A sphere has a volume of 1,436 in3. What is its radius?

A photograph measuring 4 inches wide and 5 inches long is enlarged to make a wall mural. If the mural is 82 inches wide, how lon

Aliun [14]

I say it around 150 inches that what I think

6 0

2 years ago

£6000 is divided between Adam, Ben and Chris in the ratio 1:3:4. How much does Ben receive?

Gala2k [10]

Answer:

Chris gets £3000

Step-by-step explanation:

A : B : C

1 : 3 : 4 = 8 (add all the parts together)

£6000 ÷ 8 = 750

so the multiplier is x 750

1 : 3 : 4

↩ x 750

750 : 2250 : 3000

Chris gets £3000

3 0

2 years ago

Solve the following logarithmic equations. log[(x^2 + 2x − 3)^4] = 0

saw5 [17]

Answer:

The solutions are x = 1.24 and x = -3.24

Step-by-step explanation:

Hi there!

First, let´s write the equation:

log[(x² + 2x -3)⁴] = 0

Apply the logarithm property: log(xᵃ) = a log(x)

4 log[(x² + 2x -3)⁴] = 0

Divide by 4 both sides

log(x² + 2x -3) = 0

if log(x² + 2x -3) = 0, then x² + 2x -3 = 1 because only log 1 = 0

x² + 2x -3 = 1

Subtract 1 at both sides of the equation

x² + 2x -4 = 0

Using the quadratic formula let´s solve this quadratic equation:

a = 1

b = 2

c = -4

x = [-b± √(b² - 4ac)]/2a

x = [-2 + √(4 - 4(-4)·1)]/2 = 1.24

and

x = [-2 - √(4 - 4(-4)·1)]/2 = -3.24

The solutions are x = 1.24 and x = -3.24

Have a nice day!

4 0

2 years ago

After a college football team once again lost a game to their archrival, the alumni association conducted a survey to see if alu

valentina_108 [34]

Answer:

P-value for this hypothesis test is 0.00175.

Step-by-step explanation:

We are given that the alumni association conducted a survey to see if alumni were in favor of firing the coach.

A simple random sample of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach.

Let p = proportion of all living alumni who favored firing the coach

SO, Null Hypothesis, $H_0$ : p = 0.50 {means that the majority of alumni are not in favor of firing the coach}

Alternate Hypothesis, $H_A$ : p > 0.50 {means that the majority of alumni are in favor of firing the coach}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of the alumni in the sample who were in favor of firing the coach = $\frac{64}{100}$ = 0.64

n = sample of alumni = 100

So, test statistics = $\frac{0.64-0.50}{{\sqrt{\frac{0.64(1-0.64)}{100} } } } }$

= 2.92

Now, P-value of the hypothesis test is given by ;

P-value = P(Z > 2.92) = 1 - P(Z $\leq$ 2.92)

= 1 - 0.99825 = 0.00175

Therefore, the P-value for this hypothesis test is 0.00175.

4 0

3 years ago

Sofia has 25 coins in nickels and dimes in her pocket for a total of $1.65 how many of each type of coin does she have?

Simora [160]

Answer:

She has 23 nickels and 5 dimes.

Step-by-step explanation:

Let n = the number of nickles and d = the number of dimes.

The number of each = 28. Set up the equation:

n + d = 28

Solve for n:

n = 28 - d

The total amount is $1.65 or 165 cents:

5n + 10d = 165

Substitute:

5(28 - d) + 10d = 165

140 - 5d + 10d = 165

140 + 5d = 165

5d = 165 - 140

5d = 25

d = 5, the number of dimes.

Solve for n:

n = 28 - d

n = 28 - 5 = 23, the number of nickles.

Proof:

5n + 10d = 165

5(23) + 10(5) = 165

115 + 50 = 165

165 = 165

Hope this Helps! Have an Awesome Day!!! <3

Step-by-step explanation:

8 0

3 years ago

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