A woman making $2000 per month has her salary reduced by 20% because of sluggish sales. One year later, after a dramatic improvement in sales, she is given a 30% raise over her reduced salary. Find her salary after the raise. $ per month What percent change is this from the $2000 per month? %

Answer:

54degrees

Step-by-step explanation:

From the given diagram;

2<P + 136 + 74 + 42  = 360 (sum of angle at a point is 360degrees)

2<P +252 = 360

2<P = 360 - 252

2<P = 108

<P = 108/2

<P = 54

Hence the measure of <P is 54degrees

Answer:

20%decrease? id.k if its decrease or increase but its 20%

Step-by-step explanation:

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Explanation:

He sold $4950 worth of items. Take 12% of this amount to get

12% of 4950 = 0.12*4950 = 594

So he earns $594 in commission on top of the $350 base salary paid every week. In total, he earns 594+350 = 944 dollars for that week

This isn't the per week pay because he would need to sell exactly $4950 worth of goods each week to keep this same weekly pay.

This question is incomplete, the complete question is;

A Driver's Ed program is curious if the time of year has an impact on numer of car accidents in the U.S.

They assume that weather may have a significant impact on the ability of drivers to control their vehicles. They take a random sample of 150 car accidents and record the seasons each occurred in. They found that 27 occurred in the Spring, 39 in the Summer, 31 in the Fall, and 53 in the Winter. Can it be concluded at the 0.05 level of significance that car accidents are not equally distributed throughout the year

a) Yes, because the p-value = 0.0145

b) No, because the p-value = 0.0145

c) Yes, because the p-value = 0.0291

d) No, because the p-value = 0.0291

Answer:

p-value = 0.0145

Since p-value ( 0.0145 ) is less than Significance level ∝ ( 0.05 ),

We reject Null hypothesis.

Hence, There is sufficient evidence to conclude that car accidents are NOT equally distributed through out the year.

[ Option a) Yes, because the p-value = 0.0145 ] is the correct answer.

Step-by-step explanation:

Given the data in the question;

number of car accident = 150

Observed Frequencies O are;

Spring = 27

Summer = 39

Fall = 31

Winter = 53

Significance level ∝ = 0.05

Hypothesis

Null hypothesis            H₀ : The car accidents are equally distributed through out the year

Alternative hypothesis H₀ : The car accidents are NOT equally distributed through out the year

Now, Expected Frequency E will be;

Spring = 150/4 = 37.5

Summer = 150/4 = 37.5

Fall = 150/4 = 37.5

Winter = 150/4 = 37.5

Test Statistics;

[tex]X^2_{stat^[/tex] = ∑[ ( O-E )² / E ]

so

[tex]X^2_{stat^[/tex] = [ ( 27-37.5 )² / 37.5 ] + [ ( 39-37.5 )² / 37.5 ] + [ ( 31-37.5 )² / 37.5 ] + [ ( 53-37.5 )² / 37.5 ]

[tex]X^2_{stat^[/tex] = 2.94 + 0.06 + 1.1267 + 6.4067

[tex]X^2_{stat^[/tex] = 2.94 + 0.06 + 1.1267 + 6.4067

[tex]X^2_{stat^[/tex] = 10.5334

Degree of Freedom DF = n-1 = 4 -1 = 3

Now,

p-value = P( [tex]X^2[/tex] - [tex]X^2_{stat^[/tex] ) = P( [tex]X^2[/tex] - 10.5334 ) = 0.0145

p-value = 0.0145

Since p-value ( 0.0145 ) is less than Significance level ∝ ( 0.05 ),

We reject Null hypothesis.

Hence, There is sufficient evidence to conclude that car accidents are NOT equally distributed through out the year.

[ Option a) Yes, because the p-value = 0.0145 ] is the correct answer.

Answer:

V =110 in ^3

Step-by-step explanation:

The volume is

V = l*w*h

V = 10 * 2 * 5.5

V =110 in ^3

Answer:

Step-by-step explanation:

The total number of ways of selecting 3 gems of any kind without replacement is 35 * 34 * 33 = 39270

Now selecting 2 gems from 25 is 25C2

25 C 2 = 25 * 24/2 = 300

Selecting one good gem is 10

Total selection = 300 * 10 = 3000

P(gems) = 3000 / 39270

P(gems) = 300/3927

P(gems) = 100/1309

Answer: Is there a picture?

Step-by-step explanation:

Answer:

[tex]x = \pi \div 4 [/tex]

h(-9) = 32

h(0)= 2

h(2) =11

h(7)= 16

c. 5/12

Step-by-step explanation:

tan= opposite/adjacent

[tex]{\huge{\underline{\bf{\pink{Hello \: mate \: (◕ᴗ◕✿)}}}}} \\ \\ = > \mathcal\blue{tan \beta = perpendicular \: \div base\: } \\ \\ \mathcal\blue{=>perpendicular = 5 \: } \\ \\\blue{=>Base = 12 \: } \\ \\ \\ \huge\mathfrak\red{=>tan \beta = 5 /12\: } \\ \\ {\huge{\boxed{\sf{\green{✓✓venom✓✓}}}}}[/tex]

The answer is in the picture. To be honest, I am not 100% sure about it.

Answer:

that there is no significant evidence that there is an increase in mean number of arrivals per hour

Step-by-step explanation:

The hypothesis :

H0 : μ = 195

H1 : μ > 195

We obtain the test statistic :

(xbar - μ) ÷ (σ/√(n))

xbar = 200 ; n = 30 ; σ = 16

Test statistic :

(200 - 195) ÷ (16/√(30))

5 ÷ 2.9211869

= 1.712

Using the Pvalue calculator :

Pvalue from Test statistic = 0.043

At α = 0.025

Pvalue > α ; we fail to reject the Null and conclude that there is no significant evidence that there is an increase in mean number of arrivals per hour.

Answer:

3

Step-by-step explanation:

A ratio is always expressed in the form a : b = a / b ; where, a = antecedent ; b = consequent

With antecedent = 15 ; consequent = b

Value of ratio = 5

15 / b = 5

Cross multiply

15 = 5b

b = 15 / 5

b = 3

Answer:

[tex]\displaystyle \int\limits^0_\infty {cos(x)} \, dx = sin(\infty)[/tex]

General Formulas and Concepts:

Pre-Calculus

Calculus

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^0_\infty {cos(x)} \, dx[/tex]

Step 2: Integrate

Since we are dealing with infinity of functions, we can do a numerous amount of things:

∴  [tex]\displaystyle \int\limits^0_\infty {cos(x)} \, dx = sin(\infty) \ or \ \text{unde}\text{fined}[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Improper Integrals

Book: College Calculus 10e

Answer:

the answer to this question would be percentiles

Answer:

15/25, simplified to 3/5. As a decimal, 0.6, or a 60% as a percentage.

Step-by-step explanation:

everything can be found in the picture

Answer:

h = [tex]\frac{K^2}{17}[/tex]

Step-by-step explanation:

Given

K = [tex]\sqrt{17h}[/tex] ( square both sides )

K² = 17h ( divide both sides by 17 )

[tex]\frac{K^2}{17}[/tex] = h

9514 1404 393

Answer:

  103 square units

Step-by-step explanation:

There is a way to find the area by counting grid points, but the fairly large number of them suggests that could be both tedious and prone to error. Instead, we'll chop up the figure into a trapezoid and two triangles.

From the top corner of the right edge draw a horizontal line across the figure. This will make the bottom portion a trapezoid and the top portion two triangles. The length of that horizontal line is 13 units, the height of the trapezoid, and the sum of the triangle bases.

The bottom trapezoid has a left-side base of 7 units and a right-side base of 6 units. Its area is ...

  A = 1/2(b1 +b2)h

  A = 1/2(7 +6)(13) = 1/2(13)(13) = 169/2 = 84.5 . . . square units.

The right top triangle has a base of 11 and a height of 3, so its area is ...

  A = 1/2bh

  A = 1/2(11)(3) = 33/2 = 16.5 . . . square units

The left top triangle has a base and height of 2 units each, so its area is ...

  A = 1/2(2)(2) = 2 . . . square units

Then the total area of the figure is ...

  84.5 +16.5 +2 = 103 . . . square units

_____

Check

Here is the check by counting grid points. The number of grid points on the outline of the figure is i=22. The number of grid points inside the figure appears to be b=93. Then the area by Pick's theorem is ...

  b +i/2 -1 = 93 + 22/2 -1 = 103 . . . square units

Answer:

w=18

Step-by-step explanation:

-1-2 = =3

w/-6 = -3

-6x-3 = 18

w=18

Answer:

w = 18

Step-by-step explanation:

[tex]\frac{w}{-6}+2=-1\\\frac{w}{-6}=-3\\w=18[/tex]

Can you please show attachments.

Answer:

Step-by-step explanation:

can you give the question? XD

Answer:

36 cupcakes per hour

Step-by-step explanation:

288 cupcakes divided by 8 hours

288/8=36

Answer:

32

Step-by-step explanation:

p=8/1/4

p=8÷¼

p=8×4

p=32

hope this helps

please like and mark as brainliest

Answer:

The 95% confidence of interval to estimate the difference in the proportion of the residents in these regions who support the construction is (-0.0849, 0.0013).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

North:

274 out of 1000. So

[tex]p_N = \frac{274}{1000} = 0.274, s_N = \sqrt{\frac{0.274*0.726}{1000}} = 0.0141[/tex]

South

240 out of 760. So

[tex]p_S = \frac{240}{760} = 0.3158, s_S = \sqrt{\frac{0.3158*0.6842}{760}} = 0.0169[/tex]

Distribution of the difference:

[tex]p = p_N - p_S = 0.274 - 0.3158 = -0.0418[/tex]

[tex]s = \sqrt{s_N^2+s_S^2} = \sqrt{0.0141^2+0.0169^2} = 0.022[/tex]

Confidence interval:

The confidence interval is:

[tex]p \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Lower bound:

[tex]p - zs = -0.0418 - 1.96*0.022 = -0.0849[/tex]

Upper bound:

[tex]p + zs = -0.0418 + 1.96*0.022 = 0.0013[/tex]

The 95% confidence of interval to estimate the difference in the proportion of the residents in these regions who support the construction is (-0.0849, 0.0013).

Given the proportion and number of residents in the North and South of

0.274, 1000, and approximately 0.316, 760, we have;

The given parameter presented in a tabular form are;

[tex]\begin{array}{|c|c|c|}Support \ Constructtion&North&South\\Yes&274&240\\No&726&520\\Total & 1000& 760\end{array}\right][/tex]

Which gives;

Proportion of the North resident that support, [tex]\mathbf{\hat p_N}[/tex] = 274 ÷ 1000 = 0.274

The number of people sampled in the north, n₁ = 1,000

Proportion of the South resident that support, [tex]\mathbf{\hat p_S}[/tex] = 240 ÷ 760 ≈ 0.316

The number of people sampled in the south, n₂ = 760

The confidence interval for the difference of two proportions are given

as follows;

[tex]\hat{p}_N-\hat{p}_S\pm \mathbf{ z^{*}\sqrt{\dfrac{\hat{p}_N \cdot \left (1-\hat{p}_N \right )}{n_{1}}+\dfrac{\hat{p}_S \cdot \left (1-\hat{p}_S \right )}{n_{2}}}}[/tex]

Where;

The z-score at 95% confidence level is 1.96

Which gives;

[tex]C.I. = \left(0.274-0.316 \right)\pm 1.96 \times \sqrt{\dfrac{0.274 \times \left (1-0.274 \right )}{1000}+\dfrac{0.316 \times \left (1-0.316 \right )}{760}}[/tex]

C.I. ≈ (-0.085, 0.00109)

The 95% confidence interval, C. I. of the difference in the proportion of

the residents in the regions who support the construction, [tex]\hat p_N[/tex] -  [tex]\hat p_S[/tex] is

therefore;

Learn more calculating the confidence interval here:

https://brainly.com/question/15308274

Answer:

m<1 = ½(b - d)

Step-by-step explanation:

Recall: when two secants intersect to form an exterior angle outside a circle, the measure of the exterior angle equals half of the difference of the major and minor arcs intersected.

Thus, in the problem given,

m<1 is the exterior angle

b and d are the arcs intersected.

Therefore,

m<1 = ½(b - d)

The equation that is correct regarding the measure of <1 is; m<1 = ½(b - d)

According to the secant theorem, it states that when two secants intersect to form an exterior angle outside a circle, then the measure of the exterior angle will be equal to half of the difference of the major and minor arcs intersected.

In the given question, we can see that;

The exterior angle = m<1

The arcs intersected are b and d

Thus, from applying the secant theorem, we can express that;

m<1 = ½(b - d)

Read more about the secant theorem at; https://brainly.com/question/26340897

Answer: [tex]50\frac{2}{5}[/tex]  or 50.4 pounds

Step-by-step explanation:

You multiply:

[tex]9*5\frac{6}{10} \\\\=9*\frac{56}{10} (5\frac{6}{10} =\frac{5(10)+6}{10} =\frac{50+6}{10} =\frac{56}{10} )\\\\=\frac{9*56}{10} =\frac{504}{10}\\\\ =\frac{2(252)}{2(5)}=\frac{252}{5} =50.4[/tex]

Answer:

Bottom left corner and bottom right corner

Step-by-step explanation:

the orange one and the blue one on the bottom