$D:x\geq-5 \wedge x\geq10\\
D:x\geq10\\\\
\sqrt{n+5}-\sqrt{n-10}=1\\
\sqrt{n+5}=1+\sqrt{n-10}\\
n+5=1+2\sqrt{n-10}+n-10\\
2\sqrt{n-10}=14\\
\sqrt{n-10}=7\\
n-10=49\\
n=59$

7 0

3 years ago

If a number is decreased by 36 and the result is 76 less than twice the number, what is the number?

olga_2 [115]

A - 36 = B
B = 76 - A * 2.
the number is 40.
A = 40
:D

5 0

3 years ago

Steven just got a new summer job painting fences in his neighborhood. He will be paid $7.25 an hour. His first customer paid him

mote1985 [20]

Answer:

a). The equation; 7.25 h-36.25=0

b). total number of hours Steven work=5 hours

Step-by-step explanation:

Part A

The expression for the total money earned is as follows;

T=E×h

where;

T=total earnings

E=earnings per hour

h=number of hours worked

In our case;

T=$36.25

E=$7.25

h=h

replacing;

36.25=(7.25×h)

36.25=7.25 h

The equation would be; 7.25 h=36.25, or 7.25 h-36.25=0

Part B

7.25 h=36.25

h=36.25/7.25

h=5

total number of hours Steven work=5 hours

5 0

3 years ago

Grades on a standardized test are known to have a mean of 1000 for students in the United States. The test is administered to 45

krok68 [10]

Answer:

The 95% confidence interval is $1003 < \mu$

Yes there is statistically significant evidence that students in Florida perform differently from other students in the United States

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 1000$

The sample size is $n = 453$

The sample mean is $\= x = 1013$

The standard deviation is $s = 108$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 100 - 95$

=> $\alpha = 5\%$

=> $\alpha = 0.05$

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

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

Generally the margin of error is mathematically represented as

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

=> $E = 1.96 * \frac{108}{\sqrt{453} }$

=> $E = 9.946$

Generally the 95% confidence interval is mathematically represented as

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

=> $1013 - 9.946 < \mu < 1013 + 9.946$

=> $1003 < \mu$

Given that the population mean(1000) is not within the 95% confidence interval for l for the average test score for students in Florida, then it means that there is statistically significant evidence that students in Florida perform differently from other students in the United States

4 0

3 years ago