In politics, marketing, etc. We often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Describe the conclusion about p using an absolute value inequality.

Answers

Answer 1

Answer: |p-72% |≤ 4%

Step-by-step explanation:

Let p be the population proportion.

The absolute inequality about p using an absolute value inequality.:

[tex]|p-\hat{p}| \leq E[/tex] , where E = margin of error, [tex]\hat{p}[/tex] = sample proportion

Given:  A poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% .

|p-72% |≤ 4%

⇒    72% - 4% ≤ p ≤ 72% +4%

⇒  68%  ≤ p ≤  76%.

i.e. p is most likely to be between 68% and 76% (.

Answer 2

The conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.

What is absolute value inequality?

An expression using absolute functions and inequality signs is known as an absolute value inequality.

We know that the absolute value inequality about p using an absolute value inequality is written as,

[tex]|p-\hat p| \leq E[/tex]

where E is the margin of error and [tex]\hat p[/tex] is the sample proportion.

Now, it is given that the poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76%. Therefore, p can be written as,

[tex]|p-0.72|\leq 0.04\\\\(0.72-0.04)\leq p \leq (0.72+0.04)\\\\0.68 \leq p\leq 0.76[/tex]

Thus, the p is most likely to be between the range of 68% to 76%.

Similarly, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Therefore, p can be written as,

[tex]|p-\hat p|\leq E\\\\|p-0.32|\leq 0.022\\\\(0.32-0.022)\leq p \leq (0.32+0.022)\\\\0.298\leq p\leq 0.342[/tex]

Thus, the p is most likely to be between the range of 29.8% to 34.2%.

Hence, the conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.

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Related Questions

Sams building a suspension bridge for the playground at the elementary school I needed some chain-link and some rope he bought a total of 80 feet of materials and The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135 how much of each did he buy

Answers

Answer:

Amount of material for chain link = 30 feet

Amount of material for rope = 50 feet

Step-by-step explanation:

Let the amount of chain link = X

The amount of rope be represented by Y

He bought a total of 80 feet of materials

Hence we have:

X + Y = 80 ....... Equation 1

Y = 80 - X

The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135

X × $2 + Y × $1.50 = $135

2X + 1.5Y = 135 ......Equation 2

Substitute 80 - X for Y in Equation 2

2X + 1.5(80 - X) = 135

2X + 120 - 1.5X = 135

Collect like terms

2X - 1.5X = 135 - 120

0.5X = 15

X = 15/0.5

X = 30 feet

Substitute 30 feet for X in Equation 1

X + Y = 80 ....... Equation 1

30 + Y = 80

Y = 80 - 30

Y = 50 feet

Hence the amount of material he used for the chain link = 30 feet and the amount of material he used for the rope was = 50 feet

Need help give you a good rating pls.

Answers

Answer:

x^(1/2)

Step-by-step explanation:

For this, we need to understand exponent rules.  This one is like this, "A power to a power, you multiply the exponents".  This is simply, because this expression would be equivalent to 3 base terms:

(x^(1/6))^3 = (x^(1/6)) * (x^(1/6)) * (x^(1/6))

And when you perform this multiplication "Powers of like bases, you add the exponents", you will get the following

(x^(1/6)) * (x^(1/6)) * (x^(1/6)) = x^(1/6 + 1/6 + 1/6) = x^(3/6) = x^(1/2)

Hence, this expression simplifies to x^(1/2).

Cheers.

Answer:

[tex] \boxed{ {x}^{ \frac{1}{2} } }[/tex]

Option D is the correct option.

Step-by-step explanation:

[tex] \mathrm{ ({x}^{ \frac{1}{6} } ) ^{3} }[/tex]

[tex] \mathrm{simplify \: the \: expression \: by \: multiplying \: exponents}[/tex]

[tex] \mathrm{ = {(x)}^{ \frac{1}{6} \times 3 } }[/tex]

[tex] \mathrm{ = {x}^{ \frac{1}{2} } }[/tex]

Hope I helped!

Best regards!

A recipe for peanut butter cookies calls for 1 cup of sugar, 1 cup of chunky peanut butter, and 1 medium egg. The recipe yields 18 cookies. If the baker has 12.5 cups of sugar, 15 cups of chunky peanut butter, and 10 eggs. How many full batches of cookies can the baker make

Answers

Answer:

10 batches - they only have 10 eggs, so they can't make any more batches without them

Which of the following statements is false? A. A rectangle is an equiangular quadrilateral. B. Opposite sides of a parallelogram are congruent. C. A square is a regular quadrilateral. D. The diagonals of a rectangle are perpendicular.

Answers

Answer:

D.

Step-by-step explanation:

Choices A., B., and C. are always true.

Choice D. is true only for rectangles with congruent sides, which are squares.

Answer: D.


[tex]2x + x { }^{2} + x[/tex]


Answers

Answer:

[tex]\huge \boxed{x(x+3)}[/tex]

Step-by-step explanation:

[tex]2x+x^2 +x[/tex]

Combine like terms.

[tex]x^2 +(2x+x)[/tex]

[tex]x^2 +3x[/tex]

Factor out [tex]x[/tex] from the expression.

[tex]x(x+3)[/tex]

Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.

Answers

there is no visible graph

Step-by-step explanation:

An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses.H0: The product does not change the height of the plant.Ha: The product makes the plant grow taller.Is the following an example of a type I or type II error?The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.a) Type Ib) Type II

Answers

Answer:

The error made here is a Type I error.

Step-by-step explanation:

A Type I error is the rejection of a null hypothesis (H₀) when indeed the null hypothesis is true. It is symbolized by α.

A Type II error is failing to discard a null hypothesis when indeed the null hypothesis is false. It is symbolized by β.

The hypothesis in this case is defined as follows:

H₀: The product does not change the height of the plant.

Hₐ: The product makes the plant grow taller.

The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.

So, the sample suggests to reject the null hypothesis when in fact the null hypothesis is true.

Thus, the error made here is a Type I error.

Which phrase best describes the relationship indicates by the scatter plotting?

Answers

Answer: negative correlation

Step-by-step explanation: If you look at the points in this graph here, I would say that those points are very close to a perfect line.

Notice that the slope of the line is negative.

This means it will be a negative correlation.

So the line is a very good estimate of the points.

A line passes through the point (–1,–2) and is perpendicular to the line with the equation y= –x – 1. What's the equation of the line?

Question 16 options:

A) 
y = x – 5

B) 
y = –x + 3

C) 
y = –x + 7

D) 
y = x – 1

Answers

Answer:

D) y = x - 1

Step-by-step explanation:

First we need the general equation of point slope form:

(y - y0) = m(x - x0)

Where y0 is the y coordinate and x0 is the x coordinate and m is the slope.

For the line to be perpendicular, we need the slope to be the negated opposite of the other equation.  So the negated opposite of -1 is 1.

So our m = 1, y0 = -2, and x0 = -1.  Now let's plug this into the equation and reform the equation into slope-intercept form

(y - (-2)) = 1 (x - (-1))

y + 2 = 1 (x + 1)

y + 2 = x + 1

y = x - 1

So the equation of the line that goes through the point (-1,-2) and is perpendicular to the line y = -x -1, is y = x - 1.

Cheers.

Answer:

B) y = -x - 3

Step-by-step explanation:

slope = -1

y = mx + b

-2 = -1(-1) + b

-3 = b

y = -x - 3

I need help will rate brainliest please

Answers

Answer:

the stone fell in the air for 7 sec and fell in the water for 5 sec

Answer:

Let time taken in air be 'a'

And the time taken in water be 'b'

a+b=12

Distance covered in air = 16a

′′′′′ ′′″″ water= 3b

16a + 3b = 127

Solve the two equations simultaneously

a= 7 secs

b= 5 secs

6
PO
2. In school of 900 studonts, it was
found that 600 students participate
in singing 500 students
in dancing and 125
do not participate
in both the activities.
participate​

Answers

Answer:

[tex]B = 325[/tex]

Step-by-step explanation:

Given

Total = 900

Singing = 600

Dancing = 500

None = 125

Required

Determine the number of students that participate in both

Representing; Singing with S, Dancing with D, Both singing and dancing with B and None with N;

In Set Notation;

[tex]Total = (S - B) + (D - B) + N + B[/tex]

Substitute 900 for Total, 600 for S, 500 for D and 125 for N

[tex]900 = (600 - B) + (500 - B) + 125[/tex]

Open Brackets

[tex]900 = 600 - B + 500 - B + 125 + B[/tex]

Collect Like Terms

[tex]900 = 600 + 500 + 125 - B - B + B[/tex]

[tex]900 = 1225- B - B + B[/tex]

[tex]900 = 1225- B[/tex]

Collect Like Terms

[tex]900 - 1225 = -B[/tex]

[tex]-325 = -B[/tex]

Multiply both sides by -1

[tex]-1 * -325 = -B * -1[/tex]

[tex]325 = B[/tex]

Reorder

[tex]B = 325[/tex]

Hence, the number of students that do not participate in both is 325

Please help I did the first 2 already.

Answers

The answer to C is 1.5 or 3/2

Since we know that 2x is equal to 3 because the solution is three and 3+3=6 then we divide 3 by 2 to get 3/2

Kevin ordered some books online for seven dollars each he paid a total of six dollars for shipping the total cost of the purchase was $97 how many books did he buy?

Answers

Answer:

a) 7b+6=97

b)b=13

Step-by-step explanation:

Total cost = $97

Cost of each book = $7

Cost of shipping =$6

Therefore ,

Cost of the total no. of books+ Cost of shipping = Total Cost

=>7b+6= 97   <------- Answer to part(a)

=>7b=97-6

=>7b=91

=>b=13

No. of books = 13 <--------- Part (b)

the difference between y and 3/8 is 3/4. workout the possible values of y

Answers

Answer:

y-3/8 =3/4y=3/4-3/8y=3/8

Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100100100 pieces of sushi in total. Sofia had already ordered and paid for 242424 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 121212 pieces and costs \$8$8dollar sign, 8. Let RRR represent the number of additional rolls that Sofia orders.

Answers

Answer:

Sofia will order 7 more rolls of sushi (84 pieces) and pay $56

Step-by-step explanation:

They need at least 100 pieces of sushi

Sofia had ordered and paid for 24 pieces of sushi already

Sushi comes in rolls

Each roll=12 pieces at $8

R=additional rolls that Sofia orders

Additional sushi= Needed sushi - ordered sushi

=100-24

=76 pieces of sushi

Each roll has 12 pieces

76/12=6.33

Sofia has to order in rolls

So, she will order 7 more rolls of sushi of 12 pieces each

12*7=84 pieces

Recall, that they needed at least 100 pieces, so the number of pieces could be more than 100

If Sofia orders 84 pieces + the already ordered 24 pieces

Total pieces=108 pieces

She has paid for 24 pieces (3 rolls) at $8 per roll

7 rolls=$8*7

=$56

♡ The Question/Task(s)! ♡

✦ || 1) Which inequality describes this scenario?

✦ || 2) What is the least amount of additional money Sofia can spend to get the sushi they need?

︶꒦︶꒷︶︶ʚ♡ɞ︶︶꒷︶꒦︶

♡ The Answer(s)! ♡

✦ || 1) The inequality is, "24 + 12R ≥ 100"!

✦ || 2) They need 56 Dollars!

I apologize if the answer is incorrect! ♡

︶꒦︶꒷︶︶ʚ♡ɞ︶︶꒷︶꒦︶

♡ The Step-By-Step Process! ♡

✦ || Sofia needs the sushi she's already ordered plus the additional sushi to be at least 100 pieces. We can represent this with an inequality whose structure looks something like this:

(sushi already ordered) + (additional sushi) [≤ or ≥] 100

Then, we can solve the inequality for R to find how many additional rolls Sofia needs to order. Sofia has already ordered and paid for 24 pieces. Each roll has 12 pieces, and R represents the number of additional rolls, so the number of additional pieces from these rolls is 12R. The number of pieces she's already ordered plus the additional pieces needs to be greater than or equal to 100 pieces. Since she can't order partial rolls, Sofia needs to reserve 7 additional rolls. And each roll costs $8, so ordering 7 additional rolls costs 7 ⋅ $8 = $56.

︶꒦︶꒷︶︶ʚ♡ɞ︶︶꒷︶꒦︶

♡ Tips! ♡

✦ || No Tips Provided!ヽ(>∀<☆)ノ

2x/9 +x/3 = 13/6, solve for x

Answers

Answer:

x = 3 9/10

Step-by-step explanation:

2x/9 +x/3 = 13/6

Get a common denominator on the left side

2x/9 + x/3 *3/3 = 13/6

2x/9 + 3x/9 = 13/6

5x/9 = 13/6

Multiply each side by 9/5 to isolate x

5x/9 *9/5 = 13/6 * 9/5

x = 117/30

Divide the top and bottom by 3

x = 39/10

x = 3 9/10

Answer:

[tex]\bold{\red{\boxed{\blue{ x = 3.9}}}}[/tex]

Step-by-step explanation:

[tex] \frac{2x}{9} + \frac{x}{3} = \frac{13}{6} \\ \frac{2x + 3x}{9} = \frac{13}{6} \\ \frac{5x}{9} = \frac{13}{6} \\ use \: \: cross \: \: multipication \\ 5x \times 6 = 9 \times 13 \\ 30x =11 7 \\ \frac{30x}{30} = \frac{117}{30} \\ x = 3.9[/tex]

Please answer this question now in two minutes

Answers

Answer:

m∠C = 102°

Step-by-step explanation:

This diagram is a Quadrilateral inscribed in a circle

The first step is to determine what m∠B

is

The sum of opposite angles in an inscribed quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

Second step is we proceed to determine the exterior angles of the circle

m∠ADC = 2 × m∠B

m∠ADC = 2 × 100°

m∠ADC = 200°

m∠ADC = m∠CD + m∠AD

m∠AD = m∠ADC - m∠CD

m∠AD = 200° - 116°

m∠AD = 84°

The third step is to determine m∠BAD

m∠BAD = m∠AD + m∠AB

m∠BAD = 84° + 120°

m∠BAD = 204°

The final step Is to determine what m∠C is

It is important to note that:

m∠BAD is Opposite m∠C

Hence

m∠C = 1/2 × m∠BAD

m∠C = 1/2 × 204

m∠C = 102°

The Three Stooges are having a pie eating contest. In 3 hours, Moe can eat 36 pies, Larry can eat 30, and Curly can eat 60. How many hours does it take them to eat 126 pies?

Answers

Answer:

3 hours

the information states in 3 hours they eat 36+30+60 = 126 pies.

Answer:

Altogether, the three stooges will consume 126 pies in three hours.

Step-by-step explanation:

1. In one hour, the three stooges can eat their total divided by three: Moe can eat 12 in one hour, Larry can eat 10 in one hour, and Curly can eat 20 in one hour. Therefore, the three stooges can eat 42 pies in one hour altogether. So, we have the equation 126 = 42h where h = the number of hours. Solving for 126 gives us 126/42 = h. h = 3. The three stooges can eat 126 pies in three hours.

Kareem wants to find the number of hours the average sixth-grader at his school practices an instrument each week. Which is the best way Kareem can get a representative sample?

Answers

This question is incomplete because the options are missing; here is the complete question:

Kareem wants to find the number of hours the average sixth-grader at his school practices an instrument each week. Which is the best way Kareem can get a representative sample?

A. He can randomly survey 50 boys in the school.

B. He can survey 30 students in the school band.

C. He can randomly survey 50 6th graders in the school.

D. He can survey 20 friends from his neighborhood.

The correct answer is C. He can randomly survey 50 6th graders in the school.

Explanation:

A representative sample is a portion of a population that shows the characteristics of all the population. In this context, for a sample to be representative it needs to include only individuals of the population that is studied. Also, ideally, individuals should be selected randomly as this guarantees the sample is not influenced by the researcher. According to this, option C is the best as this is the only one that focuses on the target population (6th graders) and the sample is random, which contributes to the sample being objective and representing the behavior of 6th-graders.

Answer:

He can randomly survey 50 sixth-graders in the school.

Step-by-step explanation:

Which of the binomials below is a factor of this trinomial? URGENT!!!

Answers

Answer:

C

Step-by-step explanation:

10×-28=-280

35-8=27

35×(-8)=-280

10x²+27x-28

=10x²+(35-8) x-28

=10x²+35x-8x-28

=5x(2x+7)-4(2x+7)

=(2x+7)(5x-4)

Answer: C) 2x+7

=========================================================

Explanation:

One way we can factor is through use the of the quadratic formula.

Let [tex]10x^2+27x-28 = 0[/tex]

For now, the goal is to find the two roots of that equation.

Plug a = 10, b = 27, c = -28 into the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(27)\pm\sqrt{(27)^2-4(10)(-28)}}{2(10)}\\\\x = \frac{-27\pm\sqrt{1849}}{20}\\\\x = \frac{-27\pm43}{20}\\\\x = \frac{-27+43}{20} \ \text{ or } \ x = \frac{-27-43}{20}\\\\x = \frac{16}{20} \ \text{ or } \ x = \frac{-70}{20}\\\\x = \frac{4}{5} \ \text{ or } \ x = -\frac{7}{2}\\\\[/tex]

The two roots are x = 4/5 and x = -7/2

For each root, rearrange the equation so we have 0 on the right hand side, and it's ideal to get rid of the fractions

x = 4/5

5x = 4

5x-4 = 0 gives us one factor

and

x = -7/2

2x = -7

2x+7 = 0 gives the other factor

The two factors are 5x-4 and 2x+7

Note how (5x-4)(2x+7) = 0 leads to the two separate equations of 5x-4 = 0 and 2x+7 = 0 due to the zero product property. Solving each individual equation leads to the two roots we found earlier.

Alternative methods to solve this problem are the AC factoring method (which leads to factor by grouping), using the box method, or you could use guess and check.

12 people can paint the orchard in one hour How long would it take five people Give your answer in minutes

Answers

Answer:

[tex] \boxed{144 \: \: \: minutes}[/tex]

Step-by-step explanation:

Let's solve :

[tex] \mathsf{ \: people \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:time \: ( \: in \: minutes)}[/tex]

[tex] \mathsf{12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 \: hour \: = \: 60 \: minutes }[/tex]

[tex] \mathsf{5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: t }[/tex]

The amount of time needed for completion is inversely proportional to the number of people working on the orchard. Let t be the amount of time ( in minutes ) needed when there are 5 people working.

[tex] \mathsf{ \frac{12}{5} = \frac{t}{60} }[/tex]

Apply cross product property

[tex] \mathsf{5t = 12 \times 60}[/tex]

Multiply the numbers

[tex] \mathsf{5t = 720}[/tex]

Divide both sides of the equation by 5

[tex] \mathsf{ \frac{5t}{5} = \frac{720}{5} }[/tex]

Calculate

[tex] \mathsf{t = 144 \: minutes}[/tex]

Hope I helped!

Best regards!!

It will take five people 144 minutes to paint the orchard.

12 people can paint the orchard in one hour, which is 60 minutes.

If there are five people, it will take them 12 × 60 / 5 = 144 minutes to paint the orchard.

So the answer is 144

Here's the explanation:

We know that the number of people and the time it takes to paint the orchard are inversely proportional. This means that if we increase the number of people, the time it takes to paint the orchard will decrease.

We can also set up a proportion to find the time it takes five people to paint the orchard. The proportion will look like this:

12 people : 5 people :: 60 minutes : x minutes

Cross-multiplying, we get:

12 × x = 5 × 60

x = 5 × 60 / 12

x = 144 minutes

Therefore, it will take five people 144 minutes to paint the orchard.

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Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles? ∠T ≅ ∠C ∠T ≅ ∠A ∠T ≅ ∠D

Answers

Answer:

∠T ≅ ∠A

Step-by-step explanation:

Since, ∆MTW ≅ ∆CAD

Therefore, ∠T ≅ ∠A (cpct)

the area of a trapezium is 14.7cmsquare. if the parallel sides are 5.3cm and 3.1cm long,find the perpendicular distance between them

Answers

The perpendicular distance of the trapezoid is 3.5 cm

How to determine the perpendicular distance?

The given parameters are:

Parallel sides = 5.3 cm and 3.1 cmArea = 14.7 square cm

The area of a trapezoid is:

Area = 0.5 * (Sum of parallel sides) * perpendicular distance

So, we have:

14.7 = 0.5 *(5.3 + 3.1) * perpendicular distance

Evaluate

Perpendicular distance = 3.5

Hence, the perpendicular distance of the trapezoid is 3.5 cm

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What is the possibility that a red or green marble will be selected from a bag containing 9 red marbles, 6 blue marbles , 7 green marbles and 11 yellow marbles

Answers

Answer:

16/33

Step-by-step explanation:

We have a bag of :

9 red marbles

6 blue marbles

7 green marbles

11 yellow marbles

Total number of marbles = 33 marbles.

The possibility that a red or green marble will be selected from a bag

P( Red or Green) = P(Red) + P(Green)

In the question we are not told if it is with replacement or without. We do both

With replacement

P( R or G) = P(Red) + P(Green)

P(Red)= 9/33

P(Green) = 7/33

= 9/33 + 7/33

= 16/33

Therefore, the possibility that a red or green marble will be selected from a bag is 16/33

Please show your work. I will give brainliest to the right answer!

Answers

Answer:

[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]

Step-by-step explanation:

Given:

Focus of parabola: (-4, 6)

Directrix: y = 2

Required:

Equation for the parabola

SOLUTION:

Using the formula, [tex] y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) [/tex] , the equation for the parabola can be derived.

Where,

a = -4

b = 6

k = 2

Plug these values into the equation formula

[tex] y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) [/tex]

[tex]y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)[/tex]

[tex]y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}[/tex]

[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]

In pentagon ABCDE, A = 87º, B = 1250, C = 63º, and E = 95º. Find
D.
A. 160
B. 169
C. 170
D 530​

Answers

Answer:

[tex]D = 170\º[/tex]

Step-by-step explanation:

Given

Shape: Pentagon

[tex]A = 87\º[/tex]

[tex]B = 125\º[/tex]

[tex]C = 63\º[/tex]

[tex]E = 95\º[/tex]

Required

Find D

From the sum of angles in a Pentagon; we have that

[tex]A + B + C + D + E = 540[/tex]

Substitute values for A, B, C and E

[tex]87\º + 125\º + 63\º + D + 95\º = 540\º[/tex]

Collect Like Terms

[tex]87\º + 125\º + 63\º + 95\º + D = 540\º[/tex]

[tex]370\º + D = 540\º[/tex]

Collect Like Terms

[tex]D = 540\º - 370\º[/tex]

[tex]D = 170\º[/tex]

Hence, from the list of given options, the correct answer is 170

Solve for x : 2^(x-5) . 5^(x-4) = 5​

Answers

Answer:

x = 5

Step-by-step explanation:

Notice that there is also a base 5 on the right hand side of the equation, therefore, let's move [tex]5^{x-4}[/tex] to the right by dividing both sides by it. and then re-writing the right hand side as 5 to a power:

[tex]2^{x-5}\,*\,5^{x-4}=5\\2^{x-5}=5/5^{x-4}\\2^{x-5}=5\,*\,5^{4-x}\\2^{x-5}=5^{5-x}[/tex]

Now apply log to both sides in order to lower the exponents (where the unknown resides):

[tex](x-5)\,log(2)=(5-x)\,log(5)[/tex]

Notice that when x = 5, this equation is true because it makes it the identity: 0 = 0

So, let's now examine what would be the solution of x is different from 5, and we can divide by (x - 5) both sides of the equation:

[tex]log(2)=\frac{5-x}{x-5} \,log(5)\\log(2)=-1\,\,log(5)\\log(2)=-log(5)[/tex]

which is an absurd because log(2) is [tex]\neq[/tex] from log(5)

Therefore our only solution is x=5

Answer:

if decimal  no solution

if multiply x =5

Step-by-step explanation:

If this is a decimal point

2^(x-5) . 5^(x-4) = 5

Rewriting .5 as 2 ^-1

2^(x-5)  2 ^ -1 ^(x-4) = 5

We know that a^ b^c = a^( b*c)

2^(x-5)  2 ^(-1*(x-4)) = 5

2^(x-5)  2 ^(-x+4) = 5

We know a^ b * a^ c = a^ ( b+c)

2^(x-5 +-x+4) = 5

2^(-1) = 5

This is not true so there is no solution

If it is multiply

2^(x-5)  * 5 ^(x-4) = 5

Divide each side by 5

2^(x-5)  * 5 ^(x-4) * 5^-1 = 5/5

We know that a^ b * a^c = a^ ( b+c)

2^(x-5)  * 5 ^(x-4 -1)  = 1

2^(x-5)  * 5 ^(x-5)  = 1

The exponents are the same, so we can multiply the bases

a^b * c*b = (ac) ^b

(2*5) ^ (x-5) = 1

10^ (x-5) = 1

We know that 1 = 10^0

10^ (x-5) = 10 ^0

The bases are the same so the exponents are the same

x-5 = 0

x=5

When factoring 6x2−7x−20 by grouping, how should the middle term be rewritten? It should be written as 8x−15x. It should be written as −2x−5x. It should be written as x−8x. It should be written as −x−7x. I think it should be B but im not quite sure Is the given equation a quadratic equation? x(x−6)=−5 The equation is not a quadratic equation because there is no x2-term. The equation is a quadratic equation because there is an x2-term. The equation is not a quadratic equation because the expression is not equal to zero. The equation is not a quadratic equation because there is a term with degree higher than 2. For this one i think its A but once again im not sure. Which of the following is an example of the difference of two​ squares? x2−9 x3−9 (x+9)2 (x−9)2 this one i have no clue i would appreciate it if anyone could explain this one.

Answers

Answer:

(3x+4)(2x-5)

Step-by-step explanation:

Factor by grouping.

Find the volume of the given shapes. Round to the nearest tenth if necessary.

Answers

Answer:

Step-by-step explanation:

5.

volume=l×w×h=8×6×7=336 mi³

6.

diameter=16 yd

radius=16/2=8 yd

[tex]volume=\frac{4}{3} \pi \times 8^3=\frac{2048}{3} \pi \approx 2144.67 \approx 2144.7 yd^3[/tex]

The time required to drive a fixed distance varies inversely as the speed. It takes 2 hr at a speed of 200 km/h to drive a fixed distance. How long will it take to drive the same distance at a speed of 80 km/h?

Answers

Answer:

5 hours

Step-by-step explanation:

From the question, we are told that:

Time required to drive a fixed distance varies inversely as the Speed

T ∝ 1/S

k = proportionality constant hence,

T =k × 1/S

T = k/S

Step 1

Find k

It takes 2 hr at a speed of 200 km/h to drive a fixed distance

T = 2 hours, S = 200km/h

T = k/S

2 = k / 200

k = 2 × 200

k = 400

Step 2

How long will it take to drive the same distance at a speed of 80 km/h?

S = 80km/h

T = k/S

k = 400

T = 400/80

T = 5

Therefore, it takes 5 hours to drive the same distance at a speed of 80km/hr

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