The sum of three consecutive integers is 108. What are the integers?



smallest integer

middle integer

largest integer

The measure of the missing angles are d= 77° , e= 31° ,and f = 72°.

As given in the question,

Angle e is vertically opposite to the given angle 31°

⇒Measure of angle e = 31°

Angle d is vertically opposite to the given angle 77°

⇒Measure of angle d = 77°

Angle e , Angle f and angle d are linear pairs

⇒∠e +∠f +∠d =180°

⇒31° +∠f + 77°=180°

⇒ ∠f =180° -108°

⇒ ∠f =72°

Therefore, the measure of the missing angles are d = 77° , e = 31° and

f = 72°.

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50 books can be purchased with $ 350.

We have the data:

Books Cost (dollars)    Amount left (dollars)

            1                                    343

            2                                   336

            3                             336 - 7 = 329

            4                             329 - 7 = 322

            7                             322 - 21 = 301

           14                             301 - 49 = 252

Cost of 1 book = $ 7

Cost of b books = 7 × b = 7 b    

Amount of budget after b books = 350 - 7 b

We can buy = 350 / 7 = 50 books before spending the entire amount.

Therefore, we get that 50 books can be purchased with $ 350.

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Answer:

y=-5x-7

Step-by-step explanation:

For lines to be parallel with one another, that means they have to have the same slope. The slope of this equation is -5

From there we have to find the b (or the y-intercept) of the new equation. To do this we plug in the slope and the x and y from the given point (-2,3) into the equation y=mx+b and solve for b:

3=-5(-2)+b

3=10+b

-7=b

Finally, we make a new equation with the b (-7) and slope (-5):

y=-5x-7

DON'T READ IF YOU DON'T WANT TO/ALREADY KNOW HOW TO DO THIS FOR A LINE PERPENDICULAR TO THE GIVEN LINE:

To find a line perpendicular to (y=-5x+1), you do everything the same as before but instead of using -5 as the slope for your new equation (including the one you use for solving for the new b) you use it's negative reciprocal. That basically means you switch the numbers numerator and denominator and switch the sign. Remember, every whole number has a denominator of 1, so it'll look like this:

-5/1 turns into 1/5

Then you use 1/5 as the slope for the new equation by plugging in the x and y of the given point and solving for b like we did before. Finally you take the 1/5 as the slope and the b you solved for and put those into a equation like you did before and bam.

If you're confused after reading that then forget everything I said.

hope this helps :D

Answer:

Since there are a total of six friends and they each use a $2 off coupon then what you first want to do is multiply:

2 times 6 = 12

Then you want to add:

42 + 12 = 54

So the total that they would have spent without the discount would be $54.

Step-by-step explanation:

Hope it helps! =D

The correct option is b. 16.67 acres would the lot next to it contain if it has a 900' frontage and is the same width as the first rectangular lot.

The quantity of space occupied by a flat surface with a specific shape is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.). The quantity of unit squares that can fit inside a rectangle called its area. Blackboards, painting canvases, laptop monitors, and other flat surfaces are a few instances of rectangular shapes.

Area of a Rectangle = (Length × Breadth) square units.

We know that the Area = Length × Width.

For first lot:

43,560 (sq. ft. in acre) × 25 acres = 1,089,000 sq. ft.

We know that 1,089,000 sq. ft. = Width × 1,350 (length). Therefore width =1,089,000 / 1,350 = 806.67.

From the problem the lots were of the same width.

In second lot: Area =806.67 (width) × 900( length)= 726,000 sq. ft. Therefore:

⇒726,000 (area) / 43,560 = 16.67 acres.

The correct answer is:  b. 16.67 acres

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Answer:

32ft

Step-by-step explanation:

Answer:

give me one second brooo

Explanation:

The coordinates of the given points are:

Refer to the diagram to know the coordinates of the given points.

Therefore, the coordinates of the given points are:

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The minimum will be $ 0. If the theft occurs , company will have to pay the claim. Hence Option B will be correct.

What is probability and example?

The variety of strategies for success. the total number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

$ 0 and $ 200

This is because both the insured will pay $ 100 premium each , hence total revenue of company can be $ 200 maximum.

The minimum will be $ 0. If the theft occurs , company will have to pay the claim. Hence Option B will be correct.

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It will take 4 hours for both companies to equal the same price and it will cost $ 90 at that time.

There are two companies:

Company A-
It charges $ 50 to come and $ 10 per hour to work.

Let the number of hours worked be x

The equation will be:

Price of Company A = 50 + 10 x   …(1)

Company B-

It charges $ 30 to come and $ 15 per hour to work.

The equation will be:

Price of Company B = 30 + 15 x    …(2)

Now, for the same prices, we will equate (1) with (2):

50 + 10 x = 30 + 15 x

15 x - 10 x = 50 - 30

5 x = 20

x = 20 / 5

x = 4

At x = 4, price of the companies will be:

A = 50 + 10 (4) = 50 + 40

A = $ 90

B = 30 + 15(4)

B = 30 + 60

B = $ 90.

Therefore, it will take 4 hours for both companies to equal the same price and it will cost $ 90 at that time.

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Answer:− 9/56

​

Step-by-step explanation: hope this helps you!!!!

We can be 99% certain the baseball game will end by 5.22pm.

A cut-off Number is a number mentioned in the applicable Final Terms as such, or if no number is provided, the Specific Number is presumed to be five.

In binary classification, the threshold or cut-off represents the chance that the prediction is correct. It represents the cost of false positives or false negatives.

Let the cutoff be A.

so,

P(X ≤ A) = 0.99

[tex]P\left(\frac{X-\mu}{\sigma} \leq \frac{a-2.5}{0.37}\right)=0.99[/tex]

[tex]P\left(Z \leq \frac{a-2.5}{0.37}\right)=0.99[/tex]

[tex]\Phi\left(\frac{a-2.5}{0.37}\right)=\Phi(2.33)\\[/tex]

(a - 2.5)/.37 = 2.33

a = 3.3621

a = 3hours and (0.3621 * 60) = 22 minutes

We can be 99% certain the baseball game will end by 5.22pm.

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I understand that the question you are looking for is:

The probability that the baseball game will cut into the program is 0.0885.

Can you provide a cut-off time by which you can be 99% sure that the baseball game would end?

According to the question, let us consider the random variable for the discrete uniform distribution to be x.

What is the discrete uniform distribution?

Uniform distribution is another name for the rectangular distribution. And it is the family of the symmetric probability distribution. It has constant probability and the outcomes are equal in nature.

The standard formula for the mean and the variance of the distribution in terms of the lower bounds(L) and the upper bounds(U) is as follows:

Mean = (L+U)/2 ;

Variance = (L+U)/12

The value of the lower bound(L) is 1000 and the upper bound(U) is 1500.

The calculation is as follows:

Mean = (1000+1500)/2 = 1250

Variance =  (1000+1500)/12 = 208.3

Therefore, the values are: mean = 1250 and variance = 208.3

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The discount rate, as a percent is 20%

The given parameters are:

Cost of 1 T-shirt = $15.97

Also, we have

4 purchases gives 1 free item

So, the discount rate is

Discount = 1/(1 + 4) * 100%

Evaluate the sum

Discount = 1/5 * 100%

Evaluate the product

Discount = 20%

Hence, the discount rate, as a percent is 20%

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The runner has to run more 8.808 km to finish the race.

So, the runner ran 1.192 km out of 10 km.

Then, the remaining distance:

Therefore, the runner has to run more 8.808 km to finish the race.

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Answer:

Step-by-step explanation:

[tex]\displaystyle\\ax+by=c\\\\by=c-ax\\\\\frac{by}{b}=\frac{c-ax}{b} \\\\y=\frac{c-ax}{b}[/tex]

Answer: Basically, bottom is first. The top is second, and the middle one is last.

Step-by-step explanation:

1. Super Duper Easy, first, subtract ax, making it by = c - ax

2. Then, divide b , so by/b = c/b - ax/b

3. Becoming y = c/b - ax/b

Answer:

27-7=4d+6d

20=10d

d=20/10

therefore; d=2

The population that would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases is All 513 bolts that were randomly selected.

Generalizing the conclusions from a study can only be done with a sample that is well-represented. The question here says that all 513 bolts were chosen without bias. This means that a fair conclusion can be reached from the sample.

So, the results that occur from studying the 513 bolts can be sure to produce accurate results. Moreso, the population is large, thus, the population can be used to generalize conclusions.

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The values of the exponential expressions are follows;

3. [tex] {x}^{m \times n} [/tex]

4. [tex] {\frac{1}{4} }^{16} [/tex]

5. [tex] {( - 3)}^{5} [/tex]

6. [tex] 5.3 \cdot {( - 4)}^{11}[/tex]

7. [tex] {(2.9)}^{10} [/tex]

The given expression that can be used to show the Power of a Power Exponent law are as follows;

3. The Power of a Power Exponent law states that;

[tex] {( {x})^{m} }^{n} = {x}^{m \times n} [/tex]

4. The given expression is presented as follows;

[tex] { ({( \frac{1}{4} )}^{2} )}^{8} ={\frac{1}{4} }^{2 \times 8} = {\frac{1}{4} }^{16} [/tex]

5. [tex] {( - 3)}^{4} \times - 3 = {( - 3)}^{4 + 1} = {( - 3)}^{5} [/tex]

6. [tex]5.3 \cdot {( - 4)}^{11} = 5.3 \cdot {( - 4)}^{11}[/tex]

7. [tex] {(2.9)}^{2} \cdot {(2.9)}^{5} \cdot {(2.9)}^{3} = {(2.9)}^{2+5+3} [/tex]

[tex] {(2.9)}^{2+5+3}={(2.9)}^{10} [/tex]

Therefore;

[tex] {(2.9)}^{2} \cdot {(2.9)}^{5} \cdot {(2.9)}^{3} = {(2.9)}^{10} [/tex]

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The inequality that represents the possible area of the triangle is 2/7a < 10

The solution to the inequality is a < 35

From the question, we are to write and solve an inequality that represents the possible area, a, of the triangle

From the given information,

The base of the triangle is given by

b = 2/7a

Also, from the given information,

The base of the triangle is less than 10

That is,

b < 10

Then,

we can write that

2/7a < 10

This is the inequality that represents the possible area of the triangle

Now, solve the inequality

2/7a < 10

Multiply both sides of the equation by 7/2

7/2× 2/7a < 7/2× 10

a < 7 × 5

a < 35

Hence, the inequality that represents the possible area of the triangle is 2/7a < 10

The solution to the inequality is a < 35

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Answer:

3.73

Step-by-step explanation:

The hundredths place is two places to the right of the decimal so the number doesn't need to change.

The solutions for the expressions are given as follows:

6. y = 12.

7. w = -20.

8. x = 30.

The expression is given by:

4/3y = 16.

Applying cross multiplication:

4y = 48

y = 48/4

y = 12.

The expression is given by:

w/(-2.5) = 8

Applying cross multiplication:

w = -2.5 x 8

w = -20.

The expression is given by:

(1/5)x - 2 = 4.

Isolating x:

(1/5)x = 6.

Applying cross multiplication:

x = 6 x 5

x = 30.

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Supplementary angles have a sum of 180°

Therefore, we can add the expressions for Angles A and B and set their sum equal to 180.

( 7x - 15 ) + ( 2x - 3 ) = 180

Now we can combine like terms and use inverse operations to find the value of x:

( 7x - 15 ) + ( 2x - 3 ) = 180

9x - 18 = 180

9x - 18 + 18 = 180 + 18

9x  = 198

9x/9 = 198/9

x = 22

Then Angle A will have a measure of 7x - 15 or 7• 22 -15 = 154 - 15 = 139°

m∠A = 139°

The measure of Angle b will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°

m∠ B = 41°

NOTE:  139 + 41 = 180

The value of the other angle will be 40°.

It should be noted that the value of the angle on a straight line equals to 180°.

In this case, the adjacent angles (two angles that share a common side and vertex) form a straight

angle and one of the angles measures 140°.

The value of the other angle will be:

= 180° - 140°

= 40°

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The measure of angle COD will be 85° and it will be an acute angle.

If an angles is less than 90°, it is known as an acute angle. If it is more than 90°, it will be an obtuse angle. And if it is equal to 90, then it is called a right angle.  

Here, we are given a a figure and we need to find the measure of ∠COD.

∠COD can be written as ∠AOB - ∠AOC - ∠DOB

Here, ∠AOB = 180° (straight line)

∠AOC = 30°

and ∠DOB = 65°

Thus, ∠COD = 180 - 30 - 65

∠COD = 180 - 95

∠COD = 85°

As ∠COD is less than 90°, it will be an acute angle.

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Answer:D

Step-by-step explanation:

√81 - √25 = 9 - 5 = 4

√64 + √25 = 8 + 5 = 13

√64 - 31 = 8 - 31 = -23

14 left handed people would you expect in a group of 140 people .

According to the question, 3 people are left handed out of every 30 people.

We can solve this using unitary method ,

14 left handed people would you expect in a group of 140 people.

Another method:

Based on the given conditions, formulate : 140 * 3 / 30

Reduce the fraction : 14

get the result 14

Answer 14

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The smallest n such that 1 can be written as a sum of n

special numbers is 8.

A number is a mathematical concept that is used for counting, measuring, and labeling. The natural numbers 1, 2, 3, 4, and so forth are the original examples. Number terms in language can be used to represent numbers. More commonly, individual numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five. Basic numerals are frequently arranged in a numeral system, which is an ordered manner to represent any number, as only a very small number of symbols can be learned. The most widely used numeral system is the Hindu-Arabic numeral system, which enables the depiction of any number using a combination of 10 basic numerical symbols, or "digits."

Calculations:

Suppose 1 = x1 + x2 + · · · + xn where x1, x2, . . . , xn are special and

n ≤ 9. For k = 1, 2, 3, . . . , let ak be the number of elements of {x1, x2, . . . , xn}whose kth decimal digit is 7. Then

1 =7a1}/10 +7a2/10 +7a3/10 + ... ,

which yields

1/7 = 0.142857 =a1 /10 +a2/[tex]10^{2}[/tex] +a3/[tex]10^{3}[/tex] + ... ,

Hence a1 = 1, a2 = 4, a3 = 2, a4 = 8, etc. In particular, this implies that n ≥ 8. On

the other hand,

x1 = 0.700, x2 = x3 = 0.07, x4 = x5 = 0.077777, and x6 = x7 = x8 = 0.000777

are 8 special numbers whose sum is

(700700+2(70707)+2(77777)+3(777))/{999999} =1

Thus the smallest n is 8.

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