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3 years ago

Can someone please explain?

Mathematics

1 answer:

geniusboy [140]3 years ago

6 0

This is an isosceles triangle. The angles at the base are congruent (they have the same measures).

Look at the picture.

We know: The sum of the measures of angles in a triangle is equal 180°.

Therefore we have the equation:

$2x-10+2x-10+3x+25=180$ <em>combine like terms</em>

$(2x+2x+3x)+(-10-10+25)=180$

$7x+5=180$ <em>subtract 5 from both sides</em>

$7x=175$ <em>divide both sides by 7</em>

$x=25$

$m\angle A=2x-10\to m\angle A=2(25)-10=50-10=40\\\\m\angle C=m\angle A=40\\\\m\angle B=3x+25\to m\angle B=3(25)+25=75+25=100^o$

<h3>Answer: D. m∠C = 40</h3>

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Gabe went to the amusement park with $40 to spend. His ticket cost $26.50. Write and solve an inequality to show how much he mig

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<h3><u>An inequality to show how much he might spend on souvenirs and snacks is:</u></h3>

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<h3><u>Solution:</u></h3>

Given that,

Gabe went to the amusement park with $40 to spend

His ticket cost $26.50

Therefore,

Total amount she has = $ 40

Ticket cost = $ 26.50

Let "x" be the amount he might spend on souvenirs and snacks

Therefore,

Remaining amount = 40 - 26.50

Remaining amount = 13.5

Thus she can spend less than or equal to $ 13.5 on souvenirs and snacks

Which is represented in inequality as:

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3 years ago

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Step-by-step explanation:

The confidence interval for population mean is given by :-

$\mu\pm\ z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : n= 35 , large sample (n>30)

Mean difference : $\overline{x}=12$

Standard deviation : $\sigma=3$

Significance level : $\alpha=- 1-0.999=0.001$

Critical value : $z_{\alpha/2}=z_{0.0005}=3.4807567$

Now, the 99.9% confidence interval for the mean difference between the marks scored last week and marks scored this week by all the students will be :-

$12\pm\ (3.4807567)\dfrac{2}{\sqrt{35}}\\\\=12\pm1.18\\\\=(10.82\ , 13.18)$

Hence, the 99.9% confidence interval for the mean difference between the marks scored last week and marks scored this week by all the students = $(10.82\ , 13.18)$

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Answer:

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