Factor.
-7x2 + 49x

-7(x - 7)
01 - 7x2 + 49x)
-x(x – 7)
-7x(x – 7)

Answer:

F'(-3) = 18

Step-by-step explanation:

Let g(x) = u and apply the chain rule

[tex]F(x)=f(g(x))=f(u)\\F'(x)=\frac{df(u)}{du}[/tex]

[tex]\frac{du}{dx}=g'(x)[/tex]

[tex]\frac{df(u)}{du}*\frac{du}{dx} = \frac{df(u)}{dx}\\F'(x)= \frac{df(u)}{du}*g'(x)\\F'(x)= f'(u)*g'(x)\\F'(x)= f'(g(x))*g'(x)[/tex]

We now have all of the necessary definite values to solve the expression for x= -3:

[tex]F'(-3)= f'(g(-3))*g'(-3)\\F'(-3)= f'(-4)*6\\F'(-3)= 3*6\\F'(-3)= 18[/tex]

Finally, we have that F'(-3)= 18.

Answer:

23 dimes, 32 nickels

Step-by-step explanation:

Let n equal the number of nickels and d be the number of dimes. We can use the information given to create a system of equations, as follows:

The total number of coins (the number of nickels plus the number of dimes) is 55, giving us the equation n + d = 55.

The total amount is $3.90. Since each nickel is worth $0.05 and each dime is worth $0.10, we get the equation 0.05n + 0.10d = 3.90.

Multiplying the second equation by 20, we get n + 2d = 78. We can subtract the first equation to get d = 23. Substituting this into the first equation, we get that n = 32.

Therefore, there are 23 dimes and 32 nickels.

Answer: 100 penny 2 qtrs 50 noclke

Step-by-step explanation:

Answer: (a) No, the data suggests it is possible to reject the hypothesis which states that the 2 methods provide same mean value.

(b) (-10.957,-0.063)

Step-by-step explanation:

(a) Hypotheses for this data are:

[tex]H_{0}[/tex]: [tex]\mu_{1} = \mu_{2}[/tex]

[tex]H_{a}: \mu_{1} \neq \mu_{2}[/tex]

First find the differences in values:

1 => -0.31

2 => -0.63

3 => -2.85

4 => -3.46

5 => -6.43

6 => -7.52

7 => -17.39

Now, find the mean and standard deviation of the differences:

mean = [tex]\frac{-0.31+(-0.63)+...+(-17.39)}{7}[/tex] = - 5.51

sd = [tex]\sqrt{\frac{(-0.31-(-5.51))^{2}+...+(-17.39-(-5.51))^{2}}{7-1} }[/tex] = 5.89

The value of test statistics is:

t = [tex]\frac{mean}{\frac{s}{\sqrt{n} } }[/tex] = [tex]\frac{-5.51}{\frac{5.89}{\sqrt{7} } }[/tex] = - 2.4750

Analysing Student's T distribution, at a df = 7-1 = 6:

p-value = 0.025*2 = 0.05

To reject the null hypothesis, p-value must be less or equal than α. Since they are equal, reject the null hypothesis, i.e., reject the claim suggesting the 2 methods provide the same mean value for natural vibration frequency.

(b) For a CI = 95%:

t-score for α = 0.025 and df = 6 is 2.447.

mean ± [tex]t.\frac{s}{\sqrt{n} }[/tex]

-5.51 ± 2.447.[tex]\frac{5.89}{\sqrt{7} }[/tex]

-5.51 ± 5.4471

lower limit: -5.51 - 5.4471 = - 10.957

upper limit: -5.51 + 5.4471 = - 0.063

The interval on the mean difference is (-10.957,-0.063)

Complete question:

The line graph relating to the question was not attached. However, the line graph has can be found in the attachment below.

Answer:

17,209

Step-by-step explanation:

The line graph provides information about alcohol-related highway fatalities between year 2001 to 2010.

Determine the average number of alcohol-related fatalities from 2001 to 2006. Round to the nearest whole number.

The average number of alcohol related fatalities between 2001 - 2006 can be calculated thus :

From the graph:

Year - - - - - - - - - - Number of fatalities

2001 - - - - - - - - - - 17401

2002 - - - - - - - - -  17525

2003 - - - - - - - - -  17013

2004 - - - - - - - - - 16694

2005 - - - - - - - - - 16885

2006 - - - - - - - - - 17738

To get the average :

Sum of fatalities / number of years

(17401 + 17525 + 17013 + 16694 + 16885 + 17738) / 6

= 103256 / 6

= 17209.333

Average number of alcohol related fatalities is 17,209 (to the nearest whole number)

Answer: B) 22

Step-by-step explanation:

y coordinate of line = 3

y coordinate of point = -19

On a number line, distance between 3 & -19 = 22

Answer:

Step-by-step explanation:

In double angle, sin2x = sin(x+x) = sinxcosx+cosxsinx

sin2x = 2sinxcosx ... 1

Applying this formula to prove that sin(4x) = 4 sinx cosx(1 − 2sin2x is shown below;

sin(4x) = sin(2x+2x)

= sin2xcos2x+cox2xsin2x

sin4x = 2sin2xcos2x ..2

also cos2x = cos(x+x) = cosxcox-sinxsinx

cos 2x = cos²x - sin²x ...3

Substituting equation 1 and 3 into 2, we will have;

sin4x = 2(2sinxcosx(cos²x - sin²x ))

sin4x = 4sinxcosx(cos²x - sin²x )

From sin²x+cos²x =1; cos²x = 1-sin²x

Substituting the expression into the resulting equation will give;

sin4x = 4sinxcosx(1-sin²x - sin²x )

sin4x = 4sinxcosx(1-2sin²x) Verified!  

Answer:

[0, infinity)

Step-by-step explanation:

clarence, I believe you meant y = |3x + 1|.  The absolute value of 3x + 1 is never less than 0, so the range of the given function (above) is [0, infinity).

Answer:  i) θ = 30°, 60°, 210°, & 240°

              ii) θ = 20° &  200°

Step-by-step explanation:

i) sin (2θ) = cos 30°

[tex]\sin(2\theta)=\dfrac{\sqrt3}{2}\\\\.\quad 2\theta=\sin^{-1}\bigg(\dfrac{\sqrt3}{2}\bigg)\\\\.\quad 2\theta=60^o\qquad 2\theta=120^o\\\\.\quad \theta=30^o\qquad \theta=60^o[/tex]

To include all of the solutions for one rotation, add 360/2 = 180 to the solutions above.   θ = 30°, 60°, 210°, 240°

If you need ALL of the solutions (more than one rotation), add 180n to the solutions.   θ = 30° + 180n   &   60° + 180n

*********************************************************************************************

ii) cos α = sin (50 + α)

Use the Identity: cos α = sin (90 - α)

Use Transitive Property to get:   sin (50° + α) = sin (90° - α)

50° + α = 90° - α

50° + 2α = 90°

        2α = 40°

          α = 20°

To find all solutions for one rotation, add 360/2 = 180 to the solution above.

α = 20°, 200°

If you need ALL of the solutions (more than one rotation), add 180n to the solution. α = 20° + 180n

Answer:

30 cm

Step-by-step explanation:

1 inch is 2.54 centimeters, and 2.54 times 12 is 30.48, which would be the closest.

The following metric units of measure is 30 cm

The correct option is (A)

Measurement” is the act of determining a target's size, length, weight, capacity, or other aspect.

Step 1: Write the conversion as a fraction.

Step 2: Multiply or divide, as required.

Step 3: Cancel the units (same units from top and bottom)

Step 4: Write the simplified answer with its correct unit.

Now, as we know that

1 inch = 2.54 cm

So, we can write

12 inch = 2.54 * 12

12 inch= 30.48 cm

Hence, the closest unit is  30 cm in the given metric system.

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Answer:

The volumes of the cubes are 6³ = 216, 8³ = 512, 10³ = 1,000 and 12³ = 1,728 for a combined volume of 216 + 512 + 1,000 + 1,728 = 3456 which means that each side of the scale must have a combined volume of 3456 / 2 = 1728. This means that in order for the scale to be balanced we need to put the 12 cm cube on one side and the other 3 cubes on the other side.

Answer:

[tex]\boxed{ \sf 41.81}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trigonometric functions.

[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]\sf sin(?)=\frac{2}{3}[/tex]

[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]

[tex]\sf ?= 41.81031489...[/tex]

Answer:

[tex]\boxed{41.81}[/tex]

Step-by-step explanation:

∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.

The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).

However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.

Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.

Answer:

87.92 ft³

Step-by-step explanation:

The formula for the volume of a cylinder is πr² · h

1. Set up the equation

π2² · 7

2. Solve

(3.14)(4)(7) = 87.92

The volume of a cylindrical water tank with a diameter of 4 feet  and a height of 7 feet is 87.92 cubic feet.

Given that, a cylindrical water tank with a diameter of 4 feet and a height of 7 feet.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

We know that, the volume of a cylinder πr²h

Here, radius =4/2 = 2 feet

The volume of a cylinder = 3.14×2²×7

= 3.14×4×7

= 87.92 cubic feet

Therefore, the volume of a cylindrical water tank with a diameter of 4 feet  and a height of 7 feet is 87.92 cubic feet.

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Answer:

t= 1.89736659

Step-by-step explanation:

We have a known hypotenuse, but unknown opposite side. Use the sine ratio to tie the two together to be able to solve for x.

sin(angle) = opposite/hypotenuse

sin(50) = x/6.5

6.5*sin(50) = x

x = 6.5*sin(50)

x = 4.97928888027336 make sure your calculator is in degree mode

x = 4.98

Answer is choice B

Answer:

b

Step-by-step explanation:

Answer:

161/184 or 0.875

Step-by-step explanation:

Total number of cans = 24 cans

Total number of diet soda = 3 cans

Total number of regular soda = 21 cans

We are asked to find the probability that:that at least one contain regular soda if two cans are selected randomly

We have two ways for this happening

a) two of the cans are regular soda

b) one of the cans is regular , while one is diet

Hence,

Probability (that at least one contain regular soda) = Probability(that two of the cans are regular soda) + Probability ( one of the cans is regular , while one is diet)

Probability(that two of the cans are regular soda) = 21/24 × 20/23

= 35/46

Probability ( one of the cans is regular , while one is diet) = 21/24 × 3/23

= 21/184

Probability (that at least one contain regular soda) = 35/46 + 21/184

We find the Lowest common multiple of the denominators = 184

= 35/46 + 21/184

= (35 × 4) + (21 × 1)/184

= 140 + 21/184

= 161/184

= 0.875

Therefore, the probability that at least one can contains regular soda = 161/184 or 0.875

3*5 ≡ 15 ≡ 3 (mod 12)

3*7 ≡ 21 ≡ 9 (mod 12)

3*9 ≡ 27 ≡ 3 (mod 12)

5*7 ≡ 35 ≡ 11 (mod 12)

5*9 ≡ 45 ≡ 9 (mod 12)

7*9 ≡ 63 ≡ 3 (mod 12)

Your table should look like the attached.

It's unclear what you're supposed to evaluate for part (b)...

Answer:

-3a

Step-by-step explanation:

3(-a)

Expand brackets.

3 × -1a

-3a

Answer:

this is all i got for the second question.

Step-by-step explanation:

That is, the average rate of change of from 3 to 0 is 1. That is, over the interval [0,3], for every 1 unit change in x, there is a 1 unit change in the value of the function. Here is a graph of the function, the two points used, and the line connecting those two points.

hope this kinda helps

-lvr

Answer:

The maximum one-day percentage loss = -1.15%

Step-by-step explanation:

Let assume that with the  normal distribution, 95% of observations are smaller than 1.65 standard deviations above the mean.

Given that:

Cerra estimates the standard deviation of daily percentage changes of the euro to be 1 percent over the last 100 days.

if the expected percentage change of the euro tomorrow is 0.5 percent

and that Z value at 95% C.I level = 1.65

∵ The maximum one-day percentage loss = (expected percentage change -   Z-Value) × standard deviation

The maximum one-day percentage loss =  (0.5 - 1.65) ×  1

The maximum one-day percentage loss = -1.15  ×  1

The maximum one-day percentage loss = -1.15%

Answer:

0.8 < x < 16.8

Step-by-step explanation:

8.0 + 8.8 = 16.8

The range of possible sizes for the side x are 0.8 < x < 16.8.

A triangle is a geometrical shape in two dimensional geometry which has three sides, three vertices and three angles.

The sum of all the three angles inside the triangle is supplementary.

This implies that if a, b and c are the three interior angles of a triangle, then, a + b + c = 180°.

If two sides of a triangle are given, then the third side of the triangle will always be in between the difference of the length of the other two sides and the sum of the length of the other two sides.

Here two lengths are given as 8.0 and 8.8.

Difference of the lengths = 8.8 - 8.0 = 0.8

Sum of the lengths = 8.8 + 8.0 = 16.8

So the x lies between 0.8 and 16.8.

Hence the range of the possible length of the given triangle is 0.8 < x < 16.8.

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Answer:

1) [tex](a+ib)(a-ib)[/tex]

2) [tex]a^2+i^2b[/tex]

Step-by-step explanation:

1) [tex]a^2+b^2[/tex]

=> [tex]a^2 - (-1)b^2[/tex]      (We know that -1 = [tex]i^2[/tex] )

=> [tex]a^2-i^2b^2[/tex]

=> [tex](a)^2-(ib)^2[/tex]

Using Formula [tex]a^2 -b^2 = (a+b)(a-b)[/tex]

=> [tex](a+ib)(a-ib)[/tex]

2) [tex]a^2-b[/tex]

=> [tex]a^2+(-1)b[/tex]      (We know that -1 = [tex]i^2[/tex] )

=> [tex]a^2+i^2b[/tex]  (It cannot be simplified further)

Answer:

[tex]\boxed{(a+ib)(a-ib)}[/tex]

[tex]\boxed{a^2+i^2b}[/tex]

Step-by-step explanation:

[tex]a^2 + b^2[/tex]

Rewrite expression.

[tex]a^2- (-1)b^2[/tex]

Use identity :  [tex]-1=i^2[/tex]

[tex]a^2- i^2 b^2[/tex]

Factor out square.

[tex]a^2-(ib)^2[/tex]

Apply difference of two squares formula : [tex]a^2-b^2 =(a+b)(a-b)[/tex]

[tex](a+ib)(a-ib)[/tex]

[tex]a^2-b[/tex]

Rewrite expression.

[tex]a^2+(-1)b[/tex]

Use identity :  [tex]-1=i^2[/tex]

[tex]a^2+i^2b[/tex]

Answer:

156.7 miles

Step-by-step explanation:

Since [tex]x[/tex] is tangent to the circle, then it is also a right angle with the radius, from here, just do Pythagorean theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to solve for [tex]x[/tex].

Since 1 leg and the hypotenuse is given to you, you want to solve for the other leg, which is [tex]x[/tex] (either [tex]a[/tex] or [tex]b[/tex]). Lets use [tex]b[/tex] for [tex]x[/tex] and set up the equation.

[tex]b^{2}=c^2-a^2[/tex]

[tex]b^2=(3959+3.1)^2-3959^2[/tex]

[tex]b^2 = 3962.1^2 - 3959^2[/tex]

[tex]b^2 = 15,698,236.41 - 15,673,681[/tex]

[tex]b^2 = 24,555.41[/tex]

[tex]\sqrt{b^2}=\sqrt{24,555.41}[/tex]

[tex]b=156.7016592[/tex]

[tex]b=156.7[/tex] (round to nearest tenth)

The distance to the earth’s horizon from point P is 281.6 miles

The distance between two points is the length of the line joining the two points. Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

here, we have,

to determine the distance to the earth’s horizon from point P:

The tangent line from P meets the radius of the earth at a right angle.

This means that the triangle is a right triangle.

The length of x is then calculated as:

(3959 + 10)^2= 3959^2 + x^2

Rewrite as:

x^2 = (3959 + 10)^2- 3959^2

Evaluate

x^2 = 79280

Take the square root of both sides

x = 281.6

Hence, the distance to the earth’s horizon from point P is 281.6 miles

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Answer:

P(9) = 1/9

Step-by-step explanation:

From the contingency table, we see that 9 appears 4 times out of the 36 possible outcomes, therefore the probability of having a sum of 9 is

P(9) = 4/36 = 1/9

The probability that the sum is 9 is 1/18.

The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The sample space of rolling two dice has 36 possible outcomes.  

Remember that the sample space is a set that contains all possible outcomes.  

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

Let E = the event of getting a sum of that number is 9

favorable outcomes = (5,4) (4,5)

So, n(E) = 2

Sample space n(S) = 36

p(E) = n(E)/n(S)

p(E) = 2/36

p(E) = 1/18

Hence, the probability that the sum is 9 is 1/18.

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Answer:

Step-by-step explanation:

3(−2a - 4)+3a

=-6a - 12 +3a

A: -6a - 12 +3a

[tex]hope \: this \: helps[/tex]

Answer:

the answer is A

Step-by-step explanation:

you have to distribute the number 3 throughout the parentheses so (3*-2a-3*4)+3a = -6a-12+3a

Answer:8

Step-by-step explanation:

The smallest prime is 2

cube of 2 is equal to 8

2*2*2=8

Answer:

729

Step-by-step explanation:

The second smallest prime number is 3 (preceded by 2). We have (3^2)^3=3^6=729.

Hope this helped! :)

Answer:

An apple a day keeps the doctor away

Step-by-step explanation:

Type in the answer

Its gonna be right

Answer:

Step-by-step explanation:

Let the first number be x

Let the second number be y

For the first equation

2x + 3y = 22

For the second equation

3x + 4y = 31

Multiply the first one by 3 and the second one by 2

That's

First equation

6x + 9y = 66

Second equation

6x + 8y = 62

Subtract the second equation from the first one

That's

6x - 6x + 9y - 8y = 66 - 62

Substitute y = 4 into 2x + 3y = 22

That's

2x + 3(4) = 22

2x = 22 - 12

2x = 10

Divide both sides by 2

Hope this helps you

We have

[tex]\dfrac{1-i}{1+i}=\dfrac{e^{-i\frac\pi4}}{e^{i\frac\pi4}}=e^{-i\frac\pi2}[/tex]

which reduces to -i.

Answer:

slope = 4

The line is increasing

Step-by-step explanation:

slope can be found through the equation [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]. So, if we plug these points in, we get [tex]\frac{7-3}{8-7}[/tex], which simplifies to 4. So, the slope is 4.

Since the slope is positive, the line is increasing.