Mike wants to save $1,750 in the next 12 months. He plans to save $150 each month for the first 11 months. What is the total amount of money Mike will save during the first 11 months if he saves $150 each month?

Please need steps

Answer:

Step-by-step explanation:perp. 3/2

y + 8 = 3/2(x - 4)

y + 8 = 3/2x - 6

y = 3/2x - 14

Answer:

The number of softballs that would fill the room is 221796 softballs

Step-by-step explanation:

First we will determine the Volume of the room.

The volume of a room is given by

\(Volume = lwh\)

From the question, the given dimension of the room is  10 by 12 by 24 foot

Hence the volume of the room = 10 × 12 × 24

= 2880 cubic feet (ft³)

Convert to cubic inches

To do this, multiply the answer in cubic feet by (12 × 12 × 12)

(NOTE: 1 foot = 12 inches)

Hence, 2880 cubic feet = 2880 × 12 × 12 × 12 cubic inches

= 4976640 cubic inches

This is the volume of the room.

To estimate the number of softballs that would fill the room, we will determine the number of softballs which would give a total volume that is equal to the volume of the room.

First, we will find the volume of one softball

Diameter of softball = 3.5 inches

∴ Radius of softball, r = 3.5/2 inches = 1.75 inches

∴ r = 1.75 inches

Now, for the volume of one softball

From,

V = 4/3 (3.14)r^3

\(V = \frac{4}{3}(3.14)r^{3}\)

\(V = \frac{4}{3}(3.14)\) × \(1.75^{3}\)

\(V = 22.43791667\) cubic inches

This is the volume of one softball

The number of softballs that would fill the room will be

= Volume of the room / Volume of one softball

= 4976640 cubic inches / 22.43791667 cubic inches

=221795.9926

≅221796

Hence, the number of softballs that would fill the room is 221796 softballs

The interval of convergence, i, of the given series is (-∞, ∞).

The given series is

[infinity] xn 4 / 4n! n = 0.

Lets find the radius of convergence, r:

The general term of the given series is xn 4 / 4n!.

So, the ratio of two consecutive terms is given by;

|xn+1 4 / 4(n + 1)!| / |xn 4 / 4n!| = |xn+1| / |xn| * 1 / (n + 1) * 4 / 4 = |xn+1| / |xn| * 1 / (n + 1)

To find the radius of convergence, we take the limit of the above expression as n approaches infinity:

limn→∞ |xn+1| / |xn| * 1 / (n + 1) = LHere, L = limn→∞ |xn+1| / |xn| * 1 / (n + 1)

Because xn+1 and xn are two consecutive terms of the series;

0 ≤ L = limn→∞ |xn+1| / |xn| * 1 / (n + 1)≤ limn→∞ 4 / (n + 1) = 0

The above inequality implies L = 0.

Hence, the radius of convergence, r, is given by:r = 1 / L = ∞

The radius of convergence of the given series is ∞.

The given series is [infinity] xn 4 / 4n! n = 0.

We know that the radius of convergence of the series is ∞.

The interval of convergence, i, is given by;[-r, r] = [-∞, ∞]

To know more about infinite series please visit :

https://brainly.com/question/30221799

#SPJ11

Answer:

MS and QS

Step-by-step explanation:

Finished the test!!! Hope u have a great day or night wherever u are :)

ΔMNQ is said to be an isosceles triangle, and a side is bisected at S, based on the definition of bisector, the segments that are congruent are: MS and QS.

Thus, since ΔMNQ is said to be an isosceles triangle, and a side is bisected at S, based on the definition of bisector, the segments that are congruent are: MS and QS.

Learn more about isosceles triangle theorem on:

https://brainly.com/question/1591730

The instantaneous rate of change of the ball is (b) 1/√2

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

f'(x) = 1/√x

When was the ball is travelling 2 ft/s, we hav

x = 2

Substitute the known values in the above equation, so, we have the following representation

f'(2) = 1/√2

Hence, the instantaneous rate of change is (b) 1/√2

Read more about instantaneous rate at

https://brainly.com/question/14666106

#SPJ4

Answer:

3/10 or three-tenths

Step-by-step explanation:

Hope this helps=D

Answer:

O.3 = 1/3

Step-by-step explanation:

divide 1÷3

you will get 0.3 to infinity

The value of side length w is 13.75 .

Given right angled triangle,

Perpendicular = w

Hypotenuse = 17

Angle of triangle = 54°

So,

According to the trigonometric ratios,

tanФ = p/b

cosФ = b/h

sinФ = p/h

By using sinФ,

sinФ = p/h

sin 54° =  w/ 17

0.809 = w/17

w = 13.75 .

Thus after correction w will be 13.75

Know more about trigonometry,

https://brainly.com/question/25618616

#SPJ1

answer 33

because i had abd and ur mum jk but yea

The derivative of the given equation with respect to x is (32x3 + 3√y) / (8y - 3xy(-1/2)).

The given equation is:8x4 + 6√xy = 8y2We are to find dy/dx.To solve this, we need to use implicit differentiation on both sides of the equation.

Using the chain rule, we have: (d/dx)(8x4) + (d/dx)(6√xy) = (d/dx)(8y2).

Simplifying the left-hand side by using the power rule and the chain rule, we get: 32x3 + 3√y + 6x(1/2) * y(-1/2) * (dy/dx) = 16y(dy/dx).

Simplifying the right-hand side, we get: (d/dx)(8y2) = 16y(dy/dx).

Simplifying both sides of the equation, we have:32x3 + 3√y + 3xy(-1/2) * (dy/dx) = 8y(dy/dx)32x3 + 3√y = (8y - 3xy(-1/2))(dy/dx)dy/dx = (32x3 + 3√y) / (8y - 3xy(-1/2))This is the main answer.

we can provide a brief explanation on the topic of implicit differentiation and provide a step-by-step solution. Implicit differentiation is a method used to find the derivative of a function that is not explicitly defined.

This is done by differentiating both sides of an equation with respect to x and then solving for the derivative. In this case, we used implicit differentiation to find dy/dx for the given equation.

We used the power rule and the chain rule to differentiate both sides and then simplified the equation to solve for dy/dx.

Finally, the conclusion is that the derivative of the given equation with respect to x is (32x3 + 3√y) / (8y - 3xy(-1/2)).

T know more about chain rule visit:

brainly.com/question/31585086

#SPJ11

Answer:

\(\sqrt{17.3}\) = 4.159.....  so approx 4.2

Step-by-step explanation:

Answer:

17:19

Step-by-step explanation:

yesssssirrrrrrrrrr

Step-by-step explanation:

Triangles ABX and DCX are similar.

Since they are similar, AX/DX = AB/DC.

Hence AX/2.8 = 8/4 and AX = 5.6.

Step-by-step explanation:

We need to simply like terms. Let's break this out into four different problems that are easy to solve, then we can put it all back together for the final answer.

There are four like terms in both the numerator (top) and denominator (bottom) of the fraction. Numbers, m, p, and v. We will look at each of these seperately.

What is \(45/15\)? Easy right, just 3.

Let's move on to the harder parts.

\(\frac{m^{-6}}{m^{-2}}\)

Remember that negavite exponents mean to divide.

For example, \(2^{-2} = \frac{1}{2^2} = 1/4\)

So we just need to apply this rule to both of these exponents to get,

\(\frac{m^2}{m^6}\)

Now remember that when dividing by exponents, the exponents subtract from each other\(\frac{x^y}{x^z} = x^{y-z}\)

So we get, \(m^{2-6} = m^{-4} = \frac{1}{m^4}\)

So far we have

\(\frac{3}{m^4}\)

Keep applying the same rules for the other two terms. Reply back if you need more help and I can keep working through with you.

Answer:

8

Step-by-step explanation:

First, you want to substitute your a, b, c, and d, which you would get 3(2) + 3(8) divided by sign 2 - 2(5). According to PEMDAS, we will multiply our numbers in the parenthesis with the outside number next to it, so you should have gotten 6 + 24 divided by sign 2 - 10. Next, you will divided 24 by 2 to get 12, so the equation will now look like 6 + 12 - 10. Finally, just work it out 6 + 12 is 18 minus 10, is 8. I hope this helps :)

Answer:

Answer is 18

Step-by-step explanation:

a2+3b/c-2d

when

a=3

b=8

c=2

d=5

2*3+3*8/2-2*5

6+24/2-10

6+12-10

18-10

8. answer

Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.

In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.

To know more about cell frequencies,

https://brainly.com/question/30482788

#SPJ11

After working 8 hours and grading 9 papers per hour, it is expected Autumn has 11 papers left.

To calculate the number of papers she can grade during this time, let's use the rate provided:

This means in 9 hours she can grade 72 papers.

Now, let's calculate the number of papers left:

Based on this, the total of papers left after working for 8 hours is 11 papers.

Learn more about grade in: https://brainly.com/question/14853329

#SPJ1

\(Ainsley \: walked \: in \: \frac{1}{3} \: \: of \: a \: day \ \: = \frac{3}{5} mile\)

\( = \frac{1}{3} \times 24 = \frac{3}{5} \)

\(8 \: hours = \frac{3}{5} \: miles\)

\(Sarah \: walked \: in \: \frac{2}{6} of \: a \: day \: = \frac{5}{8} miles\)

\( \frac{2}{6} \times 24 = \frac{5}{8} \)

\(8 \: hours \: = \frac{5}{8} \: miles\)

Let us see who walked more :

\(Ainsley \: walked \: = \frac{3 \times 8}{40} \)

\( = \frac{24}{40} \: miles\)

\(Sarah \: walked \: = \frac{5 \times 5}{40} \)

\( = \frac{25}{40} \: miles\)

\( \frac{24}{40} < \frac{25}{40} \)

Sarah walked farther than Ainsley .

\( \frac{25}{40} - \frac{24}{40} = \frac{1}{40} \: miles\)

∴ Sarah walked farther than Ainsley by 1/40 miles .

Answer:

the height is 6ft

Step-by-step explanation:

2 x 3 = 6ft

Answer:

m=15w

Step-by-step explanation:

i did the test before :)

The probability that, both tries to own a dog is 0.2500.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

P(A) = f / N determines probability, which quantifies the possibility of an event happening. Probability and odds are related, but probability is necessary for odds to exist. Prior to calculating the likelihood that an event will occur, probability is required.

Here, 50% of people own dog.

P(people own dog) = 50/100

= 0.5

P(both people own dog) = 0.5×0.5 = 0​​​​​​.2500

Learn more about probability Visit : brainly.com/question/13604758

#SPJ4

a) The probability of selecting a red marble is 3/17.

b) The probability of selecting a green marble is 14/17.

c) The probability of selecting a purple marble is 0/17.

d) The probability of selecting a red or a green marble is 1.

We have,

a) The probability of selecting a red marble is 3/17.

This is because there are 3 red marbles in the bag, and the total number of marbles in the bag is 3 (red) + 14 (green) = 17.

b) The probability of selecting a green marble is 14/17. There are 14 green marbles in the bag, and the total number of marbles is 17.

c) The probability of selecting a purple marble is 0/17. This is because there are no purple marbles in the bag, so the probability of selecting one is zero.

d) The probability of selecting a red or a green marble is:

= (3 + 14)/17

= 17/17

= 1.

This is because there are 3 red marbles and 14 green marbles in the bag, and the total number of marbles is 17.

Therefore, you are guaranteed to select either a red or a green marble when picking from the bag.

Thus,

a) The probability of selecting a red marble is 3/17.

b) The probability of selecting a green marble is 14/17.

c) The probability of selecting a purple marble is 0/17.

d) The probability of selecting a red or a green marble is 1.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ4

The zeros of f(x) are x = 1, x = 2, and x = 3.

There are two main theorems used to factor and find the real zeros of polynomial functions: the Factor Theorem and the Rational Zeros Theorem.

Factor Theorem: If (x - a) is a factor of a polynomial function f(x), then f(a) = 0. In other words, if we can factor a polynomial as (x - a) times some other polynomial, then we know that a is a zero of the polynomial (meaning that f(a) = 0).

Rational Zeros Theorem: If a polynomial function f(x) with integer coefficients has a rational zero p/q (where p and q have no common factors other than 1) then p is a factor of the constant term and q is a factor of the leading coefficient.

To find all the zeros of a polynomial, we can use synthetic division or long division to divide the polynomial by its factors. Here's an example using a polynomial of degree 3:

Let's say we want to find all the real zeros of the polynomial f(x) = x^3 - 6x^2 + 11x - 6.

Step 1: Use the Rational Zeros Theorem to find possible rational zeros. The constant term is -6 and the leading coefficient is 1, so the possible rational zeros are ±1, ±2, ±3, and ±6.

Step 2: Use synthetic division to test each possible rational zero. We start with 1:

1 | 1 -6 11 -6

|___ 1 -5 6

1 -5 6 0

Since the remainder is 0, we know that (x - 1) is a factor of f(x). We can write f(x) as:

f(x) = (x - 1)(x^2 - 5x + 6)

Step 3: Use the Factor Theorem to find the other zeros. We already know that x = 1 is a zero, so we need to find the zeros of the quadratic factor (x^2 - 5x + 6). We can use the quadratic formula or factor it as:

x^2 - 5x + 6 = (x - 2)(x - 3)

Therefore, the zeros of f(x) are x = 1, x = 2, and x = 3.

To learn more about polynomial visit:

https://brainly.com/question/11536910

#SPJ11

Answer:

3/y

Step-by-step explanation:

15x÷5xy

15x/5xy....you will cancel x by x and simplify by 5(GCF)

3/y ...... it is the simplify form of the given equetion.

There are 7 women and 6 men signed up to join a ballroom dance class. There are 155 different ways the instructor can choose 4 people to join the ballroom dance class, ensuring that at least 3 of them are men.

To calculate the number of ways the instructor can choose 4 people with at least 3 men, we consider two cases:

Case 1: 3 men and 1 woman

The number of ways to select 3 men from the 6 available is given by the combination formula: C(6, 3) = 20. For the woman, there are 7 available choices. Therefore, the number of combinations with 3 men and 1 woman is 20 * 7 = 140.

Case 2: 4 men

The number of ways to select 4 men from the 6 available is given by the combination formula: C(6, 4) = 15.

To find the total number of ways, we add the combinations from both cases: 140 + 15 = 155.

Visit here to learn more about combinations:

brainly.com/question/29089154

#SPJ11

Answer:

21.16 x 10^6 or 2.116 x 10^7

Step-by-step explanation:

First, rewrite 9200 in scientific notation. This can be expressed as 9.2 x 10^3.

Now you can multiply and add the exponents.

9.2 x 2.3 = 21.16

3 + 3 = 6

21.16 x 10^6 or 2.116 x 10^7