Solve for the length of x.

the bottom of a ladder must be placed 7 ft from a wall the ladder 19 feet how far above the ground dose ladder touch the wall

Natali5045456 [20]

Answer:

Distance between bottom of the wall and bottom of the ladder = 7 ft

Length of the ladder = 19 ft

Let the distance between the ground and top of the ladder be x

Using Pythagoras theorem,

x^2 + 7^2 = 19^2

x^2 + 49 = 361

x^2 = 312

Therefore x = √312 = 2√78 ft

3 0

4 years ago

find the size of each sample needed to estimate the difference between the proportions of boys and girls under 10 years old who

Alex Ar [27]

Answer:

sample

Step-by-step explanation:

6 0

3 years ago

PLEASE help me with this question and I WILL love you forever But yeah please help me with the question.And EXPLAIN in words how

Rufina [12.5K]

Well on this problem recall area of a rectangle is defined by:

A = lw our w = 1/6 and our l = (x + $\frac{2}{3}$ ) we have let 'x' represent our original length.
$(x + \frac{2}{3} )( \frac{1}{6} )= \frac{11}{72}$
$\frac{1}{6} x+ \frac{2}{18} = \frac{11}{72}$
12x + 8 = 11
12x = 11 - 8
12x = 3
x = $\frac{3}{12} = \frac{1}{4}$ So our original length is $\frac{1}{4}$

5 0

4 years ago

In one community, a random sample of 26 foreclosed homes sold for an average of $443 comma 555 with a standard deviation of $

alexandr1967 [171]

Answer:

i) a) Normality : We assume that the data follows approximately a normal distribution

ii) Random sample: The data comes from a random sample

iii) The sample size represent <10% of the population size

We assume that all the conditions are satisfied for this case.

b) $443555-2.06\frac{195381}{\sqrt{26}}=364621.22$

$443555+2.06\frac{195381}{\sqrt{26}}=522488.775$

So on this case the 95% confidence interval would be given by (364621.22;522488.775)

c) We are confident at 95% that the true mean of foreclosed homes sold's are between (364621.22;522488.775)

d) Since the lower value for the 95% confidence interval is higher than 300000 we can conclude that yes differes significantly and the true mean is different from 300000 at 5% of significance.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=443555$ represent the sample mean

$\mu$ population mean (variable of interest)

s=195381 represent the sample standard deviation

n=26 represent the sample size

Part a

We need some conditions:

a) Normality : We assume that the data follows approximately a normal distribution

b) Random sample: The data comes from a random sample

c) The sample size represent <10% of the population size

We assume that all the conditions are satisfied for this case.

Part b

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=26-1=25$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,25)".And we see that $t_{\alpha/2}=2.06$

Now we have everything in order to replace into formula (1):

$443555-2.06\frac{195381}{\sqrt{26}}=364621.22$

$443555+2.06\frac{195381}{\sqrt{26}}=522488.775$

So on this case the 95% confidence interval would be given by (364621.22;522488.775)

Part c

We are confident at 95% that the true mean of foreclosed homes sold's are between (364621.22;522488.775)

Part d

Since the lower value for the 95% confidence interval is higher than 300000 we can conclude that yes differes significantly and the true mean is different from 300000 at 5% of significance.

8 0

3 years ago

4 cups is equivalent to ____ quart

olga nikolaevna [1]

Answer:

1 quart is equal to 4 cups

Step-by-step explanation:

4 cups is equivalent to __1__ quart

5 0

2 years ago

Solve for the length of x.​

Solve for the length of x.