Need help asap please! If you don’t know the answer, don’t comment.

Answer:

(d) <-21, -7>.

Step-by-step explanation:

To find 7u, we simply multiply each component of u by 7:

7u = 7<-3, -1> = <-37, -17> = <-21, -7>

Answer:

1. w = [tex]\bold{e^{7+6x}}[/tex]

2. [tex]\bold{t = 2(log_a(7) - log_a(3))}[/tex]

Step-by-step explanation:

1.

a. The exponential form of a logarithmic equation is given by:

[tex]\bold{log_a(b) }[/tex]= c is equivalent to [tex]a^c = b[/tex]

Using this rule, we can rewrite the equation:

ln w = 7 + 6x as w = [tex]\bold{e^{7+6x}}[/tex]

Therefore, the exponential form of the given equation is w = [tex]\bold{e^{7+6x}}[/tex]

2.

a. To solve for t using a logarithm with base a, we can take the logarithm of both sides of the equation:

[tex]\bold{3a^\frac{t}{2} = 7 }\\\bold{log_a3a^\frac{t}{2}= log_a(7)}[/tex]

Using the rule of logarithms that log_a(b^n) = n*log_a(b), we can simplify the left side:

[tex]\bold{log_a(3) +\frac{t}{2} log_a(a) = log_a(7)}[/tex]

Since log_a(a) = 1 for any base a, we can simplify the expression further:

[tex]\bold{log_a(3) + \frac{t}{2}*1= log_a(7)}[/tex]

Now we can solve for t by isolating it on one side of the equation:

[tex]\bold{ \frac{t}{7} = (log_a(7) - log_a(3))} \\ \bold{t = 2(log_a(7) - log_a(3))}[/tex]

Therefore, the solution for t using a logarithm with base a is[tex]\bold{t = 2(log_a(7) - log_a(3))}[/tex]

Answer:

[tex]\textsf{1.} \quad w = e^{7 + 6x}[/tex]

[tex]\textsf{2.} \quad t= \log_a\left(\dfrac{49}{9}\right)[/tex]

Step-by-step explanation:

Exponential form is a way to represent a number using an exponent, where the base is raised to a power.

The natural logarithm function is the inverse of the exponential function:

[tex]\boxed{\ln x=y \iff x=e^y}[/tex]

Therefore we can use this definition to change the given equation to exponential form:

[tex]\begin{aligned}\ln w & = 7 + 6x\\\\e^{\ln w} & = e^{7+6x}\\\\w&=e^{7+6x}\end{aligned}[/tex]

Therefore, the exponential form of the equation is:

[tex]w = e^{7 + 6x}[/tex]

[tex]\hrulefill[/tex]

To solve for t using a logarithm with base a, begin by taking the logarithm of both sides of the equation with base a:

[tex]\log_a (3a^{\frac{t}{2}})=\log_a(7)[/tex]

[tex]\textsf{Apply the log product law:} \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\log_a (3)+\log_a(a^{\frac{t}{2}})=\log_a(7)[/tex]

Subtract logₐ(3) from both sides of the equation:

[tex]\log_a (3)+\log_a(a^{\frac{t}{2}})-\log_a (3)=\log_a(7)-\log_a (3)[/tex]

[tex]\log_a(a^{\frac{t}{2}})=\log_a(7)-\log_a (3)[/tex]

[tex]\textsf{Apply the log quotient law:} \quad \log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)[/tex]

[tex]\log_a(a^{\frac{t}{2}})=\log_a\left(\dfrac{7}{3}\right)[/tex]

[tex]\textsf{Apply the log power law:} \quad \log_ax^n=n\log_ax[/tex]

[tex]\dfrac{t}{2}\log_a(a)=\log_a\left(\dfrac{7}{3}\right)[/tex]

Apply the log law:  logₐ(a) = 1

[tex]\dfrac{t}{2}(1)=\log_a\left(\dfrac{7}{3}\right)[/tex]

[tex]\dfrac{t}{2}=\log_a\left(\dfrac{7}{3}\right)[/tex]

Multiply both sides of the equation by 2:

[tex]2 \cdot \dfrac{t}{2}=2 \cdot \log_a\left(\dfrac{7}{3}\right)[/tex]

[tex]t=2 \log_a\left(\dfrac{7}{3}\right)[/tex]

Finally, apply the log power law:

[tex]t= \log_a\left(\dfrac{7}{3}\right)^2[/tex]

[tex]t= \log_a\left(\dfrac{7^2}{3^2}\right)[/tex]

[tex]t= \log_a\left(\dfrac{49}{9}\right)[/tex]

Therefore, the solution for t in terms of logarithm with base a is:

[tex]\boxed{t= \log_a\left(\dfrac{49}{9}\right)}[/tex]

An equation for f', the inverse function is: f¹(x) = (x - 3)/7, for x ≥ 4.

The equation is correct as it has been shown that f(f'(x)) = x and f'(f(x)) = x.

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this exercise, you are required to determine the inverse of function f. This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

f(x) = y = 7x + 3

x = 7y + 3

7y = x - 3

y' = f¹(x) = (x - 3)/7, for x ≥ 4.

Proof:

f(f'(x)) = f[(x - 3)/7] = 7[(x - 3)/7] + 3

f(f'(x)) = f[(x - 3)/7] = x - 3 + 3

f(f'(x)) = f[(x - 3)/7] = x.

f'(f(x)) = x

f'(f(x)) = f¹[(7x + 3)]

f'(f(x)) = (7x - 3 + 3)/7

f'(f(x)) = 7x/7

f'(f(x)) = x

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The critical points of h are -2 and 3

Recall that  a critical point of a function y = f(x) is a point (c, f(c)) on the graph of f(x) at which either the derivative is 0 (or) the derivative is not defined.

The given function is h(x) = [(x+2)(x-3)]

Finding the product of the brackets

(x+2)(x-3) = x²-3x+2x-6

Collecting like terms to have

h(x) = x²-x -6

h(x) = [(x+2)(x-3)] =  x²-x -6

factorizing this to get

(x²-3x)+(2x-6) = 0

x(x-3) + 2(x-3) = 0

x+2 = 0 or x-3 = 0

x=-2 or x = 3

Therefore the critical points are -2 and 3

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The value of h is 0.895, the arc cosine of h is 0.462 and it terminates in the correct quadrant

Lastly, the measure of angle θ is 1.46 π

Given that

Terminal point = (-1.79, -0.89)

This means that

(x, y) = (-1.79, -0.89)

Also, we have

Radius, r = 2 units

So, the value of h is

h = |x|/r

This gives

h = |-1.79|/2

Evaluate

h = 0.895

In part (a) of this solution, we have

h = 0.895

Take the arc cos of both sides

So, we have

cos⁻¹(h) = cos⁻¹(0.895)

Evaluate the arc cos using a calculator

So, we have the following representation

h = 0.462 rad

This angle is in the first quadrant

It means that the angle terminates in the correct quadrant

For the value of θ, we have the following

This is calculated as

θ = π + tan⁻¹(-0.89/-1.79)

Evaluate

θ = π + 0.46 π

Evaluate

θ = 1.46 π

Hence, the measure of angle θ is 1.46 π

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Step-by-step explanation:

well, do the division. a fraction is nothing else.

13 divided by 20.

13/20 = 0.65

Answer:

15.7 inches

Step-by-step explanation:

Circumference of circle = d x 3.14

d = 5 inches

Let's solve

5 x 3.14 = 15.7 inches

So, the circumference of the circle is 15.7 inches.

Step-by-step explanation:

the equality is: 4 × π × r × r

so the answer is

4 • π • 81

= 324π

Answer:

Step-by-step explanation:

SA= 4[tex]\pi[/tex]r²

    =4[tex]\pi[/tex]9²

    =324[tex]\pi[/tex] m² or 1017.88 m²

Step-by-step explanation:

Slope  = rise / run

Using points ( -1/2  - 1/2 ) and (1/2, 0 )  

  rise = 1/2    run = 1

     rise / run = 1/2 /1 = 1/2 = slope

Answer:

the median is 100

Step-by-step explanation:

the numbers are already in order so the number in the middle is 100.

Percent decrease =

(difference in prices)/(original price) × 100

(2.85 - 2.78)/2.85 × 100

= (0.07)/2.85 ×100 ≈ 2.5%

Answer:

a) Area = 144, so Side length = √144 = 12

b) Area = 96, so Side length = √96 = 4√6

= sqrt96

c) Area = 36, so Side length = √36 = 6

d) Area = 35, so Side length = √35

= sqrt35

In the Venn diagram , we can conclude that the statement is valid.

What is Venn diagram?

Venn diagrams are frequently used in mathematics, statistics, logic, teaching, linguistics, computer science, and business. They are also known as Set diagrams or Logic diagrams.

Here "Pen" and "Pencil". Since we know that every student brought a pen or a pencil, we know that there are no elements outside the 2 sets (these would be students who brought neither a pen or a pencil). Also, since every student brought a pencil or a pen, we also know that the overlap between the 2 sets is empty (this would be students who brought a pencil and a pen). So there are 2 areas remaining where students can be situated (1 and 2 in the picture).

We know that Marcie brought a pencil, so she is situated in area 2. This means she is outside the set "pen", and so she didn't bring a pen, and we can conclude that the statement is valid.

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A:dentrite

B: cell body

C:axon terminal

D:axon

E: nucleus

The expression for the nth term of the sequence is 6 + 9(n - 1)

From the question, we have the following parameters that can be used in our computation:

6,15,24,33,

In the above sequence, we can see that the current term is added to 9 to gett the next term

So, we have

First term, a = 6

Commin difference, d = 9

The nth term is

Tn = a + (n - 1)d

So, we have

Tn = 6 + 9(n - 1)

Hence, teh nth term is 6 + 9(n - 1)

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Solving the radical expression √(x + 3) + 4 = 5 for x gives x = -2

From the question, we have the following parameters that can be used in our computation:

√(x + 3) + 4 = 5

Subtract 4 from both sides of the equation

So, we have

√(x + 3) = 1

Take the square of both sides

x + 3 = 1

So, we have

x = -2

Hence, the solution for x is -2

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Answer:

Let x be the width of the flag in feet. Then the length of the flag is x + 60 feet. The perimeter of the flag is the sum of the lengths of its four sides, which is:

2(x + x + 60) = 4x + 120 feet

Setting this equal to 480 feet, we have:

4x + 120 = 480

Solving for x, we get:

4x = 360

x = 90

Therefore, the width of the flag is 90 feet and the length is 150 feet.

Three situations to which this system of equations could be applied are:

A farmer wants to plant a rectangular field of flowers. He knows the perimeter of the field but needs to determine the length and width in order to calculate the area and decide how many flowers to buy.

A carpenter wants to build a rectangular frame for a painting. She knows the perimeter of the frame but needs to determine the length and width in order to calculate the amount of wood needed and the cost.

A city planner wants to design a rectangular park. She knows the perimeter of the park but needs to determine the length and width in order to calculate the area and decide how many trees and benches to place in the park.

We fail to reject the null hypothesis, and hence conclude that: Sex of the respondent is independent of the choice for the cause of global warming.

The problem boils down to the following hypotheses:

H0: The sex of the respondent is independent of the choice for the cause of global warming.

H1: The sex of the respondent is dependent on the choice for the cause of global warming.

Chosen level of significance: 0.01

Original Table ,also showing marginals and grand total

Human Activity Natural Patterns Don't Know Marginal Total

Male 323 158 39 520

Female 340 152 38 530

Marginal Total 663 310 77 1050(= Grand total)

Table of expected values :

Human Activity Natural Patterns Don't know

Male 328.343 153.524 38.133

Female 334.657 156.476 38.867

Test Statistic: X2 = (323-328.343)2 / 328.343 + (158-153.524)2 /153.524 + (39-38.133)2 / 38.133 + (340-334.657)2 /334.657 + (152-156.476)2 / 156.476 + ( 38-38.867)2 /38.867

= 0.46974 (approx) = (value of test statistic)

degree of freedom = (2-1)*(3-1)= 2

Therefore, X2 critical (critical value) = 9.210

So, we see that the value of the chi-square test statistic is less than the critical value for alpha=0.01

( 0.46974 < 9.210)

So, we fail to reject the null hypothesis,

and hence conclude that: Sex of the respondent is independent of the choice for the cause of global warming.

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Answer:

$68,486.79

Step-by-step explanation:

the first 10 years:

23,500(1.051)^10=38,645.1522

the remaining 13 years:

38,645.1522(1.045)^13=68,486.78798

(round it)

The density of the small rocks is 21 rocks per square feet.

To find the density of rocks per square feet, we need to take the quotient between the total number of rocks and the area covered.

We know that the patio has an area of 200 square feet, and the total number of rocks is 4200, then here we only need to take the quotient between these two values.

Density = (4200 rocks)/(200 ft²) =  21 rocks per ft²

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Complete question:

"Jen's patio has an area of 200 square feet. She is covering the area with 4200 small rocks.

What is the density of the rocks on the patio?"

The measure of other angles of the triangle in degrees are 90 and 50 degrees

From the question, we have the following parameters that can be used in our computation:

Triangle = right triangle

Angle = 40 degrees

The sum of angles in a triangle is 90 degrees

using the above as a guide, we have the following:

40 + 90 + Other angle = 180

Evaluate

Other angle = 50

Hence, the other angle = 50 degrees

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The value of x when lines MN and PQ are equal is 7

Let take note of the properties of a quadrilateral, they include;

From the information given in the diagram, we have that;

Line MN = Line PQ

Also, the expressions are;

MN = 7x + 13

PQ = 10x - 8

Now, equate the values, we get;

7x + 13 = 10x - 8

collect the like terms

7x - 10x = -8 - 13

subtract the like terms

-3x = -21

Divide both sides by the coefficient of x, we get

x = 7

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The result of multiplication of complex numbers is ¹/₈sin5π/3 -√3/8 cos5π/3 + i¹/₈(cos5π/3 - √3sin5π/3).

The result of the multiplication of the complex number is determined as follows;

-√3 + i  x ¹/₈ (cos 5π/3  + i sin 5π/3)

Multiply the bracket by grouping them as shown below;

= -√3 x ¹/₈ (cos 5π/3  + i sin 5π/3) + i x ¹/₈ (cos 5π/3  + i sin 5π/3)

Multiply out the bracket;

= -√3/8 cos5π/3 -  i√3/8 sin5π/3 + i¹/₈cos5π/3 + ¹/₈sin5π/3

note: i x i = 1

Collect similar terms together and add them if any;

= ¹/₈sin5π/3 -√3/8 cos5π/3 + i¹/₈(cos5π/3 - √3sin5π/3)

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Answer:

603.36 cubic inches.

Step-by-step explanation:

To find the approximate volume of the mailing cylinder for posters, we can use the formula for the volume of a cylinder, which is given by:

Volume of cylinder = π * r^2 * h

where π is the mathematical constant pi, r is the radius of the cylinder, and h is the height of the cylinder.

Given that the diameter of the cylinder is 8 inches, we can find the radius by dividing the diameter by 2:

Radius (r) = Diameter / 2 = 8 inches / 2 = 4 inches

Given that the length of the cylinder is 12 inches, we can use these values to calculate the approximate volume:

Volume of cylinder = 3.14 * (4 inches)^2 * 12 inches

Volume of cylinder = 3.14 * 16 square inches * 12 inches

Volume of cylinder = 603.36 cubic inches

So, the approximate volume of the mailing cylinder for posters is 603.36 cubic inches.

Answer:

6.8 with a sum of 09.28282

Step-by-step explanation:  

To find the approximate volume of the mailing cylinder for posters, we can use the formula for the volume of a cylinder, which is given by:

Volume of cylinder = π * r^2 * h

where π is the mathematical constant pi, r is the radius of the cylinder, and h is the height of the cylinder.

Given that the diameter of the cylinder is 8 inches, we can find the radius by dividing the diameter by 2:

Radius (r) = Diameter / 2 = 8 inches / 2 = 4 inches

Given that the length of the cylinder is 12 inches, we can use these values to calculate the approximate volume:

Volume of cylinder = 3.14 * (4 inches)^2 * 12 inches

Volume of cylinder = 3.14 * 16 square inches * 12 inches

The volume of cylinder = 603.36 cubic inches

So, the approximate volume of the mailing cylinder for posters is 603.36 cubic inches.

hope it helps!!!

The total miles of run covered by Mark on Thursday is equal to  9 miles.

Mark ran 3 3/5 miles on Wednesday.

On Thursday, he ran 2 1/2 times as far as he did on Wednesday.

To find out how far he ran on Thursday,

We need to multiply his Wednesday distance by 2 1/2,

2 1/2 × 3 3/5

First, we need to convert both mixed numbers to improper fractions which is equal to,

2 1/2 = 5/2

3 3/5 = 18/5

Now, we can multiply,

5/2 × 18/5

= (5 × 18) / (2 × 5)

= 90/10 = 9

Therefore, the total miles Mark ran on Thursday is equal to  9 miles.

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The required probability of getting at least 3 sixes in 5 rolls of a fair die is 0.033.

The probability of getting exactly k sixes in n rolls of a fair die is given by the binomial distribution formula:

[tex]P(k) = (n C k) * p^k * (1-p)^{(n-k)}[/tex]

(n choose k) = n! / (k! * (n-k)!)

Using this formula, we can calculate the probability of getting exactly 3, 4, or 5 sixes in 5 rolls:

P(3) = (5 choose 3) * (1/6)³ * (5/6)² = 0.032

P(4) = (5 choose 4) * (1/6)⁴ * (5/6)¹ = 0.001

P(5) = (5 choose 5) * (1/6)⁵ * (5/6)⁰ = 0.00003

To get the probability of getting at least 3 sixes, we need to add up these probabilities:

P(at least 3 sixes) = P(3) + P(4) + P(5) = 0.032 + 0.001 + 0.00003 = 0.03303

Rounding to the nearest thousandth, the probability of getting at least 3 sixes in 5 rolls of a fair die is 0.033.

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The approximate amount of rotations it would take the monster truck to travel one mile is 1260 rotations.

Now, Based on the tire experiment, it will take fewer rotations for a monster truck with 6ft (which is 72 inches) tires to travel one mile compared to the other 3 tires from before.

This is because larger tires have a greater circumference, which means they are able to cover more distance with each rotation.

Hence, For calculate the approximate amount of rotations it would take the monster truck to travel one mile, we need to use the formula:

Number of rotations = Distance traveled / Circumference of the tire

Since the distance traveled is one mile, which is equal to 5280 feet, we need to convert the tire diameter from feet to inches, and then calculate the circumference:

Hence, We get;

Circumference = π x Diameter Circumference

                        = 3.14 x 72 Circumference

                        = 226.08 inches

Now, we can calculate the number of rotations:

Number of rotations = 5280 feet / (12 inches/foot x 226.08 inches/rotation)

Number of rotations = 5280 / 2712.96

Number of rotations ≈ 1.947 rotations

or ≈ 1260 rotations per mile

Therefore, the approximate amount of rotations it would take the monster truck to travel one mile is 1260 rotations.

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