f(x) = 2x – 1 g(x) = 7x – 12 What is h(x) = f(x) + g(x)?

Answer:

It will have a population of 61,779 in 2000.

Step-by-step explanation:

The population for the city, in t years after 1900, can be modeled by a exponential function with constant growth rate in the following format:

[tex]P(t) = P(0)(1+r)^{t}[/tex]

In which P(0) is the population in 1900 and r is the growth rate.

Population of 24,000 in 1900

This means that [tex]P(0) = 24000[/tex]

Population of 29,000 in 1920.

1920 is 1920 - 1900 = 20 years after 1900.

This means that P(20) = 29000. So

[tex]P(t) = P(0)(1+r)^{t}[/tex]

[tex]29000 = 24000(1+r)^{20}[/tex]

[tex](1+r)^{20} = \frac{29000}{24000}[/tex]

[tex]\sqrt[20]{(1+r)^{20}} = \sqrt[20]{\frac{29000}{24000}}[/tex]

[tex]1 + r = 1.0095[/tex]

So

[tex]P(t) = P(0)(1+r)^{t}[/tex]

[tex]P(t) = 24000(1.0095)^{t}[/tex]

What population will it have in 2000

2000 is 2000 - 1900 = 100 years after 1900. So this is P(100).

[tex]P(t) = 24000(1.0095)^{t}[/tex]

[tex]P(100) = 24000(1.0095)^{100} = 61779[/tex]

It will have a population of 61,779 in 2000.

Answer: Significantly low.

Step-by-step explanation:

Ok, we know that out of 1700 randomly selected, only 4 of them are girls.

Then the frequency is:

p = 4/1700

Now, using the subjective judgement (meaning that it is based on the opinion only, there is no real math involved)

I can conclude that the number of girls is significantly low, meaning that out of 1700 births we have 4 girls, then the other 1694 must be boys.

Answer:

I would say the second one

Step-by-step explanation:

f(x) has a range of y<0, because it is reflected over the x axis

g(x) = -5/7(3/5)^-x is also reflected over the x axis, except also in the y axis. Regardless of the reflection in the y-axis, y still cannot be equal to or greater than 0. Therefore, I believe it is the second choice.

(The third and forth choice are the same, which rules them both out. The first on reflects it over the y-axis, meaning that x can be greater than 0.)

Answer:

Blocking in a paired design

Completed randomized design

Step-by-step explanation:

Orringer et. al used blocking in a paired design. He use the special type of randomized block design; a matched pair design wherein there is just two treatment conditions (laser treatment and the sham treatment) and the subjects are then group the subjects in pairs using the blocking variable which is a treatment applied to one side of face randomly chosen.

While Seaton et. al. used a completely randomized design. Here the subjects/participants are just merely assigned albeit randomly to either the laser or the sham treatment.

Answer:

y=(5/2)x-3

Step-by-step explanation:

slope of the line=(y2-y1)/(x2-x1)=(-3-2)/(0-2)=5/2

use any point to get the line:

y-(-3)=(5/2)(x-0)

y=(5/2)x-3

Answer:

[tex] P(X>14)= 1-P(X<14) =1- F(14)[/tex]

And replacing we got:

[tex] P(X>14)= 1- \frac{14-8}{22-8}= 0.5714[/tex]

The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714

Step-by-step explanation:

We define the random variable of interest as x " time it takes a barber to complete a haircuts" and we know that the distribution for X is given by:

[tex] X \sim Unif (a= 8, b=22)[/tex]

And for this case we want to find the following probability:

[tex] P(X>14)[/tex]

We can find this probability using the complement rule and the cumulative distribution function given by:

[tex] P(X<x) = \frac{x-a}{b-a} ,a \leq x \leq b[/tex]

Using this formula we got:

[tex] P(X>14)= 1-P(X<14) =1- F(14)[/tex]

And replacing we got:

[tex] P(X>14)= 1- \frac{14-8}{22-8}= 0.5714[/tex]

The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714

Answer:

To find a we use sine

sin 60° = a / 4√3

a = 4√3sin60°

a = 6

To find b we use sine

sin 45° = a / b

a = 6

b = 6 / sin 45°

b = 6√2

To find c we use cosine

cos 60° = c / 4√3

c = 4√3 cos 60°

c = 2√3

To find d we use tan

tan 45° = a / d

a = 6

d = 6 / tan 45°

d = 6

Therefore a = 6 b = 6√2 c = 2√3

d = 6

That's option A.

Hope this helps

Answer:

P = 0.006

Step-by-step explanation:

If the first team have a probability of 0.9 to complete the task, we can said that the probability to not complete the task in time is 0.1. It is calculated as:

1 - 0.90 = 0.1

At the same way, the probability to not complete the task for the second and third team are 0.2 and 0.3 respectively and they are calculated as:

1 - 0.80 = 0.2

1 - 0.70 = 0.3

Finally, the the probability that the task will NOT be completed in time is the probability that any of the teams completed the task. So, it is equal to:

P = 0.1 * 0.2 * 0.3 = 0.006

Answer:

Step-by-step explanation:

a) All of the arcs show point A is the center of rotation.

__

b) The angle marked at point A is 90°.

__

c) The arrows indicate the direction of rotation is counterclockwise.

The process used to collect data will affect the validity and the bias of the study.

The way data is gathered is very important for making sure a study is accurate and doesn't have any unfair influences. Validity means how well the information collected correctly shows the things the study is trying to find out. If the way data is collected is not done correctly, it can cause incorrect or untrustworthy results, making the study less reliable

Bias means when we make mistakes or go away from the correct value or truth. If the way we collect data is biased, it can lead to unfair outcomes or favor certain groups.

Learn more about validity  from

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Answer:

At a plus or minus 5%

Her claim is wrong

Step-by-step explanation:

Ok..

Let's calculate the total amount of result first.

6 +14+22+8+4= 54.

Let's take the percentage of each.

For A

6/54= 0.11

11.1%

11.1%*5%= 10.5

For B

14/54

=0.25925

= 25.9%

25.9%*5%= 24.605

For C

22/54

0.4074

40.7%

40.7*5%= 42.73%

For D

8/54

= 0.148

14.8%

14.8%*5% = 14.06%

For E

4/54

= 0.074

= 7.4%

7.4%*5%=7.77%

But she suggested

10% A's, 23% B's, 45% C's, 14% D's, and 8% F's

Answer: SAS

Step-by-step explanation:

Answer:

V ≈ 670.2 [tex]ft^3[/tex]

Step-by-step explanation:

Use the formula of the volume of a cone, which is [tex]V=\pi r^{2} \frac{h}{3}[/tex]

Plug in your given components and solve for V:

[tex]V=\pi (8)^2\frac{10}{3} \\V=\pi (64)\frac{10}{3} \\V=\pi (64)(3.33)\\V=\pi (213.33)\\V=670.2[/tex]

Answer:

98

Step-by-step explanation:

Z as Zach; W as Wendy; L as Lee; C as Chen

We know that average score of Z,W, and L is 91, so:

(z + w + l)/3 = 91

z + w + l = 273

Average score W, L, C = 89, so:

(w + l + c)/3 = 89

w + l + c = 267

We take both:

(z + w + l) – (w + l + c) = 273 – 267

z – c = 6

Average score Z and C = 95

(z + c)/2 = 95

z + c = 190

(z + c) – (z – c) = 184

2c = 184

c = 92

z + c = 190

z + 92 = 190

z = 98

So, Zachs score is 98

Answer:

a = 49°

Step-by-step explanation:

OB = OC ( both radii of the circle ), thus

Δ BOC is isosceles and the base angles are congruent, that is

∠ OBC = ∠ OCB = 41° , so

∠ BOC = 180° - (2 × 41)° = 180° - 82° = 98°

The angle on the circumference BAC is half the angle at the centre for angles subtended on the same arc , thus

a = 0.5 × 98° = 49°

If the measure of the angle ∠BOC will be 98°. Then the measure of the angle ∠BAC will be 49°.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The central angle is double the angle at the periphery that was subtended by the same chords.

The measure of the angle ∠BCO is 41°.

The angle ∠BCO and angle ∠CBO will be congruent. Because they are angles of an isosceles triangle.

We know that the sum of all the interior angles of the triangle will be 180°. Then the measure of the angle ∠BOC will be given as,

∠BOC + ∠CBO + ∠BCO = 180°

∠BOC + 41° + 41° = 180°

∠BOC = 98°

Then the measure of the angle ∠BAC will be

∠BAC = (1/2) ∠BOC

∠BAC = 1/2 x 98°

∠BAC = 49°

If the measure of the angle ∠BOC will be 98°. Then the measure of the angle ∠BAC will be 49°.

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Answer:

90.35% probability that a test result will be negative

Step-by-step explanation:

We have these following probabilities:

0.05 = 5% probability that an individual adult has the disease.

If the adult has the disease, 1 - 0.98 = 0.02 = 2% probability of a negative test.

1 - 0.05 = 0.95 = 95% probability that an individual adult does not have the disease.

If the adult does not have the disease, 1 - 0.05 = 0.95 = 95% probability of a negative test.

What is the probability that a test result will be negative

2% of 5% or 95% of 95%. So

p = 0.02*0.05 + 0.95*0.95 = 0.9035

90.35% probability that a test result will be negative

Answer:

We can factor this into (5x+12y)^2

Step-by-step explanation:

Answer :

x1 = -1

x2= +3

x3 = +4

I hope it helps

If you are doing it by roots how ever it would be 3

Answer:

a) 0.0026

P- value is 0.0026

Step-by-step explanation:

Step(i):-

Given data

first sample size n₁= 80

mean of the first sample  x⁻₁= $6.75

Standard deviation of the first sample   (σ₁) = $1.00

second sample size (n₂) = 60

mean of the second sample( x₂⁻) = $6.25

Standard deviation of the second sample (σ₂) = $0.95

step(ii):-

Test statistic

[tex]Z = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{\frac{(S.D)_{1} ^{2} }{n_{1} } +\frac{(S.D)_{2} ^{2} }{n_{2} } } }[/tex]  

  Null Hypothesis :H₀: There is no significant difference in wages across the two employers.

x⁻₁= x₂⁻

Alternative Hypothesis :H₁: There is significant difference in wages across the two employers.

x⁻₁≠ x₂⁻

[tex]Z = \frac{6.75 -6.25 }{\sqrt{\frac{(1^{2} }{80 } +\frac{((0.95)^{2} }{60} } }[/tex]

Z = 3.01

P- value:-

Given data is two tailed test

The test statistic Z = 3.01

First we have to find the Probability of z-statistic

P(Z>3.01) =  1- P( z <3.01)

                 = 1- (0.5 + A(3.01)

                = 0.5 - A(3.01)

             =    0.5 - 0.49865   ( from normal table)

             = 0.0013

P(Z>3.125) = 0.0013

Given two tailed test

   P- value = 2 × P( Z > 3.01)

                 = 2 × 0.0013

                = 0.0026

Final answer:-

The calculated value Z = 3.125 > 1.96 at 0.05 level of significance

null hypothesis is rejected

Conclusion:-

P- value is 0.0026

Answer:

1.  x = 4

2. x = -1

3. x = 0

Answer:

Step-by-step explanation:

Answer:

x = -9

Step-by-step explanation:

Step 1: Write out expression

5(x + 13) = 20

Step 2: Distribute

5x + 65 = 20

Step 3: Isolate x

5x = -45

x = -9

And we have our answer!

Answer:

-9

Step-by-step explanation:

Let the number be x.

5(x+13) = 20

Expand.

5x+65 = 20

Subtract 26 on both sides.

5x = 20 - 65

5x = -45

Divide 5 into both sides.

x = -45/5

x = -9

The number is -9.

Answer:

Step-by-step explanation:

To evaluate 4P2, we will use the permutation formula as shown;

nPr = [tex]\frac{n!}{(n-r)!}[/tex]

4P2 = [tex]\frac{4!}{(4-2!}[/tex]

[tex]= \frac{4!}{2!} \\= \frac{4*3*2!}{2!}\\ = 4*3\\= 12[/tex]

4P2 = 12

Answer:

[tex]x^{36}-x^{16}[/tex] is already at its simplest form

Step-by-step explanation:

You cannot factor or GCF anything out of it, and you cannot just subtract exponents. Therefore, it is simplified already.

Answer:

The sample size for the data set = 56

Step-by-step explanation:

The sample size or number of individuals (n) is gotten from a histogram by summing up the total frequencies of occurrences.

In this example, the frequencies are: 2 4 6 8 10 12 14

Therefore, the sample size (n) is calculated as follows:

n = 2 + 4 + 6 + 8 + 10 + 12 + 14 = 56

Therefore the sample size for the data set = 56

The sample size for the data set = 56

Given that,

The calculation is as follows:

= 2 + 4 + 6 + 8 + 10 + 12 + 14

= 56

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Answer:

Hi there!

The correct answers are: A, B, D, E

Step-by-step explanation:

First of all, perpendicular means when two lines intersect to form a 90° angle.

Second ⊥ means perpendicular.

When something is a bisector it means it evenly slices a line in half.

Answer:

8

Step-by-step explanation:

Answer:

8 and 6.

Step-by-step explanation:

2.86 has tenths and hundredths place.

After the decimal point is the tenths place and after the tenths place is hundredths place.

The number 8 is the tenths place and the number 6 is in the hundredths place.

Answer:

y = -2x - 1

Step-by-step explanation:

Step 1: Find the parallel line

y = -2x + b

Step 2: Solve for b

-3 = -2(1) + b

-3 = -2 + b

b = -1

Step 3: Write parallel equation

y = -2x - 1

Answer:

2,095,636,800,000 possible passwords.

Step-by-step explanation:

There are:

26 lower case characters.

10 decimal digits.

Passwords with 6 characters:

The first character must be a lower case letter, so 26 possible outcomes.

Any of the other 6 - 1 = 5, there are 36 possible options. So

[tex]T_{6} = 26*36^{5} = 1572120576[/tex]

Passwords with 7 characters:

Same logic as above, just the last 6 with 36 possible options. So

[tex]T_{7} = 26*36^{6} = 56596340736[/tex]

Passwords with 8 characters:

7 with 36 possible options

[tex]T_{8} = 26*36^{7} = 2037468300000[/tex]

Total:

[tex]T = T_{6} + T_{7} + T_{8} = 1572120576 + 56596340736 + 2037468300000 = 2095636800000[/tex]

2,095,636,800,000 possible passwords.

Answer:

There are no choices on your question

Step-by-step explanation:

Maybe 2/1 or 4/2 or 10/5.

Hey there! :)

Answer:

a. 3

b. -22

c. -2

d. -2

e. 5a + 8

f. a² + 6a + 3

Step-by-step explanation:

Calculate the answers by substituting the values inside of the parenthesis for 'x':

a. f(1) = 5(1) - 2 = 3

b. f(-4) = 5(-4) - 2  = -22

c. g(-3) = (-3)² + 2(-3) - 5 = 9 - 6 - 5 = -2

d. g(1) = 1² + 2(1) - 5 = 1 + 2 -5 = -2

e. f(a+ 2) = 5(a+2) - 2 = 5a + 10 - 2 = 5a + 8

f. g(a + 2) = (a + 2)² + 2(a + 2) - 5 = a² + 4a + 4 + 2a + 4 - 5 =

a² + 6a + 3