Solve for x.

7-3x/2 = 8

x = [?]

Because of the SSS postulate for proving triangles congruent, you can say that triangles DEG and FEG are congruent. Corresponding parts of congruent triangles are congruent (CPCTC) means that angles DEG and FEG are congruent, which means their measures are equal. So 3y + 4 = 5y - 10.

4 = 2y - 10

14 = 2y

7 = y

The measure of angle DEF is 50 degrees

Answer:

Height = 16

Step-by-step explanation:

Area = (Base * Height) / 2

Height = (2 * Area) / Base

Height = (2 * 10) / (5/4)

Height = (2 * 10) / (5/4) * (4/4)

Height = (2 * 10 * 4) / 5

Height = (80 / 5)

Height = 16

The weight of the other children are 37.5 kg and 31.25 kg

The weight of the three children are 6:5:4

6x, 5x and 4x

The weight of the smallest child is 4x

4x= 25

x= 6.25

The weight of the other two children can be calculated as follows

6(6.25)

= 37.5

5(6.25)

= 31.25

Hence the weight of the other two children are 37.5 kg and 31.25 kg

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Answer:

[tex]x=\pm\,9i[/tex]

Step-by-step explanation:

[tex]x^2=-81\\x=\pm\,9i[/tex]

Answer: 1/4

Step-by-step explanation:

To find the product of two fractions, you simply multiply the numerators together and multiply the denominators together. That is:

(5/8) x (6/15) = (5 x 6) / (8 x 15)

Simplifying the numerator and denominator by dividing both by their greatest common factor, which is 2, we get:

(5 x 6) / (8 x 15) = 30 / 120

Further simplifying the fraction by dividing both the numerator and denominator by their greatest common factor, which is 30, we get:

30 / 120 = 1 / 4

Therefore, the product of 5/8 and 6/15 is 1/4.

Answer:

To multiply two fractions, you simply multiply their numerators (top numbers) and denominators (bottom numbers), respectively.

So, 5/8 x 6/15 = (5 x 6) / (8 x 15) = 30 / 120

To reduce this fraction to its simplest form, we can divide both the numerator and denominator by their greatest common factor, which is 30.

30 / 120 = (30 ÷ 30) / (120 ÷ 30) = 1/4

Therefore, the product of 5/8 x 6/15 is 1/4

Answer:

60 square inches

Step-by-step explanation:

Measure of length in scale drawing = Measure of actual length

                                             6 inches = 24 feet

                                               ∴ 1 inch = [tex]\frac{24}{6}[/tex] feet

∴Unit multiplier applied:

                  ∴1 inch in scale drawing = 4 feet of actual measurement

         
Measure of width in scale drawing = Measure of actual width

                                             x inches = 40 feet

                                           ∴ x inches = (40 feet) × ([tex]\frac{1 inch}{4 feet}[/tex])

Measure of width in scale drawing   = 10 inches

Area of rectangular floor in the scale drawing = (Length) × (Width)

                                                                                = (6 inches) × (10 inches)

                                                                                = 60 square inches                                          

Answer: To find the critical value for a 80.4% confidence interval for a normal approximation of a binomial distribution, we need to find the z-score that corresponds to the 80.4% confidence level. We can do this using a standard normal table or using a z-score calculator.

Using a z-score calculator, we can find that the z-score corresponding to 80.4% confidence level is approximately 0.931. This means that 80.4% of the data falls within 0.931 standard deviations of the mean.

So, the critical value that corresponds to a confidence level of 80.4% is approximately 0.931.

Step-by-step explanation:

The estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is 0.45 which is denoted as option C.

This is referred to as a number that indicates how likely the event is to occur.

Probability for drawing at least 5 beads before she picks a grey bead from her collection

= 1-Probability for drawing at least one grey bead in the first 5 draws.

No of grey beads drawn in first 5 trials = (5, 80/80+160+240)

                                                                 = (5, 1/6)

Probability for drawing at least one grey bead in the first 5 draws.

=1 - Prob of no grey

Required probability = P(X=0 in first 5 draws) = (1/6)⁵ = 0.4018 and th nearest value is therefore 0.45.

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The possible number of equal sized group is given by set N = 5 groups

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the total number of pencils be represented as n = 5 dozen = 60 pencils

The number of equal groups should be at least 3 and less than 11

So , the groups are represented by sets A , B , C , D , E

where the value of set A is

Set A = { 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 , 6 }

The set A contains 6 pencils of 10 groups

Set B = { 10 , 10 , 10 , 10 , 10 , 10 }

The set B contains 10 pencils of 6 groups

Set C = { 12 , 12 , 12 , 12 , 12 }

The set C contains 12 pencils of 5 groups

Set D = { 15 , 15 , 15 , 15 }

The set D contains 15 pencils of 4 groups

Set E = { 20 , 20 , 20 }

The set E contains 20 pencils of 3 groups

Therefore , the total number of sets N = 5 sets

Hence , the sets are solved

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A congruent triangles worksheet is a type of educational resource that provides practice problems and exercises for students to work on to help them understand and apply the concept of congruent triangles.

The worksheet typically includes a variety of problems, such as identifying pairs of congruent triangles, determining congruent sides and angles, and applying congruence postulates or theorems to solve problems. The problems may involve using the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), or hypotenuse-leg (HL) congruence criteria.

Congruent triangles are triangles that have the same size and shape. In other words, they are identical in every way except for their position and orientation in space. Understanding congruent triangles is important in geometry, as it can help students to solve problems involving triangles, as well as more complex geometric figures.

Worksheets are a useful tool for students to practice and reinforce their understanding of congruent triangles, and can be used in the classroom or as homework assignments.

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Total No. of cards in a deck = 52

Total no. of suits = 4

Total number of cards in one suit = [tex]\frac{52}{4} \\[/tex] = 13

Ways of selecting combinations of 4 from 13 hearts (combination) = [tex]\frac{13!}{9! 4!}[/tex]

= 715

Ways of selecting combinations of 3 from 13 spades (combination) = [tex]\frac{13!}{10! 3!}[/tex]

= 286

Combining the two independent choices, there are  715×286=204490

ways to select a seven-card hand with 4 hearts and 3 spades.

Ways of selecting 7 cards from 52 cards = [tex]\frac{52!}{7! 45!}[/tex] = 133784560

Probability of getting 4 hearts and 3 spades on drwaing 7 cards from the deck = [tex]\frac{204490}{133784560}[/tex] = 0.0015285 (approx.)

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The work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium is 34,300 J.

First we need to calculate the total amount of water that needs to be lifted and the height it needs to be lifted to.

The volume of water in the aquarium is given by:

V = 7 m * 1 m * 1 m = 7 m^3

Since we need to pump out the top half of the water, the volume of water that needs to be lifted is:

V = (1/2) * 7 m^3 = 3.5 m^3

The mass of the water can be calculated as:

m = V * density of water = 3.5 m^3 * 1000 kg/m^3 = 3500 kg

The height that the water needs to be lifted to is equal to the height of the aquarium, which is 1 m.

The work needed to lift the water can be calculated using the formula:

W = m * g * h

where

So, the work needed is:

W = 3500 kg * 9.8 m/s^2 * 1 m = 34,300 J (joules)

Therefore, the work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium is 34,300 J.

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The line plot which can be used to represent the teachers record of how many miles each student ran during gym class is attached.

A Line plot can be defined as a graphical representation of data as points or check marks above a number line, showing the frequency of each value along a line. It is used to analyze data

Given Data:

3/4, 1/4, 1/2, 3/4, 1/2, 1/2, 1/4, 3/4, 1/4, 1/2, 1/4, 3/4

From the given Data, the frequency of

1/4 = 5

1/2 = 4

3/4 = 3

Therefore, the line plot is attached as a diagram.

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Answer:

the answer you are looking for here is 3/7

Answer:

3/7

Step-by-step explanation:

6/7 ×1/2 = 6×1 × 7×2 = 6/14 ÷ 2 = 3/7

Answer:

Y will be 65°

Step-by-step explanation:

Since angle S is 65°, angle Y will also be 65°

What are similar shape ?

Similar shapes are shapes that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Since quadrilateral QRST is similar to quadrilateral WXYZ, then angle Q = angle W , angle R = angle X and angle S = angle Y and angle T = angle Z.

Since angle S is 65° from the diagram shown, angle will be measured as 65°.

We can infer from the foregoing description that the typical annual cost of living for a retiree is (A) around $50,000.

One who has retired is known as a retiree.

Many seniors underestimate their retirement income by not accounting for inflation.

Wages, a gauge of the income that retirees must replace, will be the basis for benefits.

One who has retired is known as a retiree.

According to the U.S. Bureau of Labor Statistics most recent Consumer Expenditure Survey, the typical retiree household—one that is headed by a person 65 or older—spends $50,220 annually.

Comparatively, the average yearly household expenditure is $63,036.

So, from the above description, we can state that the average cost of living for a retiree per year is (A) around $50,000.

Therefore, we can infer from the foregoing description that the typical annual cost of living for a retiree is (A) around $50,000.

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Complete question:

What is the average cost of living for a retiree per year?

A. around $50,000

B. around $60,000

C. around $70,000

D. around $80,000

Answer:

67,914

Step-by-step explanation:

Let x = total employees.

18.7% of x = 12,700

0.187x = 12,700

x = [tex]\frac{12700}{0.187}[/tex] = 67914.438 → 67,914

Answer:

The decimal 6.25 would be 6 25/100 as a mixed number. In lowest terms, it would be 6 1/4.

The total volume in the 6 cups is  638.30 in^2

Remember that the volume of a cylinder of height H and radius R is:

V = pi*R^2*H

Here the diameter is 4.4 inches, then the radius is half of that:

R = 4.4in/2 = 2.2in

The height is 7 inches, then the volume of each cup is:

V = 3.14*(2.2in)^2*7in = 106.38 in^2

And in 6 cups the total volume will be:

volume = 6*106.38 in^2 = 638.30 in^2

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The total surplus at the equilibrium point is: $200,000

This is the maximum total surplus that can be achieved in the market for the digital camera.

To compute the maximum total surplus, we need to find the equilibrium quantity and price in the market for the digital camera, and then calculate the consumer and producer surplus at that point.

First, we need to set the demand and supply functions equal to each other to find the equilibrium quantity:

50 - 2P = 2P - 10

4P = 60

P = 15

Substituting this equilibrium price into either the demand or supply function, we can find the equilibrium quantity:

Q = 50 - 2(15) = 20

So the equilibrium price is $15, and the equilibrium quantity is 20,000 digital cameras.

Next, we can calculate the consumer and producer surplus at the equilibrium point. Consumer surplus is the difference between the maximum price a consumer is willing to pay for a good and the market price, summed over all consumers in the market. Producer surplus is the difference between the market price and the minimum price a producer is willing to accept for a good, summed over all producers in the market.

The demand function gives us the maximum price consumers are willing to pay for each quantity of digital cameras:

P = 25 - 0.5Q

So at the equilibrium quantity of 20,000 digital cameras, the maximum price consumers are willing to pay is:

P = 25 - 0.5(20) = 15

This is exactly the same as the market price, so there is no consumer surplus at the equilibrium point.

The supply function gives us the minimum price producers are willing to accept for each quantity of digital cameras:

P = 0.5Q - 5

So at the equilibrium quantity of 20,000 digital cameras, the minimum price producers are willing to accept is:

P = 0.5(20) - 5 = 5

The market price is $15, so the producer surplus is:

(15 - 5) * 20 = $200,000

Therefore, the total surplus at the equilibrium point is:

$200,000

This is the maximum total surplus that can be achieved in the market for the digital camera.

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The values of the variable are:

x is 45.

y is 18.

z is 18.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

From the figure,

Sin 45 = z / (18√2)

Sin 45 = 1 /√2

So,

1/√2 =z / 18√2

z = 18

Cos 45 = y / (18√2)

1/√2 = y/18√2

y = 18

Tan x = y / z

Tan x = 18/18

Tan x = 1

x = [tex]tan^{-1}[/tex]1
x = [tex]tan^{-1}[/tex] tan 45

x = 45

Thus,

x is 45.

y is 18.

z is 18.

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Given:-

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

The volume of the cylinder is 90π in³

[tex] \: [/tex]

hope it helps!:)

The antiderivative of 1x (or simply x) is (1/2)x² + C, where C is the constant of integration. In other words, the antiderivative of x is the function whose derivative is equal to x.

This is a basic result in calculus, and it is derived using the power rule of integration. The antiderivative of 1x (or simply x) is the function whose derivative is equal to x. This function is (1/2)x² + C, where C is the constant of integration. To find the antiderivative, one can use the power rule of integration, which states that the antiderivative of xⁿ is (1/(n+1))x⁽ⁿ⁺¹⁾ + C. In the case of x, n is equal to 1, so the antiderivative is (1/2)x² + C. The constant of integration represents the family of functions that have the same derivative, so it is added to the antiderivative to reflect this.

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The probability of hitting the bullseye if the dart is thrown 40 times is approx. 3 times.

The quantity of occurrences of an event is referred to as its frequency. The concept of relative frequency is experimental rather than theoretical. It is experimental, therefore if we repeat the trials, we can get different relative frequencies. To determine the frequency, we must first:

Number of occurrences for the entire population

Frequency count for a particular demographic segment

If we know the two frequencies mentioned above, we can use the following formula to get the relative frequency probability. A subgroup's formula is as follows:

Subgroup Count / Overall Count: Relative Frequency

Given that, a player hits the bullseye with a dart 8% of the time.

The probability of hitting the dart is = 8/100.

Now, the probability of hitting the bullseye if the dart is thrown 40 times is:

p = 40 (8/100) = 3.2 times = 3 times.

Hence, the probability of hitting the bullseye if the dart is thrown 40 times is approx. 3 times.

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The square root function involves the square root symbol √ which is  mostly read as "square root of", the rule says that the square root of a number 'x' is a number 'y' such that y² = x.

We know that the square root of a number can be either positive or negative, but while defining the square root function, we restrict its range to be the set of all positive real numbers and hence making all square roots possible to be positive.

If the range for the square root of a number is set to be positive as well as negative it wont be a function that is why there is a restriction to the range of this set allowing only positive real numbers.

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Answer:

C

Step-by-step explanation:

-4 is greater than -7

2/10 Net 30 represents credit given to the buyer for the sale of goods or services. 2/10 net 30 means that the customer gets a 2% discount if the outstanding balance is paid within 10 days. Otherwise, full payment is due within 30 days.

2/10 Net 30:

The terms and conditions of the transaction are set forth in the purchase order and the corresponding invoice. These terms include terms of credit between the seller (also known as the payee) and the buyer (also known as the payer). A typical net credit period of 30 means the balance must be paid within 30 days of the invoice date. 2/10 Net 30 (also known as 2 10 Net 30) means that if a buyer pays within the first 10 days, their balance will be reduced by 2%. So "2" is the discount amount (2%) and "10" is the due date (10 days).

For example, if your company purchased $500 worth of goods or services on June 1st, you have entered into a loan agreement with the seller. If your company pays the net amount between June 1st and June 10th, you get a 2% discount, bringing the total amount to $490.

This example 2/10 net 30 step by step.

Day Start counting days from the invoice date.

Quick Formula: 100% Discount % x Invoice Amount.

100% - 2% = 98% x $500 = $490.

Formula:

(immediate discount) x (invoice amount) = less payment

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From the calculations, the best loan option is

A. 3-year loan with a 7% annual simple interest rate

To determine which loan option would allow the customer to pay the least amount of interest, we need to compare the amount of interest charged by each loan option.

For the 3-year loan with a 7% annual simple interest rate,

the interest charged would be $15,000 x 7% x 3 = $2,550.

For the 4-year loan with a 5% annual simple interest rate,

the interest charged would be $15,000 x 5% x 4 = $3,000.

For the 5-year loan with a 4.5% annual simple interest rate,

the interest charged would be $15,000 x 4.5% x 5 = $3,375.

For the 6-year loan with a 3.7% annual simple interest rate,

the interest charged would be $15,000 x 3.7% x 6 = $3,870.

From the calculations, it is clear that the 3-year loan with a 7% annual simple interest rate would result in the least amount of interest charged, with $2,550.

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The average speed with the given distance and time is 119/40 miles per hour.

Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.

Given that, number of miles jogged = [tex]3\frac{2}{5}[/tex] = 17/5 miles and the time taken = 7/8 hours

Here, average speed = 17/5 ÷ 7/8

= 119/40 miles per hour

Therefore, the average speed is 119/40 miles per hour.

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Coordinates of the circumcenter are (7.7, -6.6)

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

we first need to find the midpoint of each side, and then find the intersection of the perpendicular bisectors of each side.

Midpoint of AB is (7, -3)

Midpoint of BC is (2.5, -1.5)

Midpoint of AC is (4.5, -2.5)

The slope of the line passing through A and B is:

m= (-4 - (-2))/(9 - 5) = -1/2

the slope of the perpendicular bisector is 2

By point slope form

y - (-3) = 2(x - 7)

y = 2x - 17

And the equation of the perpendicular bisector of AC is:

y - (-2.5) = -1/2(x - 4.5)

y = -1/2x + 5

Now 2x - 17 = -1/2x + 2.25

2.5x = 19.25

x = 7.7

Substituting x = 7.7 into the equation for the perpendicular bisector of AB, we get:

y = 2(7.7) - 17

y = -6.6

Hence, coordinates of the circumcenter are (7.7, -6.6)

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