4(x+1) - 7 = 3(x-1) + x

When the smaller of two consecutive integers is added to two times the larger, the result is 35. Find the integers.

Aleonysh [2.5K]

x+2(x+1)=35

x+2x+2=35

3x=35-2=33

x=33/3=11

smaller number=11

larger number=11+1=12

4 0

3 years ago

What is the area of the right trapezoid?

zhenek [66]

Answer:

c

Step-by-step explanation:

because are of trapizium =( a+b/2) × h

5 0

2 years ago

A national study, that revealed a normal distribution, revealed that the average time a student spends studying statistics on a

Neporo4naja [7]

Answer:

Null hypothesis = H0 : μ = 60

Alternative hypothesis = H1 : μ < 60

Step-by-step explanation:

From the question given :

μ = 60 minutes

xbar = 44.27 minutes

s = 20.4 minutes

The alternative hypothesis is the claim ; which is to hypothesize that the average studying time is 44.27 (which is less than the population average studying time)

The null hypothesis is the initial truth and it is the opposite of the alternative hypothesis.

The hypothesis are :

H0 : μ = 60

H1 : μ < 60

5 0

3 years ago

Billy Found The Slope of the line through the points (2,5) and (-2, -5) using the equation shown in the picture below. What mist

Nady [450]

Answer: the numbers were negative so he needed to add the positive numbers to that equation (I think sorry if I’m wrong)

Step-by-step explanation:

7 0

2 years ago

Suppose you do not know the population mean fee charged to H&R Block customers last year. Instead, suppose you take a sample

puteri [66]

Answer:

i $\to$ a

$n = 96040000$

i $\to$ b

$n_1 =24010000$

i $\to$ c

$n_2 =41602500$

ii $\to$ a

$E = 58.16$

ii $\to$ b

$291.84 < \mu < 408.16$ \

ii $\to$ c

There is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval

Step-by-step explanation:

From the question we are told that

The sample size is $n = 8$

The sample mean is $\= x = \$ 350$

The sample standard deviation is $\$ 100$

Considering question i

i $\to$ a

At $E = 0.02$

given that the confidence level is 95% = 0.95

the level of significance would be $\alpha =1-0.95 = 0.05$

The critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{ \alpha }{2} } = 1.96$

So the sample size is mathematically evaluated as

$n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2$

=> $n =[ \frac{ 1.96 * 100}{ 0.02} ]^2$

=> $n = 96040000$

i $\to$ b

At $E_1 = 0.04$ and confidence level = 95% => $\alpha_1 = 0.05$ => $Z_{\frac{\alpha_1 }{2} } = 1.96$

$n_1 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_1} ]^2$

=> $n_1 =[ \frac{ 1.96 * 100}{ 0.04} ]^2$

=> $n_1 =24010000$

i $\to$ c

At $E_2 = 0.04$ confidence level = 99% => $\alpha_2 = 0.01$

The critical value of $\frac{\alpha_2 }{2}$ from the normal distribution table is

$Z_{\frac{ \alpha_2 }{2} } = 2.58$

=> $n_2 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_2} ]^2$

=> $n_2 =[ \frac{ 2.58 * 100}{ 0.04} ]^2$

=> $n_2 =41602500$

Considering ii

Given that the level of significance is $\alpha = 0.10$

Then the critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

substituting values

$E = 1.645 * \frac{100 }{\sqrt{8} }$

$E = 58.16$

Generally the 90% confidence interval is mathematically evaluated as

$\= x - E < \mu < \= x + E$

=> $350 - 58.16 < \mu < 350 + 58.16$

=> $291.84 < \mu < 408.16$

So the interpretation is that there is 90% confidence that the mean fee charged to H&R Block customers last year is in the interval .So there is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval.

8 0

3 years ago