Can someone explain to me how to do this

Answer:

  a. 3 (see below for explanation)

  b. Ln = 4 + 3(n -1)

  c. 48

  d. dn = 6n +2

Step-by-step explanation:

a. The common difference is found by subtracting any given term from the next one: 7 -4 = 3, or 10 -7 = 3. The common difference is 3.

__

b. The general expression for an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 + d(n -1)

Here, the first term is 4 and the common difference is d. We choose to name the n-th term of Levy's sequence "Ln", so we can fill in the numbers to get ...

  Ln = 4 + 3(n -1)

__

c. We can call the terms of Zack's sequence Zn, so we have ...

  Zn = 3·Ln = 3·(4 + 3(n -1)) = 12 +9(n -1)

Putting 5 where n is in this equation, we find ...

  Z5 = 12 +9(5 -1) = 48

The 5th term of Zack's sequence is 48.

__

d. The difference of n-th terms of the two sequences is ...

  dn = Zn -Ln = (3·Ln) - Ln = 2Ln = 2(4 +3(n -1)) = 8 +6(n -1)

  dn = 6n +2

Final answer:

To find the time it took for Austin to catch up with Amber, we calculated the distance Amber had covered before Austin started, and then divided that distance by the difference in their speeds, yielding a catch-up time of 5.5 hours.

Explanation:

The question is asking after how many hours Austin will catch up with Amber if they are driving the same route, but start at different times and drive at different speeds. To solve this problem, we can use the concept of relative speed and the equation Distance = Speed × Time. Since Amber left 2 hours earlier, by the time Austin starts, Amber has already covered a certain distance. We can calculate this distance by multiplying Amber's speed (55 mph) by the time she drove alone (2 hours), which gives us 110 miles. Now, Austin catches up by covering the difference in the distance at a relative speed, which is the difference of their speeds. So, the relative speed is Austin's speed (75 mph) minus Amber's speed (55 mph), resulting in 20 mph.

Now we can find the time it took Austin to catch up by dividing the distance Amber covered alone (110 miles) by the relative speed (20 mph). This comes out to 5.5 hours. Thus, Austin catches up with Amber after driving for 5.5 hours.

Answer:

  58 in^2

Step-by-step explanation:

The area of one face of the 3" cube is (3 in)^2 = 9 in^2. Then the 6 faces of that will have an area of ...

  6·9 in^2 = 54 in^2

The area of the top of the paperweight is unaffected by the area of the added cube: the area the smaller cube covers is exactly the same as its exposed top area. So, the net effect of the added 1" cube is to increase the total area by that cube's lateral area: 4 faces at 1 in^2 for each face, a total of 4 in^2.

Then the total surface area of the paperweight is ...

  54 in^2 + 4 in^2 = 58 in^2

Answer:

Option 3.

Step-by-step explanation:

The domain of a function is the complete set of possible values of the independent variable.

The argument of a square root can take negative values, then:

So x+3 must be greater than 0. So x+3> 0 -> x> -3.

Then, the domain of the function is: [-3, +inf)  

The range of a function is the complete set of all possible resulting values of the dependent variable after we have substituted the domain.

So in this case, we know that the square root always is going to throw a positive value, but given that the square rooth is multiplied by a minus, the result is always going to be negative.

The least value the square root can take is 0, so in that case, the maximum value the function can take is y = -2.

So the range is (-inf, -2]

So, the correct option is option 3

Answer:

15.50+n=325.00

Step-by-step explanation:

15.50+what she had in the bank already = what she has now

Answer:

The answer is $15.50 + n = $325.00.

Step-by-step explanation:

Fifteen dollars plus "n" (her account balance before the deposit) equals $325.00. Hope this helps! :D

What number do

You need help with

Answer:

The number of faces is 29

Step-by-step explanation:

we know that

The Euler's formula state that, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

[tex]V- E + F = 2[/tex]

In this problem we have

[tex]V=16[/tex]

[tex]E=43[/tex]

Substitute in the formula and solve for F

[tex]16- 43 + F = 2[/tex]

[tex]-27 + F = 2[/tex]

[tex] F = 2+27[/tex]

[tex] F = 29[/tex]

[tex]\displaystyle\\\text{If we have the radius of the circle, we use the formula: }\\V=\pi R^2\cdot h\\\\\text{If we have the diameter of the circle, we use the formula: }\\\\V=\frac{\pi D^2}{4}\cdot h\\\\\text{It is given:}\\{\bf D=3~in}\\{\bf h=3~in}\\\\\text{Is required:}\\{\bf V=?}\\\\\text{Solution:}\\\\V=\frac{\pi D^2}{4}\cdot h=\frac{\pi 3^2}{4}\cdot 3=\frac{27\pi}{4}=\boxed{\bf6.75\pi~in^2}[/tex]

C is the median.

to find the median we need to put all the numbers given in order from smaller to largest

12, 18, 34, 55, 59, 67, 80, 80

then find the middle number of these

well we have to middle numbers 59 and 55

so we need to find the mid number between these two which 57.

The answer to this question is 57

hope this helped

Answer:

The answer is 18

Answer:

  (0, -3), (-1, 1)

Step-by-step explanation:

The equation can be simplified to a form more helpful for graphing.

Subtract 7:

  24x +18 = -6y

We note that all of the coefficients are multiples of 6, so we can divide by -6:

  y = -4x -3

This is slope-intercept form, so it tells you that the y-intercept is -3, which means one point on the graph is (0, -3).

The slope is -4, so an x-value in the negative direction will give a more positive y-value. We can choose x=-1 and find y:

  y = -4(-1) -3 = 4 -3 = 1

Then another point on the graph is (-1, 1).

Two points on the graph are (0, -3) and (-1, 1).

ANSWER

D. 22-8√5

EXPLANATION

We want to expand

[tex](2 \sqrt{5} - 4)(3 \sqrt{5} + 2)[/tex]

We use the distributive property to obtain,

[tex]2 \sqrt{5} (3 \sqrt{5} + 2) - 4(3 \sqrt{5} + 2)[/tex]

We expand to get,

[tex]6(5) + 4 \sqrt{5} - 12 \sqrt{5} - 8[/tex]

Simplify to get,

[tex]22 - 8 \sqrt{5} [/tex]

The correct answer is D.

Final answer:

The statement is true, as adding the probabilities of walking with the beagle (20%) and with the golden retriever (70%) correctly calculates the probability of walking with any dog as 90%.

Explanation:

The question involves calculating the probability of an event occurring, specifically the event of a neighbor walking with any dog. To determine whether the statement "We could find the probability of walking with a dog by adding P(beagle) and P(golden retriever)" is true or false, let's examine the given percentages. According to the information, the neighbor walks 20% of the time with her beagle, 70% of the time with her golden retriever, and 30% of the time she walks alone.

Adding the probabilities of walking with the beagle (20%) and with the golden retriever (70%) gives us a total of 90%. This calculation suggests that the neighbor walks with a dog 90% of the time, which is a valid way to find the probability of walking with any dog. Hence, the statement is true. However, it is important to ensure that the events (walking with the beagle and walking with the golden retriever) are exclusive and do not overlap, which is implied in this scenario.

Depends really:

If you think about it everywhere has a different temperature my lowest on Friday was 45 degrees and that was the lowest that week.

SO PLEASE CLARIFY

Answer:

y=-2/3x -6

Step-by-step explanation:

y=-6 so b=-6

rise/run=-2/3

Put that into an equation of y=mx+b and you get y=-2/3x -6

For this case we have the following function:

[tex]f (x) = 7x ^ 2 + 4[/tex]

By definition, we have that a linear equation is of the form [tex]y = mx + b[/tex]

On the other hand, a quadratic equation is of the form[tex]y = ax ^ 2 + bx + c[/tex]

Then, the given equation is not a linear equation, it is not of the form [tex]y = mx + b[/tex]

Answer:

No, the equation is not linear. It is not of the form [tex]f (x) = mx + b.[/tex]

Hey there!

Here goes your answer ↓

Question:- State whether the given equation or function is linear. Write yes or no. Explain your reasoning. f(x) = 7x² + 4

(a) Yes, the equation is linear. It is of the form f(x) = m + b

(b) Yes, the equation is linear form. It is of the form f(x) = mx + b.

(c) No, the equation is not linear. It is in the form x + y = c.

(d) No, the equation is not linear. It is not of the form f(x) = mx + b.

Answer :- Option (D)

Explanation :-

Given equation :- f(x) = 7x² + 4

•The form of any equation should be → y - mx + b

The given equation does not satisfy the above rule, and hence it is not a linear equation.

Hope it helps.

Have a great day ahead!

De l'Hospital rule applies to undetermined forms like

[tex]\dfrac{0}{0},\quad\dfrac{\infty}{\infty}[/tex]

If we evaluate your limit directly, we have

[tex]\displaystyle \lim_{x\to 0}(1+2x)^{-\frac{3}{x}} = 1^\infty[/tex]

which is neither of the two forms covered by the theorem.

So, in order to apply it, we need to write the limit as follows: we start with

[tex]f(x)=(1+2x)^{-\frac{3}{x}}[/tex]

Using the identity [tex]e^{\log(x)}=x[/tex], we can rewrite the function as

[tex]f(x)=e^{\log\left((1+2x)^{-\frac{3}{x}}\right)}[/tex]

Using the rule [tex]\log(a^b)=b\log(a)[/tex], we have

[tex]f(x)=e^{-\frac{3}{x}\log(1+2x)}[/tex]

Since the exponential function [tex]e^x[/tex] is continuous, we have

[tex]\displaystyle \lim_{x\to 0} e^{f(x)} = e^{\lim_{x\to 0} f(x)}[/tex]

In other words, we can focus on the exponent alone to solve the limit. So, we're focusing on

[tex]\displaystyle \lim_{x\to 0} -\frac{3}{x}\log(1+2x) [/tex]

Which we can rewrite as

[tex]\displaystyle \lim_{x\to 0} -\frac{3}{x}\log(1+2x) = -3\lim_{x\to 0}\frac{\log(1+2x)}{x}[/tex]

Now the limit comes in the form 0/0, so we can apply the theorem: we derive both numerator and denominator to get

[tex]\displaystyle -3\lim_{x\to 0}\frac{\log(1+2x)}{x} = -3 \lim_{x\to 0}\dfrac{\frac{2}{1+2x}}{1} = -3\cdot 2 = -6[/tex]

So, the limit of the exponent is -6, which implies that the whole expression tends to

[tex]e^{-6}=\dfrac{1}{e^6}[/tex]

By applying L'Hospital's rule to the given expression, the limit is found to be 1 as x approaches 0.

L'Hospital's rule can be applied to find the limit of the expression (1+2x)^(-3/x) as x approaches 0. This rule states that if we have an indeterminate form 0/0 or ∞/∞, we can take the derivative of the numerator and denominator separately and then evaluate the limit again.

After simplifying the expressions and substituting x = 0, we find that the limit is equal to 1.

The distance between him and school is 1.59 miles. Of course this distance is linear to make this problem simple. He walks with a speed of 3 miles per hour or 0.00083 mile per second.

To calculate time from distance and speed we use this formula: [tex]t=\frac{d}{s}=\frac{3mil}{0.00083mil/s}\approx3614.46sec[/tex] seconds. To convert minutes we divide number of second by 60. [tex]t\div60=3614.46sec\div60\approx\boxed{60.24min}\approx\boxed{1h}[/tex].

It will take him approximately 60 minutes to get to school.

Answer:

20 minutes

Step-by-step explanation:

The wording of this question is a bit strange.  Are you saying that Zeke can walk to school 3 times per hour?  

If so, then the total distance he'd walk in 1 hour would be 3(1.59 miles), or

4.77 miles.  So he walks 4.77 mph.

How long to talk to school?  Divide 1.59 miles by 4.77 mph.  The result is:

1/3 hour or 20 minutes.

Answer:

  ∠H = 120°

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary:

  ∠H +∠T = 180

  (2x +60) + (x +30) = 180

  3x = 90 . . . . . . . subtract 90, collect terms

  x = 30 . . . . . . . . divide by the coefficient of x

Then the measure of angle H is ...

  ∠H = 2·30 +60 = 120 . . . . . degrees

Answer:

A

Step-by-step explanation:

sin is opposite/hypotenuse, which is 24/26, simplifying to 12/13

For this case, we have that by definition:

[tex]Sin (C) = \frac {24} {26}[/tex]

That is, the sine of angle C will be given by the leg opposite the angle C divided by the hypotenuse of the traingule.

[tex]Sin (C) = \frac {24} {26}[/tex]

Simplifying:

[tex]Sin (C) = \frac {12} {13}[/tex]

Answer:

Option A

Answer:

[tex]f(x)=3^x[/tex]

Step-by-step explanation:

From the table;

When x=2, [tex]y=9=3^2[/tex]

When x=3, [tex]y=27=3^3[/tex]

When x=4, [tex]y=81=3^4[/tex]

We can infer from the pattern that;

[tex]f(x)=3^x[/tex]

Answer:

Explanation:

1) Principal quantum number, n = 2

2) Second quantum number, ℓ

The possible values of ℓ are from 0 to n - 1.

Hence, since n = 2, there are two possible values for ℓ: 0, and 1.

This gives you two shapes for the orbitals: 0 corresponds to "s" orbitals, and 1 corresponds to "p" orbitals.

3) Third quantum number, mℓ

The possible values for mℓ are from - ℓ to + ℓ.

Hence, the poosible values for mℓ when n = 2 are:

4) Fourth quantum number, ms.

Therfore the full set of possible states (different quantum number for a given atom) for n = 2 is:

That is a total of 8 different possible states, which is the answer for the question.

Answer: Option C

[tex]g(x) = 4 ^ x-1[/tex]

Step-by-step explanation:

If we have a function f(x) and we want to move its graph vertically then we apply the transformation:

[tex]g (x) = f (x) + k.[/tex]

So:

If [tex]k> 0[/tex] the function g(x) will be the function f(x) displaced k units up

If [tex]k <0[/tex] the function g(x) will be the function f(x) displaced k units down.

In this case we know that the graph of f(x) moves 5 units up.

then [tex]k> 0[/tex] and [tex]k = 5[/tex]

Therefore [tex]g (x) = f(x) +5[/tex]

[tex]g(x) = 4 ^ x - 6 +5\\\\g(x) = 4 ^ x-1[/tex]

Answer:

A

Step-by-step explanation:

sin(60) can be simplified into sqrt(3)/2.

The sine of 60° is √3/2.

The ratio between the hypotenuse and the leg opposite the angle, when viewed as a component of a right triangle, is the trigonometric function for an acute angle.

Given

height = √3

hypotenuse = 2

sin θ = height/ hypotenuse

sin θ = √3/2

To know more about sine of an angle refer to :

https://brainly.com/question/2920412

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Answer:

13

180-125-42=13

You can find the measure of the missing angle by identifying the fraction of the total circle that the time period represents. For example, the movement from 12 to 3 on a clock represents a quarter of the clock's cycle, which corresponds to a 90 degrees angle.

To find the measure of the missing angle, we must first identify the type of problem it is. Based on the information shared, it seems like it's a problem involving angles in a circle, specifically, how the hour hand of the clock moves.

When the hour hand moves from 12 to 3, we are looking at a quarter (1/4) of a 360 degrees circle, which is identified by 90 degrees.

So, if you're trying to find the measure of a missing angle over a certain period, you can use the fraction of the total circle that the period represents. For example, the quarter period from 12 to 3 on the clock would represent a 90 degrees angle.

https://brainly.com/question/33833061

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The answer is 4. Any absolute value of a negative number is positive

Answer: 4

Step-by-step explanation: It's important to understand what absolute value really means and that is the absolute value of a number represents that numbers distance from zero on a number line.

The absolute value of -4 is 4. The reason the absolute value of -4 is 4 is that if we graph -4 down here on the number line, you can see that its distance from zero is 4 units.

I have attached a number line below showing the absolute value of -4

Answer: $10

Step-by-step explanation:

Let's analize the information given: We know that  she had $94 to spend on 8 books and after buying these books she had $14. So, we need to calculate the amount of money she spent. Subtract $94 and $14:

[tex]Total\ spent=\$94-\$14\\Total\ spent=\$80[/tex]

Then, to calculate the cost of each book, we need to divide the "Total spent" by 8:

[tex]cost\ of\ each\ book=\frac{Total\ spent}{8}\\\\cost\ of\ each\ book=\frac{\$80}{8}\\\\cost\ of\ each\ book=\$10[/tex]

Answer:

D. Cylinder

Step-by-step explanation:

Consider the rectangle that has to be rotated about the axis as shown in the picture. In attached diagrams this rectangle is black rectangle ABCD.

While rotating each point of the rectangle will describe the circle. The circles with the greatest radii will be circles made by the points from the side that is opposite to the side on the axis of rotation.

Formed figure appear to be cylinder.

Answer:

  see below

Step-by-step explanation:

Each point moves to a location 3 times its current distance from the center of dilation. The dilated figure connects those moved vertices.

___

In the attached figure, the orange lines show how the points move to their new location (3 times the original distance). The blue lines connect the dots to make the dilated figure.

-4 x -4d=16d

-4 x-5=20

16d+20

Answer: -36d

Step-by-step explanation:

-4(-4d-5)

You have to multiply -4x-4d= -16d

Then do -4x5=-20

After you have to solve -16-20d

Which equals to -36d

Answer:

  5 times as large

Step-by-step explanation:

You can think of "10^5" as "green marbles" if you like. Then your question is ...

  5 green marbles is how many times as large as 1 green marble.

Hopefully, the answer is all too clear: it is 5 times as large.

_____

In math terms, when you want to know how many times as large y is as x, the answer is found by dividing y by x:

  y/x . . . . . tells you how many times as large as x is y.

Here, that looks like ...

  [tex]\dfrac{5\times 10^5}{1\times 10^5}\\\\=\dfrac{5}{1} \qquad\text{the factors of $10^5$ cancel}\\\\=5[/tex]

Answer:

5 times as large

Step-by-step explanation:

I did the question