Write in index form using a unit fraction : 6√19

Find the SLANT HEIGHT of the pyramid, then calculate its SURFACE AREA.

Vedmedyk [2.9K]

Answer:

13 cm

Step-by-step explanation:

slant height = $\sqrt{12^2 +\frac{10^2}{4} }$

= $\sqrt{144 + \frac{100}{4} }$

= $\sqrt{144 + 25}$

= $\sqrt{169}$

=13 cm

a=10 cm

l =

surface area = $a^{2} + 2a \sqrt{\frac{a^{2} }{4} +h^{2} }$

= $10^{2} +2*10 \sqrt{\frac{10^{2} }{4} +12^{2} } \\100 + 20 \sqrt{\frac{100}{4} + 144} \\100 + 20\sqrt{25 + 144} \\100 + 20 \sqrt{169} \\100 + 20*13\\100 + 260\\360 cm^2$

3 0

3 years ago

Some investments in the stock market have earned 10% annually. At this rate, earning can be found using the formula A=p(1.10)n,

GalinKa [24]

Answer:

c. 13.899.79

Step-by-step explanation:

Exponential function

Two variables y and x have an exponential relation if

$y=Ce^{kx}$

where C and k are real numbers. Many natural phenomena are modeled by using exponentials, finance included, where the growing of the investments can be computed through the use of the exponential function

The situation described in the question is modeled as

$A=p1.1^{n}$

being A is the total value of the investment, p is the initial value of the investment, and n is the number of years the money is invested. We know p=2,500 and n=18, so we compute A

$A=(2,500)1.1^{18}$

$A=$13,899.79$

Answer: c. 13.899.79

5 0

3 years ago

A study was conducted to estimate the difference in the mean salaries of elementary school teachers from two neighboring states.

umka21 [38]

Answer:

$(28900-30300) -2.07 \sqrt{\frac{2300^2}{10} +\frac{2100^2}{14}} = -3301.70$

$(28900-30300) +2.07 \sqrt{\frac{2300^2}{10} +\frac{2100^2}{14}} = 501.698$

The confidence interval would be $-3301.70 \leq \mu \leq 501.698$ and since the confidence interval contains the value of 0 we don't have enough evidence to conclude that the difference between the two states for the salary of teachers are significantly different.

Step-by-step explanation:

We have the following info given by the problem

$\bar X_1 = 28900$ the sample mean for the salaries of teachers in Indiana

$s_1 = 2300$ the sample deviation for the salary of teachers in Indiana

$n_1 =10$ the sample size from Indiana

$\bar X_2 = 30300$ the sample mean for the salaries of teachers in Michigan

$s_2 = 2100$ the sample deviation for the salary of teachers in Michigan

$n_2 =14$ the sample size from Michigan

We want to find a confidence interval for the difference in the two means and the formula for this case is given by;

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}$

The degrees of freedom for this case are:

$df = n_1 +n_2 -2= 10+14-2 =22$

The confidence is 95%so then the significance is $\alpha=0.05$ and the $\alpha/2 =0.025$ , we need to find a critical value in the t distribution with 22 degrees of freedom who accumulates 0.025 of the area on each tail and we got:

$t_{\alpha/2}= 2.07$

And now replacing in the formula for the confidence interval we got:

$(28900-30300) -2.07 \sqrt{\frac{2300^2}{10} +\frac{2100^2}{14}} = -3301.70$

$(28900-30300) +2.07 \sqrt{\frac{2300^2}{10} +\frac{2100^2}{14}} = 501.698$

The confidence interval would be $-3301.70 \leq \mu \leq 501.698$ and since the confidence interval contains the value of 0 we don't have enough evidence to conclude that the difference between the two states for the salary of teachers are significantly different.

6 0

3 years ago

Solve each system by elimination

MaRussiya [10]

X-y=11
2x+y=19
add them

x-y=11
2x+y=19 +
3x+0y=30

3x=30
divide 3
x=10

sub baack
x-y=11
10-y=11
minus 10
-y=1
times -1
y=-1

(x,y)
(10,-1)

3 0

3 years ago

Idk a? or no? like im really bad

kozerog [31]

Answer:

c

Step-by-step explanation:

0.0125

so it is 1.25 because the thousand place onward, it is in the decimal place of the percent

6 0

3 years ago