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3 years ago

Please helppp. Solve for x in the diagram below

Mathematics

2 answers:

REY [17]3 years ago

7 0

Answer:

Step-by-step explanation:

The diagram shows a right angle, therefore (6x-2) + 20 = 90.

Find x

(6x - 2) + 20 = 90

6x - 2 = 70

6x = 72

x = 12

Confirmation

[6(12) - 2] + 20 = 90

Yuri [45]3 years ago

4 0

The answer is [6(12)-2]+20=90

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Name the property that justifies the statement: If 3x = 6 then x = 2.

SVETLANKA909090 [29]

The property is Multiplication Property of Equality.

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3 years ago

Read 2 more answers

Test the claim that the mean GPA of night students is larger than 2 at the .025 significance level. The null and alternative hyp

exis [7]

Answer:

$H_0: \, \mu = 2$ .

$H_1:\, \mu > 2$ .

Test statistics: $z \approx 2.582$ .

Critical value: $z_{1 - 0.025} \approx 1.960$ .

Conclusion: reject the null hypothesis.

Step-by-step explanation:

The claim is that the mean $\mu$ is greater than $2$ . This claim should be reflected in the alternative hypothesis:

$H_1:\, \mu > 2$ .

The corresponding null hypothesis would be:

$H_0:\, \mu = 2$ .

In this setup, the null hypothesis $H_0:\, \mu = 2$ suggests that $\mu_0 = 2$ should be the true population mean of GPA.

However, the alternative hypothesis $H_1:\, \mu > 2$ does not agree; this hypothesis suggests that the real population mean should be greater than $\mu_0= 2$ .

One way to test this pair of hypotheses is to sample the population. Assume that the population mean is indeed $\mu_0 = 2$ (i.e., the null hypothesis is true.) How likely would the sample (sample mean $\overline{X} = 2.02$ with sample standard deviation $s = 0.06$ ) be observed in this hypothetical population?

Let $\sigma$ denote the population standard deviation.

Given the large sample size $n = 60$ , the population standard deviation should be approximately equal to that of the sample:

$\sigma \approx s = 0.06$ .

Also because of the large sample size, the central limit theorem implies that $Z= \displaystyle \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}}$ should be close to a standard normal random variable. Use a $Z$ -test.

Given the observation of $\overline{X} = 2.02$ with sample standard deviation $s = 0.06$ :

$\begin{aligned}z_\text{observed}&= \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}} \\ &\approx \frac{\overline{X} - \mu_0}{s / \sqrt{n}} = \frac{2.02 - 2}{0.06 / \sqrt{60}} \approx 2.582\end{aligned}$ .

Because the alternative hypothesis suggests that the population mean is greater than $\mu_0 = 2$ , the null hypothesis should be rejected only if the sample mean is too big- not too small. Apply a one-sided right-tailed $z$ -test. The question requested a significant level of $0.025$ . Therefore, the critical value $z_{1 - 0.025}$ should ensure that $P( Z > z_{1 - 0.025}) = 0.025$ .

Look up an inverse $Z$ table. The $z_{1 - 0.025}$ that meets this requirement is $z_{1 - 0.025} \approx 1.960$ .

The $z$ -value observed from the sample is $z_\text{observed}\approx 2.582$ , which is greater than the critical value. In other words, the deviation of the sample from the mean in the null hypothesis is sufficient large, such that the null hypothesis needs to be rejected at this $0.025$ confidence level in favor of the alternative hypothesis.

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3 years ago

Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}

Olin [163]

Answer:

B {6, 6, 7}

Step-by-step explanation:

Which set of numbers may represent the lengths of the sides of a triangle? (A) {2,5,9} (B) {6,6,7} (C) {6,4,2} (D) {7,8,1}

For a given triangle with 3 sides, the sun of the length of any two sides must be greater Than the third side. This can be expressed mathematically as;

Let the side be ;

x, y and z

Then:

x > (y + z) or

y > (x + z) or

z > (x + y)

For A{2,5,9}

(2 + 5) < 9 (does not meet criteria)

For B {6,6,7}

(6 +6) > 7

(7 +6) > 6

Meets all criteria

For C {6,4,2}

(4 +2) is not greater Than 6 (does not meet criteria)

For D {7,8,1}

(7 +1) is not greater Than 8 ( does not meet criteria)

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3 years ago

X Find the value of x. Show 3 10 your work.

pickupchik [31]

Step-by-step explanation:

Hello, there!!!

Let ABC be a Right angled triangle, 

where, AB = 3

BC= 10

and AC= x

now,

As the triangle is a Right angled triangle, taking angle C asrefrence angle. we get,

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p= AB = 3

b= BC= 10

now, by Pythagoras relation we get, 

 $h = \sqrt{ {p}^{2} + {b}^{2} }$ 

 $or ,\: h = \sqrt{ {3}^{2} + {10}^{2} }$ 

by simplifying it we get, 

h = 10.44030

Therefore, the answer is x= 10.

Hope it helps...

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3 years ago

A soccer ball is kicked toward the goal. the height of the ball is modeled by the function h(t) = −16t2 48t, where t equals the

mamaluj [8]

It takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.

<h3>What is the axis of symmetry?</h3>

Axis of symmetry is a line that divides an object into two equal halves, thereby creating a mirror-like reflection of either side of the object.

1. The function is a parabola of the form . The the formula for the axis of symmetry of a parabola is . We can infer from our function that a= -16 and b = 48, so lets replace those values in our formula:

$x = \frac{-b}{2a}$

$x = \frac{(-48)}{-2(16)}$

$x = \frac{-48}{-32}$

x = 1.5

We can conclude that to the left of the line of symmetry the ball is reaching its maximum height, and to the right of the line of symmetry the ball is falling.

2. Lets check how much time the ball takes to reach its maximum height and return to the ground. To do that we are going to set the height equal to zero:

$-16t^{2} +48t = 0$

$-16t(t-3)=0$

t = 0, (t-3) = 0

t = 0, t = 3

From our previous point we know that the ball reaches its maximum time at , which means that it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.

To learn more about axis of symmetry from the given link:

brainly.com/question/9444537

#SPJ4

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1 year ago