

The answer to this question can be found by using the trigonometric formula of Tangent. To calculate the height of the balloon, we must find the length of the hypotenuse in the triangle formed by the two towns and the balloonist.

Using the formula for tangent, we can calculate the length of the hypotenuse. The formula is:

tan (angle) = opposite side/adjacent side

In this case, the opposite sides are the two towns, and the adjacent side is the height of the balloon.

For the first town, the formula is:

tan 36° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the first town to be 2.8 miles.

For the second town, the formula is:

tan 32° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the second town to be 2.9 miles.

Since the hypotenuse is the total distance between the two towns and the balloonist, the height of the balloon can be calculated by subtracting the total length of the two towns (1.6 miles) from the hypotenuse of the second town (2.9 miles).

The height of the balloon is 1.3 miles above the ground.

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Answer:

What is height?

Height:

When a rectangle is drawn with horizontal and vertical sides, the word height makes it clear which dimension is meant; height labels how high (how tall) the rectangle is. That makes it easy to indicate the other dimension—how wide the rectangle is from side to side—by using the word width. And if the side-to-side measurement is greater than the height, calling it the length of the rectangle is also acceptable, as it creates no confusion.

The answer to this question can be found by using the trigonometric formula of Tangent. To calculate the height of the balloon, we must find the length of the hypotenuse in the triangle formed by the two towns and the balloonist.

Using the formula for tangent, we can calculate the length of the hypotenuse. The formula is:

tan (angle) = opposite side/adjacent side

In this case, the opposite sides are the two towns, and the adjacent side is the height of the balloon.

For the first town, the formula is:

tan 36° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the first town to be 2.8 miles.

For the second town, the formula is:

tan 32° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the second town to be 2.9 miles.

Since the hypotenuse is the total distance between the two towns and the balloonist, the height of the balloon can be calculated by subtracting the total length of the two towns (1.6 miles) from the hypotenuse of the second town (2.9 miles).

The height of the balloon is 1.3 miles above the ground.

Answer:

x = -3/5

Step-by-step explanation:

Given the equation:
[tex]\displaystyle{8x+9=3x+6}[/tex]

Solve for the variable x by isolating x-term, first move subtract both sides by 3x:

[tex]\displaystyle{8x+9-3x=3x+6-3x}\\\\\displaystyle{5x+9=6}[/tex]

Subtract both sides by 9:

[tex]\displaystyle{5x+9-9=6-9}\\\\\displaystyle{5x=-3}[/tex]

Divide both sides by 5:

[tex]\displaystyle{\dfrac{5x}{5}=\dfrac{-3}{5}}\\\\\displaystyle{x=-\dfrac{3}{5}}[/tex]

Therefore x = - 3/5

Answer:

x = -3/5 (or) x = -0.6

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 8x + 9 = 3x + 6

Then the value of x will be,

→ 8x + 9 = 3x + 6

→ 8x - 3x = 6 - 9

→ 5x = -3

→ x = -3 ÷ 5

→ [ x = -3/5 ]

Hence, the answer is -3/5.

Answer:

there were 15 almonds in the snack pack.

Step-by-step explanation:

Let's use variables to represent the unknown quantities. Let's call the number of almonds in the snack pack "a", and the number of cashews in the snack pack "c".

we can use the following equations to represent the problem:

c = 2a (the number of cashews is twice the number of almonds)

c - 10 = a + 5 (there are 5 more cashews than almonds after Sylvia eats 10 cashews)

Substituting the first equation into the second equation, we get:

2a - 10 = a + 5

Solving for "a", we get:

a = 15

So there were 15 almonds in the snack pack.

Answer:

The answer is (A) 8.1%.

Step-by-step explanation:

The probability of flipping a coin and getting heads is 1/2 or 0.5. Assuming the coin is fair, the probability of getting heads 4 times in 11 flips is given by the binomial probability formula:

P(4 heads in 11 flips) = (11 choose 4) * (0.5)^4 * (0.5)^(11-4) = 330 * 0.5^11

Using a calculator, we get:

P(4 heads in 11 flips) ≈ 8.1%

Therefore, the answer is (A) 8.1%.