In triangle def, m∠d = (2x 19)°, m∠e = (3x 24)°, and m∠f = 87°. determine the degree measure of the exterior angle to ∠d. 54° 39° 141° 126°

The three numbers that are in the ratio 7:3:2 are 70, 30, and 20.

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

So, let 7x, 3x, and 2x be the three numbers.

7x+2x = 9x is the product of the lowest and greatest number.

In accordance with:

9x-30=2(3x)

To make the equation easier:

9x-30=6x

30 extra on both sides:

9x=6x+30 or,9x-6x=30

3x=30, x=10,

So, the numbers will be:

7x=7(10) = 70

3x=3(10) = 30

2x=2(10) = 20

Therefore, the three numbers that are in the ratio 7:3:2 are 70, 30, and 20.

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Answer:

[tex]\huge\boxed{\sf 3}[/tex]

Step-by-step explanation:

y = 3x + 5

Comparing it with standard form of slope-intercept equation i.e. y = mx + b.

Where,

m = slope = 3

b = y-intercept = 5

A line that is parallel to this line will have the same slope as this line.

So, it will also have a slope of 3.

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

|x+1|=2-5

|x+1|= -3

statement doesn't have solution

The probability flipping of four coin that will give head is 0.93

Probability:

In statistics, Probability defines the possible way of occurring a particular event.

Given,

A flipped coin can land in one of two states: heads or tails.

Here we need to find the probability while flipping four coins then  how many of these coins land in the heads state.

In order to calculate the probability of these event, we have to know the values of the sample space and the possible number of events,

Here the value of sample space is written as,

S = {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH}

So, the value of n(S) = 16

The possible number of way to obtain the head state is,

E = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH}

the value of n(E) = 15.

Therefore, the probability of getting head state is

=> P(E) = 15/16

=> P(E) = 0.93

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The slope and intercept of the line will be 2 and 80 respectively.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that, the total amount of tourist spending in Florida from 2013 to 2017 can be predicted using the equation y=2x+80, where x is the number of years since 2013, to the tune of billions of dollars.

Compare the equation with the standard equation,

y=mx+ c

Where m is the slope and c is the intercept of the line.

Thus the slope and intercept of the line will be 2 and 80 respectively.

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Answer:

Step-by-step explanation:

Base angles are congruent.

[tex]\tt y=128^o[/tex]

Let's solve for x first:-

[tex]\tt x+y=180^o[/tex]

[tex]\tt x=180-y[/tex]

[tex]\tt x=180-128[/tex]

[tex]\tt x=52^o[/tex]

Therefore, x = 52° and y = 128°

_________________

Hope this helps you!

Have a nice day! :)

The social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical process, and extraction of roots

Main body:

Cumulative Earnings before this pay period = $128,300

pay amount this period = $3000

tax rate of 6.2% on social security = 6.2%

effective earning = 128300 = 3000

                           = 125300

social security deduction = 6.2 % of 125300

⇒ 6.2 *125300 /100

⇒$7768

Medicare deductions = 1.45%

⇒ 1.45*125300/100

⇒$1816

Hence , the social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

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Website B is cheaper then website A.

What are headphones?

A user wears headphones, which are a pair of small loudspeaker drivers, on or near their head over their ears.

They function as electroacoustic transducers, converting an electrical signal into an associated sound.

People can listen to music and carry on conversations at any time and from any location thanks to headphones. It is impossible to overstate how simple it is to use headphones and how much mobility they provide.

There are two types of headphones, website A and website B.

First to find the cost for website A.

Cost of website A = Cost of headphone + cost of postage

                              = 47.68 + 16.96

Cost of website A = 64.63

Cost of website B = Cost of headphone + cost of postage

                              = 49.95 + 14.39

Cost of website B = 64.34

The cost of website B is less than the cost of website A.

Hence, website B is cheaper then website A.

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The value of the mentioned expression is -43.24.

To solve the expression, firstly rewriting the equation followed by keeping the values of x, y and z at their respective places.

Equation = (4x³ - 10)/(3y² + 5) - (4x³ (z² - 8))/(y³ + 5)

Now keeping the values of each variable in the equation

Equation = (4×2³ - 10)/(3×(-5)²) - (4×2³ ((-7)² - 8))/((-5)³ + 5)

Taking cube and square on Right Hand Side of the equation

Equation = (4×8 - 10/(3×15)) - (4×8 (49 - 8))/(25 + 5)

Solving the bracket first where we will perform multiplication on the Right Hand Side

Equation = (32 - 10/45) - ((32 × 41)/30)

Equation = 22/45 - 1312/30

Now performing division on Right Hand Side of the equation

Equation = 0.49 - 43.73

Performing subtraction on Right Hand Side of the equation

Equation = -43.24

Hence, the value is -43.24.

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The statement that is true about the triangle ABC with vertices A(-6, 6), B(4, 2), and C(-4, 0) is C. Since two of the sides have slopes that are negative reciprocals, it is a right triangle.

Right triangles are triangles with have perpendicular relationships

The lines will be checked for perpendicularity by calculating the slopes, if any two slopes are negative reciprocals then they are perpendicular and the triangle is a right triangle'

the points A(-6, 6), B(4, 2), and C(-4, 0)

Using point A(-6, 6) and B(4, 2)

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - 6) / (2 - -6)

m = -1/2

Using point B(4, 2), and C(-4, 0)

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - -4) / (2 - 0)

m = 2

Comparing the slopes shows that slopes calculated are negative reciprocals

Therefore the triangle is a right triangle

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The required system of equation for the cost of shirt and tie are-

For the stated question-

Let 's' be the cost of each shirt.

Let 't; be the cost of each tie.

Then, the equations become-

4s + 2t = 95

3s + 3t = 84 are the required system of equation.

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The following ways of measuring weight loss are more appropriate than correlation, i.e.,Skin calipers, Impedance scales, DEXA scanning, Body measurements.

Calories factor into the equation while trying to maintain a healthy weight. The key to losing weight is to burn more calories than you consume. You may do this by consuming fewer calories than you need and increasing the number of calories you burn via physical exercise.

A realistic, efficient, and lasting weight loss plan might be difficult to follow even if it may appear straightforward.

You don't have to do it by yourself, though. Seek advice from your doctor, family, and friends. Consider whether this is the right time and whether you're prepared to make the essential changes. Plan wisely as well: Consider how you'll respond to circumstances that put your determination to the test and the inevitable slight setbacks.

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The measured height of the tree is found as 3.2 yards.

Let 'h' be the height of the three.

Let distance between student A and tree =  x.

Using trigonometric relation;

tan 57 = h/x

x = h/tan 57   ......eq 1

tan 46 = h/(x + 1)

x + 1 = h/tan 46   ......eq 2

Equation eq 1 and eq 2.

h/tan 57 + 1 = h / tan 46

h / tan 46 - h / tan 57 = 1

Further solving,

h(tan 57 - tan 46) = tan 46.tan 57

h = tan 46 tan 57 / (tan 57 - tan 46)

h = 3.2 yards

Thus, the measured height of the tree is found as 3.2 yards.

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The complete question is-

Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°.

What is h, the height of the tree? Use the law of sines to first find AT. Then use that measure to find the value of h.

A) 3.0 yards

B) 3.2 yards

C) 3.8 yards

D) 4.4 yards

Answer: 3.2 is correct

Step-by-step explanation:

edge 2023

70% of students had scores that were within (±) one standard deviation of the mean.

For the stated question-

Total number of students = 20

Scores received; 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73.

Mean = Sum of all/ Total number

Mean x = 79.7

standard deviation = 8.7

Thus, (±) one standard deviation SD of the mean becomes;

-1 SD; 79.7 - 8.7 ≈ 70.994

+1 SD; 79.7 + 8.7 ≈ 88.406

Thus, 71 to 88

Percentage = scores between  71 to 88/ total scores

Percentage = 14/20 x 100 %

Percentage = 70%

Thus, 70% of students had scores that were within (±) one standard deviation of the mean.

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Answer:

w=7/2=3.5

Step-by-step explanation:

width =w

length = l = 2w+2

25=2(l+w)= 2(2w+2+w) =2(3w+2)=6w+4

25=6w+4

6w=21

w= 21/6 = 7/2

Answer:

A. Symmetric Property

Step-by-step explanation:

The Symmetric Propertry states that if x = y, then y = x.

Since XY = WX, and WX = XY, its the Symmetric Property.

The value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.

For the given question-

The length of the side are-

a = 3 units

Angle B = 64°.

Then,

Applying trigonometric properties-

Tan B = b/a

b = a tan B

b = 3 tan 64°

b = 12.47 units

Now,

Sin B = b/c

c = b sin B

c = 12.47 sin 64°

c = 11.21 units.

Thus, the value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.

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The distance covered by the car with 12 gallons of gasoline is 200 miles.

Given,

Distance travelled by a car with full  tank gasoline = 300 miles

The capacity of the car's tank = 18 gallons

We have to find the distance covered by the car with 12 gallons of gasoline;

Here,

x be the distance covered by the car with 12 gallons of gasoline

Then,

300/18 = x/12

x = (300 x 12) / 18

x = (300 x 2) / 3

x = 100 x 2

x = 200 miles

That is,

The car will cover 200 miles with 12 gallons of gasoline.

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The depth of the given rectangular lot is 60 yards.

Here, we are given that the area of a rectangular lot is 1,200 square yards.

Further the width of the lot is 60 feet

As the area and the width are given in different units, we first need to convert them into the same units.

Now, 1 foot = 0.33 yards

⇒ 60 feet = 0.33*60 yards

= 20 yards

Further, we know that the area of a rectangle is given by the formula-

area = length × breadth

Thus,

1,200 = 20 × breadth

1,200/20 = breadth

breadth = 60 yards

Thus, we find that the depth of the given rectangular lot is 60 yards.

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Answer: 11 miles each day for the remaining 5 days

Step-by-step explanation:

First, you subtract the miles already done (25) from the total (80) to get 55 (miles left to do) then next divide 55 by 5 (days left), and then your left with 11. Finally, check the work and see how 11x5=55 then 55+25=80.

That's how to get the answer :)

the regression line indicates whether the slope of the regression line is positive or negative is a proportion will be between 0 to 1

Regression is a statistical method that links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether variations in the dependent variable are related to variations in one or more of the explanatory variables.

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If Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

So, the probability that the base construction company did not bid:

[tex]\begin{aligned}& P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B \mid A) P(A)+P\left(B \mid A^{\prime}\right) P\left(A^{\prime}\right)} \\& P\left(B^{\prime} \mid O\right)=\frac{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)}{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)+P(O \mid B) P(B)} \\& P\left(B^{\prime} \mid O\right)=\frac{(0.5)(0.3)}{(0.5)(0.3)+(0.25)(0.7)} \\& P\left(B^{\prime} \mid O\right)=\frac{0.15}{0.15+0.175} \\& P\left(B^{\prime} \mid O\right)=0.4615\end{aligned}[/tex]

Therefore, if Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

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The equation v in terms of other variables is v = kr/2h

It is a variable which is expressed in terms of other variables involved in the formula.

Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.

2(vh) / k = r

by cross multiplication

2(vh) = kr

divide both sides by 2h

v = kr/2h

In conclusion, v in terms of other variables is  kr/2h

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Step-by-step explanation:

A group of friends wants to go to the amusement park. They have no more than $115 to spend on parking and admission. Parking is $15, and tickets cost $25 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park.

115 ≥ 25p + 15

115 ≥ 25p + 15

subtract 15 from both sides:

115 - 15 ≥ 25p + 15 - 15

100 ≥ 25p

divide both sides by 25:

100/25 ≥ 25p/25

4 ≥ p

4 people

The number of people who can go to the amusement park is 4.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number lineby their size.

Given that, the money to be spend, is no more than $115 to spend on parking and admission.

Parking is $15, and tickets cost $25 per person, including tax.

we need to determine the maximum number of people that can go to the park,

115 ≥ 25p + 15

115 ≥ 25p + 15

subtract 15 from both sides:

115 - 15 ≥ 25p + 15 - 15

100 ≥ 25p

divide both sides by 25:

100/25 ≥ 25p/25

4 ≥ p

Hence, the number of people who can go to the amusement park is 4.

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Answer:

No.

Step-by-step explanation:

Below I should you two ways to get the correct answer.

The required evaluation to the given expression is 5/12.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

The expression is given in the question as:

1 3/4  - 1/3 (4)(3) - 1/3

We have to determine the evaluation to the given expression

As per the given question, we have

⇒ 1 3/4  - 1/3 (4)(3) - 1/3

⇒ 7/4  - 1/3 (12) - 1/3

Apply the subtraction operation,

⇒ 7/4  - 4 - 1/3

Take the LCM in the above fractions,

⇒ (21 - 12 - 4)/12

⇒ 5/12

Thus, the required evaluation to the given expression is 5/12.

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The difference between the value of two signed numbers and the absolute value is that

Positive and negative numbers are referred to as signed numbers. The number is automatically regarded as positive if no sign is present.

On a number line, positive numbers are those to the right of zero. Negative numbers are those to the left of 0

Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.

A number can never have a negative absolute value.

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