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Solution

We want to get why

Reason 1: Commutation Law Does Not Hold For Division (or quotient)

Generally,

Reason 2: Actual Computation

First

Secondly

It is now obvious that

Solution:

Given;

Divide both sides by 14, we have;

Take the logarithm of both sides; we have;

Applying logarithmic laws;

Divide both sides by 0.5;

(b)

The solution of the system of equations is where both lines cross each other.

solution = (0,1)

Step 1: Problem

There is a class with 6 women and 12 men. a) If I randomly pick 5 students, with replacement. What is the probability that at least 4 of them will be man? b) If I randomly pick 6 students, what is the probability that at least one of them will be a man?​

Step 2: Concept

For this problem, we are given the distance a construction crew built a road and the time in days it took to build it. We need to determine the unit rate for this problem, which is achieved by dividing the distance and time. We have:

The unit rate is 3 miles per day.

Solution:

5/6 divided by 2, i.e.

Applying the fraction rule

Hence, the answer is 5/12

3 milles ---> 45 minutes

7 miles ---> x minutes

then

answer: 105 minutes for walk 7 miles

When looking at the graph, we can discard two of the options, rotation (as they don't have any intersection, there are no possibilities of having a rotation axis) and reflection. It occured a translation. To know which of the options is correct, we can see the y intercepts of both lines. The y intercept of f(x) is 0 and the y intercept of g(x) is -4, which means that the line was translated down 4 units.

It means the right answer is D. Vertical Translation down 4 units.

Answer

7 remainder 3

Explanation

38 : 5 can be written as 38/5

And we know that that will give

(38/5) = 7 remainder 3

Hope this Helps!!!

Step 1

The domain includes all the x-values that fall within the function

Hence, the domain of this function is [ All real values of x]

Step 2

Find the range

The range includes all values of y that fall within the function

Hence the range of the function is [-∞, 9]

Given

Number of patients = 6,663

- For Sunday

Patients = 1,187

Percent is:

- For Monday

Patients = 755

Percent:

Monday is correct.

- For Tuesday

Patients = 1,085

Percent:

Tuesday is correct.

- For Wednesday

Patients = 1,031

Percent:

Wednesday is correct.

- For Thursday

Patients = 1,024

Percent:

- For Friday

Patients = 808

Percent:

Friday is correct.

- For Saturday

Patients = 773

Percent:

Saturday is correct.

Answer:

Errors

Sunday ---> 17.8%

Thursday ---> 15.4%

Let 'j' be the cost of the jacket and let 's' be the cost of the shirt. Then, if they cost $75.08, then we have the following expression:

since the price of the jacket was 5.32 less than the shirt, then, we have:

using this equation on the first equation, we get the following:

now that we have that the shirt costs $40.20, we can find the price of the jacket:]

therefore, the price of the jacket is $34.88 and the price of the shirt costs $40.20

The required sample sizes for the confidence intervals are given as follows:

a) Estimate of 38%: 566.

b) No estimate: 601.

The margin of error for a confidence interval of proportions, using the z-distribution, is calculated as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The parameters of the equation are listed as follows:

The desired margin of error in this problem is of:

M = 0.04.

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For item a, the estimate is of [tex]\pi = 0.38[/tex], hence the sample size is obtained as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 1.96\sqrt{\frac{0.38(0.62)}{n}}[/tex]

[tex]0.04\sqrt{n} = 1.96\sqrt{0.38(0.62)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.38(0.62)}}{0.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.38(0.62)}}{0.04}\right)^2[/tex]

n = 566.

For item b, when there is no estimate, we use [tex]\pi = 0.5[/tex], hence:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2[/tex]

n = 601.

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the initial expression is:

We can see that they have in common a factor of 4 so we can rewrite it like:

We define the following variables for our problem:

P = population of mooses

t = number of years since 1990

m = growth ratio

In terms of the variables that we defined above and the fact that the population of moose in terms of the year is linear, we have the following equation:

Now, we use the data of the problem:

1) In 1994 the moose population was 4930, so we have:

2) In 1999 the moose population was 6180, so we have:

Now, using the data above and the equation for P(t) we construct the following system of equations:

We solve the system of equations.

First, we solve the equations for P0:

Now, because the right-hand-side of both equations is equal to P0, we equal them and then we solve for the variable m:

Finally, we replace the value of m in one of the equations of P0 and solve for it:

A) The formula for the moose population, P, in terms of t, the years since 1990 is:

B) We want to know the value of the moose population in 2006.

First, we compute the value of t:

Now, we replace the value of t in the equation of P(t) above:

Answer: 7930

Given the question

4 (3x -6) + 2x + 18

To simplify the above expression, we will observe the following steps

Step 1: Expand the parenthesis (bracket)

Step 2: Simplify the expression by collecting like terms

Answer = 14x - 6

Let the minimum score be x

(85 + 77 + 63 + 90 + x)/5 = 80

315 + x = 400

x = 400 - 315

= 85

Julia must get a minimum score of 85 to get a B average

B) (-5,3)

1) We need to locate the vertex location since the point here is to find the coordinates of C'. So, let's do it before applying the required transformation.

C(5,3)

2) Since we want to know the coordinates of C', and there was a reflection across the y-axis, we can write the following:

C(5,3) Rule (x,y) --> (-x,y) C'(-5,3)

3) Thus, the answer is (-5,3)

The square feet of wall space in your room if paint cost $25 per gallon and will cost you $175 to paint the room is 2,310 square feet

Number of latex paint need to paint your room = Total cost of paint / Cost of latex paint per gallon

= $175 / $25

= 7 gallons

Number of square feet of wall space in your room = Number of latex paint need to paint your room × Square feet covered by each gallon

= 7 × 330

= 2,310 square feet

In conclusion, the square feet of wall space in your room is 2,310 square feet

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The required (a) cost per ream becomes 59.99 and (b) the markdown per ream is  30.

Given that,
Printer Paper Store normally sells laser paper for 89,99 per ream, It has a special, 1 ream free with the purchase of 2. If you buy 2 reams and get 1 free.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Cost of the 1 ream = 89,99
Cost of the 2 reams = 179.98
According to the question,
Cost of the 3 reams = 179.98
Cost of the one ream among the 3 reams = 179.88/3 = 59.99
markdown per ream = 89.99 - 59.99 = 30

Thus, the required (a) cost per ream becomes 59.99 and (b) the markdown per ream is  30.

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Answer:

Step-by-step explanation:

9+4=

13

13*2=

26

Answer:

Step-by-step explanation:

(9 multiplied by 4) multiplied by 2

= 72

The functions [tex]F(x)=-\frac{1}{2}x^{4}-x^{3}+x+2[/tex] could have created this graph of downward parabola.

Option D is correct because the leading coefficient of given function is negative. That's why it is making the downward parabola.

As we can see from the graph that the the parabola is downward.

And we know that if the leading coefficient is less than zero, thus the graph will be downward parabola.

Lets check all the option:

For option A:

[tex]F(x)=x^{3}+x^{2}+x+1[/tex], this is a cubic polynomial and the graph will be a cubic curve.

For option B:

[tex]F(x)=x^{2}+5[/tex], this is a quadratic polynomial and leading coefficient is positive, so the graph will be upward parabola.

For option C:

[tex]F(x)=x^{4}-2x[/tex], for x = 0, F(x) =0, so it will not intersect the y-axis. Also the graph will be upward parabola.

Hence, the option D, [tex]F(x)=-\frac{1}{2}x^{4}-x^{3}+x+2[/tex], could have created this graph of downward parabola.

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x - 9 = 35x

Subtract x from both sides:

x - 9 -x = 35x - x

-9 = 34x

Divide both sides by 34:

-9/34 = 34x/34

x = -9/34

Given:

Total distanced traveled is 200 miles.

speed is 60 mph, but as the congestion got bad, they had to slow to 10 mph.

Time = 6 hours.

Let, x be the travel time at 60 mph

The equation is,

It mean at the speed of 60 mph, the distance traveled is,

So, the distance traveled for the speed of 10 mph is,

Answer: The family traveled 32 miles at reduced speed.

Step 1)

We used angles alpha and betta from the original triangle

Step 2)

Then,

Step 3)

Notice that the two triangles are similar due to the AAA postulate. (The length of DE is different than that of AB)

Recall the following identities:

Since sin(t)=12/13 and cos(t)=5/13, then:

To be able to determine how many dogs can Jimmy Jump per hour, let's divide how many dogs can Jimmy Jump by the number of hours he took to complete that certain number of jumps. Thus, we generate this equation,

Given:

Jimmy jumped = 40 dogs

No. of hours Jimmy took to jump 40 dogs = 5 hours

We get,

Therefore, Jimmy can jump 8 dogs per hour.

Okay, here we have this:

We need to meke the composition (f•g)(x), so in the function f we will replace x with the function g:

Now let's find the domain of (f•g)(x):

2X+8≥0

2X≥-8

X≥-4

Finally we obtain the following domain: [-4,∞)

We are given two complementary angles (QRS and SRT).

Two angles are called complementry if they sum up to 90 degrees.

Therefore, by defination

mQRS + mSRT = 90

(8x+10) + (8x) = 90

8x + 8x + 10 = 90

16x = 90-10

16x = 80

x = 80/16

x = 5

Now, put the values in both the euqations and we will get the values of both the angles.

mQRS = 8x + 10 = 8(5) + 10 = 40 + 10 = 50 degrees

mSRT = 8x = 8(5) = 40 degrees

If Vegetable Oil costs $3.47 for 48 ounces, the cost of 1 tablespoon of vegetable oil is 4 cents.

1 tablespoon has alomst 0.5 ounce

If Vegetable Oil costs $3.47 for 48 ounces

Cost of 48 ounces of vegetable oil = $3.47

cost of 1 ounce of vegetable oil = $ 3.47 / 48 = $0.0722

cost of 0.5 ounce of vegetable oil = $0.0722/2 = $0.0361

cost of 0.5 ounce of vegetable oil is $0.0361

1 dollar = 100 cents

0.0361 dollar = 0.0361 x 100 cents

0.0361 dollar = 3.6 cents = 4 cents (approx)

Therefore, if Vegetable Oil costs $3.47 for 48 ounces, the cost of 1 tablespoon of vegetable oil is 4 cents.

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