which is equivalent to the expression shown below

Answer:

AC

Step-by-step explanation:

First, let's find m∠B and m∠C by solving for x. Since the sum of interior angles in a triangle is 180°, we know that:

60 + 3x - 2 + 2x + 7 = 180

5x + 65 = 180

5x = 115

x = 23° so m∠B = 3(23) - 2 = 67° and m∠C = 2(23) + 7 = 53°. The longest side of a triangle is always opposite to the largest angle of the triangle, and since m∠B is the largest, we know that the side opposite to ∠B is the longest. That side is AC.

In triangle ABC, the longest side is AC, since it is opposite the biggest angle ∠B.

According to the angle sum property of a triangle, the sum of the three interior angles is 180°.

In a triangle, the longest side is on the opposite side of the biggest angle, and the shortest side is on the opposite side of the smallest angle.

We are given the angles of the triangle ABC. We are asked to find the longest side in the triangle ABC.

By the angle sum property of a triangle, we know that,

m∠A + m∠B + m∠C = 180°

or, 60° + (3x - 2)° + (2x + 7)° = 180°

or, 5x + 65° = 180°

or, 5x = 180° - 65° = 115°

or, x = 115/5 = 23.

∴ m∠A = 60°.

m∠B = (3x - 2)° = (3(23) - 2)° = (69-2)° = 67°.

m∠C = (2x + 7)° = (2(23) + 7)° = (46 + 7)° = 53°.

∵ m∠B is the largest angle, the side opposite to it, that is, AC is the longest side of the triangle.

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Answer:

13 weeks

Step-by-step explanation:

V = -15 x + 200 x 213.33 weeks 6 = -15x + 200 after 13 weeks.

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

The number of weeks Micah needs to spend so that her birthday money of $200 will be gone is 13 weeks.

Given,

Micah was given $200 for his birthday.

Each week he spends $15 on comic books.

We need to find in how many weeks will his birthday money be gone.

We need to make sure we get the required value on the left side.

If 1 week = 7 days

Find how many days in 2 weeks

2 weeks = ​2 x 7 days = 14 days

We have  2 weeks on the left side.

If 2 items = $5

5/2 x 2 items = 5/2 x $5

5 items = $25/2 = $12.5

Find the total amount Micah has.

= $200

Find the amount spend each week.

= $15

Find how many weeks she must spend to spend $200.

We have,

$15 = 1 week

Multiply 200/15 on both sides.

200/15 x $15 = 200/15 x 1 week

$200 = 13.33 weeks

This means 13 weeks.

Thus the number of weeks Micah needs to spend so that her birthday money of $200 will be gone is 13 weeks.

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Answer:

21

Step-by-step explanation:

tcctvucycyccyctctctchu ycuvuvuvy t r y y g g t g

Answer:

x is greater than 4

Step-by-step explanation:

4x + 5 is greater than 13

you want to find out what x is

4 - 4 x + 5 is greater than 13 - 4 ( whatever you do to one side you have to do to the other)

x + 5 is greater than 9

x + 5 - 5 is greater than 9 - 5

x is greater than 4

the answer is 7-7y i think if not the it should be 7+7y

Answer:

0.10

Step-by-step explanation:

Average age of Iowa residents = 37 years

Amy believes that the average age in her hometown in Iowa is not equal to this average

Alternative hypothesis : µ ≠ 37

Sample size = 30

t - test statistic = 1.311

The p-value of the test statistic can be obtained using the online p-value calculator :

The p- value obtained using a t-test statistic value of 1.311 and a degree of freedom (df =N-1; 30 - 1 = 29) at a 0.05 significance level = 0.100072 = 0.10 ( nearest hundredth)

Answer:

0.20

Step-by-step explanation:

In order to find the p-value we first need the degrees of freedom because we are running a t-test. The df = n-1 = 30-1 = 29. If Amy is using the alternative hypothesis, µ ≠ 531, this is a two-tailed test. In order to find the p-value, we simply need to find the probability of being as extreme or more extreme as our current test statistic in one-tail and then multiply it by 2. Another way to describe this is it is the tail probability/area. If we go to the df row of 29 and then scan to the right we see 1.311 is in the 0.10 column. So if we multiply this by 2, we find 0.20 or 20% in both of the tails. So the p-value is 0.20.

Answer:

399.17 miles

Step-by-step explanation:

Gunnar's car gets 22.4 miles per gallon. His gas tank can hold 17.82 gallons of gas.

Gunnar's car travels with one gallon of gas = 22.4 miles

He can travel with 17.82 gallon of gas = 17.82 × 22.4

                                                             = 399.168 ≈ 399.17 miles

Gunnar can travel 399.17 miles if he uses all of the gas in the gas tank.

Answer: 0.8

Step-by-step explanation:

Given the following :

Sum of Square Error Error (SSE) = 100 which is the difference between the actual and predicted value.

Sum of Square due to regression (SSR) = 400

The Coefficient of determination (R^2) :

(Sum of Square Regression(SSR)) / Sum of Squared total (SST))

Sum of Squared total (SST) = SSE + SSR

Sum of Squared Total = (100 + 400) = 500

R^2 = 400 / 500

R^2 = 0.8

Complete Question

The  complete question is shown on the first uploaded image  

Answer:

a

  [tex]n(t) = 120 e^{(0.056t)}[/tex]

b

  [tex]n(36) = 901 \ rats[/tex]

c

 [tex]t = 50 \ months[/tex]

Step-by-step explanation:

From the question we are told that

    The  original number of  rats that swim from the wreckage to a deserted island is

   The population on the island grows exponentially according to the model

          [tex]n(t) = n_o e^{rt}[/tex]

     The  number of rats after t =  15 months is  280

So

     [tex]n(15) = 120 e^{15 * r } = 280[/tex]

=>   [tex]120 e^{15 * r } = 280[/tex]

=>   [tex]e^{15r} = 2.33[/tex]

=>  [tex]15r = 0.8459[/tex]

=>   [tex]r = 0.056[/tex]

Therefore the population t months after the arrival of the rats is mathematically represented as

      [tex]n(t) = 120 e^{(0.056t)}[/tex]

Here t is in months

Considering question b

   For  t =  3 years  =  12 * 3 =  36 months

   Then the number of rats that will be present is mathematically represented as

     [tex]n(36) = 120 e^{0.056 * 36 }[/tex]

      [tex]n(36) = 901 \ rats[/tex]

Considering question c

Now  the number of rats considered is  n(t) =  2000

So  

     [tex]n(t) = 2000 = 120e^{0.056t}[/tex]

=>    [tex]2000 = 120e^{0.056t}[/tex]

=>  [tex]16.67 = e^{0.056t}[/tex]

Taking natural log of both sides

=>   [tex]0.056 t = 2.81[/tex]

=>   [tex]t = 50 \ months[/tex]

Answer:

y = x - 1

Step-by-step explanation:

Answer:

b would be a negative number

Answer:  The sign of b is negative or  -

Step-by-step explanation:

If you multiply two negative numbers you will have a positive number. And if you multiply a positive and negative numbers you will have  a negative answer.

Answer:

1684

Step-by-step explanation:

x ÷ 17 > 99

x > 17 * 99

x > 1683

The least whole number that is greater than 1683 is 1684.

Answer: 1684

Answer:

1683

Step-by-step explanation:

To undo the problem you do 99 times 17 which is 1683. Then you know that 1683 divided by 17 is 99.

Answer:

 The  test statistics is [tex]t = -1.40[/tex]

  The critical value is  [tex]Z_{\alpha } = 2.33[/tex]

   The null hypothesis is rejected

Step-by-step explanation:

From the question we are told that

   The sample size  for men is  [tex]n_1 = 80[/tex]

    The sample  proportion of men that own a cat is  [tex]\r p _M = 0.40[/tex]

     The  sample  size for  women is [tex]n_2 = 80[/tex]

     The sample  proportion of women that own a cat is  [tex]\r p_F = 0.51[/tex]

     The level of significance is  [tex]\alpha = 0.10[/tex]

   The  null hypothesis is  [tex]H_o : \r p _M = \ r P_F[/tex]

    The alternative hypothesis is  [tex]H_a : \r p _M < \r p_F[/tex]

Generally the test statistic is mathematically represented as

        [tex]t = \frac{(\r p_M - \r p_F)}{\sqrt{\frac{(p_M*(1-p_M)}{n_1 } } + \frac{p_F*(1-pF)}{n_2 } }[/tex]

=>  [tex]t = \frac{(0.40 - 0.51)}{\sqrt{\frac{(0.40 *(1-0.41)}{80} } + \frac{0.51*(1-0.51)}{80 } }[/tex]

=>   [tex]t = -1.40[/tex]

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

     [tex]Z_{\alpha } = 2.33[/tex]

The p-value  is obtained from the z-table ,the value is  

    [tex]p-value = P( Z < -1.40) = 0.080757[/tex]

=>    [tex]p-value = 0.080757[/tex]

Given that the [tex]p-value < \alpha[/tex] then we reject the null hypothesis

Answer:

1/4x + 3

Step-by-step explanation:

The question said one-third(1/3) not one-fourth(1/4).

1/3x + 4 can also be written as x/3 + 4.

Answer:

1/4x + 3

Step-by-step explanation:

expressions does not represent "four more than one-third x"

1/3x + 4 --- No.

x/3 + 4  --- No.

1/4x + 3 --- Yes. it does not represent 4 + 1/3x. you can tell it by +3

Answer:

newzz new new me he new new

Answer:

oiuhj90pkomnjhb vcfgtyu789i0op,lmkn bvghyu7890opklmnjbhgvfty67890-p[lkjhngvty67u890-op[l;',

Step-by-step explanation:

Answer:

True

Explanation:

1/2 (up the hill) - 1/2 (down the hill) = 0

Answer: A

16 minutes

Step-by-step explanation:

The required time to inflate the balloon to Two-thirds of its maximum Volume is 16 minutes.

The rate of change is defined as the change in value with the rest of the time is called rate of change.

Here,
radius = 55 / 2 = 27.5
Since volume is directly proportional to the cube of the radius,
So,
For maximum volume,
V ∝ R³

and
2/3V = v
2/3R³ = r³
r = 27.5 ∛2/3
r = 24
Now,
the radius increases at a rate of 1.5 feet per minute.
Time to reach a radius of 24 feet,
= 24 / 1.5
= 16 minutes

Thus, the required time to inflate the balloon to Two-thirds of its maximum Volume is 16 minutes.

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Step-by-step explanation:

Hey, there!!

Let's solve it simply,

angle ONP = 60°+55° { as exterior angle is equal to the sum of opposite interior angle}.

Therefore, angle ONP = 115°.

Now, let's solve for x,

x+ 115°=180° { because the sum of co-interior angle is 180°}.

x= 180°-115°

Therefore, the measure of angle x is 65°.

Hope it helps...

Answer:

[tex]\Huge \boxed{{x=65\° }}[/tex]

Step-by-step explanation:

l and m are parralel lines.

The third angle in the triangle is also x, because of corresponding angles.

Angles in a triangle add up to 180 degrees.

Create an equation and solve for x.

x + 60 + 55 = 180

Add the numbers.

x + 115 = 180

Subtract 115 from both sides.

x = 65

Answer:

D. $10,909.09

Step-by-step explanation:

The class recovery period for residential rental property each year = 27.5 years

The cost basis for the residential property = $300,000

The amount he will be able to depreciate

= Cost basis/ Number of years

= $300000/ 27.5 years

=$10, 909.090909

Approximately ≈ $10,909.09

The amount he will be able to depreciate  using the class recovery period for residential rental property each year is: D. $10,909.09.

Using this formula

Depreciation=Rental unit amount/ MACRS residential rental property recovery period

Where:

Rental unit amount=$300,000

MACRS Residential rental property recovery period=27.5 years

Let plug in the formula

Depreciation=$300,000/27.5

Depreciation=$10,909.09

Inconclusion the amount he will be able to depreciate  using the class recovery period for residential rental property each year is: D. $10,909.09.

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Answer:

110 cupcakes are left

Step-by-step explanation:

200-90 is 110

Answer:

110 cupcakes

Step-by-step explanation:

If you have 200 cupcakes and you give away 90, that means you only have [tex]200-90[/tex] cupcakes left.

[tex]200 - 90 = 110[/tex]

So you have 110 cupcakes left.

Hope this helped!

Answer:

p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]

Step-by-step explanation:

Given equations:

2p - 3q = 4        -----------(i)

3p + 2q = 9       ------------(ii)

Let's solve this equation simultaneously using the elimination method

(a) Multiply equation (i) by 3 and equation (ii) by 2 as follows;

[2p - 3q = 4]        x 3

[3p + 2q = 9]       x 2

6p - 9q = 12            -------------(iii)

6p + 4q = 18            -------------(iv)

(b) Next, subtract equation (iv) from equation (iii) as follows;

     [6p - 9q = 12]        

 -   [6p + 4q = 18]    

            -13q = -6      -----------------(v)

(c) Next, make q subject of the formula in equation (v)

      q = [tex]\frac{6}{13}[/tex]

(d)  Now substitute the value of q = [tex]\frac{6}{13}[/tex] into equation (i) as follows;

     2p - 3([tex]\frac{6}{13}[/tex]) = 4

(e)  Now, solve for p in d above

Multiply through by 13;

26p - 18 = 52

Collect like terms

26p = 52 + 18

26p = 70

Divide both sides by 2

13p = 35

p = [tex]\frac{35}{13}[/tex]

Therefore, p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]

Answer:

Mercury, Venus, Earth, Mars, and Uranus

Step-by-step explanation:

Calculate the escape velocity for each planet, using the equation v = √(2gR).

[tex]\left[\begin{array}{cccc}Planet&R(m)&g(m/s^{2})&v(m/s)\\Mercury&2.43\times10^{6}&3.61&4190\\Venus&6.07\times10^{6}&8.83&10400\\Earth&6.37\times10^{6}&9.80&11200\\Mars&3.38\times10^{6}&3.75&5030\\Jupiter&6.98\times10^{7}&26.0&60200\\Saturn&5.82\times10^{7}&11.2&36100\\Uranus&2.35\times10^{7}&10.5&22200\\Neptune&2.27\times10^{7}&13.3&24600\end{array}\right][/tex]

The rocket's maximum velocity is double the Earth's escape velocity, or 22,400 m/s.  So the planets the rocket can escape from are Mercury, Venus, Earth, Mars, and Uranus.

Answer:

28

Step-by-step explanation:

83 - [59 - (22-18)]

= 83 - [59 - 4]

= 83 - 55

= 28

Answer:

#9 x=21

#10 a. QP  b. 8  c. 18

Step-by-step explanation:

#9 use the theorem where the ratio between a midline and the base of the triangle is 1:2

as we know the midline and the base is 1:2

this means

2(4x-65)=2x-4

  4x-65=x-2

    3x=63

      x=21

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

#10

a. RS|| QP (Remember to write the letters accordingly)

b. 8 (As mentioned before of the ratio 1:2)

c. 18

Answer:

The answer is not complete. I will explain the concept of profit to you.

Step-by-step explanation:

We can determine profit deducting direct costs (cost price) of commodities from sales (selling prices) of the commodities.

Profit = Selling Price - Cost Price

Example:

A trader buys some dresses for #2,500 in May and agrees to pay for it in three months’ time. He sells off all the dresses in August for #4,500. The profit for the month is #2,000.

The formula for percentage profit is [tex]\frac{profit * 100}{cost price}[/tex]

The formula for gross profit is Revenue – Cost of Sold Items

Profit Margin =  [tex]\frac{Total Income}{Net Sales}[/tex] * 100

While Gross Profit Margin can be calculated as [tex]\frac{Gross Profit}{Net Sales}[/tex] * 100

Any of these formulas can be used to calculate profit-related questions.

Answer: p = 13.9

Step-by-step explanation: 7(p-9) = 34.3 multiply 7 into p and -9

7p - 63 = 34.3  add 63 into both sides

7p = 97.3  divide 7 into both sides.

p = 13.9

This question can be solved in  two ways

the equation given is  7(p-9)=34.3

The first step to take is to divide both sides of the equation by 7

p - 9 = 34.3 / 7

p - 9 = 4.9

The second step is to combine similar terms

p = 4.9 + 9 = 13.9

A second method

the equation given is  7(p-9)=34.3

1. expand the bracket

7p - 63 = 34.3

2. Combine similar terms

7p = 34.3 + 63

7p = 97.3

3. Divide both sides of the equation by 7

p = 13.9

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Answer:

[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]

Step-by-step explanation:

The question is incomplete; However

[tex]A = (-2, -4)[/tex]

[tex]B = (6, 1)[/tex]

Required

Determine coordinates of P

When line segment is divided in ratios, the following formula calculates the coordinates;

[tex]P(x,y) = \{\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\}[/tex]

In this case;

[tex]m:n = 2:1[/tex]

[tex](x_1,y_1) = (-2, -4)[/tex]

[tex](x_2,y_2) = (6, 1)[/tex]

So, the coordinates of P is calculated as thus

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

[tex]P(x,y) = \{\frac{12 -2}{3}, \frac{2 -4}{3}\}[/tex]

[tex]P(x,y) = \{\frac{10}{3}, \frac{-2}{3}\}[/tex]

Hence, the coordinates of P is

[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]

The question is incomplete, the points A and B are:

A = (-2, -4)

B = (6, 1)

We want to find a point P in the segment AB such that the ratio of AP to PB is 2:1

We will find that:

[tex]P = (\frac{2}{3} , \frac{7}{3} )[/tex]

The general formula for two points (x₁, y₁) and (x₂, y₂), the coordinates of a point that separates the segment in a ratio j:k is

[tex]P = (\frac{j*x_1 + k*x_2}{j + k} , \frac{j*y_1 + k*y_2}{j + k})[/tex]

So we only need to use that general formula:

[tex]P = P = (\frac{2*(-2) + 1*6}{3} , \frac{2*(-4) + 1*1}{3})\\\\P = (\frac{2}{3} , \frac{7}{3} )[/tex]

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Answer:

0.083

Step-by-step explanation:

To solve the above question, we use the combination method.

C(n, r) = nCr = n!/r!(n - r)!

Probability of answering (all 5 correctly)

= Probability of answering ( 5 out of 7 correctly)/ Probability of answering (5 out of 10 problems)

Probability of answering ( 5 out of 7 correctly) = 7C5

nCr = n!/r!(n - r)!

= 7!/5! (7 - 5)!

= 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (2 × 1)

= 21 ways

Probability of answering (5 out of 10 problems) = 10C5

nCr = n!/r!(n - r)!

= 10!/5! (10 - 5)!

= 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/( 5 × 4 × 3 × 2 × 1) × (5 × 4 × 3 × 2 × 1)

= 252 ways

Probability of answering (all 5 correctly)

= 21/252

= 0.0833333333

Approximately = 0.083