The areas of two circles are 92 2 and 62 2
respectively. Find the radius of the circle
having its area equal to the sum of the areas of the two circles.

The required Jane is approximately 59.28 inches tall.

Height is a measurement of vertical distance, either in terms of vertical extent (how tall an object or person is) or in terms of vertical position (how high a point is). "The height of that building is 50 meters" or "The height of an airplane in flight is approximately 10,000 meters" are two examples.

Sylvia's height can be represented as:

Sylvia’s height =56[tex]\frac{3}{4}[/tex] inches

Bill is [tex]\frac{1}{3}$[/tex] of 8 inches taller than Sylvia, which means that Bill's height is:

[tex]$\begin{align*}\text{Bill's height} &= \text{Sylvia's height} + \frac{1}{3} \times 8\ \text{inches} \&= 56 \frac{3}{4}\ \text{inches} + \frac{8}{3}\ \text{inches} \&= 58 \frac{7}{12}\ \text{inches}\end{align*}[/tex]

Jane is [tex]1 \frac{1}{5}$[/tex] inches taller than Bill, which means that Jane's height is:

[tex]$\begin{align*}\text{Jane's height} &= \text{Bill's height} + 1 \frac{1}{5}\ \text{inches} \&= 58 \frac{7}{12}\ \text{inches} + 1 \frac{1}{5}\ \text{inches} \&= 59 \frac{17}{60}\ \text{inches}\end{align*}[/tex]

Therefore, Jane is approximately 59.28 inches tall.

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The information makes sense in different scenarios like manufacturing, baking, researching survey, etc.

A sample is a portion of a population that is used to represent the full population in statistics. Researchers frequently utilise samples to draw conclusions about the population since it might be difficult or impossible to collect data from the complete population. In order for the conclusions made from the sample to be applicable to the entire population, it is important to pick a sample that is representative of the wider population. Many techniques, such as cluster sampling, stratified sampling, and random sampling, can be used to choose samples.

The knowledge of biscuit preferences may come in handy in a variety of situations. Here are three potential instances:

A biscuit manufacturer wants to launch a brand-new taste. They may opt to create a chocolate chip or peanut butter flavor as those are the most popular ones based on the preferences data.

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Complete question -

A national sampling of cookie preferences showed that 75% of people like chocolate chip, 50% like peanut butter, and only 3% like coconut. The use of this information makes sense in which of the following scenarios? A. The school cafeteria decides to make 3 coconut cookies for each 100 students who buy lunch, even though it puts them over budget for desserts. B. A national cookie company is thinking of changing the recipe in their peanut butter cookies. C. A national cookie company decides to spend $5 million in advertising to convince people to eat coconut cookies. D. Tom is about to open a small bakery and is using the result of the sampling to decide what kind of cookies to offer.

Answer:

C. Approximately 3 hens per square meter

When the pressure is 2.6 g/m² then the depth is 3.9 m.

The term proportionality describes any relationship that is always in the same ratio. The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.

Given that

the pressure varies directly with the depth. When the pressure is 320 g/m² the depth is 480 m.

We need to find the depth if the pressure is 2.6 g/m².

So, here we will use the concept of proportionality,

Let the unknown depth be x,

So,

320 / 480 = 2.6 / x

2 / 3 = 2.6 / x

2x = 7.8

x = 3.9

Hence when the pressure is 2.6 g/m² then the depth is 3.9 m.

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complete question:

Pressure varies directly with the depth. When the pressure is 320 grams per square meter the

depth is 480 meters. What is the depth, in meters, when the pressure is 2.6 grams per square

meter? (Round to the nearest tenth)

A 1.7 grams

B 1.9 grams

C 3.7 grams

D 3.9 grams

The area of the Tri-Tri-Again board game is 3 1/8 square feet.

To calculate the area of a triangle, we need to know the length of its base and its height. In this case, Bridget's Tri-Tri-Again board game is in the shape of a triangle with a base of 1 1/4 feet and a height of 2 1/2 feet. To find the area of the triangle, we can use the formula for the area of a triangle, which is 1/2 x base x height.

We first convert the mixed numbers to improper fractions. The base is 5/4 feet and the height is 5/2 feet. We can then substitute these values into the formula to get:

Area of triangle = 1/2 x 5/4 feet x 5/2 feet

Area of triangle = 25/8 square feet

We can simplify the answer by dividing the numerator and denominator by the greatest common factor of 25 and 8, which is 1. This gives us:

Area of triangle = 25/8 square feet

Area of triangle = 3 1/8 square feet

Therefore, the area of the Tri-Tri-Again board game is 3 1/8 square feet.

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Answer:

6.00 %

Step-by-step explanation:

Percent = amount donated/total sales × 100 %

              = 429/7150 × 100 %

              = 6.00 %

The store donated 6.00 % of its sales to charity.

the height of point P after the windmill blade rotates by an angle of a is approximately 1.1908 feet.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

To find the height h of point P, we can use the sine function, which relates the opposite side of a right triangle (in this case, the height h) to the hypotenuse (in this case, the length of the windmill blade, which is 1.5 feet). The angle between the opposite side and the hypotenuse is the complement of the angle of rotation a, which is π/4 radians minus the angle between the ground and the windmill blade, which is arctan(6/1.5) or approximately 1.3258 radians.

So, the equation for the height h of point P after the windmill blade rotates by an angle of a is: h = 1.5 sin(π/4 - arctan(6/1.5))

Therefore, the height of point P after the windmill blade rotates by an angle of a is approximately 1.1908 feet.

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Below are the three angles listed out in both radians and degrees:

Let us assume that point P is initially at the topmost point of the wheel, and Q is directly to the right of P.

When the wheel rotates counterclockwise, point P moves along a circle with radius 1 foot, centered at the center of the wheel. To end up at position Q, point P needs to move a quarter of the way around the circle, or pi/2 radians. Therefore, one angle that the wheel can rotate is pi/2 radians (or 90 degrees).

Another angle that the wheel can rotate is 5*pi/2 radians (or 450 degrees), which corresponds to rotating the wheel counterclockwise almost all the way around the circle, but stopping just short of completing a full rotation.

A third angle that the wheel can rotate is 9*pi/2 radians (or 810 degrees), which corresponds to rotating the wheel counterclockwise almost twice around the circle, but stopping just short of completing two full rotations.

Therefore, Note that there are a lot of many other angles that the wheel can rotate to end up at position Q, but these three examples give an idea of the possibilities.

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The new dimensions of the poster will be 5 in by 6 in.

In mathematics, scaling is the process of adjusting a geometric form or figure's size by a predetermined factor or ratio. With scaling, a shape's dimensions are all multiplied by the same quantity. Depending on whether the scaling factor is more than 1 or less than 1, respectively, scaling can either make the form larger or smaller. In addition to science, engineering, and computer graphics, scaling is frequently utilised in trigonometry, geometry, and other areas of mathematics.

Given that the scale factor = 1/3.

Thus, the new dimensions are:

New length = 15 in x (1/3) = 5 in

New width = 18 in x (1/3) = 6 in

Hence, the new dimensions of the poster will be 5 in by 6 in.

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The expression that is equal to 9 is 10 − (one-fifth x 10) + 1.

Basic mathematical procedures known as arithmetic are used to calculate using numbers. Addition, subtraction, multiplication, and division are the four fundamental arithmetic operations. Finding the sum of two or more numbers is done using addition, finding the difference between two numbers is done using subtraction, finding the product of two or more numbers is done using multiplication, and finding the quotient of two numbers is done using division. There are more operations outside these four, such as square root and exponentiation (increasing a number to a power) (finding the root of a number).

For the given expressions we have:

4 x (one-half x 6) ÷ 3 = 4 x 3 ÷ 3 = 4 --> not equal to 9

6 ÷ (one-fourth x 3 x one and one-fourth) = 6 ÷ (3/4 x 5/4) = 6 ÷ (15/16) = 96/15 --> not equal to 9

8 + (one-third x 6) ÷ 5 = 8 + 2 ÷ 5 = 8.4 --> not equal to 9

10 − (one-fifth x 10) + 1 = 10 - 2 + 1 = 9 --> equal to 9

Hence, the expression that is equal to 9 is 10 − (one-fifth x 10) + 1.

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Answer:

$1529

Step-by-step explanation:

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the final amount (balance) in the account

P = the initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = the annual interest rate (as a decimal)

t = the time period (in years)

Plugging in the given values, we get:

A = 1000e^(0.0855)

A = 1000*e^0.425

A = 1000*1.529

A = 1529

Therefore, the balance after 5 years with continuous compounding at 8.5% interest rate is $1529.

The solution for x is -21 when rectangle JKLM below, JN = 44.

If MN = -2x + 2,

What is the rectangle?

A rectangle is a geometric shape with four sides and four right angles. It is a quadrilateral in which opposite sides are equal in length and parallel to each other, and adjacent sides are perpendicular to each other.

To solve for x, we can use the given information that JN = 44 and MN = -2x + 2 in the rectangle JKLM.

Since JN is a side of the rectangle and is equal to 44, and MN is also a side of the rectangle and is equal to -2x + 2, we can set up the equation:

JN = MN

44 = -2x + 2

Now we can solve for x:

Add 2x to both sides:

44 + 2x = 2

Subtract 2 from both sides:

44 + 2x - 2 = 0

42 + 2x = 0

Subtract 42 from both sides:

42 + 2x - 42 = 0 - 42

2x = -42

Finally, divide both sides by 2 to isolate x:

2x / 2 = -42 / 2

x = -21

Hence, the solution for x is -21.

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The equation of the line of reflection is y = (−13 / 45)x − (1376 / 45) in point-slope form.

To find the equation of the line of reflection between the points (-9, 12) and (17, -78), we first need to find the midpoint of the line segment joining these two points, which will lie on the line of reflection. The midpoint formula is:

[(x₁ + x₂) / 2, (y₁ + y₂) / 2]

Using the coordinates of the two given points, we get:

[(−9 + 17) / 2, (12 − 78) / 2] = [4, −33]

So, the midpoint is (4, −33).

Next, we need to find the slope of the line of reflection. This is equal to the negative reciprocal of the slope of the line passing through the two given points, since the line of reflection is perpendicular to this line. The slope of the line passing through the two given points is

m = (y₂ − y₁) / (x₂ − x₁) = (−78 − 12) / (17 − (−9)) = −90 / 26 = −45 / 13

So, the slope of the line of reflection is:

m' = −1 / m = −13 / 45

Finally, we can use the point-slope form of the equation of a line, with the midpoint we found as the point and the slope we calculated as the slope which is

y − (−33) = (−13 / 45)(x − 4)

y + 33 = (−13 / 45)x + (52 / 45)

or

y = (−13 / 45)x − (1376 / 45)

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[tex]x^4y^2-2x^3y^3\\\\x^2y^2(x^2-2xy)[/tex]

Answer is the second one.

In a parallelogram, The statement "angle A and angle D are supplementary" is not correct.

The same-side interior angles theorem states that if a transversal intersects two parallel lines, then the same-side interior angles are supplementary. However, in this case, we are dealing with a parallelogram, which has two pairs of parallel sides.

When we say that "ab||dc", we are stating that side AB is parallel to side DC. We cannot assume that side AD is a transversal between these two sides, as it could intersect the sides at some other angle. Therefore, we cannot conclude that angle A and angle D are angles.

However, we do know that opposite angles in a parallelogram are congruent. Therefore, we can conclude that angle A is congruent to angle C, and angle B is congruent to angle D.

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Population proportion: The proportion of people aged under 40 who have savings accounts is the population proportion. This can be calculated as follows:Population proportion = (number of savings accounts belonging to people under 40) / (total number of savings accounts).

Population proportion = 4675/13500Population proportion = 0.3463 (rounded to four decimal places)Mean and standard deviation of the sampling distributionFor a given sample size, the mean and standard deviation of the sampling distribution can be calculated as follows:

Mean of sampling distribution = population proportionStandard deviation of sampling distribution = sqrt[(population proportion * (1 - population proportion)) / n]where n is the sample size.For this question, the sample size is not given, so we cannot calculate the mean and standard deviation of the sampling distribution.

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The correct option for the quadratic function g are-

Mathematical expressions with a two as the highest power are called quadratic functions. A function or numerical statement of degree two is a quadratic function. This indicates that two is the function's highest power.

The correct option for the given quadratic function g from the graph are-

Correction for the incorrect statements:

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It is not possible for a study to have practical significance without statistical significance because statistical significance provides evidence that the observed effect is unlikely to have occurred by chance.

The Practical significance and statistical significance are two different concepts that are often used in hypothesis testing.

The Statistical significance refers to the probability that the observed results of a study occurred by chance, given a particular level of significance or alpha.

The Practical significance refers to whether the observed effect size is large enough to be meaningful in a real-world context.

It is possible for a study to have statistical significance without practical significance. For example, a study may find a statistically significant difference between two groups, but the difference may be so small that it is not meaningful in practice.

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Answer: [tex]6x^{2}[/tex] + 24x + 18

Step-by-step explanation: To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

Answer:

the length of the rectangle is 21 feet.

Step-by-step explanation:

Let's use "w" to represent the width of the rectangle. According to the problem, the length is three times the width, so we can use "3w" to represent the length.

The perimeter of a rectangle is given by the formula:

Perimeter = 2(length + width)

Substituting the expressions for length and width, we get:

56 = 2(3w + w)

Simplifying the right side, we get:

56 = 2(4w)

56 = 8w

w = 7

So the width of the rectangle is 7 feet. To find the length, we can use the expression we derived earlier:

length = 3w = 3(7) = 21

Therefore, the length of the rectangle is 21 feet.

well, the amount off from the original 125 is just 125 - 87.50 = 37.50.

now, if we take 125(origin amount) as the 100%, what's 37.50 off of it as a percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 125 & 100\\ 37.50& x \end{array} \implies \cfrac{125}{37.50}~~=~~\cfrac{100}{x} \\\\\\ 125x=3750\implies x=\cfrac{3750}{125}\implies x=30[/tex]

To determine what percent off the sale for something was, we need to use the formula for percent off calculation.

What is percent off? The percent off is used to refer to the reduction in price or value of something. The percent off calculation is used to determine the amount of discount in percentage of the original price or value.

What is the formula for percent off calculation? The formula for percent off calculation is as follows:

percent off = (discount / original price) x 100, where,discount = original price - sale price

original price = $125 sale price = $87.50

Substitute the given values into the formula and simplify.

percent off = (discount / original price) x 100percent off =

(($125 - $87.50) / $125) x 100percent off

(37.50 / 125) x 100percent off

⇒ 0.3 x 100percent off = 30%

Therefore, the percent off the sale was 30%.

Step-by-step explanation:

3.2  liters    divided by 300 ml / bottle is

3200 ml / 300 ml/bottle = 10 2/3 bottles  

             10 full bottles plus 2/3 of a bottle left over

                        2/3 bottle * 300 ml/bottle = 200 ml left over

According to the solution we have come to find that, The possible coordinates of point A are (2,-2) and (2,4).

Geometry is a branch of mathematics that deals with the study of spatial relationships and properties of objects. It is concerned with the study of shape, size, position, and relative orientation of objects, as well as their properties such as angles, lines, curves, surfaces, and solids. Geometry is used extensively in various fields, including architecture, engineering, physics, astronomy, and computer graphics. The study of geometry involves using logic and reasoning to analyze and solve problems related to shapes and spatial relationships. It is an important subject that has practical applications in many areas of everyday life.

To find the possible coordinates of point A, we need to use the distance formula and the fact that the x-coordinate of point A is 2.

The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) are the coordinates of point A, (x2, y2) are the coordinates of point B, and d is the distance between the two points.

We know that the distance between point A and point B is 5 units:

5 = √((5 - 2)² + (1 - y1)²)

Squaring both sides:

25 = (5 - 2)²+ (1 - y1)²

Simplifying:

9 = (1 - y1)²

Taking the square root of both sides:

3 = 1 - y1 or 3 = y1 - 1

Solving for y1 in each case:

y1 = -2 or y1 = 4

Therefore, the possible coordinates of point A are (2,-2) and (2,4).

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Answer:

[tex]n = \frac{m - 2p}{3} \\ \\ p = \frac{m - 3n}{2} [/tex]

Step-by-step explanation:

[tex]1. \: m - 2p = 3n \\ 2. \: \frac{m - 2p}{3} \\ 3. \: n = m - 2p \\ \\ 1. \: m - 3n = 2p \\ 2. \: \frac{m - 3n}{2} = p \\ 3. \: p = \frac{m - 3n}{2} [/tex]

Answer:

b = 8.485

c = 23.995 ≈ 24

Step-by-step explanation:
Part b:

[tex]\sqrt{(10-4)^2+(9-3)^2}[/tex]

√(36 + 36)

= 8.485

Part c:

Base = [tex]\sqrt{(6-2)^2+(1-5)^2}[/tex]

Base = 5.656

Area = Base x Height x 0.5

Area = 5.656 x 8.485 x 0.5

Area = 23.995 ≈ 24

Step-by-step explanation:

ans is 2 nd option

first bracket multiply with 7 and second multiply with 2 multiply the sign also carefully.

Answer:

1/72

Step-by-step explanation:

There are a total of 17 students in the class, and we want to choose one boy from 9 and one girl from 8 without replacement. The total number of ways to choose two students from the class is:

17C2 = (17!)/(2!15!) = (1716)/(21) = 136

To choose a boy and a girl, we can choose the boy in 9 ways and the girl in 8 ways, for a total of 9*8 = 72 ways.

Now, since the brother and sister are both in the class, there is only one way to choose them together. Therefore, the probability of choosing the brother and sister is:

1/72

So the probability is 1/72, written as a fraction in simplest form.

step-by-step explanation:

Part A. We can see that within only for a 0-2 second interval, the height of the water balloon increases from 60ft to approximately 80ft.

Part B. In two intervals, 2-4 seconds to approximately 80 ft and 10-14 seconds to 0 ft.

Part C. Between 4 and 6 seconds, the water balloon height changes from approximately 80ft to 40ft, whereas between 6-8 seconds and 8-10 seconds, the height only changes by 20ft.

Part D. According to the graph, we can suppose that the water balloon was thrown up, and after beginning to fall, at 10 seconds touched the floor, so in 16 seconds kept staying on the floor, at 0ft.  

Hope it helps.

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

The probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

What is probability?

The probability of the spinner landing on blue is 2/6, which simplifies to 1/3.

The probability of rolling an even number on a six-sided die is 3/6, which simplifies to 1/2.

To find the probability of both events occurring together, we multiply the probabilities:

P(blue and even number) = P(blue) x P(even number)

P(blue and even number) = (1/3) x (1/2)

P(blue and even number) = 1/6

Therefore, the probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

What is spinner?

A spinner is a device or a toy used to randomly select or generate a value or outcome. It consists of a circular board or disc, often divided into sections of different colors or with different values or symbols, and a pointer or arrow that is spun around the disc to land on a particular section. Spinners are commonly used in games, educational activities, and statistical experiments to create random outcomes or to simulate probability distributions.

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Complete question is: The probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

Answer:

Step-by-step explanation:

The probability of the spinner landing on blue is 2/6, which simplifies to 1/3.

The probability of rolling an even number on a six-sided die is 3/6, which simplifies to 1/2.
To find the probability of both events occurring together, we multiply the probabilities:

P(blue and even number) = P(blue) x P(even number).

P(blue and even number) = (1/3) x (1/2).

P(blue and even number) = 1/6.

Therefore, the probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.

As per the mentioned informations and values provided, the mean from this sample frequency distribution is calculated to be approximately 160.50.

To find the mean from the given sample frequency distribution, we need to first calculate the midpoint for each class interval, then multiply it by the corresponding frequency, sum all of these products, and finally divide by the total frequency.

Using the formula: mean = (sum of midpoint x frequency) / (sum of frequency)

Midpoint for the first interval = (0 + 70) / 2 = 35

Midpoint for the second interval = (70 + 200) / 2 = 135

Midpoint for the third interval = (200 + 500) / 2 = 350

Now we can calculate the sum of midpoint x frequency:

35 x 73 + 135 x 37 + 350 x 182 + 232 x 500 = 84,166

The total frequency is the sum of all frequencies: 73 + 37 + 182 + 232 = 524

Finally, we can calculate the mean:

mean = (sum of midpoint x frequency) / (sum of frequency) = 84,166 / 524 ≈ 160.50

Therefore, the mean from this sample frequency distribution is approximately 160.50.

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The angles that form a linear pair is 6 and 8.

option C.

Linear pair angles are two adjacent angles formed by two intersecting lines. These two angles are always supplementary, which means that their sum is equal to 180 degrees. In other words, if we add the measure of one angle to the measure of the other angle, we will get a total of 180 degrees.

A linear pair of angles can be easily identified by observing the angles formed when two straight lines intersect each other. For example, if line AB intersects line CD at point E, then the two pairs of adjacent angles formed are:

Each pair of adjacent angles in a linear pair is supplementary, which means that ∠AED + ∠DEB = 180 degrees and ∠CEB + ∠BED = 180 degrees.

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