(7a3 – 2a - 2) + (-5a + 3) =

kkurt [141]

Answer:

62.83 cm is the length of the ribbon needed

6 0

3 years ago

Compute a 99% confidence interval for the mean weight of toxic substance per gram of mold culture. State the assumption you make

kow [346]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The 99% confidence interval is $2.4309 < \mu < 4.9328$

Step-by-step explanation:

From the question we are told that

The data is 3, 2,5, 3, 2, 6, 5,4.5, 3, 3, and 4

The sample size is n = 11

Generally the sample mean is mathematically represented as

$\= x = \frac{\sum x_i}{n}$

=> $\= x = \frac{3+ 2+5+ \cdots +4 }{11}$

=> $\= x = 3.6818$

Generally the sample standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{\sum [ x_i - \= x ] }{n} }$

=> $\sigma = \sqrt{\frac{[ 3 - 3.6818 ]^2 +[ 2 - 3.6818 ]^2 + \cdots + [ 4 - 3.6818 ]^2 }{11} }$

=> $\sigma = 1.3091$

Given that the confidence interval is 99% then the level of significance is mathematically represented as

$\alpha= (100 - 99) \%$

=> $\alpha= 0.01$

Given that the sample size is small we will making use of t distribution table

Generally from the t distribution table the critical value of at a degree of freedom of is

$t_{\frac{\alpha }{2} , 10 } =3.16927267$

Generally the margin of error is mathematically represented as

$E = 3.16927267 * \frac{1.3091 }{\sqrt{11} }$

$E = 1.251$

Generally 99% confidence interval is mathematically represented as

$3.6818 -1.251 < p < 3.6818 + 1.251$

=> $2.4309 < \mu < 4.9328$

8 0

3 years ago

Write an equivalent expression for 7¹² × 7⁴

Anika [276]

Answer:

$\huge\boxed{7^{16}}$

Step-by-step explanation:

We can use exponent rules to try and simplify this expression down.

Exponent rules tell us that $x^a + x^b = x^{a+b}$ .

This means that since we have the same base on both terms (7 and 7), we can add the exponents to get a simplified expression.

$12 + 4 = 16$

So our simplified expression is $7^{16}$ .

Hope this helped!

3 0

4 years ago

What is the equation of the line that passes through the point (-4,6)(−4,6) and has a slope of -\frac{5}{4}−

AysviL [449]

Answer:

5x + 4y - 4 = 0 is the given line equation.

Step-by-step explanation:

The slope m of the line is given as $-\frac{5}{4}$

The point of the equation is (x0, y0) = (-4, 6)

Now, by POINT SLOPE formula of a line:

Equation of a line is : ( y -y0) = m (x - x0)

Hence, the equation is $(y - 6) = -\frac{5}{4} (x -(-4))$

On further simplifying $4(y - 6) = -5 (x + 4)\\or, 4y - 24 = -5x- 20$ ,

⇒ 5x + 4y - 24 + 20 = 0

or, 5x + 4y - 4 = 0 is the given line equation.

4 0

3 years ago

Please help! Need answer ASAP!

REY [17]

ANSWER:

A ) It also increases.

EXPLANATION:

When the measure of angle A increases im the trianes, the measure of angle A on line p also increases. This is angle A in the triangle and angle A on line p are equivalent to each other. Hence, if there is an increase to one of the angle As then there is also an increase to the other.

Therefore, the answer must be:

A ) It also increases.

8 0

3 years ago

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