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Answer:

1. tan(65) = x/3

x = 3tan(65)

= 6.434

≈ 6.4

(nearest 10th)

2. cos(43) = AB/17

AB = 17cos(43)

= 12.433

≈ 12.43

(nearest 100th)

Answer:

3 1/3 each

Step-by-step explanation:

10/3=3 1/3

Solution :

Transforming given equations :

[tex]1)\ P = 600( 1 + \dfrac{12}{100})^t\\\\2)\ P = 1000( 1 + \dfrac{3}{100})^t\\\\3)\ P = 200( 1 + \dfrac{8}{100})^t\\\\4)\ P = 900( 1 - \dfrac{10}{100})^t[/tex]

From above equations we can see that equation 1) has largest percentage growth rate and the percent growth rate is 12% .

Hence, this is the required solution.

Answer: (i), 12%

Step-by-step explanation:

Given

The Population of four towns is given

(i) [tex]P=600(1.12)^t[/tex] i.e.

[tex]\Rightarrow P=600(1+0.12)^t\\\Rightarrow P=600(1+12\%)^t[/tex]

rate=12%

(ii) [tex]P=1000(1.03)^t[/tex]

[tex]\Rightarrow P=1000(1+0.03)^t\\\Rightarrow P=1000(1+3\%)^t[/tex]

rate=3%

(iii) [tex]P=200(1.08)^t[/tex]

[tex]\Rightarrow P=300(1+0.08)^t\\\Rightarrow P=300(1+8\%)^t[/tex]

rate=8%

(iv) [tex]P=900(0.90)^t[/tex]

[tex]\Rightarrow P=900(1-0.10)^t\\\Rightarrow P=900(1-10\%)^t[/tex]

rate=10% fall

So, the largest growth rate is for town (i)  i.e. 12%

Answer:

there are 52 cards in a deck so the chance is a red card (or not a red card) is 26 out of 52.

Step-by-step explanation:

The solution is 12/13

The probability that the selected card is not an ace but a red card is 12/13

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

The value of probability lies between 0 and 1

Given data ,

Let the probability of the selected card is not an ace but a red card be P

Now , the equation will be

Mason randomly chooses a card from a standard deck of playing cards

So , the probability that the card is a red card is

There are 26 red cards in the deck of 52 cards

So , the probability of selecting a red card = 26/52

Now , from the 26 red cards , the probability that the card is not an ace would be = 26 - ( Ace of hearts + Ace of diamonds )

And ,

The probability of the selected card is not an ace but a red card P = 24/26

The probability of the selected card is not an ace but a red card P = 12/13

Therefore , the value of P is 12/13

Hence , the probability is 12/13

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Answer:

$1.33

Step-by-step explanation:

Determine the cost per ounce of the larger bottle

cost per ounce = cost of larger bottle / total ounces

$12.99 / 150 = $0.0866

Multiply cost per ounce by 100

$0.0866 x 100 = $8.66

Subtract the above figure from 9.99

9.99 -  $8.66 = $1.33

Answer:

1

Step-by-step explanation:

Assuming your mean we have the points

(6, -10) and ( 3, -13)

We can use the slope formula

m = (y2-y1)/(x2-x1)

m = ( -13 - -10)/( 3 - 6)

    = (-13+10)/( 3-6)

   = -3 / -3

    = 1

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the regression line is not given.

However, I will give a general explanation of how to calculate the degree of freedom of a slope of regression line

The degree of freedom is calculated using:

[tex]df = n - k[/tex]

Where

[tex]k \to number\ of\ parameters[/tex]

[tex]n \to sample\ size.[/tex]

For a regression line; there are two parameters that are being estimates;

The intercept and the slope. So:

[tex]k = 2[/tex]

Hence, the degree of freedom of a slope of regression line is:

[tex]df = n -2[/tex]

So; if for example

[tex]n =101[/tex]

the degree of freedom will be:

[tex]df =101 - 2[/tex]

[tex]df =99[/tex]

Answer:

$32.50

Step-by-step explanation:

The total amount of candy bars is 26. Half of that is 13. 13 times the $2.50 for each is $32.50.

Answer:

c

Step-by-step explanation:

yeah tha answer is c I can't explain it rn but for now put c

Answer:

False

Step-by-step explanation:

There might be a chance I am wrong though sorr for the inconvinience

Answer: How are we going to point it?

Step-by-step explanation:

Answer:

57639 employees in total.

Step-by-step explanation:

28.8% of X = 16600

X = 16600 / 28.8%

= 16600 / 0.288

= 57638.89

=57639

Answer: 1.5

mean: 104

S.D: 6

110-104/6=1.5

Answer:

Domain: [tex][3,\infty)[/tex]

Range: [tex][6,\infty)[/tex]

Step-by-step explanation:

I assume you mean [tex]y=\sqrt{x-3} +6[/tex]?

Take note of how x cannot be less than 3 because it would result in a negative number under the radical, which isn't real. However, x CAN be 3 because [tex]\sqrt{3-3}+6=\sqrt{0}+6=0+6=6[/tex] which is real.

Therefore, the domain of the function is [tex][3,\infty)[/tex]

As for the range of the function, we saw previously that the minimum of the domain resulted in the minimum of the range, which was 6.

Therefore, the range of the function is [tex][6,\infty)[/tex]

See attached graph below for a visual.

Answer:

C

4712 cm³ exactly

Step-by-step explanation:

10² * pi is the area of the circle

then just multiply with the height

Answer:

C. 1500π ≈ 4710 cm³

Step-by-step explanation:

Volume = πr²h

Volume = π * 100 * 15

Volume = 1500π ≈ 4710 cm³

If my answer is incorrect, pls correct me!

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-Chetan K

9514 1404 393

Answer:

  (3)  35·cos(57°)

Step-by-step explanation:

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

For the given triangle, this is ...

  cos(57°) = QR/QS

Multiplying by QS gives ...

  QS·cos(57°) = QR

Filling in the value of QS, we have ...

  QR = 35·cos(57°)

Answer:

1 1/6

Step-by-step explanation:

5/6 + 3/9

Simplify 3/9 by dividing the top and bottom by 3

5/6 + 1/3

Get a common denominator of 6

5/6 + 1/3 *2/2

5/6 + 2/6

7/6

Rewriting

6/6 +1/6

1 1/6

Answer:

D

Step-by-step explanation:

because in standard form the first number can not be greater than 10 above 10 it should be in points. e.g. D must be 6.12×10^5

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the image of the polygon is not given.

I will answer this question with the attached image (similar to your question)

The attached polygon is a trapezoid of the following dimensions.

[tex]Height = 4ft[/tex]

Parallel sides

[tex]Side\ 1 = 4ft[/tex]

[tex]Side\ 2 = 4ft+1ft = 5ft[/tex]

So, the area is:

[tex]Area = \frac{1}{2} * (Side\ 1 + Side\ 2) * Height[/tex]

[tex]Area = \frac{1}{2} * (4ft + 5ft) * 4ft[/tex]

[tex]Area = \frac{1}{2} * 9ft * 4ft[/tex]

[tex]Area = 18ft^2[/tex]

Answer:

What exactly is the question?? u only gave the statement -_-

Step-by-step explanation:

Answer:

433 in.²

Step-by-step explanation:

Divide the figure into 2 rectangles

Area of the figure = area of the bigger rectangle + area of smaller rectangle

✔️Area of bigger rectangle = L*W

L = 29 in.

W = 13 in.

Area of the bigger rectangle = 29*13

= 377 in.²

✔️Area of the smaller rectangle = L*W

L = 7 in.

W = 8 in.

Area of the bigger rectangle = 7*8

= 56 in.²

✅Area of the figure = 377 + 56 = 433 in.²

Answer:

a. 0.008 = 0.8% probability that the person will answer all three questions correctly.

b. 0.096 = 9.6% probability that the person will answer exactly two questions correctly.

c. 0.384 = 38.4% probability that the person will answer exactly one question correctly.

d. 0.512 = 51.2% probability that the person will answer no questions correctly.

e. The expected value of the person’s score for the three questions is -0.2.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the person answers it correctly, or they do not. The probability of a person answering a question correctly is independent of any other question. This 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 X happening.

Each question has five possible answers.

Person has no idea which option is correct, so the probability of answering correctly is:

[tex]p = \frac{1}{5} = 0.2[/tex]

Three questions:

This means that [tex]n = 3[/tex]

a. What is the probability that the person will answer all three questions correctly?

This is [tex]P(X = 3)[/tex]. So

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

[tex]P(X = 3) = C_{3,3}.(0.2)^{3}.(0.8)^{0} = 0.008[/tex]

0.008 = 0.8% probability that the person will answer all three questions correctly.

b. What is the probability that the person will answer exactly two questions correctly?

This is [tex]P(X = 2)[/tex]. So

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

[tex]P(X = 2) = C_{3,2}.(0.2)^{2}.(0.8)^{1} = 0.096[/tex]

0.096 = 9.6% probability that the person will answer exactly two questions correctly.

c. What is the probability that the person will answer exactly one question correctly?

This is [tex]P(X = 1)[/tex]. So

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

[tex]P(X = 1) = C_{3,1}.(0.2)^{1}.(0.8)^{2} = 0.384[/tex]

0.384 = 38.4% probability that the person will answer exactly one question correctly.

d. What is the probability that the person will answer no questions correctly?

This is [tex]P(X = 0)[/tex]. So

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

[tex]P(X = 0) = C_{3,0}.(0.2)^{0}.(0.8)^{3} = 0.512[/tex]

0.512 = 51.2% probability that the person will answer no questions correctly.

e. Suppose that the person gets one point of credit for each correct answer and that 1/3 point is deducted for each incorrect answer. What is the expected value of the person’s score for the three questions?

The expected number of correct answer is:

[tex]E(X) = np = 3*0.2 = 0.6[/tex]

And the expected number of wrong answers is 3 - 0.6 = 2.4. So, the expected score is:

[tex]S(x) = 0.6 - \frac{2.4}{3} = 0.6 - 0.8 = -0.2[/tex]

The expected value of the person’s score for the three questions is -0.2.

Answer:

The answer is 0.60b + 0.30w = 150; 60 + 0.30w = 150

Step-by-step explanation:

Answer:

Solution given:

side1=2units

side2=8units

height[h]=6units.

now

area of trapezoid=½h(side1+side2)=½*6(8+2)=

30units².

Answer:

471.24

Step-by-step explanation:

V=πr2h/3

radius = 5 and length = 18

answer = 471.24

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Answer:

The answer Plato wants is 150Pi,

Step-by-step explanation:

Answer:

the answer would be B: 2.125lb.

Answer: B; 2.125lb

Step-by-step explanation: 34 ounces to pounds is 2.13lb (rounded, the exact number is 2.125lb

Step-by-step explanation:

Question 264138: How many liters of a 40% alcohol solution must be mixed with a 65% solution to obtain 20 liters of a 50% solution? x=8 gallons of 65% solution is used. 20-8=12 gallons of 40% solution is used.

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