The function f(x)=2x2−x+4; f ( x ) = 2 x 2 − x + 4 is defined over the domain 0 ≤ x ≤ 3 Find the range of this function. A. 4 < f(x) < 7 B. 4 < f(x )< 19 C. 4 ≤ f(x) ≤ 19 D. 4 ≤ f(x) ≤ 25

Answer:

csc ø = 5/3 ; sec ø = 5/4

Step-by-step explanation:

cot ø = adj/opp

adj = 4

opp = 3

after that, we must find the hypotenuse by using phytagoras theorem

hpy² = adj² + opp²

hpy² = 4² + 3²

hpy² = 25

hpy = 5

now let's find the other

csc ø (not scs) = hyp/opp = 5/3

sec ø = hyp/adj = 5/4

Answer:

3 Pages

Step-by-step explanation:

In the first instance, the student has time to read 50 pages of psychology and 10 pages of economics.

The student could read 30 pages of psychology and 70 pages of economics.

Since the two situations take the same amount of time, we have:

50p+10e=30p+70e

Collect like terms

50p-30p=70e-10e

20p=60e

Divide both sides by 20

p=3e

Therefore, in the time it will take the student to read 1 page of psychology, the student can read 3 pages of economics.

75km convert to m 75x1000=75000m

converted I hour to seconds that is 3600seconds

If 75000m=3600seconds

? =5seconds

that id 75000x5=375000/3600

=104.26…metres

The distance will be 104.16 meters if the car is driving at 75 kilometers per hour.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

A car is driving at 75 kilometers per hour.

Let x be the distance.

As we know from the distance time relation:

Distance = speed×time

Speed = 75 km/h

Speed = 75 km/(3600)seconds

Speed = 0.0208 km/s

x = 0.0208×5

x = 0.10416 km

in meters

x  = 0.104x1000

x = 104.16 meters

Thus, the distance will be 104.16 meters if the car is driving at 75 kilometers per hour.

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Answer:

[tex]7x+1+6x+101=180\\13x=78\\x=6[/tex]

Answer:

[tex]-8(y+4) =(x-6)^{2}[/tex]  

Step-by-step explanation:

The standard form of a parabola is given by the following equation:

[tex](x-h)^{2} =4p(y-k)[/tex]

Where the focus is given by:

[tex]F(h,k+p)[/tex]

The vertex is:

[tex]V=(h,k)[/tex]

And the directrix is:

[tex]y-k+p=0[/tex]

Now, using the previous equations and the information provided by the problem, let's find the equation of the parabola.

If the focus is (-6,6):

[tex]F=(h,k+p)=(6,-6)[/tex]

Hence:

[tex]h=6\\\\k+p=-6\hspace{10}(1)[/tex]

And if the directrix is [tex]y=-2[/tex] :

[tex]-2-k+p=0\\\\k-p=-2\hspace{10}(2)[/tex]

Using (1) and (2) we can build a 2x2 system of equations:

[tex]k+p=-6\hspace{10}(1)\\k-p=-2\hspace{10}(2)[/tex]

Using elimination method:

(1)+(2)

[tex]k+p+k-p=-6+(-2)\\\\2k=-8\\\\k=-\frac{8}{2}=-4\hspace{10}(3)[/tex]

Replacing (3) into (1):

[tex]-4+p=-6\\\\p=-6+4\\\\p=-2[/tex]

Therefore:

[tex](x-6)^{2} =4(-2)(y-(-4)) \\\\(x-6)^{2} =-8(y+4)[/tex]

So, the correct answer is:

Option 3

Answer:

x = -3        x=8

Step-by-step explanation:

(x+3)(x-8)=0

Using the zero product property

x+3 =0   x -8 = 0

x = -3        x=8

Answer:

[tex] z= \frac{9832- 10000}{\frac{714.2857}{\sqrt{49}}}= -1.646[/tex]

[tex] z= \frac{10200- 10000}{\frac{714.2857}{\sqrt{49}}}= 1.96[/tex]

And we can use the normal standard distribution table or excel and we can  find the probability with this difference:

[tex] P(-1.646 <z< 1.96) =P(z<1.96) -P(z<-1.646) =0.975-0.0499= 0.9251[/tex]

Then the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200 is 0.9251

Step-by-step explanation:

For this case we have the following info given:

[tex] \mu = 10000[/tex] represent the mean

[tex] \sigma = 714.2857[/tex] represent the deviation

[tex] n = 49[/tex] represent the sample size selected

For this case since the sample size is large enough n>30 we have enough evidence to use the central llmit theorem and the distribution for the sample mena would be given by:

[tex] \bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}}) [/tex]

And we want to find the following probability:

[tex] P(9832 < \bar X< 10200)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we use the z score formula for the limits  given we got:

[tex] z= \frac{9832- 10000}{\frac{714.2857}{\sqrt{49}}}= -1.646[/tex]

[tex] z= \frac{10200- 10000}{\frac{714.2857}{\sqrt{49}}}= 1.96[/tex]

And we can use the normal standard distribution table or excel and we can  find the probability with this difference:

[tex] P(-1.646 <z< 1.96) =P(z<1.96) -P(z<-1.646) =0.975-0.0499= 0.9251[/tex]

Then the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200 is 0.9251

Answer:

c. line

Step-by-step explanation:

the intersection of two planes is called a line

Answer:

Hello dear,

two planes intersect and forms line

so yaa your answer is C)

Hope I helped you ;)

please thank me !!!

satsriakal ji

Answer:

1) Antonio's statement

2) <A = 123

Step-by-step explanation:

1) Antonio's statement is incorrect. This is because the opposite angles of a quadrilateral add up to 180°. Erin was incorrect because the opposite angles of this quadrilateral are unequal.

2) 2x+7+5x-2 = 180° (opposite angles of quadrilateral)

Now

7x+5 = 180

7x = 175

x = 25

<A = 5x-2

= 5(25)-2

= 125-2

= 123

Answer:

square root of 72

Step-by-step explanation:

Answer:

(c) square root of 72

Step-by-step explanation:

khan academy answer :)

Answer: the answer is 4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4 on edgunity 2020

Answer:

Look at the money bags below!!! (but I'll give you the answer)

Step-by-step explanation:

John F: 7 full bags - 1 half

Juan A: 9 full bags

Jason A: 3 full bags

Nick J: 3 full bags- 1 half

Alfonso S: 8 full bags

Hope this helped and wasn't confusing!!! xx - Asia

Answer:

The answer is A

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

60% * 160 = 0.6 * 160 = 96.

Answer:

None

Step-by-step explanation:

There is no Forest Green iPhone XR's only the 11 Pros have that color.

Answer:

[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]

[tex]CI = (527 - 439) \pm 25.75\\\\CI = 88 \pm 25.75\\\\CI = 88 - 25.75 \:\: and \:\: 88 + 25.75\\\\CI = (62.2 \: ,\: 113.8 )[/tex]

The correct answer choice is a. (62.2, 113.8)

Step-by-step explanation:

Of the 500 customers who were told the increase applied to charges above $1000 each month, the average increase in spending was $527 with a standard deviation of $225.

Sample size = n₁ = 500

Sample mean = x₁ = $527

Standard deviation = s₁ = $225

Of the 500 customers who were told the increase applied to charges above $2000 each month, the average increase in spending was $439 with a standard deviation of $189

Sample size = n₂ = 500

Sample mean = x₂ = $439

Standard deviation = s₂ = $189

We are asked to find the 95% confidence interval for the difference between two means.

The given group of answer choices are

a. (62.2, 113.8)

b. (86.2, 120.5)

c. (10.3, 23.8)

d. (55.6, 67.8)

The confidence interval for the difference between two means is given by

[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]

Where [tex]\bar{x_{1} }[/tex] and [tex]\bar{x_{2} }[/tex] are the given sample means and margin of error is given by

[tex]$ MoE = z_{\alpha/2} \cdot \sqrt{\frac{s_{1}^2}{n_1} + \frac{s_{2}^2}{n_2}} $[/tex]

The z-score corresponding to 95% confidence level is given by

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

From the z-table at α = 0.025 the z-score is 1.96

[tex]$ MoE = 1.96 \cdot \sqrt{\frac{225^2}{500} + \frac{189^2}{500}} $[/tex]

[tex]MoE = 1.96 \cdot 13.14[/tex]

[tex]MoE = 25.75[/tex]

Finally,

[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]

[tex]CI = (527 - 439) \pm 25.75\\\\CI = 88 \pm 25.75\\\\CI = 88 - 25.75 \:\: and \:\: 88 + 25.75\\\\CI = (62.2 \: ,\: 113.8 )[/tex]

Therefore, the correct answer choice is a. (62.2, 113.8)

How to use z-table?

In the z-table find the probability of 0.025

Note down the value of that row, it would be 1.9.

Note down the value of that column, it would be 0.06.

Add the two numbers together.

The z-score is 1.9 + 0.06 = 1.96

Answer: y

Step-by-step explanation:

Answer:

He earns $2,100 in two weeks.

Step-by-step explanation:

We know that this street performers earn $60 per day at the Barclays center subway station, and that this earning represents 40% (or a proportion of 0.4) of his daily earnings. We can calculate his daily earnings as:

[tex]0.4D=\$\,60\\\\D=\dfrac{\$\,60}{0.4}=\$\,150[/tex]

If the daily earnings are $150, the earnings in 2 weeks (14 days) will be:

[tex]W=14\cdot\$\,150=\$\,2100[/tex]

Answer:

Step-by-step explanation:

2 3x6

the 3 is an exponet so supost to be smaller

the answer-  2^3 x^6

i think its right

Answer:

No. There is not enough evidence to support the claim that the proportion of liberals is higher than that reported by the polling​ organization (P-value = 0.0366).

Step-by-step explanation:

The question is incomplete: there is no information about the results of the survey. We will assume that 55 of the subjects answer "liberal", and test the claim.

This is a hypothesis test for a proportion.

The claim is that the proportion of liberals is higher than that reported by the polling​ organization.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.22\\\\H_a:\pi>0.22[/tex]

The significance level is 0.01.

The sample has a size n=200.

The sample proportion is p=0.275.

[tex]p=X/n=55/200=0.275[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.22*0.78}{200}}\\\\\\ \sigma_p=\sqrt{0.000858}=0.029[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.275-0.22-0.5/200}{0.029}=\dfrac{0.053}{0.029}=1.792[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>1.792)=0.0366[/tex]

As the P-value (0.0366) is greater than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion of liberals is higher than that reported by the polling​ organization.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

A sports physician conducts an observational study to learn the average amount of time that 3,000 swimmers in the town can hold their breath underwater. He uses 150 sampling of 60 people. The average of the means of all the samplings is 72.7, and the standard deviation is 0.92. This is a histogram of the sampling distribution of the sample mean. Based on this data, with a 95% confidence interval the researchers can determine that the actual average amount of time the entire population can hold their breath under water is?

Given Information:

sample mean time = 72.7

sample standard deviation = 0.92

Sampling size = n = 150

Confidence level = 95%

Required Information:

95% confidence interval = ?  

Answer:

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]

Step-by-step explanation:

The confidence interval is given by

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean time and Margin of error is given by

[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]

Where n is the sampling size, s is the sample standard deviation, and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to 95% confidence level.

The t-score corresponding to 95% confidence level is

Significance level = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 150 - 1 = 149

From the t-table at α = 0.025 and DoF = 149

t-score = 1.975

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 1.975\cdot \frac{0.92}{\sqrt{150} } \\\\MoE = 1.96\cdot 0.07512\\\\MoE = 0.14836\\\\[/tex]

So the required 95% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]

Therefore, we are 95% confident that actual average amount of time the entire population can hold their breath under water is within the range of (72.552, 72.848)

If the area of ΔBAC = 24 in², the area of ΔEDF is 6 in².

If two triangles' angles are congruent and their corresponding sides are proportionate, they are considered similar. To put it another way, similar triangles are the same in shape but not necessarily in size. If ΔPQR and ΔMNO are two similar triangles, then we can write it as ΔPQR ∼ ΔMNO.

The square of the ratio of any pair of their respective sides is equal to the ratio of the areas of two similar triangles.

Since ΔBAC ∼ ΔEDF, we can use the above statement to find the area of ΔEDF. Let the area of ΔEDF be x in². Given that length of EF and BC is 2 in and 4 in respectively.

So, we have to solve this equation,

24/x = 4²/2²

Now, 24/x = 16/4

i.e. 24/x = 4

i.e. 4x = 24

i.e. x = 24/4 = 6

Therefore the area of ΔEDF is 6 in².

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Answer:

They are parallel because they are vertical lines, and all vertical lines are parallel.

Step-by-step explanation:

Answer:

i dont really know what it is

Answer:

=3651 km^2

Step-by-step explanation:

The rectangle at the top is 11 km by 32 km

The area is 11*32 =352

The rectangle at the bottom is 9 km by 11 km

The area is 9*11 = 99

Add the two areas together

352+99 =451 km^2

Answer:

149.14 [tex]m^{2}[/tex]

Step-by-step explanation:

Area of a circle = π[tex]r^{2}[/tex]

so A = π * 6.89^2 = 149.14 (to 2d.p.)

Complete Question:

The Giant Machinery has the current capital structure of 65% equity and 35% debt. Its net income in the current year is $250 000. The company is planning to launch a project that will requires an investment of $175 000 next year. Currently the share of Giant machinery is $25/share. Required: a. How much dividend Giant Machinery can pay its shareholders this year and what is dividend payout ratio of the company. Assume the Residual Dividend Payout Policy applies? b. If the company is paying a dividend of $2.50/share and tomorrow the stock will go ex-dividend. Calculate the ex-dividend price tomorrow morning. Assuming the tax on dividend is 15%? c. Little Equipment for Hire is a subsidiary in the Giant Machinery and currently under the liquidation plan due to the severe contraction of operation due to corona virus. The company plans to pay total dividend of $2.5 million now and $ 7.5 million one year from now as a liquidating dividend. The required rate of return for shareholders is 12%. Calculate the current value of the firm’s equity in total and per share if the firm has 1.5 million shares outstanding?

Answer:

a) Total dividend for the current year = $136,250

Dividend Payout Ratio = 0.545

b) Ex-dividend price = $22.875

c) Total current value = $9,196,428.57

Current value per share = $6.13

Step-by-step explanation:

a) Equity = 65%

Debt = 35%

Net Income for year 0 = $250,000

proposed Investment for year 1= $175,000

Current price = $25/share

Tax on dividend = 15%

Total dividend for year 0 = 250000 - (65% of 175000)

Total dividend for year 0= 250000 - 113750

Total dividend for the current year = $136,250

Dividend Payout Ratio = total dividends/ total earning

Dividend Payout Ratio = 136250/250000

Dividend Payout Ratio = 0.545

b) Dividend = $2.5/ share

Ex-dividend price = current price - Dividend * (1-tax on dividend)

Substituting the appropriate values:

Ex-dividend price = 25 - 2.5 * (1-15%)

Ex-dividend price = 25 - 2.125

Ex-dividend price = $22.875

c) Current value of the firm = Dividend paid in year 0 + (Dividend to be paid in year 1/discount rate)

Dividend paid in year 0 = $2,500,000

Dividend to be paid in year 1 = $7,500,000

Discount rate = 12%

Total current value = 2,500,000 + (7,500,000 / 1.12)

Total current value = $9,196,428.57

Numbe of shares = 1,500,000

Current value per share = Total current value / number of shares

Current value per share = 9,196,428.57/1,500,000

Current value per share = $6.13

Answer:

Is there any options if so just repost with the options and i will answer it

Step-by-step explanation:

Answer:

[tex]A = \dfrac{40}{P}[/tex]

Step-by-step explanation:

Pressure [tex]p(in lbs/in^2)[/tex]  varies inversely with the area [tex]A(in$ in^2)[/tex] of the sole of the shoe.

This is written as:

[tex]P \propto \frac{1}{A}\\ $Introducing the constant of variation$\\P = \dfrac{k}{A}[/tex]

When:

[tex]When: A= 40 in^2, P =4 lbs/in^2\\$Substituting into the equation\\P = \dfrac{k}{A}\\4 = \dfrac{k}{40}\\$Cross multiply\\k=4*40\\k=160\\Therefore, the equation that connect these variables is given as:\\P = \dfrac{40}{A}\\$In terms of P\\AP=40\\\\A = \dfrac{40}{P}[/tex]

Answer:

The number of female faculty in the Department with a PhD is 8.

Step-by-step explanation:

There are 14 + 30 = 44 faculty members.

Of those, x are male and y are female.

Then

x + y = 44.

The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.

y = z + w

z is the number of females with PhD.

w is the number of females without PhD.

w = z + 10

If a third of the male faculty in the Department have a PhD

[tex]\frac{x}{3} + z = 14[/tex]

Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.

The objective is:

To find z from the first equation, that is:

[tex]x + y = 44[/tex]

To do this, we have to write x and y as functions of z.

Writing x and y as functions z.

[tex]\frac{x}{3} + z = 14[/tex]

[tex]\frac{x}{3} = 14 - x[/tex]

[tex]x = 3(14 - z)[/tex]

[tex]x = 42 - 3z[/tex]

And

[tex]y = z + w[/tex]

In which

[tex]w = 10 + z[/tex]

So

[tex]y = z + 10 + z[/tex]

[tex]y = 2z + 10[/tex]

Replacing:

[tex]x + y = 44[/tex]

[tex]42 - 3z + 2z + 10 = 44[/tex]

[tex]-z + 52 = 44[/tex]

[tex]z = 52 - 44[/tex]

[tex]z = 8[/tex]

The number of female faculty in the Department with a PhD is 8.

Answer:

<1 = 91

Step-by-step explanation:

<2 + <3 = 180

5 x + 14 +  (7 x -14) = 180

Combine like terms

12x = 180

Divide by 12

12x/12 = 180/12

x =15

We want <1

<1 = <3 since they are vertical angle

<1 = 7x-14 = 7*15 -14 =105-14=91

Answer:

D, 91 degrees

Step-by-step explanation:

First, solve for x. Angles 2 and 3 add up to 180, so set up an equation:

(5x + 14) + (7x - 14) = 180

12x = 180

x = 15

Then, you know angles 1 and 2 also add up to 180, so solve for Angle 2

5(15) + 14= 89

180-89= 91, so angle 1 is 91 degrees.