Need help with this ASAP

Answer: See bolded below

Step-by-step explanation:

With the given f(x) and g(x) given, we can directly plug them in to solve. The inverse is to replace the y with x and x with y, then solve for y.

A. f(g(-4))=143

g(-4)=3(-4)+1

g(-4)=-12+1

g(-4)=-11

With g(-4), we plug that into f(x) to find f(g(-4)).

f(-11)=(-11)²-2(-11)

f(-11)=121+22

f(-11)=143

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B. 9x²-1

(3x+1)²-2(3x+1)

(9x²+6x+1)-6x-2

9x²-1

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C. g⁻¹(x)=(x-1)/3

x=3y+1

x-1=3y

(x-1)/3=y

Answer:

x = ln6

Step-by-step explanation:

e^2x - 2e^x - 24 = 0

a = e^x

=> a^2 - 2a - 24 = 0

=> (a + 4)(a - 6) = 0

=> a = -4 => e^x = -4 (invalid because e^x > 0)

=> a = 6 => e^x = 6 => x = ln6

Answer:

0.492

Step-by-step explanation:

According to the given situation,  the calculation of Δy and dy is shown below:-

[tex]y = e^x, x = o, \Delta x = 0.6[/tex]

[tex]dy = f'(x) = e^x[/tex]

[tex]dy = e^x dx[/tex]

[tex]= e^x (0.4)[/tex]

[tex]dy = 0.4e^x[/tex]

[tex]\Delta y = f(0.4) - f(0)[/tex]

[tex]= e^{0.4} - e^0[/tex]

Now we use the scientific calculator or spreadsheet to determine the exponential value

= 1.491824698  - 1

= 0.491824698

or

= 0.492

Therefore for computing the  Δy and dy we simply applied the above formula.

Hence, the answer is 0.4918

Answer:

10

Step-by-step explanation:

for this you need to sub the value of -3 for x

Q(-3)=(-3)^2-(-3)-2

=9+3-2

=10

Answer:

Q= x - X/x - 2/x

Step-by-step explanation:

hope this helps !

Answer:

Confirming Trapezoid as the correct answer just for verification.

Step-by-step explanation:

The shape of cross section is trapezoid.

A rectangular pyramid is a pyramid, where four triangular sides correspond to each side of rectangular base.

A vertex is a point where edges of a pyramid meet or intersect.

A cross-section is a shape which is obtained by the intersection of any solid object by a plane.

For given situation consider a rectangular pyramid ABCDE,

If pyramid is sliced so the cross section is perpendicular to its base but does not pass through its vertex, then from figure the cross section will be PQRS.

The cross section PQRS is perpendicular to the base BCDE.

This means, the shape of the cross section PQRS is trapezoid.

Hence, the shape of cross section is trapezoid.

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Answer:

[tex]\frac{y}{3}[/tex]

Step-by-step explanation:

Well the quotient is the answer if y divided by 3.

So y divided by 3 is y over 3 y/3.

Answer:

Step-by-step explanation:

From the information given,

p represents the probability of success.

x represents the number of success

n represents the number of samples

Therefore,

1) b(x|n,p): b(3|8, .35)

x = 3

n = 8

p = 0.35

From the binomial probability distribution calculator,

P(x = 3) = 0.28

1) b(x|n,p): b(5|8, .6)

x = 5

n = 8

p = 0.6

From the binomial probability distribution calculator,

P(x = 5) = 0.28

c) n = 7

p = 0.6

P(3 ≤ X ≤ 5)

P(x ≥ 3) = 0.904

P(x ≤ 5) = 0.841

P(3 ≤ X ≤ 5) = 0.904 - 0.841 = 0.063

d) n = 9

p = 0.1

P(1 ≤ X) = p(x ≥ 1)

p(x ≥ 1) = 0.61

Answer:

Her initial money she started with us $800.00

Step-by-step explanation:

Let the initial money Ann began with be x.

So she spent 1/3 of x on transport,

2/5 of x on food

1/6 of x on clothing

And the remaining is $80.00.

Let's find the value of x

X(1/3) +x(2/5) + x(1/6) +80 = x

X(1/3) +x(2/5) + x(1/6) -x = -80

Taken 30 as the lowest common multiple of the factors gives

(10x + 12x + 5x -30x)/30 = -80

(10x + 12x + 5x -30x)= -2400

-3x = -2400

X = -2400/-3

X= 800

Answer:

113

Step-by-step explanation:

Let the number of adult tickets sold =a

Let the number of student tickets sold =s

A total of 259 tickets were sold, therefore:

a+s=259

Adult tickets were sold for $24 each and student tickets were sold for $16 each.

Total Revenue = $5,312

Therefore:

24a+16s=5,312

We solve the two derived equations simultaneously.

From the first equation

a=259-s

Substitute a=259-s into 24a+16s=5,312

24(259-s)+16s=5,312

6216-24s+16s=5,312

-8s=5,312-6216

-8s=-904

Divide both sides by -8

s=113

Therefore, 113 student tickets were sold.

Answer:

white

Step-by-step explanation:

plato

The solution is Option D.

The missing color from the tree diagram is given by the equation A = white

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the missing color from the tree diagram be represented as A

Now , the value of A is

Jenson has 3 clean T-shirts of white , red and orange

Jenson has 2 clean pairs of jeans of blue and gray

Now , substituting the values in the equation , we get

For every blue jeans = { white , red , orange }

For every gray jeans = { A , red , orange }

From the equation , we get

The value of A = white

Therefore, the value of A is white

Hence , the missing color is white

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Answer:

40

Step-by-step explanation:

(34 + 43 + 45 + 35)/4 = 39.25

To the nearest 10th = 40

Answer:

(CX3)+10

Step-by-step explanation:

Answer:

c×3+10= j

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

Our input is function f( x ), but to find the derivative of this function, you must convert this f ( x ) into a " [tex]d / dx[ f( x )] / f'x[/tex] " format. In this case it can be done multiplying the numerator by 7, and squaring the denominator. We would have to separate this into two fractions, as the following -

[tex]\frac{4}{7x-18}-\frac{28x}{\left(7x-18\right)^2}[/tex]

Now all that has to be done is to simplify this expression! The least common multiple of 7x - 18, ( 7x - 18 )^2 is ( 7x - 18 )^2. That, respectively makes it our denominator. Based on the LCM we would receive the following -

[tex]\frac{4\left(7x-18\right)}{\left(7x-18\right)^2}-\frac{28x}{\left(7x-18\right)^2}[/tex]

Now the denominators are equal, so we can combine the two fractions and simplify -

[tex]\frac{4\left(7x-18\right)-28x}{\left(7x-18\right)^2} - ( Simplify ),\\\\-\frac{72}{\left(7x-18\right)^2}[/tex]

Hence, the solution is option c. Hope that helps!

Answer:

x=1/2, x=5

Step-by-step explanation:

2x^2-11x+5=0

Factor them

(x-0.5)(x-5)

x=0.5 or 1/2

x=5

Answer:

12x/2 or 52/2

Step-by-step explanation:

Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.

Answer:

one side is [tex]\sqrt{10}[/tex] and other 3[tex]\sqrt{10}[/tex]

in decimal one side = 3.16

other side =  9.48

Step-by-step explanation:

In right angle

if two sides containing right angle is a and b and h is hypotenuse then

by Pythagoras theorem

a^2 + b^2 = h^2

__________________________________

let one side be x

given

One of the triangle’s legs is 3  times the length of the other leg

then other leg = 3x

given h = 10 cm

applying Pythagoras theorem

[tex]a^2 + b^2 = h^2\\x^2 + (3x)^2 = 10^2\\x^2 + 9x^2 = 100\\10x^2 = 100\\x^2 = 100/10 = 10\\x = \sqrt{10}[/tex]

Thus, one side is [tex]\sqrt{10}[/tex] and other 3[tex]\sqrt{10}[/tex]

[tex]\sqrt{10} = 3.16\\[/tex]

thus, in decimal one side = 3.16

other side = 3.16*3 = 9.48

Answer:

We conclude that the sample is from a population of songs with a mean greater than 210 seconds.

Step-by-step explanation:

We are given that a simple random sample of 40 current hit songs results in a mean length of 252.5 seconds.

Assume that the standard deviation of song lengths is 54.5 sec.

Let [tex]\mu[/tex] = population mean length of the songs

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 210 seconds      {means that the sample is from a population of songs with a mean smaller than or equal to 210 seconds}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 210 seconds      {means that the sample is from a population of songs with a mean greater than 210 seconds}

The test statistics that will be used here is One-sample z-test statistics because we know about population standard deviation;

                              T.S.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean length of songs = 252.5 seconds

            [tex]\sigma[/tex] = population standard deviation = 54.5 seconds

            n = sample of current hit songs = 40

So, the test statistics =  [tex]\frac{252.5-210}{\frac{54.5}{\sqrt{40} } }[/tex]

                                   =  4.932

The value of z-test statistics is 4.932.

Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 4.932 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the sample is from a population of songs with a mean greater than 210 seconds.

Answer:

It's written as

[tex]89.7 \times {10}^{9} [/tex]

Or

[tex]8.97 \times {10}^{10} [/tex]

Hope this helps you

Answer:

8.97 * 10 ^10

Step-by-step explanation:

We want one nonzero digit to the left of the decimal

8.97

We moved the decimal 10 places to the left

The exponent is positive 10 since we moved 10 places to the left

8.97 * 10 ^10

Answer:

657.96

Step-by-step explanation:

use formula A=P(1+r/n)^nt

A=500(1+.04/1)^1*7

A=500(1.04)^7

A=500(1.3159~)

A= 657.96~

Answer:

i think it is a

Step-by-step explanation:

Answer:

a) Graph A has a stronger correlation, so it is more likely to provide an accurate prediction.

Step-by-step explanation:

Answer: [tex]2\sqrt{1+tant}+C[/tex]

Step-by-step explanation:

To integrate means to find the antiderivative of the function. For this problem, we can use u-substitution.

[tex]\int\limits {\frac{dt}{cos^2t\sqrt{1+tant} } } \[/tex]

Let's first use our identities to rewrite the function. Since [tex]\frac{1}{cosx} =secx[/tex], we can use this identity.

[tex]\int\limits {\frac{sec^2t}{\sqrt{1+tant} } } \,[/tex]

[tex]u=\sqrt{1+tant}[/tex]

[tex]du=\frac{sec^2t}{2\sqrt{1+tant} } dt[/tex]

Now that we have u and du, we can plug them back in.

[tex]\int\limits {2} \, du[/tex]

[tex]\int\limits{2} \, du=2u[/tex]

Since we know u, we can plug that in.

[tex]2\sqrt{1+tant}[/tex]

This may seem like the correct answer, but we forgot to add the constant.

[tex]2\sqrt{1+tant}+C[/tex]

Answer:

The area of the sheet is approximately 50.59 m² or 50.6 m²

Step-by-step explanation:

The area of a rectangle is given by the following expression:

[tex]area = width*height[/tex]

Since breadth is the same as the width of the sheet, we can calculate its area as shown below:

[tex]area = 9.96*5.08 = 50.59[/tex]

The area of the sheet is approximately 50.59 m² or 50.6 m²

Answer:

Step-by-step explanation:

The hypotenuse is given by the Pythagorean theorem:

  h = √(3² +5²) = √34

The trig functions are the ratios of sides:

  Tan = Opposite/Adjacent

  tan(θ) = 5/3

__

  Sin = Opposite/Hypotenuse

  sin(θ) = 5/√34 = (5/34)√34

__

  Sec = Hypotenuse/Adjacent

  sec(θ) = √34/3

Answer:

B

Step-by-step explanation:

Answer:

-2 < x < 35

Step-by-step explanation:

We have that the larger side has a larger opposite angle and the smaller sides and a smaller opposite angle.

The opposite angle of the 14 unit side is 37 °.

The opposite angle of the 13-unit side is (x + 2) °.

Since 13 <14, it would be:

x + 2 <37

we subtract 2 on both sides

x <35

The value of x must be less than 35.

Now, to form a triangle, the angle must be greater than 0.

x + 2> 0

we subtract 2 on both sides

x> -2

The value of x must be greater than - 2.

Therefore the answer would be:

-2 <x <35

Answer:

Step-by-step explanation:

y + 8 = 0(x - 0)

y + 8 = 0

y = -8

Answer:

We have our answer as approximately 10 %

Step-by-step explanation:

We are simply expected to express the sum of money spent on insurance as a percentage of the total sales in this question.

The first step is to set up a fraction, having the sum spent on insurance as the numerator, and the total sales as the denominator. This is shown below

[tex]\frac{66,170}{713,200}[/tex]

To convert this fraction to a percentage, we will have to multiply it by 100 and reduce it to its lowest term.

Here we have

[tex]\frac{66,170}{713,200} \times 100= 9.28 percent[/tex]

Rounding of to the nearest tenth, we have our answer as approximately 10 %

Answer: 12 mph

Step-by-step explanation:

20 minutes = 1/3 hour

Distance = speed x time

D = 27 x 1/3 = 09 miles

He had taken 45 minutes when he drove home

45 minutes = 3/4 hour

Speed = distance / time

Speed = 9 / 3/4

Speed = 12 mph

The average speed of Nick's journey back home is 12 mph.

Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.

The first average speed at what Nick travels is 27 mph.

One day it took Nick 20 mins to drive to work.

Here, Distance = Speed × Time

= 27 × 20/60

= 27 × 1/3

= 9 miles

Nick had drove home using the same route, it had took Nick 45 minutes.

Here, speed = Distance/Time

= 9÷45/60

= 9×4/3

= 12 mph

Therefore, the average speed of Nick's journey back home is 12 mph.

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Answer:

Step-by-step explanation:

[tex]7^{0}=1[/tex]

[tex](7^{13})^{3}*7^{0}=7^{13*3}*1\\\\=7^{39}[/tex]

Answer:

Step-by-step explanation:

Using the alternative hypothesis (µ < µ0),

To find the p-value with test statistic -1.25 and assuming a standard level of significance of 0.05, using a p value calculator, the p-value is 0.1057 which is great that 0.05. Thus, the results is not significant.

Using the p value calculation.

1. Check the left tailed z table as the test statistic is negative,

2. Then find the probabilitythat z is greater than your test statistic (look up your test statistic on the z-table- the value under 1.2 and 0.05 which is 0.8944

3. Then, find its corresponding probability, and subtract it from 1 to get your p-value- 1-0.8944 = 0.1056.