The triangle below is isosceles. Find the length of side
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x in simplest radical form with a rational denominator.

The measure of the larger acute angle of the right triangle is 73.7°. This can be calculated using trigonometry and the Pythagorean theorem.

The larger acute angle of the triangle can be found using trigonometry. First, we can find the length of the other leg using the Pythagorean theorem: a² + b² = c², where c is the hypotenuse and a and b are the legs. Plugging in the values we get: 4² + b² = 12², solving for b we get b = √(12² - 4²) = 8√3. Now we can use inverse tangent to find the larger acute angle: tan⁻¹(opposite/adjacent) = tan¹⁽⁸√³/⁴⁾ ≈ 73.7°. So, the measure of the larger acute angle is 73.7°.

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The events that are independent are,

1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.

2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.

3) Olivia choosing an ace and the dart hitting the bull's-eye

1) Henry rolling a multiple of 2 and landing on a red portion of the spinner.

2) Two pairs of socks being randomly chosen from a drawer, Hayden choosing a black pair of socks, putting them on, and then choosing another black pair.

3) Olivia choosing an ace and the dart hitting the bull's-eye.

The other events are dependent because the outcome of the first event affects the outcome of the second event. Specifically

1) Sarah picking a number less than 5 and then picking an odd number. The second event depends on the outcome of the first event.

2) A number cube being rolled and a spinner being spun. The two events are independent of each other, but the outcomes of each event are not independent.

3) Two cards being randomly chosen from a standard deck, and Eliza choosing a jack, replacing it, and then choosing a black card. The outcome of the second event depends on the outcome of the first event, and the outcome of the first event affects the composition of the deck for the second event.

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The given question is incomplete, the complete question is:

Which events are independent? Check all that apply. Each number 1 through 10 is written on a slip of paper, placed in a hat, and randomly picked. Sarah picks a number less than 5, keeps it, and then picks an odd number. A number cube is rolled and a spinner is spun. Henry rolls a multiple of 2 and lands on a red portion of the spinner. Two cards are randomly chosen from a standard deck. Eliza chooses a jack, replaces it, and then chooses a black card. Two pairs of socks are randomly chosen from a drawer. Hayden chooses a black pair of socks, puts them on, and then chooses another black pair. A card is randomly chosen from a standard deck and a dart is randomly thrown. Olivia chooses an ace and the dart hits the bull’s-eye.

Answer:49 = 7×7; 64 = 8×8; Difference Square is the answer. where a =7u; b = 8v. Hope that you carry out the rest Bianca,.. Jung Tran

Step-by-step explanation:

Answer:

7/20

Step-by-step explanation:

ok so it has 30 members, 7 are seniors it's possible. if there is multiple choice just let me know if it is not on there.

Answer:

the slope of these points is 8/3

the area of a square is always the square of its side length, and if the area cannot be expressed as the square of an integer, then we can say that it is not the power of 2.

A square is a quadrilateral that has four equal sides and four right angles. The area of a square is the product of its length and width, which are equal in the case of a square. So, the formula for the area of a square is:

Area = side × side

or

Area = side²

In other words, the area of a square is the square of its side length.

Now, when we say that the area of a square is "not the power of 2," it means that the area cannot be expressed as a perfect square of an integer. For example, if the area of a square is 25, then it is the square of 5, which is an integer, and so the area is the power of 2.

However, if the area of a square is, say, 12, then it cannot be expressed as the square of an integer, since the square of any integer is always a whole number. Therefore, we can say that the area of the given square is not the power of 2.

In summary, the area of a square is always the square of its side length, and if the area cannot be expressed as the square of an integer, then we can say that it is not the power of 2.

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We know that the temperature was 56°F at midnight, so we can plot the point (24, 56)

What is graph ?

Graph can be defined as visual representation of given data using the ordered pairs.

To graph Elroy's data, we can use the x-axis to represent the time of day in hours and the y-axis to represent the temperature in degrees Fahrenheit.

First, we can plot the point (6, 50) to represent the temperature at 6am.

Next, we can use the information that the temperature rose 3° per hour for the next 4 hours. This means that at 10am, the temperature would be 50 + 3(4) = 62°F. We can plot this point at (10, 62). Similarly, we can find the temperature at 7am, 8am, and 9am using the same formula and plot those points as well.

Then, we can use the information that the temperature rose 2° per hour for the next 6 hours. This means that at 4pm, the temperature would be 62 + 2(6) = 74°F. We can plot this point at (16, 74). Similarly, we can find the temperature at 11am, 12pm, 1pm, 2pm, and 3pm using the same formula and plot those points as well.

The temperature then stayed steady until 6pm, so we can draw a horizontal line at y = 74 from 4pm to 6pm.

For the next 2 hours, the temperature dropped 1° per hour. This means that at 8pm, the temperature would be 74 - 2 = 72°F. We can plot this point at (20, 72). Similarly, we can find the temperature at 7pm using the same formula and plot that point as well.

Therefore,  we know that the temperature was 56°F at midnight, so we can plot the point (24, 56).

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The constant of proportionality is equal to 12.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

In order to have a proportional relationship and equivalent ratios, the variables representing the earnings and time must have the same constant of proportionality:

Constant of proportionality, k = y/x

Constant of proportionality, k = 36/3 = 60/5 = 72/6 = 84/7

Constant of proportionality, k = 12.

Therefore, the required equation is given by:

y = kx

y = 12x

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After answering the prοvided questiοn, we can cοnclude that As a result, expressiοn the pizza place is abοut a mile away frοm the schοοl.

In mathematics, an expressiοn is a grοup οf representatiοns, digits, and cοnglοmerates that resemble a statistical cοrrelatiοn οr regimen. An expressiοn can be a real number, a mutable, οr a cοmbinatiοn οf the twο. Additiοn, subtractiοn, rapid spread, divisiοn, and expοnentiatiοn are examples οf mathematical οperatοrs.

Arithmetic, mathematics, and shape all make extensive use οf expressiοns. They are used in mathematical fοrmula representatiοn, equatiοn sοlutiοn, and mathematical relatiοnship simplificatiοn.  

If the pizza place is 7 miles frοm yοur friend's hοuse and her hοuse is 8 miles frοm schοοl, the distance between the twο can be calculated as fοllοws:

distance frοm pizza shοp tο schοοl = distance frοm friend's hοuse tο schοοl - distance frοm friend's hοuse tο pizza shοp

8 miles minus 7 miles = distance frοm pizza place tο schοοl

1 mile frοm the pizza place tο the schοοl

As a result, the pizza place is abοut a mile away frοm the schοοl.

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Answer:

Step-by-step explanation:

You didnt attatch anything

The ordered pair is the best approximation of the exact solution is (0.6, 1.9). The correct option is c.

A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

y = -2x + 3

y = 5x - 1

Equate the right sides of both equations:

-2x + 3 = 5x - 1,

-2x - 5x = -1 -3,

x = 4/7

then

y = -2 x 4/7 + 3 = 8/7 + 3 = 3x7-8 /7 = 13/7 = 1 x 5/7

4/7 = 0.6 and 1 x 5/7 is equal to the ordered pair (0.6, 1.9).

Therefore, the correct option is c, (0.6, 1.9).

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The question is incomplete. The full question is given below:

Which ordered pair is the best approximation of the exact solution?

The amount of the mark up is $66 and the selling price is $286.

The amount by which a product's cost is raised to determine its selling price is known as the markup percentage. Usually, it is represented as a percentage of the item's price. Markup percentage is determined by the following equation:

Markup percentage = (Selling price - Cost price) / Cost price x 100%

Given that, the mark up is 30%.

Thus,

Mark up = 0.3 x $220 = $66

The selling price is:

Selling price = $220 + $66 = $286

Hence, the amount of the mark up is $66 and the selling price is $286.

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Dividing the circumference of a pumpkin by its diameter gives a value approximately equal to pi (π)

When you divide the circumference of a pumpkin by its diameter, you get a value that is approximately equal to the mathematical constant pi (π), which is approximately 3.14159.

This is because pi represents the ratio of the circumference of a circle to its diameter, and a pumpkin is roughly spherical in shape. So, no matter how big or small the pumpkin is, if you measure its circumference and diameter and divide them, the result will be very close to pi.

Mathematically, this can be represented by the formula

pi ≈ circumference / diameter

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In approximately 11.41% of years, the rainfall will be between 50 and 70 centimeters in that town.

To solve this problem, we need to find the percentage of years where the rainfall is between 50 and 70 centimeters. We can do this by standardizing the rainfall values and using a standard normal distribution table.

First, we need to standardize the rainfall values of 50 and 70 centimeters using the formula

z = (x - μ) / σ

where

z is the standardized value

x is the rainfall value

μ is the mean

σ is the standard deviation

For x = 50

z = (50 - 95) / 28

z = -1.607

For x = 70

z = (70 - 95) / 28

z = -0.893

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two standardized values. This represents the percentage of years where the rainfall is between 50 and 70 centimeters.

Using a standard normal distribution table, we can find that the area under the curve between z = -1.607 and z = -0.893 is 0.1141. This means that approximately 11.41% of years will have rainfall between 50 and 70 centimeters in this town.

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The measure of the angle x of the polygon is 100 degrees if the polygon has 5 sides. The interior angle measures are 117°, 104°, 113°, 106°.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight line segments are joined and to end to form a closed shape. The vertices also known as corners, are the points where two lines segments meet and form an angle.

We know that the sum of the interior angles in a polygon is given by:-

180(n-2) here, n is 5.

therefore, 180(5-2) = 540° .

117°+104°+106°+x= 540°.

440°+x= 540°

x= 540°-440°

x= 100° .

Thus, the measure of the angle x is 100° .

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In the following question, Yes, the confidence interval suggests that the difference observed in this sample will also generalize to the larger population.

What is a confidence interval? A confidence interval is a probability statement that provides an interval of plausible values that are likely to contain the value of a population parameter. It is a way to infer the population parameter value from sample data.

A confidence interval is calculated as a range of values that are predicted to include the unknown population parameter, based on the sample statistic. The confidence interval suggests that the difference, if any, observed in this sample will also generalize to the larger population.

A confidence interval with a high level of confidence (e.g. 95%) would have a wider range of values and a higher probability of including the population parameter. The interpretation of the confidence interval is that we are 95% confident that the actual population parameter falls within the calculated interval. Therefore, it implies that the sample data is likely to be representative of the population data.

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If 7 cards are dealt from an ordinary deck of 52 playing cards, the probability that (a) exactly 2 of them will be face cards is 0.3601. and  (b) at least 1 of them will be a queen is 0.0008.

A) The probability that exactly 2 of the 7 cards dealt from an ordinary deck of 52 playing cards will be face cards is as follows:

      We need to use the formula for probability here. The probability formula is given by,

       Probability = Number of favorable outcomes/ Total number of possible outcomes.

The total number of possible outcomes = Number of ways 7 cards can be selected from 52 =  ₅₂C₇

A number of favorable outcomes = Number of ways 2 face cards can be selected from 12 face cards * Number of ways 5 nonface cards can be selected from 40 non-face cards

                                                      = ₁₂C₂ * ₄₀C₅

      Putting these values in the formula,

      Probability =  ₁₂C₂ * ₄₀C₅ / ₅₂C₇.

      Simplifying this gives Probability = 0.3601. (Rounded to four decimal places)

b) The probability that at least 1 of the 7 cards dealt from an ordinary deck of 52 playing cards will be a queen is as follows:

         Here, we can use the complement rule. i.e. we can calculate the probability of none of the 7 cards being a queen and subtract that from

  1. Total number of possible outcomes = Number of ways 7 cards can be selected from

                                                           52  =  ₅₂C₇

Number of favorable outcomes = Number of ways 7 non-queen cards can be selected from 48 non-queen cards = ₄₈C₇

Putting these values in the formula,

      The Probability of none of the cards being a queen = ₄₈C₇ / ₅₂C₇

Therefore, the Probability of at least 1 of the 7 cards being a queen

                     = 1 - ₄₈C₇ / ₅₂C₇ Probability of at least 1 queen

                     = 1 - 0.9992

                     = 0.0008 (rounded to four decimal places).

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4% of a number is therefore 10, or 10 by Divide both sides of the equation by 0.16 and to determine the fourth percent of the number.

Typically, an equation consists of one or more variables, which might have varying values and are typically represented by letters. Equations are frequently used to explain relationships between distinct values or to address issues in a variety of fields. An example of an equation with one variable is x + 2 = 5. It denotes that x plus 2 add up to 5 in total.

given

With the provided data, we can first determine the complete number:

If 40 is 16% of a number, then the following equation may be written:

0.16x = 40

where x is the complete number that we are looking for.

Divide both sides of the equation by 0.16 to find the value of x:

x = 40/0.16

x = 250

Hence, the total is 250.

We can now utilise this knowledge to determine the fourth percent of the number:

4% of 250 is:

0.04 × 250 = 10

4% of a number is therefore 10, or 10 by Divide both sides of the equation by 0.16 and to determine the fourth percent of the number.

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13.33 hrs long would it take juan to do the same job alone.

Here, we have,

given that,

carlos and juan take 5 hours to do a job.

carlos alone takes 8 hours to do the same job.

let, x hr long would it take juan to do the same job alone.

now, we have,

1 hr work of carlos = 1/8

1 hr work of juan = 1/x

1 hr work of both = 1/8 + 1/x = (x+8)/8x

we have,

So they together can do this job in = 5 hours

so, ATQ, we get,

(x+8)/8x = 1/5

or, (5x+40) = 8x

or, 3x = 40

or. x = 13.33

Hence, 13.33 hrs long would it take juan to do the same job alone.

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We can claim that after answering the above question, the Therefore, the solution to the original equation is: [tex]q = 9^x\\[/tex]

In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" states that the sentence "2x Plus 3" equals the value "9". The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.

given equation:

[tex]1/4xln(16q^8) - ln3 = ln24\\1/4xln(16q^8) = ln(24 * 3)\\1/4xln(16q^8) = ln72\\ln(16q^8)^(1/4x) = ln72\\16q^8^(1/4x) = 72\\16q^8 = 72^(4x)\\ln(16q^8) = ln(72^(4x))\\[/tex]

[tex]ln(16) + ln(q^8) = 4x ln(72)\\ln(q^8) = 4x ln(72) - ln(16)\\ln(q^8) = ln(72^(4x)) - ln(16^1)\\ln(q^8) = ln((72^(4x))/16)\\q^8 = e^(ln((72^(4x))/16))\\q^8 = (72^(4x))/16\\q^8 = 9^(8x)\\q = 9^x\\[/tex]

Therefore, the solution to the original equation is:

[tex]q = 9^x\\[/tex]

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Answer:

6.

[tex]2x - 1 = x + 3[/tex]

[tex]x = 4[/tex]

[tex] y = 4 + 3 = 7[/tex]

So the solution is (4, 7).

7. Substituting 4x into the second equation:

[tex]4x + x = 5[/tex]

[tex]5x = 5[/tex]

[tex]x = 1[/tex]

[tex]y = 4(1) = 4[/tex]

So the solution is (1, 4).

The two numbers that multiply to give 24 and add to give -11 are -3 and -8.

To find these numbers, you can use a system of equations. Let x and y be the two numbers. Then we have:

We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for x:

x + y = -11

x = -11 - y

We can then substitute this expression for x into the first equation:

xy = 24

(-11 - y)y = 24

Expanding and rearranging, we get:

y^2 + 11y + 24 = 0

This is a quadratic equation that we can solve using factoring or the quadratic formula. Factoring, we get:

(y + 3)(y + 8) = 0

So either y + 3 = 0 or y + 8 = 0. This means that y can be -3 or -8. Substituting each of these values into x = -11 - y, we get:

If y is -3, then x is -11 - (-3) = -8

If y is -8, then x is -11 - (-8) = -3.

Translated question "Numbers that multiply to give me 24 and add to give me -11"

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Answer:

The first step is to calculate the interest that accrues over the 3-month period:

Interest = Principal x Rate x Time

= $4,000 x 0.075 x (3/12)

= $75

The amount due on the loan is the sum of the principal and interest:

Amount due = Principal + Interest

= $4,000 + $75

= $4,075

Rounding to the nearest cent gives: $4,075.00

Answer: I'm pretty bad at math, but I made it more simple for you :)

Step-by-step explanation:

The answer is y = 4 + 5x/4

I hope it helped a bit sorryy

a) Mean time between counts is 0.3333 minutes.

b) Standard deviation of time between counts is 0.5774 minutes.

a. Mean time between counts: The mean time between counts can be computed as the inverse of the Poisson rate parameter (λ): Mean time between counts = 1/λ.

The average of 3 counts per minute is the same as the rate parameter λ in a Poisson process. Thus, the mean time between counts is: Mean time between counts = 1/λ = 1/3 = 0.3333 minutes (20 seconds approximately).

b. Standard deviation of the time between counts: The standard deviation of a Poisson process is equal to the square root of the mean.

Therefore, the standard deviation of the time between counts can be calculated as follows: Standard deviation of time between counts = sqrt(mean) = sqrt(1/λ) = sqrt(1/3) = 0.5774 minutes (approximately 35 seconds).

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Answer:

Let the maximum number of operations the computer can perform per second be x.

According to the problem, the computer is running at 65% of the maximum, so it is performing 0.65x operations per second. We also know that it is performing 30 operations per second. So we can write the equation:

0.65x = 30

Solving for x, we get:

x = 30/0.65

x ≈ 46.1538

Rounding to the nearest whole number, we get:

x ≈ 46

Therefore, the maximum number of operations the computer can perform per second is 46, which is option 2.

Answer:

2072

Step-by-step explanation:

Multiply 14 x 37

518 x 4

2072

Answer: $2,072 a month

Step-by-step explanation:

multiply 14 by 37 to see her weekly rate which is $518 a week. then multiply  518 by 4 (because there are about 4 weeks in a month). then you get the answer of $2,072