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2 years ago

Simplify 3 3^square root of 16

Mathematics

1 answer:

notsponge [240]2 years ago

6 0

Answer:

2.5198421 is yhe answer of 3^√16

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How do you solve 8y=48 one step equation

ValentinkaMS [17]

Divide each side by 8

y=6

8 0

2 years ago

Read 2 more answers

The following table gives results from two groups of students who took a nonproctored test. Use a 0.01 significance level to tes

Nana76 [90]

Answer:

Original claim is $\mu_{1} =\mu_{2}$

Opposite claim is $\mu_{1} \neq \mu_{2}$

Null and alternative hypotheses:

$H_{0}:\mu_{1} = \mu_{2}$

$H_{1} : \mu_{1} \neq \mu_{2}$

Significance level: 0.01

Test statistic:

We can use TI-84 calculator to find the test statistic and P-value. The steps are as follows:

Press STAT and the scroll right to TESTS

Scroll down to 2-SampTTest... and scroll to stats.

Enter below information.

$\bar{x_{1}}=70.29$

$Sx1=22.09$

$n_{1} = 30$

$\bar{x_{2}}=74.26$

$Sx2=18.15$

$n_{2} = 32$

$\mu_{1} \neq \mu_{2}$

Pooled: Yes

Calculate.

The output is in the attachment.

Therefore, the test statistic is:

$t=-0.78$

P-value: 0.4412

Reject or fail to reject: Fail to reject

Final Conclusion: Since the p-value is greater than the significance level, we, therefore, fail to reject the null hypothesis and conclude that the there is sufficient evidence to support the claim that the samples are from populations with the same mean.

6 0

2 years ago

What is the probability of drawing a 3 or a 4 or a heart from a deck of cards?

Effectus [21]

$\Omega=\{2\spadesuit;\ 3\spadesuit;...;A\spadesuit;2\heartsuit ;\ 3\heartsuit;...;A\heartsuit;\ 2\diamondsuit;\ 3\diamondsuit;...;A\diamondsuit;\ 2\clubsuit;\ 3\clubsuit;...;A\clubsuit\}\\\\|\Omega|=52\\\\A=\{3\spadesuit;\ 4\spadesuit;\ 3\diamondsuit;\ 4\diamondsuit;\ 3\clubsuit;\ 4\clubsuit;\ 2\heartsuit;\ 3\heartsuit;\ 4\heartsuit;...;A\heartsuit\}\\\\|A|=2+2+2+13=19\\\\P(A)=\dfrac{|A|}{|\Omega|}\to P(A)=\dfrac{19}{52}$

$Answer:\ \dfrac{19}{52}$

5 0

2 years ago

A study dealing with health care issues plans to take a sample survey of 1500 Americans to estimate the mean dollar amount that

frutty [35]

Answer:

The population parameter of this study is the population mean.

Step-by-step explanation:

A population parameter is a numerical measure representing a certain characteristic of the population. For example, population mean, population variance, population proportion, and so on.

The population parameter is computed using all the values of the population.

The population parameter can be estimated using the sample statistic. If the value of the population parameter is not known, then a random sample of large size, say n ≥ 30 can be selected from the population and the statistic value can be computed. This statistic value is considered as the point estimate of the parameter. It is also known as the unbiased estimator of the parameter.

In this case the survey involved sampling of 1500 Americans to estimate the mean dollar amount that Americans spent on health care in the past year.

The sample selected is used to compute the sample mean dollar amount that Americans spent on health care.

So, the population parameter of this study is the population mean.

7 0

2 years ago

Geometry problem help! Please refer to the image below...

Vinil7 [7]

Answer:

A. 1/3

B. √10

C. -1, 1

D. √8, 6

E. congruent and opposite pairs parallel

F. perpendicular, not congruent

G. rhombus, explanation below

Step-by-step explanation:

Hey there! I'm happy to help!

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Slope is the rise over the run. Let's look at F to G.

We are going from -1 to 2 on our x-axis (run), so our run is 3 units.

Our rise is 1 unit as we go from 2 to 3 on the y-axis.

$slope=\frac{rise}{run} =\frac{1}{3}$

This slope is the same for all of the sides.

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We will use the distance formula (which is basically just the Pythagorean Theorem) to calculate the length of each side. Let's go between F and G again, but this distance is the same for all the sides.

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+1)^2+(3-2)^2 } \\\\\sqrt{(3)^2+(1)^2 }\\\\\sqrt{9+1 }\\\\\sqrt{10}$

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The diagonals are the lines that connect the non-adjacent vertices.

Our two diagonals are FH and GE.

-----------------------------

FH

We go from x-value -1 to 1 from F to H, so our run is 2.

We go from y-value 2 to 0. so our rise is -2.

$slope=\frac{rise}{run} =-\frac{2}{2} =-1$

-----------------------------

GE

We go from x-value -2 to 2 from E to G, so our run is 4.

We go from y-value -1 to 3. so our rise is 4.

$slope=\frac{rise}{run} =\frac{4}{4} =1$

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Let's use the distance formula on each of our diagonals.

-----------------------------

FH

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(1,0)\\\\\\\sqrt{(1+1)^2+(0-2)^2 } \\\\\sqrt{(2)^2+(-2)^2 }\\\\\sqrt{4+4 }\\\\\sqrt{8}$

-----------------------------

GE

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-2,-1)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+2)^2+(3+1)^2 } \\\\\sqrt{(4)^2+(4)^2 }\\\\\sqrt{16+16 }\\\\\sqrt{36}\\\\6$

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They are congruent as they all have the same length (√10) and the opposite sides are parallel as they have the same slope (1/3)

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They are perpendicular diagonals as their slopes are negative reciprocals (1 and -1), and they are not congruent as they have different lengths (√8 and 6).

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Parallelogram- quadrilateral with opposite pairs of parallel sides.

Rhombus- a parallelogram with four equal sides

Square- a rhombus with four right angles

We can see that this is a parallelogram as we saw that the opposite sides are parallel due to having the same slope, and the perpendicular diagonals show that as well. This is also a rhombus because if we use that distance formula on all the sides, it will be the same. It is not a square though because it does not have four right angles, so this is a rhombus.

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Have a wonderful day and keep on learning!

8 0

2 years ago