The formula for the area of a trapezoid is A = {h(bi + b2), where h is the height
and bi and b2 are the two bases. Rewrite the formula to solve for h in terms of A, bi
and b2.
h=

Answer:

Step-by-step explanation:

a + 45 + 70 = 180             45 becomes an interior angle by being opposite a given vertically opposite angle.

a + 115 = 180                      Subtract 115 from both sides

a = 65

b + 68 + 65 = 180            A straight line is 180 degrees.

b +  133 = 180

b = 180 - 133

b = 47

In the triangle b + c + 100 = 180

b = 47

47 + c + 100 = 180

147 + c = 180

c = 33

If C is an exterior angle then C + 33 = 180

C = 147

You have to decide whether c is an interior angle ( in which it is 33) or an exterior angle (in which case it is 147).

Using the binomial distribution, it is found that:

0.3677 = 36.77% probability that more than 1 of these parts are defective.

-----------------

For each part, there are only two possible outcomes. Either they are defective, or they are not. The probability of a part being defective is independent of any other part, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of a success.

At a certain auto parts manufacturer, the Quality Control division has determined that one of the machines produces defective parts 18% of the time.

This means that [tex]p = 0.18[/tex]

A random sample of 7 parts produced by this machine is chosen.

This means that [tex]n = 7[/tex]

Find the probability that more than 1 of these parts are defective.

This is:

[tex]P(X \geq 1) = 1 - P(X < 1)[/tex]

In which

[tex]P(X < 1) = P(X = 0) + P(X = 1)[/tex]

Thus

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{7,0}.(0.18)^{0}.(0.82)^{7} = 0.2493[/tex]

[tex]P(X = 1) = C_{7,1}.(0.18)^{1}.(0.82)^{6} = 0.3830[/tex]

Then

[tex]P(X < 1) = P(X = 0) + P(X = 1) = 0.2493 + 0.3830 = 0.6323[/tex]

[tex]P(X \geq 1) = 1 - P(X < 1) = 1 - 0.6323 = 0.3677[/tex]

0.3677 = 36.77% probability that more than 1 of these parts are defective.

For more on the binomial probability distribution, you can check https://brainly.com/question/15557838

Answer:

−5 < x < 10

Step-by-step explanation:

−6 < x − 1 < 9

Add 1 to all sides

−6+1 < x − 1+1 < 9+1

−5 < x < 10

Answer:

B

Step-by-step explanation:

Add one to everything

-5 < x < 10

Best of Luck!

Answer:

the distributive property. or distribution

hope this helps! :)

Answer:

8.94~9.0

Step-by-step explanation:

If A squared plus B squared equals C squared. Then you can used this formula and find that 4 squared plus 8 squared equals 80. then square root 80 to find 8.94 or rounded to 9. This would equal C or the hypotenuse. Hope this helps!

The required length of the hypotenuse of the triangle is 16√5.

Given that,
If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse is to be determined.

In a right-angled triangle, its side, such as hypotenuse, perpendicular, and the base is Pythagorean triplets.

Here,
Applying the Pythagorean theorem,
Hypotenuse²  = perpendicula² + base²
Hypotenuse²  = 8² + 4²
Hypotenuse²  = 64 + 16
Hypotenuse²  = 80
Hypotenuse  = √80
Hypotenuse  =  16√5

Thus, the required length of the hypotenuse of the triangle is 16√5.

Learn  more about Pythagorean triplets here:

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Answer:

232 cars

Step-by-step explanation:

Let's say the number of cars that entered is c.

At 9:00 am, there are a total of 24 + c cars and 64 trucks. We know that this value of 64 represents 1/5 of the total number of vehicles. The total number of vehicles is (24 + c) + 64 = 88 + c. So, we have:

64/(88 + c) = 1/5

Cross-multiply:

88 + c = 64 * 5 = 320

c = 320 - 88 = 232

Thus, the answer is 232 cars.

Note: as 232 doesn't show up in the answer choices, it's possible that the problem was copied correctly.

~ an aesthetics lover

Answer:

232 cars entered between 8 and 9

Step-by-step explanation:

at 9 am there are 64 x 5 vehicles total = 320

320 - 64 - 24 = 232

Answer:

4:7

Step-by-step explanation:

4 grape candies : 7 total candies (grape + cherry)

Answer:

It is simply 4:3

Answer:

[tex]x=-\frac{11}{8}[/tex]

Step-by-step explanation:

Hi there!

[tex](x - 4) - (x + 7) = 8x[/tex]

Open up the parentheses

[tex]x - 4 - x - 7 = 8x[/tex]

Combine like terms

[tex]x -x - 4 - 7 = 8x\\-4-7=8x\\-11=8x[/tex]

Divide both sides by 8 to isolate [tex]x[/tex]

[tex]-\frac{11}{8}=x[/tex]

I hope this helps!

[tex]\huge\mathsf\green{ANSWER}:—[/tex]

[tex]option \: \: c \: \: \: \frac{3}{4} \: is \: the \: correct \: option[/tex]

Rational numbers are numbers which can be represent in the form of p/q where p and q are integers and q≠0 that's why 3/4 is the correct option

Answer:

150cm²

Step-by-step explanation:

area of trapezium=1/2h(a+b)

=1/2×20(7+8)

=10(15)

=150 cm²

Answer:

The area of the trapezium is

Step-by-step explanation:

The area of a trapezium is given by

where

h is the height

a and b are the parallel sides of the trapezium

From the question

h = 20cm

a = 7cm

b = 8 cm

Substitute the values into the above formula

We have

We have the final answer as

Hope this helps you

Answer:

I think No

Explanation:

We say two figures are similar if they have the same shape, but not necessarily the same size. If they also have the same size, we say they are congruent.

No, if two polygons are similar, it does not necessarily mean that they are congruent.

We have,

Similar polygons have the same shape but can have different sizes. This means that their corresponding angles are equal, and the ratios of their corresponding side lengths are equal.

However, the lengths of the sides themselves may be different.

On the other hand, congruent polygons have both the same shape and the same size.

This means that all corresponding angles and side lengths are equal.

So, while all congruent polygons are similar, not all similar polygons are congruent.

Similar polygons can be scaled versions of each other, but they can have different sizes.

Thus,

No, if two polygons are similar, it does not necessarily mean that they are congruent.

Learn mroe about polygons here:

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Answer:

43

Step-by-step explanation:

Using Thales theorem:

● SP/LN = RP /RN

Notice that RN = 2×RP

● SP/LN = RP/2RP

● SP /LN = 1/2

● SP / (5x-14) = 0.5

● (2x+3)/(5x-14) = 0.5

● 2x+3 = 0.5(5x-14)

● 2x+3 = 2.5x -7

Add 7 to both sides

● 2x+3+7 = 2.5x-7+7

● 2x+10 = 2.5x

Sustract 2x brom both sides

● 2x+10-2x = 2.5x-2x

● 10 = 0.5x

Multiply both sides by 2

● 10×2 = 0.5x×2

● 20 = x

Replace x with 20 in Sp expression:

● SP = 2x+3

● SP = 2×20+3

● SP = 43

Answer:

B and C

Step-by-step explanation:

The ratio of black to white is 5:6

The only mixtures that have this ratio is B and C

Answer:

$153

Step-by-step explanation:

Divide by 100-sale%

102/.66666=

$153

Check: 153x.666666=102 YES

Answer:

the original price is 153

Step-by-step explanation:

leather jacket is 102 sale price

the sale is 1/3 of original price

the original price=1/2 its price=sale price

x-1/3x=102

2/3 x=102

2x=306

x=306/2

x=153 dollars

Mukat gets 40, Usha gets 8

Step-by-step explanation:

Mukat = 5 × Usha

After Mukat gives Usha 16 books ,Usha gets (16 + initial number of books) and Mukat gets (5 × Usha - 16)

Then Mukat = final number of books for Usha

5 × Usha - 16 = Usha + 16

(5 × Usha ) - Usha = 16+16

4 × Usha = 32

Usha = 8 i.e her number of books.

Mukat = 5×8=40.

I HOPE IT'S OK

Answer:

Step-by-step explanation:

1) ABCD is a trapezium. AB ║ CD

∠ADC + ∠DAB  = 180°  { Co interior angles}

110° + ∠DAB = 180

         ∠DAB = 180 -110

∠DAB = 70°

2) Sum of all angles of trapezium = 360°

∠A + ∠B + ∠DCB + ∠D = 360

70° + 50° + ∠DCB + 110° = 360

                 230 + ∠DCB = 360

                            ∠DCB = 360 - 230

∠DCB = 130°

3) For finding the height, use Pythagorean theorem

height² + base² = hypotenuse²

      height² + 6² = 10²

      height² + 36 =100

               height² = 100 - 36

              height² = 64

               height = √64

height = 8 m

4) a = AB = x m

  b = 9 m

h = height = 8 m

Area of trapezium = 120 m²

[tex]\frac{(a+b)*h}{2}\\\\[/tex]  = 120

[tex]\frac{(x+9)*8}{2} =120\\\\\\(x +9)*4 = 120[/tex]

x + 9 = 120/4

x + 9 = 30

    x = 30 - 9

x = 21 m

AB = 21m

Step-by-step explanation:

the correct answer is option c

Answer:

They purchased 14 adult tickets and 4 kids tickets.

Step-by-step explanation:

14 x 5 = 70

3x4=12

and then add 70 plus 12 to get 82 dollars.

The number of adults tickets that were sold for the movie will be 14 tickets.

The equation to solve the question will be:

a + s = 18 .......... i

5a + 3s = 82 ......... ii

Form equation i, s = 18 - a

5a + 3s = 82

5a + 3(18 - a) = 82

5a + 54 - 3a = 82

Collect like terms

5a - 3a = 82 - 54

2a = 28.

a = 28/2

a = 14

Therefore, s will be:

s = 18 - a = 18 - 14 = 4

The number of adults ticket is 14

Read related link on:

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Answer:

C. the subtraction property of equality

Step-by-step explanation:

given

12 − x = 7x + 32

Subtract 12 from each side  using the subtraction property of equality

Step 1: -x = 7x + 20

Subtract -7x from each side using the subtraction property of equality

Step 2: -8x = 20

Answer:

D. 16 years old

Step-by-step explanation:

Step 1: Let T be Tien's age and J as Jordan's age (today),

[tex]T=\frac{1}{4}J[/tex]

Step 2: Let T be Tien's age and J as Jordan's age (in 2 years),

[tex]T+2=\frac{1}{3} (J+2)[/tex]

[tex]T=\frac{1}{3}(J+2)-2[/tex]

Step 3: As their age differences will always be similar we can have the two equations above equal to find Jordan's age,

[tex]\frac{1}{4} J=\frac{1}{3}(J+2)-2\\\frac{1}{4}J-\frac{1}{3}J=\frac{2}{3} -2 \\-\frac{1}{12}J= -\frac{4}{3} \\\\J=16[/tex]

Complete Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 164 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

Answer:

The  95%  confidence interval is  [tex]0.2392 < p < 0.3108[/tex]

No, the confidence interval includes​ 0.25, so the true percentage could easily equal​ 25%

Step-by-step explanation:

From the question we are told that

  The total sample size is  [tex]n = 432 + 164 =596[/tex]

   The  number of  offspring that is yellow peas is [tex]y = 432[/tex]

   The  number of  offspring that is green peas   is [tex]g = 164[/tex]

The sample proportion for offspring that are yellow peas is mathematically evaluated as

        [tex]\r p = \frac{ 164 }{596}[/tex]

        [tex]\r p = 0.275[/tex]

Given the the  confidence level is  95% then the level of significance is mathematically represented as

       [tex]\alpha = (100 - 95)\%[/tex]

      [tex]\alpha = 5\% = 0.0 5[/tex]

The  critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

      [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically evaluated as

        [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1- \r p )}{n} }[/tex]

=>      [tex]E = 1.96 * \sqrt{\frac{0.275 (1- 0.275 )}{596} }[/tex]

=>      [tex]E = 0.0358[/tex]

The  95%  confidence interval is mathematically represented as

      [tex]\r p - E < p < \r p + E[/tex]

=>   [tex]0.275 - 0.0358 < p < 0.275 + 0.0358[/tex]

=>   [tex]0.2392 < p < 0.3108[/tex]

Answer:

VERTICALLY OPP ANGLES

Step-by-step explanation:

Answer:

6a) i- 2hrs 36mins  ii- 3hrs 12mins

b) car A≈ 76.9km/h  car B≈ 62.5km/h

c)------

7a) 35km

b) car A=75km  car B=60km

c) 30km

d) car A≈36mins  car B≈48mins

Step-by-step explanation:

6a) Using the graph follow the lines until they finish then go downwards until you get to the x-axis. The x-axis is going up by 12mins for each square.

b) Using the answer from a, you divide 200km by the time.

For car A 2hrs 36mins becomes 2.6 because 36mins/60mins=0.6

∴ car A: 200/2.6≈ 76.92km/h

For car B 3hrs 12mins becomes 3.2 because 12mins/60mins=0.2

∴ car B: 200/3.2≈ 62.5km/h

7a) Using the graph go down from where the line of car A finished to meet car B. The y-axis is going up by 5km for each square.

b) Starting from the x-axis at 1 hour go upwards to see where you meet the car B line (60km) and car A line(75km). (sorry if that does not really make sense).

c) Difference from car A line to car B:

155km-125km=30km

d) Going across from 50km meet car A line and go down to see it has been travelling for approx. 36mins. Then continue across to car B line, go down to see it reached 50km at approx. 48mins.

Hope this helps.

Answer:

rectangular pyramid, 5, 8,5

Step-by-step explanation:

Answer:

✔ rectangular pyramid

This figure will have

✔ 5

faces,

✔ 8

edges, and

✔ 5

vertices.

the person above is correct

Answer:

Rate of gas in gallons per mile

= 0.045454545 gallon/mile

Or

Rate of gas in gallons per mile

= 1/22 gallon/mile

Step-by-step explanation:

Ava's car uses 6 gallons of gas to drive through a distance of 132 miles.

Thanks rate of gallon to distance will be given by the formula below

Rate of gas in gallons per mile

=Number of gallons/ distance covered in miles

Rate of gas in gallons per mile= 6/132

Rate of gas in gallons per mile= 1/22

Rate of gas in gallons per mile

= 0.045454545 gallon/mile

Answer:

A

Step-by-step explanation:

The sum means +, 24 or greater means ≥ 24

The product means multiplying. less than 60 means < 60

I don't really know how else to explain, so if you still don't understand, sorry.

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

Let's first find the slope.

-13 - (-8) /  2-1

-5/1

-5

The slope is -5.

The y intercept, or where the line crosses the y=axis, is equal to -3.

So, the equation is y=-5x-3

Let me know if this helps!

Answer:

please mark my answer brainliest

Step-by-step explanation:

10q (1-3)

[tex]\\ \sf\longmapsto t+\dfrac{1}{2}b=Y[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{2}b=Y-t[/tex]

[tex]\\ \sf\longmapsto \dfrac{b}{2}=Y-t[/tex]

[tex]\\ \sf\longmapsto b=2(Y-t)[/tex]

[tex]\\ \sf\longmapsto b=2Y-2t[/tex]