Find the leg and hypotenuse.

There are 216 possible outcomes for each trial of rolling three standard dice.

In probability theory, an outcome is defined as the result of a single experiment or trial. The total number of outcomes in a trial can be determined by the multiplication principle, which states that if there are m ways to do one thing, and n ways to do another, then there are m x n ways to do both.

In this case, Michelle is rolling three standard dice simultaneously, which means that there are six possible outcomes for each die. Therefore, the total number of outcomes for a single trial is calculated by multiplying the number of outcomes for each die. Using the multiplication principle, we get:

Number of outcomes for each die = 6

Total number of outcomes for a single trial = 6 x 6 x 6 = 216

It is important to note that not all outcomes are equally likely, and the probability of getting a specific outcome can be calculated by dividing the number of favorable outcomes by the total number of outcomes.

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The requried odds against Davis winning the election is 0.33 or 33%.

We can find the odds against Davis winning the election by using the formula:

odds against Davis = (number of people not voting for Davis) / (number of people voting for Davis)

Out of the 200 people, 150 said they would vote for Davis. So the number of people not voting for Davis is:

200 - 150 = 50

Therefore, the odds against Davis winning the election are:

odds against Davis = 50 / 150 = 1/3 or 0.33 (rounded to two decimal places)

This means that for every person who thinks Davis will win, there are three people who think he will lose.

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suppose that x is a normal random variable with a mean of 5. if p{x > 9} = .2, So, the approximate variance of the normal random variable X is 22.66.

To find the variance of a normal random variable X with mean 5 and given P(X > 9) = 0.2, we will follow these steps:

1. Recognize that X follows a normal distribution: X ~ N(μ, σ²), where μ = 5 and σ² is the variance we want to find.

2. Convert the probability statement P(X > 9) = 0.2 to a standard normal distribution (Z) by finding the corresponding Z-score:
  Z = (X - μ) / σ

3. Look up the Z-score that corresponds to the given probability (0.2) in a standard normal (Z) table. Since the table typically gives P(Z < z), we'll find P(Z < z) = 1 - 0.2 = 0.8. The corresponding Z-score is approximately 0.84.

4. Plug in the known values and solve for σ:
  0.84 = (9 - 5) / σ
  σ ≈ 4 / 0.84
  σ ≈ 4.76

5. Finally, find the variance, which is σ²:
  σ² ≈ 4.76²
  σ² ≈ 22.66

So, the approximate variance of the normal random variable X is 22.66.

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The approximate variance of the normal random variable X is the square of the standard deviation:

Var(X) ≈ [tex](4.76)^2[/tex] ≈ 22.65 (rounded to two decimal places).

To approximate the variance of the normal random variable X with a mean of 5, given that P(X > 9) = 0.2, we can use the z-score and standard normal distribution.

First, we calculate the z-score using the standard normal distribution formula:

z = (X - μ) / σ

where X is the value of interest (in this case, 9), μ is the mean (5), and σ is the standard deviation.

Plugging in the values, we get:

z = (9 - 5) / σ = 4 / σ

Next, we use the standard normal distribution table or a calculator to find the z-score that corresponds to a cumulative probability of 0.2. Let's assume that z = -0.84.

Now, we can use the z-score formula to solve for the standard deviation σ:

-0.84 = 4 / σ

Cross-multiplying, we get:

-0.84σ = 4

Dividing both sides by -0.84, we get:

σ ≈ 4 / -0.84 ≈ -4.76

Since the standard deviation cannot be negative, we discard the negative value and take the absolute value, resulting in:

σ ≈ 4.76

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1. If all dimension are doubled , the area will be enlarged by a factor of 4 (optionD)

2. If the dimensions are reduced by 1/4, the perimeter Is reduced by a factor of 1/4

3. If the dimensions are tripled, the perimeter will enlarge by a factor of 3

4. if the dimensions were reduced, by a factor of 1/3 , the area will reduce by a factor of 1/9

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

A linear scale factor is the dimensions for length and the relation of between linear scale factor and area scale factor is ;

area factor = (linear factor)²

Linear factor can also be used for perimeter of shape. therefore if dimension is double by 2 the perimeter will double by 2 and the area will double by 2² = 4

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The height of the kite is approximately 68.4 ft.

To solve the problem, we can use trigonometry. We know that the string is the hypotenuse of a right triangle, with the height of the kite as one of the legs. The angle of elevation, which is the angle between the string and the ground, is also given. We can use the tangent function to find the height of the kite:

tan(46°) = height / 94

Solving for height, we get:

height = 94 * tan(46°)

Using a calculator, we get:

height ≈ 68.4 ft

Therefore, the height of the kite is approximately 68.4 ft.

We use the given angle of elevation and the length of the string to set up a right triangle with the height of the kite as one of the legs. Then, we use the tangent function to relate the angle to the height of the kite. Finally, we solve for the height using a calculator and round to the nearest tenth as requested.

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Complete Question:

A kite flying in the air has a 94-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 46 °. Find the height of the kite. Round your answer to the nearest tenth.

1. The expression √b means "the square root of b".

2. The radical symbol (√) stands for the exponent 1/2.

3. The number or expression under the radical symbol is called the radicand.

A radicand is the number or expression underneath a radical symbol (√). It is the number or expression that is being operated on by the root. The square root of the radicand is the result of the operation.

The expression √6 represents the square root of 6. This is the value of x that, when multiplied with itself, results in 6.

The square root of 6 is equal to 2.44948974, which is the positive solution to the equation x² = 6.

The radical symbol (√) indicates that the expression is a root and the number or expression under the radical symbol is called the radicand, which is 6 in this case.

The exponent of the radical symbol is 1/2, which implies that the expression is a square root.

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The ounces of  beeswax needed by Leah to make 15 more small candles is equal to 49.95 ounces.

Let us consider 'x' be the ounces of beeswax required by Leah to make 15 candles.

To make 6 small candles, Leah uses 20 ounces of beeswax.

So, to make one small candle,

Ounces of beeswax used by Leah ,

= 20 ounces / 6 candles

= 3.33 ounces/candle (rounded to two decimal places)

To make 15 more small candles,

Ounces of beeswax Leah will need is equals to,

⇒ x = 15 candles x 3.33 ounces/candle

⇒ x = 49.95 ounces (rounded to two decimal places)

Therefore, Leah needs 49.95 ounces of beeswax to make 15 more small candles.

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Three distances that are equivalent to 1/2 mile are:

880 yards

1,609.34 meters

2,640 feet

Answer:3/16

Step-by-step explanation:

√1 is the same thing as 1

so (3*1)/16

3/16

Answer:

10

Step-by-step explanation:

To find the median in a set of data, organize the data from least to greatest.

Here, our data is the homework scores, those being:

10, 7, 8, 12, 9, 11, 13

Let's organize them in ascending order, like so:

7, 8, 9, 10, 11, 12, 13

The next step in finding the median is figuring out which number is in the middle. Since the amount of data we have is an odd number (7), there will be only one number in the middle.

We can find that the number in the middle is 10.

Thus, the median of the scores is 10.

The length of arc XW is 9,60 metres

The length of arc YVU is 44.93 metres

A. M<XZW = 180 degrees - M<VZW

= 180 - 108

= 72 degrees.

XV = 180/360 x 2\pi r =

r = 7.639

XW= 72/360 x 2\pi r

= 9.60 metres.

B. M<UZY = M<XZW = 72 degrees

MYVU= 85 + 180 + 72 = 337 degrees

YVU = 337/360 x 2 pi r

=44.93 metres

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The exterior angle in the figure is 10 degrees

In a triangle, the sum of all angles is 180 degrees. So we can set up an equation with the given angles:

2x + 3x + (3x + 4) = 180

Simplifying the equation, we get:

8x + 4 = 180

8x = 176

x = 22

So the value of x is 22.

To find the measures of the angles, we can substitute this value of x into the given expressions:

The first angle is 2x, so it measures 2(22) = 44 degrees.

The second angle is 3x, so it measures 3(22) = 66 degrees.

The third angle is 3x + 4, so it measures 3(22) + 4 = 70 degrees.

The exterior angle is 44 + 66 = 110

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The value of x, in the image given is calculated by applying the intersecting chords theorem, which is: x = 16.

The Intersecting Chords Theorem, also known as the Ptolemy's Theorem, states that in a circle, if two chords intersect, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

In mathematical terms, if two chords, AB and CD, intersect at point E inside a circle, then:

AE × EB = CE × ED

Applying the theorem, we have:

5(x) = (x - 6)8

5x = 8x - 48

5x - 8x = -48

-3x = -48

x = 16

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The area of the shaded region between the circle and the rectangle can be found to be 30.6 units ².

First, find the area of the rectangle. The Length would be 6 because if the midpoint to the edge of the circle is 3, then the midpoint to the edge of the circle on the left would be 3 as well:

= 3 + 3

= 6

The same is true for the width which would be 8 because the y value is 4 from the midpoint so the width is twice that and so is 8.

The radius of the circle would be 5 because this is the x value to the edge of the circle from the middle of the cirle.

The area of the shaded region is:

= Area of circle - Area of rectangle

= ( π x radius ²) - ( Length x Width)

= ( π x 5²) - ( 6 x 8 )

= 30.6 units ²

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The expected count for the cell corresponding to petals whose length is more than 5.7 cm and whose width is more than 2 cm is approximately 7.67.

What is the frequency?

The number of periods or cycles per second is called frequency. The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.

To find the expected count for the cell corresponding to petals whose length is more than 5.7 cm and whose width is more than 2 cm, we need to calculate the expected frequency for that cell using the formula:

Expected frequency = (row total * column total) / grand total

For this particular cell, the row total is 16 (from the table) and the column total is 23.

The grand total is 48 (also from the table). So, we can calculate the expected frequency as:

Expected frequency = (16 * 23) / 48 = 7.67

Rounding this to the nearest hundredth, we get the expected count as 7.67.

Therefore, the expected count for the cell corresponding to petals whose length is more than 5.7 cm and whose width is more than 2 cm is approximately 7.67.

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The solution is A, which is $13.50 as a two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.

The term "amount" designates a sum or number, typically expressed in terms of monetary value or a tangible good. It can also be used to describe the whole amount of anything, such as the total time that is spent on a work or the total amount of rain that falls in a specific location. "Amount" is frequently used synonymously with "amount" or "total."

given

A two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.

Joanna paid $7/2 ($3.50) on Friday thanks to a voucher she utilised to pay half the price.

The normal Saturday bike rental fee should be "x." Then, according to the issue, Joanna paid $4 less than double what renting a bike normally costs during the workweek. As a result, she spent $10 on Saturday (2($7) - $4).

As a result, she spent the following sum overall to rent the bike:

$3.50 + $10 = $13.50

The solution is A, which is $13.50 as a two-day bike rental normally costs $7 each day multiplied by two days for a total of $14.

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The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

A number line is a diagram that depicts numbers on a straight line. It is a tool for comparing and sorting numbers. It can represent any real number, including whole numbers and natural numbers.

Jesse currently has 520 signatures and needs at least 1000 signatures, which means he still needs to collect 1000 - 520 = 480 signatures.

He has 6 more weeks to collect the signatures he needs, so he wants to collect the same number of signatures each week. Let's call this number x, representing the number of signatures he collects each week. Then, the total number of signatures he collects in the remaining 6 weeks would be 6x.

We want to find the range of values for x that would allow Jesse to collect at least 480 signatures in the remaining 6 weeks. In other words, we want to solve the inequality:

6x ≥ 480

Dividing both sides by 6, we get:

x ≥ 80

This means that Jesse needs to collect at least 80 signatures per week in order to have enough signatures to submit the petition.

The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

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Therefore, the equation for which g = 5 is not the solution is 4g = 20.

An equation is a mathematical statement that shows the equality between two expressions or values. It typically consists of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations can be used to solve problems or to describe relationships between quantities. They are commonly written in the form of "expression 1 = expression 2" or "expression 1 - expression 2 = 0", where the goal is to find the value(s) of the variable(s) that make the equation true.

To check for which equation g = 5 is not the solution, we can substitute g = 5 into each equation and see which ones result in a false statement.

[tex]8g = 40[/tex]

Substituting g = 5 gives: 8(5) = 40, which is true. Therefore, g = 5 is a solution to this equation.

4g = 20

Substituting g = 5 gives: 4(5) = 20, which is false. Therefore, g = 5 is not a solution to this equation.

g - 2 = 3

Substituting g = 5 gives: 5 - 2 = 3, which is true. Therefore, g = 5 is not a solution to this equation.

2g = 25

Substituting g = 5 gives: 2(5) = 25, which is false. Therefore, g = 5 is not a solution to this equation.

Therefore, the equation for which g = 5 is not the solution is 4g = 20.

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Answer:

A. February 26th

B. $3,500 - Balance ≈ $6,697.26

C. $2,500 - Balance ≈ $4,263.46

D. $4,284.81

Step-by-step explanation:

a) What is the due date of the loan?

The loan term is given as 317 days, and the loan starts on April 15th. To find the due date, we will add 317 days to April 15th.

April 15th + 317 days = April 15th + (365 days - 48 days) = April 15th + 1 year - 48 days

Subtracting 48 days from April 15th, we get:

Due date = February 26th (of the following year)

b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.

First, we need to calculate the number of days between April 15th and October 12th:

April (15 days) + May (31 days) + June (30 days) + July (31 days) + August (31 days) + September (30 days) + October (12 days) = 180 days

Now, we will calculate the interest for 180 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $10,000 × 0.04 × (180 / 365)

Interest ≈ $197.26

Peter will make a payment of $3,500 on October 12th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $10,000 + $197.26 - $3,500

Balance ≈ $6,697.26

c) Calculate the interest due on January 11th and the balance of the loan after the January 11th payment.

First, we need to calculate the number of days between October 12th and January 11th:

October (19 days) + November (30 days) + December (31 days) + January (11 days) = 91 days

Now, we will calculate the interest for 91 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $6,697.26 × 0.04 × (91 / 365)

Interest ≈ $66.20

Peter will make a payment of $2,500 on January 11th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $6,697.26 + $66.20 - $2,500

Balance ≈ $4,263.46

d) Calculate the final payment (interest + principal) Peter must pay on the due date.

First, we need to calculate the number of days between January 11th and February 26th:

January (20 days) + February (26 days) = 46 days

Now, we will calculate the interest for 46 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $4,263.46 × 0.04 × (46 / 365)

Interest ≈ $21.35

Finally, we will calculate the final payment Peter must pay on the due date:

Final payment = Principal + Interest

Final payment = $4,263.46 + $21.35

Final payment ≈ $4,284.81

The solution to the system of equations is (23, -72).

The first equation is y = -72, which means that whatever the value of x is, the value of y will always be -72.

Substituting y = -72 in the second equation, we get:

7x + 2(-72) = 20

Simplifying this equation, we get:

7x - 144 = 20

Adding 144 to both sides, we get:

7x = 164

Dividing both sides by 7, we get:

x = 23.428571...

So the solution to the system of equations is the ordered pair (x, y) = (23.428571..., -72).

However, we usually express solutions as ordered pairs of integers, so we can round x to the nearest integer to get:

(x, y) = (23, -72)

Therefore, the solution to the system of equations is (23, -72).

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Answer:

-5d + 5.5 < 17

-5d < 11.5

d > -2.3

A is the correct solution.

Answer:pl z give me brainliest the crown next to the stars when two people answer :) have a good day ;)

Step-by-step explanation:

hope this helped

Janelle's intervention to increase vegetable consumption was successful and baseline period as her PND was 90%, indicating a positive outcome.

In a solitary subject review, the level of non-covering information (PND) is an action used to evaluate the viability of a mediation. It is determined by separating the quantity of examples wherein the mediation was compelling by the absolute number of occasions in which the way of behaving was noticed.

For this situation, the intercession was to expand the quantity of chomps of vegetables Janelle consumed at lunch.The PND worth of 90% actually intends that during the mediation stage, Janelle's way of behaving of taking multiple chomps of vegetables was noticed 90% of the time and that the intercession was effective in expanding her vegetable utilization.

This recommends that the intercession was viable for Janelle and can be utilized as proof to help the viability of the mediation for comparative cases. Nonetheless, it is essential to recreate the review with numerous subjects to approve the mediation's viability.

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(1) Area of triangle = 6in²

Area of rectangle of first kind=18in²

Area of rectangle of second kind= 30in²

(2) 90in²

(3) 0 as it is 2-D body

Surface area refers to the total area that covers the surface of a three-dimensional object, including all of its faces, sides, and any other surfaces that are exposed. It is measured in square units, such as square meters or square feet, and is calculated by adding up the areas of each individual surface of the object. The surface area is a fundamental property used to describe the physical characteristics of an object, and it is important in many different fields, including mathematics, physics, and engineering.

Volume is a measure of the amount of space that a substance or object occupies, typically in cubic units such as liters or cubic meters. It is commonly used to describe the size or amount of a liquid, gas, or solid.

(1) Area of triangle = 6in²

Area of rectangle of first kind=18in²

Area of rectangle of second kind= 30in²

(2) The surface area of entire figure =( 6×2+18+2×30)in²

= 90in²

(3) Volume is =0 as it is a 2-D body

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Answer:

x = 10

Step-by-step explanation:

Angle form is = 90°

therefore

5x + 25 + x + 5 = 90

6x + 30 = 90

6x = 90-30

6x = 60

6x/6 = 60/6

x = 10

We can conclude that cosh2x−sinh2x=1.

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

To show that cosh2x−sinh2x=1, we can use the identities for cosh2x and sinh2x. The identity for cosh2x is cosh2x=2cosh2x−1 and the identity for sinh2x is sinh2x=2sinh2x−1.

Substituting these identities into the equation cosh2x−sinh2x=1 yields 2cosh2x−1−2sinh2x−1=1. Simplifying this equation yields cosh2x−sinh2x=1, as required. Thus, we can conclude that cosh2x−sinh2x=1.

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Simplifying this equation yields [tex]\cosh^2x-sinh^2x=1[/tex], as required. Thus, we can conclude that [tex]\cosh^2x-sinh^2x=1[/tex].

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

We will show that [tex]\cosh^2x-sinh^2x=1[/tex].

Let us consider the expression [tex]\cosh^2x-sinh^2x.[/tex]

Then, [tex]\cosh^2x=(e^2x+e^{-2}x)/2[/tex] and [tex]sinh^2x=(e^2x+e^{-2}x)/2[/tex]

Substituting, we get [tex]\cosh^2x -\sinh^2x=(e^2x+e^{-2}x)/2\ -(e^2x+e^{-2}x)/2[/tex]

Simplifying, we have [tex]\cosh^2x -\sinh^2x=e^2x+e^{-2}x-e^2x+e^{-2}x[/tex]

[tex]=2e^{-2}x\\\\=2(e^{-2}x)\\\\=2[/tex]

Hence, [tex]cosh^2x-sinh^2x=1[/tex]

Therefore, we have shown that [tex]cosh^2x-sinh^2x=1[/tex]

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The correct form of question is Show that cosh2x−sinh2x=1 .

If the three babies consume 50 liters of milk in 20 days, then 4 babies will consume 83 liters of milk in 25 days.

We can start by using the given information to calculate the daily milk consumption rate per baby. The total milk consumed over 20 days by the three babies is 50 liters. Therefore, the daily milk consumption rate per baby is:

Daily milk consumption rate per baby = 50 liters / (3 babies x 20 days) = 0.83 liters per day per baby

If we add another baby, the total number of babies becomes 4. We want to find out how much milk they will consume in 25 days. Total milk required for 4 babies in 25 days = (number of babies) x (daily milk consumption rate per baby) x (number of days)

Substituting the given values, we get:

Total milk required = 4 x 0.83 liters per day per baby x 25 days

Total milk required = 83 liters

As a result, if three babies drink 50 liters of milk in 20 days, four babies will drink 83 liters of milk in 25 days.

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