What number am I ???

In the diagram below of triangle HJKHJK, LL is a midpoint of \overline{HJ}HJ and MM is a midpoint of \overline{JK}JK. If LM=71-9

love history [14]

Answer:

Step-by-step explanation:

Since J is the midpoint of HK, then HJ=JK and 3x+5=9x-3 solve for x

6x=8 x=8/6=4/3 so HJ=3x+5=3(4/3)+5=9 = JK HK=2(9)=18

the full segment HK is 18, each half of it is 9 =HJ=JK

3 0

3 years ago

In the figure, angle D measures 31° and angle A measures 27

patriot [66]

The acute angles of a right triangle are complementary, so:

$m\angle B=90-27=\boxed{63^{\circ}}\\m\angle F=90-31=\boxed{59^{\circ}}$

3 0

2 years ago

Frank got a gift for his sister and put it in a shoebox.

Leona [35]

Answer:

The correct answer is option C.

Step-by-step explanation:

Length of shoe box = l = 11 inches

Width of the shoes box = w = 6 inches

Height of the shoe box = h = 5 inches

Wrapping paper required t cover the shoe box will be equal to the total surface area of the shoe box.

Shoe box = Cuboid

Total surface area of the cuboid = 2(lw+wh+hl)

Total surface area of shoe box : T

$T=2\times (11 inch\times 6 inch+6 inch\times 5 inch+5 inch\times 11 inch)$

$=T = 302 inch^2$

Frank will need 302 square inches of wrapping paper to cover the shoe box.

5 0

3 years ago

Which two integers have a sum of 5 and a product of -6?

inysia [295]

Answer:

-1 and 6

Step-by-step explanation:

We can use trial and improvement for this

Pairs of numbers that have a sum of 5:

2, 3 = 6

1, 4 = 4

0, 5 = 0

-1, 6 = -6

-2, 7 = -14

-3, 8 = -24

-4, 9 = -36

-5, 10 = -50

-1 and 6 have a sum of 5 and a product of -6

7 0

2 years ago

Scores on the SAT Mathematics test are believed to be normally distributed. The scores of a simple random sample of five student

AysviL [449]

Answer:

The mean calculated for this case is $\bar X=584$

And the 95% confidence interval is given by:

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

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 mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=584$

The sample deviation calculated $s=86.776$

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

$df=n-1=5-1=4$

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(0.025,4)".And we see that $t_{\alpha/2}=2.776$

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

$584-2.776\frac{86.776}{\sqrt{5}}=476.271$

$584+2.776\frac{86.776}{\sqrt{5}}=691.729$

So on this case the 95% confidence interval would be given by (476.271;691.729)

3 0

3 years ago