All categories

3 years ago

Identify the height of the rectangle, given that A=(24x2+96x) ft2.

Mathematics

1 answer:

ch4aika [34]3 years ago

3 0

Answer:

Second option, h=( $x^{2} + 4x$ ) ft

Step-by-step explanation:

Area = Base x Height

Height = Area ÷ Base

= $\frac{24x^{2} +96x}{24}$

= $\frac{24x^{2} }{24} +\frac{96x}{24}$ (split fraction for easier simplification)

= $x^{2} +4x$

You might be interested in

Persuade Mr. Zorn whether the numbers 12, 16, and 20 make a right triangle or not. Make sure to state reasons for or against you

Darya [45]

Answer:

Yes!

Step-by-step explanation:

In Pythagorean Triples, the two legs always have to add up to be a greater number than the hypotenuse. In this case, 12 and 16 are the legs and 20 is the hypotenuse. The sum of 12 and 16 is 28. That is more than 20, so 12, 16 and 20 make a right triangle. I hope this helps you!

8 0

3 years ago

Helppppppppppp meeeeeee

Alik [6]

Answer:

Step-by-step explanation:

6 0

4 years ago

Read 2 more answers

You should know the __________ and ___________ of all safety equipment. PLS HELP ME!!!!

dezoksy [38]

You should know the instructions and rules of all safety equipment

8 0

3 years ago

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 400 babies were born, a

Masja [62]

Answer:

(a) 99% confidence interval for the percentage of girls born is [0.804 , 0.896].

(b) Yes, the proportion of girls is significantly different from 0.50.

Step-by-step explanation:

We are given that a clinical trial tests a method designed to increase the probability of conceiving a girl.

In the study 400 babies were born, and 340 of them were girls.

(a) Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

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

where, $\hat p$ = sample proportion of girls born = $\frac{340}{400}$ = 0.85

n = sample of babies = 400

p = population percentage of girls born

Here for constructing 99% confidence interval we have used One-sample z proportion statistics.

So, 99% confidence interval for the population proportion, p is ;

P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level

of significance are -2.58 & 2.58}

P(-2.58 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 2.58) = 0.99

P( $-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

P( $\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

99% confidence interval for p = [ $\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.85-2.58 \times {\sqrt{\frac{0.85(1-0.85)}{400} } }$ , $0.85+2.58 \times {\sqrt{\frac{0.85(1-0.85)}{400} } }$ ]

= [0.804 , 0.896]

Therefore, 99% confidence interval for the percentage of girls born is [0.804 , 0.896].

(b) Let p = population proportion of girls born.

So, Null Hypothesis, $H_0$ : p = 0.50 {means that the proportion of girls is equal to 0.50}

Alternate Hypothesis, $H_A$ : p $\neq$ 0.50 {means that the proportion of girls is significantly different from 0.50}

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

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

where, $\hat p$ = sample proportion of girls born = $\frac{340}{400}$ = 0.85

n = sample of babies = 400

So, the test statistics = $\frac{0.85-0.50}{\sqrt{\frac{0.85(1-0.85)}{400} } }$

= 19.604

Now, at 0.01 significance level, the z table gives critical value of 2.3263 for right tailed test. Since our test statistics is way more than the critical value of z as 19.604 > 2.3263, so we have sufficient evidence to reject our null hypothesis due to which we reject our null hypothesis.

Therefore, we conclude that the proportion of girls is significantly different from 0.50.

8 0

3 years ago

Consider the functions f(x) = 2x + 1 and g(x) = x^2 − 10 What is the value of f[g(3)]?

HACTEHA [7]

Answer:

-1

Step-by-step explanation:

Tip: Remember to always start from the inside, which would be g(3), in this case.

The first step in solving this problem is to solve for g(3).

To accomplish this, you must substitute 3 for x into the given equation g(x) = x^2 - 10

g(3) = 3^2 - 10
g(3) = 9 - 10
g(3) = -1

The next step is to substitute the answer of g(3), -1, for x in the given equation f(x) = 2x + 1.

Because the equation is asking for f[g(3)], it becomes f(-1) because g(3) = -1.

f(-1) = 2(-1) + 1
f(-1) = -2 + 1
f(-1) = -1

Therefore, f[g(3)], or f(-1), equals -1

6 0

3 years ago