When Shanaje baby-sits her nephews, she charges $8 plus $4 per hour. If

The sum of the measures of two angles of a scalene triangle is calculated, and the result is the same as the measure of one of t

ikadub [295]

The complete question in the attached figure

we know that
The Exterior Angle Theorem establishes that t<span>he measure of an exterior angle of a triangle equals to the sum of the measures of the two remote interior angles of the triangle.
so

the answer is the option
</span><span>A. the remote interior angles</span>

5 0

3 years ago

Read 2 more answers

Simplify each algebraic expression.

GREYUIT [131]

Answer:

$\huge\boxed{\sf-2x+28}\\\\\huge\boxed{\sf 10x-4}\\\\\huge\boxed{\sf 56-5x}\\\\\huge\boxed{\sf x-13}$

Step-by-step explanation:

$\sf 2x + 4(7-x) \\\\Resolving \ Parenthesis\\\\2x + 28-4x \\\\Combining\ like\ terms\\\\2x-4x +28\\\\-2x + 28\\\\\rule[225]{225}{2}$

$\sf \\12x-(4+2x)\\\\12x-4-2x\\\\Combining \ like \ terms\\\\12x-2x - 4\\\\10x-4 \\\\\rule[22]{225}{2} \\2(10-x)+3(12-x) \\\\Resolving \ Parenthesis\\\\20-2x + 36 -3x\\\\Combining \ like \ terms\\\\20+36 -2x-3x\\\\56 - 5x \\\\\rule[225]{225}{2}$

$\sf 7(x-1)-6(x+1)\\\\Resolving \ Parethesis\\\\7x-7-6x-6\\\\Combining \ like \ terms\\\\7x-6x-7-6\\\\x - 13\\\\\rule[225]{225}{2}$

Hope this helped!

~AnonymousHelper1807

3 0

3 years ago

Maths help PLZZ!!!

Slav-nsk [51]

Triangle ABC is an isosceles triangle.

Solution:

Given data:

∠ABC = 70° and ∠ACD = 55°

<em>If two parallel lines are cut by a transversal, then alternate interior angles are congruent.</em>

m∠BAC = m∠ACD

m∠BAC = 55°

<em>Sum of the angles in a straight line add up to 180°.</em>

m∠ACD + m∠ACB + m∠ABC = 180°

55° + m∠ACB + 70° = 180°

m∠ACB + 125° = 180°

Subtract 125° from both sides, we get

m∠ACB = 55°

In triangle ABC,

∠BAC = 55° and ∠ACB = 55°

∠BAC = ∠ACB

Two angles in the triangle are equal.

Therefor triangle ABC is an isosceles triangle.

6 0

3 years ago

Give a rule of the piecewise-defined function.

nataly862011 [7]

The equation of the piecewise function is $f(x) = \left[\begin{array}{ccc}3&x \le -1\\-1&x > 2\end{array}\right$

<h3>The piecewise function</h3>

On the graph, we have:

y = 3 for all x values not more than -1
y = -1 for all values greater than 2

Hence, the piecewise function is:

$f(x) = \left[\begin{array}{ccc}3&x \le -1\\-1&x > 2\end{array}\right$

<h3>The domain of the function</h3>

This is the set of input values

In (a), we have:

x ≤ -1 and x > 2

Hence, the domain is (∞, 3] u (2, ∞)

<h3>The range of the function</h3>

This is the set of output values

In (a), we have:

f(x) = 3 and f(x) -1

Hence, the range is [3] u (-1)

Read more about piecewise function at:

brainly.com/question/18859540

#SPJ1

5 0

2 years ago

Suppose a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%. A cell phon

leva [86]

Answer:

We conclude that the actual percentage of households is equal to 30%.

Step-by-step explanation:

We are given that a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%.

Their marketing people survey 150 households with the result that 43 of the households have three cell phones.

Let p = <u><em>proportion of households that have three cell phones NOT known.</em></u>

So, Null Hypothesis, $H_0$ : p = 30% {means that the actual percentage of households is equal to 30%}

Alternate Hypothesis, $H_A$ : p $\neq$ 30% {means that the actual percentage of households different from 30%}

The test statistics that would be used here <u>One-sample z-test for proportions;</u>

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of households having three cell phones = $\frac{43}{150}$ = 0.29

n = sample of households = 150

So, <u><em>the test statistics</em></u> = $\frac{0.29-0.30}{\sqrt{\frac{0.30(1-0.30)}{150} } }$

= -0.27

The value of z test statistic is -0.27.

<u>Also, P-value of the test statistics is given by;</u>

P-value = P(Z < -0.27) = 1 - P(Z $\leq$ 0.27)

= 1 - 0.6064 = <u>0.3936</u>

<u>Now, at 1% significance level the z table gives critical value of -2.58 and 2.58 for two-tailed test.</u>

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <em><u>we fail to reject our null hypothesis</u></em>.

Therefore, we conclude that the actual percentage of households is equal to 30%.

4 0

3 years ago