HELPPPP In the straightedge and compass construction of the perpendicular line
below, how do you know that CD | BE ?

Answer:

Yes, the function satisfies the hypothesis of the Mean Value Theorem on the interval [1,5]

Step-by-step explanation:

We are given that a function

[tex]f(x)=ln(x)[/tex]

Interval [1,5]

The given function is defined on this interval.

Hypothesis of Mean Value Theorem:

(1) Function is continuous on interval [a,b]

(2)Function is defined on interval (a,b)

From the graph we can see that

The function is continuous on [1,5] and differentiable at(1,5).

Hence, the function satisfies the hypothesis of the Mean Value Theorem.

Answer: The equations are

w + s = 4500

2.25s = 4500

Step-by-step explanation:

Let w represent the number of bottles of water that the football manager bought.

Let s represent the number of bottles of soda that the football manager bought.

The manager needs to buy a total of 4,500 drinks. This means that

w + s = 4500

He also needs to have 25% more water than soda.

25% of soda = 25/100 × s = 0.25s

25% more of water than soda = s + 0.25s = 1.25s

The equation would be

1.25s + s = 4500

2.25s = 4500

The probability of the pumping system failing on any given day is 0.015, or 1.5 percent.

Given data:

To find the probability that the pumping system will fail on any given day,  consider the probabilities of different failure scenarios for the two pumps.

Let's denote the events as follows:

A = Only the older pump fails

B = Only the newer pump fails

P(A) = 0.15 (probability that only the older pump fails)

P(B) = 0.10 (probability that only the newer pump fails)

To find the probability that both pumps fail, which can be denoted as the event A ∩ B.

Since the two pumps fail independently of each other, use the multiplication rule for independent events to calculate the probability of both events occurring:

P(A ∩ B) = P(A) * P(B)

Substituting the given probabilities:

P(A ∩ B) = 0.15 * 0.10

= 0.015

Hence, the probability that the pumping system will fail on any given day (when both pumps fail) is 0.015 or 1.5%.

To learn more about probability, refer:

https://brainly.com/question/17089724

#SPJ4

Answer:

a) 12

b) 129

Step-by-step explanation:

a)

[tex]w, x \in \mathbb{Z}_{\ge 0}[/tex]

[tex]w>50\\x<40[/tex]

For the smallest value of [tex]w-x[/tex], we gotta figure out the smallest value for w and the highest value for x.

[tex]w>50 \Rightarrow \text{ smallest value is } 51[/tex]

For [tex]x[/tex], once [tex]-(-x)=x[/tex], we conclude that [tex]x[/tex] cannot be negative and therefore, [tex]x=39[/tex].

[tex]51-39=12[/tex]

b)

[tex]y, z \in \mathbb{Z}_{\ge 0}[/tex]

[tex]y<70\\z\leq 60[/tex]

For the largest value of [tex]y+z[/tex], we gotta figure out the highest value for y and z.

[tex]y<70 \Rightarrow \text{ highest value is } 69[/tex]

[tex]z\leq 60 \Rightarrow \text{ highest value is } 60[/tex]

[tex]y+z=69+60=129[/tex]

Answer:

Step-by-step explanation:

The factors of the given expression are ...

  6ir +15i +8r +20 = (3i +4)(2r +5)

Which factor is current and which is resistance is not clear. Usually, resistance is referred to using the variable r, so we suppose the expressions are supposed to be ...

  resistance: (2r +5)

  current: (3i +4)

Answer:

The lines will intersect infinitely many times, because they are identical.

Step-by-step explanation:

Let's change the equations of the lines into (y=mx+b) form.

6x-4y=2 Divide by 2.

3x-2y=1 Move x and divide by -2.

-2y=1-3x ---> y= -1/2+3/2x

The equation of the first line is y=3/2x- 1/2

-2y+3x=1

-2y=1-3x

y = 3/2x -1/2

The equation of the second line is y = 3/2x- 1/2.

The lines are identical- infinitely many intersections.

Step-by-step explanation:

I think the answer is third because it doesn't has a solution.

Answer/Step-by-step explanation:

Let x = 4 (you and 3 friends)

Ticket cost per head = $5.50

Drink cost per head = $2.50

Popcorn cost per head = $4.00

Expression representing total amount of money spent = $5.50(x) + $2.50(x) + $4.00(x)

Evaluate the expression by plugging in the value of x = 4

Total amount of money spent = $5.50(4) + $2.50(4) + $4.00(4)

= $22 + $10 + $16 = $48

Total amount of money spent = $48

Answer:Yes indeed!

Step-by-step explanation:

Your right!

Answer:

[tex]-x+| \: y\: |[/tex]

Step-by-step explanation:

[tex]-x+|-y|[/tex]

[tex]\mathrm{Apply\:absolute\:rule}: \left|-y\right|\:=| \: y\: |[/tex]

[tex]-x+| \: y\: |[/tex]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 7.2

For the alternative hypothesis,

H1: µ ≠ 7.2

This is a two tailed test.

Since the population standard deviation is given, the test statistic would be the z score determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 7.2

x = 7.3

σ = 0.8

n = 250

z = (7.3 - 7.2)/(0.8/√250) = 1.976

Test statistic is 1.976

Answer:

15√20/6√125

=√20/√5

=2

Step-by-step explanation:

Answer:

Yes. At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.

The random variable is the sample mean amount of mercury in the bass fish from the lakes of Florida.

The population parameter is the mean amount of mercury in the bass fish of Florida lakes.

The alternative hypothesis (Ha) states that the amount of mercury significantly differs from 1 mg/kg.

The null hypothesis (H0) states that the amount of mercury is not significantly different from 1 mg/kg.

[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]

Step-by-step explanation:

The question is incomplete.

There is no data provided.

We will work with a sample mean of 0.95 mg/kg and sample standard deviation of 0.15 mg/kg to show the procedure.

This is a hypothesis test for the population mean.

The claim is that the fish in all Florida lakes have different mercury than the allowable amount (1 mg of mercury per kg of fish).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]

The significance level is assumed to be 0.05.

The sample has a size n=53.

The sample mean is M=0.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.15.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.15}{\sqrt{53}}=0.0206[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.95-1}{0.0206}=\dfrac{-0.05}{0.0206}=-2.427[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=53-1=52[/tex]

This test is a two-tailed test, with 52 degrees of freedom and t=-2.427, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t<-2.427)=0.019[/tex]

As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.

Answer:  Sheila today = [tex]46\dfrac{1}{3}[/tex]  yrs old

Step-by-step explanation:

   J + S = 115 v⇒  J = 115 - S

Current Ages                        Ages 14 years ago

 Joe (J) = 115 - S                      J - 14 = 2(S - 14)

 Sheila (S) = S

Substitute J = 115 - S into the "14 years ago" equation

      J    - 14 = 2(S - 14)

(115 - S) - 14 = 2(S - 14)

111 -S = 2S - 28

111 = 3S  - 28

139 = 3S

46 [tex]\frac{1}{3}[/tex] = S

It is odd that the result was not an integer.  I wonder if you meant to type "Joe was twice as old as Sheila is today.  That would change the equation to:

J - 14 = 2S

111 - S = 2S

111 = 3S

37 = S

Answer:

The answer is 60cm^2.

hope it helps..

Answer:

19cm

Step-by-step explanation:

The area  of a trapezoid [tex]=\dfrac12(a+b)h[/tex] (where a and b are the parallel sides).

Given:

Area = 189 Square cm

Height, h=14cm

a=8cm

We want to find the value of the other parallel side, b.

Substitution of the given values gives:

[tex]189=\dfrac12(8+b)14\\189=7(8+b)\\$Divide both sides by 7\\8+b=27\\Subtract 8 from both sides\\b+8-8=27-8\\b=19cm[/tex]

The length of the second parallel side is 19cm.

Answer:

B. zero

Step-by-step explanation:

If the temperature is supposed to remain constant over time (the same) when working properly, then this means that there is no increase or decrease over time.

If there were a line to represent this, then it would be a straight line with a slope of 0 because the temperature would remain the same.

Answer: 6x^2

Step-by-step explanation:

The area of a triangle is 1/2bh

Thus, simply multiply 2x*3x = 6x^2

Hope it helps <3

Answer:

Solution,

Base(b)= 3x

Height(h) = 2x

Now,

Finding the area of triangle:

[tex] \frac{1}{2} \times b \times h[/tex]

[tex] \frac{1}{2} \times 3x \times 2x[/tex]

[tex] \frac{1}{2} \times 6 {x}^{2} [/tex]

[tex]3 {x}^{2} [/tex]

Hope this helps....

Good luck on your assignment....

Answer:

1 woman Teacher

Step-by-step explanation:

We proceed as follows;

Let W and M represent the set of women and men respectively , and T represent teachers

from the information given in the question we have

n(W)=29

n(M)=23

n(T)=4

n(M U T)=24

Mathematically;

n(MUT)=n(M)+n(T)-n(MnT)

24=23+4-n(Mn T)

n(MnT)=3

that is number of men teachers is 3,

so out of 4 teachers there are 3 men ,

and remaining 1 is the women teacher .

so the number of women teachers attending the lecture is 1

Answer:

It's written as

[tex]2.6 \times {10}^{ - 3} [/tex]

Hope this helps you

Answer:

2.6 × 10⁻³

Step-by-step explanation:

To write a number in scientific notation, move the decimal to the right or left until you reach a number that is 1 or higher.

In the decimal 0.0026, the first number that is 1 or higher is 2.

0.0026 ⇒ 2.6

When trying to figure out the exponent, here are some things to keep in mind:

- when you move the decimal to the right, the exponent is negative

- when you move the decimal to the left, the exponent is positive

You moved the decimal to the right three places. So the exponent will be -3.

The result is 2.6 × 10⁻³.

Hope this helps. :)

Answer:

4.428 hours

Step-by-step explanation:

If the learning rate is 0.81, the slope of the learning curve is:

[tex]b=\frac{ln(0.81)}{ln(2)} \\b=-0.304[/tex]

The time it takes to produce the n-th unit is:

[tex]T_n=T_1*n^b[/tex]

If T1 = 8 hours, the time required to produce the seventh unit will be:

[tex]T_n=8*7^{-0.304}\\T_n=4.428\ hours[/tex]

It will take roughly 4.428 hours.

Answer:

3

Step-by-step explanation:

Triangle ABC is an isosceles triangle, so

[tex]x^2+x^2=(6\sqrt{2} )^2\\2x^2=6^2*2\\x^2=6^2\\x=6.[/tex]

Triangle BCD is a notable triangle and the sides are

BD=x, CD=[tex]x\sqrt{3}[/tex],BC=2x=6

2x=6

x=3

Answer:

Step-by-step explanation:

Answer:

Millennium Dairy Product

a) Share of the company that SBI Caps should require today to get a required rate of return of 50%.

= 50%

b) If the company had 1,000,000 (100,000 x10) shares outstanding before the private placement, SBI Caps should purchase

1,000,000 shares = 50% of (1,000,000 + 1,000,000) shares

Assuming the founding promoters are not giving up their shares, instead, new equity shares are being issued.

c) The price per share SBI Caps should agree to pay, if her required return was 50% is

Rs.50 per share, which will provide the required additional equity financing of (Rs.50 million) since Rs.50 x 1,000,000 equals Rs.50 million.

d) Pre money and post money valuations:

These are based on the calculated Market Price of Rs.1,000 per share from the Price/Earnings Ratio.

Pre money valuation will be Rs.1,000 x 1,000,000 shares = Rs.1 billion

Post money valuation will be Rs.1,000 x 2,000,000 shares = Rs.2 billion

e) Carried interests of the VC and the promoters

VC's carried interest = share of profits = 50% xRs.50 million = Rs.25 million

Promoters' carried interest = Rs.25 million

Step-by-step explanation:

a) Calculation of share in the company:

SBI Cap's required rate of return is 50%

If she invests Rs.50 million today, her expected return will be equal to Rs.50 million x 50% = Rs.25 million

Since rate of return = Net Income/Initial Investment or (Current value of investment - Initial Investment)/Initial Investment.

This return will be equal to 50% of the total net income of Rs.50 million

b) Price/Earnings P/E ratio = Market price per share/Earnings per share (EPS)

Since P/E ratio of similar companies = 20 times,

The company's P/E = 20 times x EPS

With calculated EPS = Rs.50 million /1,000,000 = Rs.50

Therefore, price per share = 20 x Rs.50 = Rs.1,000

Pre money valuation = Rs.1,000 x 1 million shares = Rs.1 billion

Post money valuation = Rs.1,000 x 2 million shares = Rs.2 billion

c) The carried interest is the share of profits to which the promoters and the Venture Capitalists are entitled.  Their respective shares are 50% of the net income = Rs.25 million each.

d) The pre money and post money valuations:  The pre money valuation is the valuation of the company before the additional equity financing.  The post money valuation is the valuation of the company after the additional equity financing.  There are many ways to value a company.  In this case, we have used the P/E ratio as a basis for the valuation.  However, we did not dilute the earnings per share post money, for simplicity.

Answer:

GCF - 4

Step-by-step explanation:

36 - 1, 2, 3, 4, 6, 9, 12, 18, 36

44 - 1, 2, 4, 11, 44

Hope this helps! :)

Answer:

x=9

Step-by-step explanation:

3x subtracted by 2y

is 1 then 1 multiplied by 2 is 2 then 7 + 2 is 9

PEMDAS

Answer:

The correct option is (A)

A. Replace row 4 by its sum with - 4 times row 3.

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]

w = 8

x = 17/2

y = 6

z = -5

Step-by-step explanation:

The given matrix is

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&4&5&-1\end{array}\right][/tex]

To solve this matrix we need to create a zero at the 4th row and 3rd column which is 4 at the moment.

Multiply 3rd row by -4 and add it to the 4th row.

Mathematically,

[tex]R_4 = R_4 - 4R_3[/tex]

So the correct option is (A)

A. Replace row 4 by its sum with - 4 times row 3.

So the matrix becomes,

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]

Now the matrix may be solved by back substitution method.

Bonus:

The solution is given by

Eq. 1

-3z = 15

z = -15/3

z = -5

Eq. 2

y + 2z = -4

y + 2(-5) = -4

y - 10 = -4

y = -4 + 10

y = 6

Eq. 3

2x - 6y + 0z = 5

2x - 6(6) = 5

2x - 12 = 5

2x = 12 + 5

2x = 17

x = 17/2

Eq. 4

w - 4x + 4y + 0z = -2

w - 4(17/2) + 4(6) = -2

w - 34 + 24 = -2

w - 10 = -2

w = -2 + 10

w = 8

Answer:

[tex]19.6-2.42\frac{5.8}{\sqrt{42}}=17.43[/tex]    

[tex]19.6+2.42\frac{5.8}{\sqrt{42}}=21.77[/tex]    

And the best option for this case would be:

a. (17.5, 21.7)

Step-by-step explanation:

Information given

[tex]\bar X= 19.6[/tex] represent the sample mean

[tex]\mu[/tex] population mean

[tex]\sigma= 5.8[/tex] represent the population deviation

n=42 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom, given by:

[tex]df=n-1=42-1=41[/tex]

Since the Confidence is 0.98 or 98%, the significance would be [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.1[/tex], and the critical value would be [tex]t_{\alpha/2}=2.42[/tex]

Replacing we got:

[tex]19.6-2.42\frac{5.8}{\sqrt{42}}=17.43[/tex]    

[tex]19.6+2.42\frac{5.8}{\sqrt{42}}=21.77[/tex]    

And the best option for this case would be:

a. (17.5, 21.7)

Answer:

The 98% confidence interval for the population mean is between 17.5 hours and 21.7 hours.

Answer:

Step-by-step explanation:

Given the equation, 2x- y = 5, if x = 3, to get y we will simply substitute the value of x into the expression given as shown;

[tex]2x - y = 5\\\\Substituting \ x = 3\ into \ the \ equation\\\\2(3) - y = 5\\\\6 - y = 5\\\\subtracting\ 6\ from\ both\ sides\\\\6-6-y = 5- 6\\\\-y = -1\\\\multiplying\ both\ sides\ by \ -1\\-(-y) = -(-1)\\\\y = 1[/tex]

Hence, the value of y is 1

Answer:

You will have $29,000 in 30 years, and you need to start with about $2,772.28 to make $14,000 in 9 years

Step-by-step explanation:

To find the total investment use the equation [tex]A = P(1 + rt)[/tex]

Where A equals total investment, P is your start investment, r is your rate, and t is time.

[tex]A=2,000(1+(0.45 * 30))[/tex]

[tex]A=2,000(1+13.5)[/tex]

[tex]A=2,000*14.5[/tex]

[tex]A=29,000[/tex]

To find the start investment use the equation [tex]P = A / (1 + rt)[/tex]

[tex]P=14,000/(1+(0.45*9))[/tex]

[tex]P=14,000/(1+4.05)[/tex]

[tex]P=14,000/5.05[/tex]

[tex]P=2,772.28[/tex]

Answer:

C

Step-by-step explanation:

undefined slope means tat the denominator=0 in the equation

m=y2-y1/x2-x1

A: m=-1-1/1+1=-2

B;2-2/2+2=0

C: 3+3/-3+3 = 6/0 undefined

D: 4+4/4+4=1