Step by step please

Answer:

Step-by-step explanation:

QR^2=PQ^2+PR^2

QR^2=(8[tex]\sqrt{3}[/tex])^2+(8)^2=8^2*(3+1)=8^2 * (4)

PR=8*2=16

answer is C

Answer:

3.7

Step-by-step explanation:

Hypotenuse is 5

Adjacent is unknown x

Cos 42 = adjacent / hypotenuse

Co's 42 = x/ 5

0.74 = x/5

Multiply both sides by 5

3.7 = x

After solving the inequalities, the values of x are [x<3/4] and [x>-1] respectively.

We can learn about the relative size of values via inequality.

It's not always about "equals" in mathematics; sometimes, all we know is whether something is bigger or less than.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

So, solve for x as follows:

3-4x<0

-4x< -3

x = -3/-4

x < 3/4

Similarly,

2x-4>-2

2x>-2+4

2x>2

x>-2/2

x>-1

Therefore, after solving the inequalities, the values of x are [x<3/4] and [x>-1] respectively.

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Finding the following percentiles for the standard normal distribution

a) P₁(61st percentile)

b) P₂(39th percentile)

c) P₃(75th percentile)

d) P₄(25th percentile)

e) P₅(15th percentile)

First of all, let's find the Z score of these percentiles with the help of the table below:

Z tableimage0.265 / 0.04 = 6.625.

This is greater than the maximum value in the table; hence we can consider it as 6.55.

P₁: When percentile is 61, z value is 0.42.

The formula to calculate percentile is as follows:

Percentile = Area to the left of Z score * 1000.42

= Area to the left of Z score * 1000.42 / 100

= Area to the left of Z score0.1664 (area to the left of Z score) + 0.5 = 0.6664 (area to the left of Z score)

P₁ = 66.64% P₂: When percentile is 39, z value is -0.26.

The formula to calculate percentile is as follows:

Percentile = Area to the left of Z score * 100-0.26

= Area to the left of Z score * 100-0.26 / 100

= Area to the left of Z score0.3950 (area to the left of Z score) + 0.5 = 0.8950 (area to the left of Z score)

P₂ = 89.50% P₃: When percentile is 75, z value is 0.68.

The formula to calculate percentile is as follows:

Percentile = Area to the left of Z score * 1000.68

= Area to the left of Z score * 1000.68 / 100

= Area to the left of Z score0.2486 (area to the left of Z score) + 0.5 = 0.7486 (area to the left of Z score)

P₃ = 74.86% P₄: When percentile is 25, z value is -0.68.

The formula to calculate percentile is as follows:

Percentile = Area to the left of Z score * 100-0.68

= Area to the left of Z score * 100-0.68 / 100

= Area to the left of Z score0.2486 (area to the left of Z score) + 0.5 = 0.7486 (area to the left of Z score)

P₄ = 25.14% P₅: When percentile is 15, z value is -1.04.

The formula to calculate percentile is as follows:

Percentile = Area to the left of Z score * 100-1.04

= Area to the left of Z score * 100-1.04 / 100

= Area to the left of Z score0.1492 (area to the left of Z score) + 0.5 = 0.6492 (area to the left of Z score)

P₅ = 64.92%.

Hence, we have found the percentiles of standard normal distribution for the given questions.

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Standard deviation

a) The distribution of IQ is exactly normal.Trueb) The distribution of the sample mean IQ is approximately normal with mean of 119 and standard deviation of 2.54c) The probability that the sample mean IQ is less than 117 is 0.114d) The probability that the sample mean IQ is greater than 117 is 0.886e) The probability that the sample mean IQ is between 117 and 123 is 0.773Step-by-step explanationa) The distribution of IQ is exactly normalGiven population mean IQ, µ = 119Standard deviation, σ = 18b) The distribution of the sample mean IQ is approximately normal with mean of 119 and standard deviation of 2.54The standard error of the sample is calculated as:SE = σ/√nwhere σ = 18 and n = 50SE = 18/√50SE = 2.54The distribution of the sample means is approximated to normal with the help of central limit theorem. The mean of sample means is μ = 119 and standard deviation of sample means is σ/√n = 2.54.c) The probability that the sample mean IQ is less than 117 is 0.114We need to calculate the z-score using the formula:z = (x-μ)/SEz = (117-119)/2.54z = -0.79Now, using z-table, the probability is calculated as:P(Z < -0.79) = 0.2146The probability that the sample mean IQ is less than 117 is 0.114d) The probability that the sample mean IQ is greater than 117 is 0.886The probability that the sample mean IQ is greater than 117 is equal to one minus the probability of less than 117:P(Z > -0.79) = 1 - 0.2146 = 0.786The probability that the sample mean IQ is greater than 117 is 0.886.e) The probability that the sample mean IQ is between 117 and 123 is 0.773We need to calculate the z-score for 117 and 123 as:z1 = (117-119)/2.54 = -0.79z2 = (123-119)/2.54 = 1.57The probability of sample means between 117 and 123 can be found as:P(-0.79 < Z < 1.57) = 0.773The probability that the sample mean IQ is between 117 and 123 is 0.773.

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On the arranged survey, the statistical margin of error is supposed to be 14.73 SEK.

In a large consumer survey, 610 randomly selected customers are interviewed in a large grocery store. They are asked, among other things, how much they have shopped for. On average, they have shopped for 412 SEK with a standard deviation of 181 SEK .

Estimate with a 95% confidence interval the average purchase amount in the entire population. The formula for finding the margin of error is given as;

Margin of Error = z * (σ/√n)

Where:

σ is the standard deviation

n is the sample size

z is the Z-score for the desired confidence level, which is 95%.

Z-score corresponding to 95% confidence level is 1.96

Margin of Error = 1.96 * (181/√610) = 14.73

The statistical margin of error is 14.73 SEK.

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Answer:

Javier has $5. He sells a video game on an online auction site for $100. He must pay a $16 fee to the auction site. Javier then splits the.   Not sure

Step-by-step explanation:

Hence, in respοnse tο the prοvided questiοn, we can say that  12x - 8 can  functiοn be factοred οut as 4(3x - 2), where 4 is a cοmmοn factοr οf 12 and 8, and (3x - 2) is the expressiοn that remains after factοring οut 4.

Mathematicians research numbers and their variants, equatiοn and related structures, οbjects and their lοcatiοns, and prοspective lοcatiοns fοr these things. The term "mοdule" is used tο describe the cοnnectiοn that exists in between set οf inputs, each οf which has a cοrrespοnding οutput. A functiοn is an input-οutput cοnnectiοn in which each inputs results in sοmething like a single, distinct return. A dοmain, cοdοmain, οr scοpe is assigned tο each functiοn. Functiοns are usually denοted by the letter f. (x). An x is used fοr entry. On capabilities, οne-tο-οne capabilities, multiple prοwess, in capabilities, and οn capabilities are the fοur majοr types οf accessible functiοns.

12x - 8 can be factοred οut as 4(3x - 2), where 4 is a cοmmοn factοr οf 12 and 8, and (3x - 2) is the expressiοn that remains after factοring οut 4.

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Complete question:

We can describe 12x-8 as an expression.

It can also be written as 4(3x-2)

4(3x-2) is a ___ of 12x-8.

What is the blank?

Step-by-step explanation:

To find the minimum height of the satellite during the given time period, we need to find the vertex of the parabolic function f(x) = 2x^2 - 16x + 800.

The vertex of a parabola with equation f(x) = ax^2 + bx + c is given by the formula:

x = -b / 2a and f(x) = -b^2 / 4a + c

In this case, a = 2, b = -16, and c = 800. Substituting these values into the formula, we get:

x = -(-16) / 2(2) = 4

f(x) = -(-16)^2 / 4(2) + 800 = 848

Therefore, the minimum height of the satellite during the given time period is 848 kilometers, and it occurs after 4 hours of flight time.

The original fraction is 5/8. The numerator of the original fraction is then n = √6, and the denominator is (√6 + 6). If we add 3 to both the numerator and denominator, we get (√6 + 3)/(√6 + 9). This fraction simplifies to 5/8.

Let the numerator be 'n'. The denominator is 6 more than the numerator, so the denominator is (n + 6).

We can represent this as an equation:

n/(n + 6) = 1

We can solve for the value of n by multiplying both sides by the denominator, (n + 6):

n*(n + 6) = 1*(n + 6)

Simplifying, we get:

n^2 + 6n = n + 6

Subtracting 6n from both sides gives us:

n^2 = 6

Taking the square root of both sides yields:

n = √6

The numerator of the original fraction is then n = √6, and the denominator is (√6 + 6). If we add 3 to both the numerator and denominator, we get (√6 + 3)/(√6 + 9). This fraction simplifies to 5/8.

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Answer: (-6,-4)

Step-by-step explanation:

Midpoint formula

(x,y) midpoint= ((x1+x2)/2, (y1+y2)/2)

X: (0-12)/2=-6

Y: (0-8)/2=-4

(-6,-4)

Answer:

A

Step-by-step explanation:

lucky for u, finding the midpoint is really easy to learn and master

alright so first you take a look at both points. we got:

-       (0,0)

-       (12,8)

we need to add the x coordinates

0+12 = 12

then divide by 2

12/2 = 6

6 the x coordinate for our segment midpoint

now we need to add the y coordinates

0+8 = 8  

divide by 2

8/2 = 4

4 is the y coordinate for our segment midpoint

How now we combine the x value and y value to create a coordinate:

(6,4)

That matches choice A

The equations that are equivalent to 5 - (6 - 2x) = (3x+4)/2 are  -1 + 2x = (3x+4)/2; and 30 - 10x = (3x+4)/2 .

By simplifying both parts of the equation and comparing the resulting expressions to each other, we can figure out which equations are equivalent to 5 - (6 - 2x) = (3x+4)/2.

5 - (6 - 2x) = (3x+4)/2

5 - 6 + 2x = 3x/2 + 2

2x - 1 = 3x/2 + 2

To get rid of the fraction, multiply both parts by two.

4x - 2 = 3x + 4

Adding 2 to both ends and subtracting 3 times:

x = 6

Let's verify which of the provided equations is equal to x = 6 now.

-1 + 2x = (3x+4)/2, where x = 6 results in:

-1 + 2(6) = (3(6) + 4)/2 \s11 = 11

The initial equation and this one are equivalent, and both are correct.

When we change x to 6, we obtain the following equation: 30 - 10(6) = (3(6) + 4)/2 -30 = -30.

In addition to being correct, this equation is also the original equation's equivalent.

If we substitute 6 for x, we obtain the following equation: 5-(6 - 2(6)) = 3/2(6)+2 1 = 8

This equation is false and does not have the same value as the initial equation.

When we replace x with 6, we obtain the formula 5- (6 - 2(6)) = 3(6)+4

3 = 22

Additionally, this equation is false and is not equal to the initial equation.

2 + 4x = 3x + 4:

When x = 6 is substituted, the result is: -2 + 4(6) = 3(6) + 4 (20) = 22.

This equation is false and does not have the same value as the initial equation.

As a result, the formulae corresponding to 5 - (6 - 2x) = (3x+4)/2 are: -1 + 2x = (3x+4)/2 30 - 10x = (3x+4)/2

A) -1 + 2x = (3x+4)/2; and C) 30 - 10x = (3x+4)/2 are the solutions.

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The purchase cost of a car 24,500 with local sales tax rate 4% has following answer,

Total tax paid = $980

Total cost of a car including tax = $25.480.

Purchasing cost of a car = $24,500

Local sales tax rate on a car = 4%

Tax paid on the car purchase = (Purchase price) × (tax rate)

Substitute the value we get,

⇒ Tax amount = 4% of 24,500

⇒ Tax amount = 0.04 x 24,500

⇒ Tax amount = $980

Total cost of a car including tax = ( Tax amount ) + (Purchase price )

Substitute the value we have,

⇒ Total cost of a car  = Purchase price + Tax amount

⇒ Total cost of a car = 24,500 + 980

⇒ Total cost of a car = $25,480

Therefore, the tax paid on the car purchase and the car's total cost including tax is equal to $980 and $25,480 respectively.

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Round to the nearest whole number A company sold 200 devices in 2007.

Number is a mathematical concept that can be used to represent an amount, value, or quantity. It is an abstract concept that can be used to count, measure, and compare. Numbers can be represented in many different forms such as words or symbols. Numbers are also used in algebra and other mathematical operations, as well as in everyday life.

The company sold 180 devices in 2008. The number of devices that the compnay sales is decreasing exponentially. If this trend continues, How many devices will the company sell in 2012?
Round to the nearest whole number. Based on the trend of the company's sales, it is estimated that the company will sell approximately 140 devices in 2012. This is a decrease of 40 devices from the sales in 2008. This trend is expected to continue into future years due to the exponential decrease in the number of devices sold.

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Rounding to the nearest whole number, the company will sell 75 devices in 2012.

Number is a mathematical concept that can be used to represent an amount, value, or quantity. It is an abstract concept that can be used to count, measure, and compare. Numbers can be represented in many different forms such as words or symbols. Numbers are also used in algebra and other mathematical operations, as well as in everyday life.

To calculate the number of devices that the company will sell in 2012 using an exponential model, we can use the following equation:

y = 200e(-0.08x)

where y is the number of devices sold, 200 is the number of devices sold in 2007, and 0.08 is the rate of decay per year.

Plugging in x=5 (for 2012), we get:

y = 200e(-0.08×5) = 200e(-0.4) = 74.7

Rounding to the nearest whole number, the company will sell 75 devices in 2012.

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The converted height of Pat’s pen pal in feet and inches when it is 1.27 meters tall is given by 4  feet 2 inches.

Height of Pat’s pen pal  = 1.27 meters

Convert the height from meters to centimeters,

1 meter = 100 centimeters

Multiply by 100 to convert meters to centimeters we get,

1.27 meters

= 1.27 x 100

= 127 centimeters

Convert the height from centimeters to inches

1 inch = 2.54 centimeters

Divide by 2.54 to convert centimeters to inches we get,

127 centimeters

= 127 centimeters ÷ 2.54

= 50 inches

Convert the total number of inches to feet and inches,

1 feet = 12 inches

Divide by 12 to convert inches to feet and inches we have,

50 inches

= 50 ÷ 12

= with 4 quotient and 2 remainder

= 4  feet 2 inches tall

Therefore, Pat's pen pal is 4 feet and 2 inches tall.

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The conclusion of question as discuss below.

The mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the values in the set and then dividing by the total number of values.

Based on the given information, we can say that there is a 95% chance that the true difference (a - b) in the mean weight of the bean burritos between Restaurant A and Restaurant B falls within the interval 0.06 ounce to 0.20 ounce.

Since the confidence interval does not include zero, we can conclude that there is a statistically significant difference between the mean weights of the bean burritos at the two restaurants. Specifically, we can say that the mean weight of the bean burritos at Restaurant A is likely to be heavier than the mean weight of the bean burritos at Restaurant B.

However, it's important to note that we cannot determine the magnitude of the difference or the direction of causation (i.e., whether Restaurant A intentionally makes their burritos heavier or whether they use different ingredients that naturally result in heavier burritos).

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We can infer that there is a statistically significant difference among the mean weights of the bean burritos at the two eateries because the confidence interval does not include zero.

The mean, which reflects the average value of a group of numbers, is a metric of central tendency. It can be calculated by adding up all of the values in the collection, dividing by the total number of values, and then taking the remainder away.

Based on the information provided, we can state that there is a 95% chance that the actual difference (a - b) between Restaurant A and

Restaurant B's mean weight of the bean burritos will lie between 0.06 ounce and 0.20 ounce.

We can infer that there is a statistically significant variance among the mean weights of the bean burritos at the two eateries because the confidence interval does not include zero. We can specifically state that the bean burritos' average weight at Restaurant A is probably heavier than the average bean burrito's weight at Restaurant B.

It's crucial to remember that we cannot establish the size of the difference or the causal relationship. (i.e., whether Restaurant A intentionally makes their burritos heavier or whether they use different ingredients that naturally result in heavier burritos).

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Answer:A. y = 0.6^x - 2

Step-by-step explanation:

This was something I put in and It worked fine. Hope this helps. If you want more help, check out Khan Academy.

From the graph, the equation that's is represented is A. 0.6x - 2.

From the equation, on the coordinate plane, the curve opens up and to the right. It crosses the x-axis at (negative 1.5, 0) and then crosses the y-axis at (0, negative 1).

Here, based on the family the graph below belongs to, the equation represented is the first equation which is 0.6x - 2.

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Answer:

Approximately 81.159

Step-by-step explanation:

First, set up the equation

56    =   (0.69)(x)

       ^ is 69% of a number

Divide each side by 0.69 to simplify

56 / 0.69 = x

x ≈ 81.159420...

1 hot dog costs amount $8.00 and 1 hamburger costs $10.80.

Steve needs to buy meat for a barbecue and he bought 15 hot dogs and 13 hamburgers for amount $192. He realized that he didn't buy enough so he bought 75 hot dogs and 45 hamburgers for $780. To calculate the cost of 1 hot dog or 1 hamburger, we need to divide the total cost of each item by the amount purchased. For the hot dogs, we divide $780 by 75, which gives us $8.00. For the hamburgers, we divide $780 by 45, which gives us $10.80. Therefore, the cost of 1 hot dog or 1 hamburger is $8.00 and $10.80 respectively.

Hot Dogs :  ($192 + $780) / (15 + 75) = $8.00

Hamburgers : ($192 + $780) / (13 + 45) = $10.80

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The tοtal area οf the shape cοmprising the rectangle and semicircle is apprοximately 2153.43 square feet.

Area is a measure οf the size οf a twο-dimensiοnal regiοn οr surface, typically expressed in square units such as square meters οr square feet. It is calculated by multiplying the length and width οf a shape, οr by using specific fοrmulas fοr different shapes.

The area οf a rectangle with sides 30' and 60' is given by multiplying the length and width, sο:

Area οf rectangle = length × width

Area οf rectangle = 30' × 60'

Area οf rectangle = 1800 square feet

The area οf a semicircle with radius 15' can be fοund by first calculating the area οf a full circle with radius 15' and then dividing by 2, since a semicircle is half οf a circle. The fοrmula fοr the area οf a circle is:

Area οf circle = π × radius²

Substituting the value οf the radius intο the fοrmula, we get:

Area οf circle = π × 15²

Area οf circle = π × 225

Area οf circle ≈ 706.86 square feet

Therefοre, the area οf the semicircle is apprοximately:

Area οf semicircle = (1/2) × Area οf circle

Area οf semicircle ≈ (1/2) × 706.86

Area οf semicircle ≈ 353.43 square feet

The tοtal area οf the shape cοmprising the rectangle and semicircle is the sum οf the areas οf the twο shapes, sο:

Tοtal area = Area οf rectangle + Area οf semicircle

Tοtal area = 1800 + 353.43

Tοtal area ≈ 2153.43 square feet

Therefοre, the tοtal area οf the shape cοmprising the rectangle and semicircle is apprοximately 2153.43 square feet.

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Based on the pattern or sequence, it can be concluded that the missing letter is K.

To understand the principle or fule the sequence follows, let's analyze the letters given:

A - C - E

These letters show the sequence follows the alphabet order but one of the letters is omitted. In the first case, the letter omitted is B and in the second case, the letter omitted is E. Based on this, the missing letter should be K.

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The probability that a student is a science major, given they are a graduate student is given as follows:

P(science|graduate) = 0.7203 = 72.03%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the probability that a student is a science major, given they are a graduate student is obtained as follows:

P(science|graduate) = 188/261

P(science|graduate) = 0.7203 = 72.03%.

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Answer:

0.72

Step-by-step explanation:

Alex feeds his cat 1/21 of the bag each day.

The fraction of the bag that Alex feeds his cat each day is 1/21. This can be calculated using the following formula:

Fraction of Bag = 1/3 / 7

Using algebra, we can solve this equation by multiplying both sides of the equation by 7, which results in the following equation:

1/3 = (1/21) * 7

Simplifying the equation, we get

1/3 = 1/21

Therefore, the fraction of the bag that Alex feeds his cat each day is 1/21.

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The equation that is true when x is equal to 3 is (x/3) = 1. By substituting the given x value and simplifying the equation we can solve.

Division is a mathematical operation that is used to split a quantity or value into equal parts or groups. It is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication.

The equation that is true when x = 3 is:

x/3 = 1

Substituting x = 3, we get:

3/3 = 1

Which is true, since 3 divided by 3 is equal to 1.

The other equations:

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6 teaspοοns οf baking sοda are needed fοr 9 cups οf sugar in Trisha's recipe.

We can set up a prοpοrtiοn using the given ratiο οf sugar tο baking sοda:

3 cups sugar : 2 teaspοοns baking sοda

We want tο find hοw many teaspοοns οf baking sοda are needed fοr 9 cups οf sugar, which we can represent as:

9 cups sugar : x teaspοοns baking sοda

Tο set up a prοpοrtiοn, we can crοss-multiply the ratiοs:

3 cups sugar * x teaspοοns baking sοda = 9 cups sugar * 2 teaspοοns baking sοda

Simplifying, we get:

3x = 18

Dividing bοth sides by 3, we get:

x = 6

Therefοre, 6 teaspοοns οf baking sοda are needed fοr 9 cups οf sugar in Trisha's recipe.

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The first four terms of the infinite geometric series are 11/2, 11/6, 11/18, and 11/54.

We can use the formula for the sum of an infinite geometric series to find the value of the first term:

S = a / (1 - r)

Where S is the sum of the infinite geometric series, a is the first term, and r is the common ratio.

Given that:

S=33/4

r=1/3

Substituting the given values:

33/4 = a / (1 - 1/3)

33/4 = a / (2/3)

a = (33/4) × (2/3) = 11/2

Now that we know the first term, we can use the formula for the nth term of a geometric series to find the first four terms:

an = a × r^(n-1)

Where an is the nth term, a is the first term, r is the common ratio, and n is the number of the term we want to find.

So the first four terms are:

a1 = 11/2

a2 = 11/2 × 1/3 = 11/6

a3 = 11/6 × 1/3 = 11/18

a4 = 11/18 × 1/3 = 11/54

Therefore, the first four terms are 11/2, 11/6, 11/18, and 11/54.

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The area of a rhombus is 15 units².

A rhombus is a quadrilateral with four sides that are all the same length. It is sometimes referred to as a lozenge or a diamond. A rhombus has equal opposite angles, and its diagonals form a right angle cut across one another.

Rhombus area can be express using the formula:

Area = (base x height) / 2

where the base and height refer to any two sides of the rhombus that form a right angle.

Given figure: base = 5 units and height = 6 units

Area of a rhombus = (5 × 6) / 2 = 30/2

Area of a rhombus = 15 units²

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The required length of the arc is 5.75 units.

A circular represents 360 degrees. A circular can be split up into smaller sections. An arc is a segment of a circle, and arcs are designated based on their angles. The three types of arcs are semicircles (v = 180°), major arcs (180° v 360°), and minor arcs (0° v 180°).

We have;

∠EFG =30° = π/6

and EF =11 units

To find; length of arc EG.

So, we know that;

∅(Radian) = arc/ radius

π/6 = arc/11

arc = 11π/6

Arc = 5.75 units.

Thus, required length of the arc is 5.75 units.

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Complete question: