My wife and I are Racing around a 400m track going opposite directions. I am running at 8 m/s and she has a head start of 50 meters running at 5 m/s, how long does it take for us to reach the same point ? Explain.

Answer:

B

Step-by-step explanation:

1) initial circumference

radius * 2 * pi = 24 * pi = 75,398224

2) final circumference

diameter * pi = 48 * pi = 150,796447

150,796447 - 75,398224 = 75.36 m

Answer:

128° because it is corresponding with <4

[tex] < 5 = \: < 3 \\ = \: < 4 \\ < 5 = 128 \degree[/tex]

Answer:

The correct option is (b).

Step-by-step explanation:

The solution of the given polynomial is :

[tex](-\dfrac{1}{3},4)[/tex]

x = 1/3 and y = -4

i.e.

Sum of roots = (1/3-4) = -11/3

Product of roots = (1/3)(-4) = -4/3

The quadratic equation is as follows :

[tex]x^2+(\text{sum of roots})x+\text{Product of roots}=0[/tex]

Put all the values,

[tex]x^2+\dfrac{-11}{3}x+\dfrac{-4}{3}=0\\\\3x^2-11x-4=0[/tex]

So, the correct option is (b).

Answer:

Started in quadrant 2, ended in quadrant 4.

Step-by-step explanation:

The coordinate plane is divided into four quadrants. Quadrant one (QI) is the top right fourth of the coordinate plane, where there are only positive coordinates. Quadrant two (QII) is the top left fourth of the coordinate plane. Quadrant three (QIII) is the bottom left fourth. Quadrant four (QIV) is the bottom right fourth.

Answer:

[tex]A_1 = 12[/tex]

[tex]A_n = A_{n-1} + 3[/tex]

Step-by-step explanation:

Given

[tex]A_n =12+(n-1)3[/tex]

Required

Write as recursive

We have:

[tex]A_n =12+(n-1)3[/tex]

Open bracket

[tex]A_n =12+3n-3[/tex]

[tex]A_n =12-3+3n[/tex]

[tex]A_n =9+3n[/tex]

Calculate few terms

[tex]A_1 =9+3*1 = 9 + 3 = 12[/tex]

[tex]A_2 =9+3*2 = 9 + 6 = 15[/tex]

[tex]A_3 =9+3*3 = 9 + 9 = 18[/tex]

The above shows that the rule is to add 3.

So, we have:

[tex]A_1 = 12[/tex]

[tex]A_n = A_{n-1} + 3[/tex]

Answer:

10x ÷ 5x=2x

10x ÷ 5x = 2x

10x÷ 5x = 2x

Answer:

[tex]e^{2x}=5[/tex]

Step-by-step explanation:

Recall that [tex]\log_b a=c\implies b^c=a[/tex].

In this case, we need to find the base of the logarithm. The logarithm [tex]\ln[/tex] denotes natural [tex]\log[/tex] with a base of [tex]e[/tex], a mathematical constant.

Therefore, we can re-write the equation as:

[tex]\log_e5=2x[/tex]

To write the equation as an exponential equation, recall the definition of log (first sentence of explanation):

[tex]\boxed{e^{2x}=5}[/tex]

Answer:

[tex](a)\ 6m(3m + 21) = 9(2m^2 + 14m)[/tex]

(b) Yes, it is divisible by 9

Step-by-step explanation:

Given

[tex]6m(3m + 21)[/tex]

Solving (a): Complete the blanks

[tex]6m(3m + 21) = 9 [\ ][/tex]

Expand the bracket

[tex]6m(3[m + 7]) = 9 [\ ][/tex]

[tex]6m*3(m + 7) = 9 [\ ][/tex]

Express 6m as 2m * 3

[tex]2m*3*3(m + 7) = 9 [\ ][/tex]

[tex]2m*9(m + 7) = 9 [\ ][/tex]

Rewrite as:

[tex]9 * 2m(m + 7) = 9 [\ ][/tex]

Multiply the bracket by 2m

[tex]9 * (2m^2 + 14m) = 9 [\ ][/tex]

Divide both sides by 9

[tex]2m^2 + 14m = [\ ][/tex]

Hence, the bracket will be filled with: [tex]2m^2 + 14m[/tex]

So:

[tex]6m(3m + 21) = 9(2m^2 + 14m)[/tex]

Solving (b): Is [tex]6m(3m + 21)[/tex] divisible by 9?

In (a), we have:

[tex]6m(3m + 21) = 9(2m^2 + 14m)[/tex]

The leading factor "9" implies that the expression is divisible by 9

Answer:

[tex]\text{C. }1[/tex]

Step-by-step explanation:

In the question, we're given that the notation [tex]\#\#(a,b,c)[/tex] produces a number [tex]a[/tex] less than the product of [tex]b[/tex] and [tex]c[/tex] raised to the [tex]a[/tex] power. Let the number produced be [tex]n[/tex]. As a mathematical equation, we can write this production as [tex]n=(bc)^a-a[/tex]

For [tex]\#\#(2, 5, x)[/tex], we can assign:

Substituting these values into [tex]n=(bc)^a-a[/tex], we get:

[tex]23=(5x)^2-2[/tex]

Add 2 to both sides:

[tex]25=(5x)^2[/tex]

Take the square root of both sides:

[tex]5=|5x|[/tex]

For [tex]y=|z|[/tex], there are two cases:

[tex]\begin{cases}y=z,\\y=-z\end{cases}[/tex]

Therefore, we have:

[tex]\begin{cases}5=5x, x=\boxed{1}\\5=-(5x), 5=-5x, x=\boxed{-1}}\end{cases}[/tex]

The only answer choice applicable is [tex]\boxed{\text{C. }1}[/tex].

Answer:

[tex]\frac{3}{17}, \\0.176, \\18\%[/tex]

Step-by-step explanation:

The area a total of 4+3+6+5=18 balls, consisting of:

After a green ball is selected (implied that it is not replaced or put back), there will be 17 balls total, consisting of:

Therefore, the probability of drawing another green one is:

[tex]\boxed{\frac{3}{17}=0.176=18\%}[/tex]

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the regression line is not given.

However, I will give a general explanation of how to calculate the degree of freedom of a slope of regression line

The degree of freedom is calculated using:

[tex]df = n - k[/tex]

Where

[tex]k \to number\ of\ parameters[/tex]

[tex]n \to sample\ size.[/tex]

For a regression line; there are two parameters that are being estimates;

The intercept and the slope. So:

[tex]k = 2[/tex]

Hence, the degree of freedom of a slope of regression line is:

[tex]df = n -2[/tex]

So; if for example

[tex]n =101[/tex]

the degree of freedom will be:

[tex]df =101 - 2[/tex]

[tex]df =99[/tex]

Answer:

-10, -1

Step-by-step explanation:

See Image below:)

Answer:

cccccccccccccccccccc

Answer:

= -9pq

Step-by-step explanation:

=8pq + (-17pq)

=8pq-17pq

= -9pq

Let n represent the interger l, the three consective intergers are represented by

[tex]n[/tex]

[tex]n + 2[/tex]

[tex]n + 4[/tex]

The second one represent

[tex](n + 2) {}^{2} + 76 =( n + 4) {}^{2} [/tex]

Simplify both sides

[tex]n {}^{2} + 4n + 4 + 76 = {n}^{2} + 8n + 16[/tex]

[tex] {n}^{2} + 4n + 4 = {n}^{2} + 8n - 60[/tex]

[tex]4n + 4 = 8n - 60[/tex]

[tex]4n + 64= 8n[/tex]

[tex]64= 4n[/tex]

[tex]n = 16[/tex]

The intergers are 16,18,20

Answer:

[tex]a_1 = 2[/tex]

[tex]a_2 = 3[/tex]

[tex]a_3 = 5[/tex]

[tex]a_4 = 8[/tex]

[tex]a_5 = 13[/tex]

Step-by-step explanation:

Given

[tex]a_n = a_{n-1} + a_{n-2}[/tex]

[tex]a_1 = 2[/tex]

[tex]a_2 = 3[/tex]

Solving (a): The first term

This has already been given as:

[tex]a_1 = 2[/tex]

Solving (b): The second term

This has already been given as:

[tex]a_2 = 3[/tex]

Solving (c): The third term

This is calculated as:

[tex]a_n = a_{n-1} + a_{n-2}[/tex]

[tex]a_3 = a_{3-1} +a_{3-2}[/tex]

[tex]a_3 = a_2 +a_1[/tex]

[tex]a_3 = 3 +2[/tex]

[tex]a_3 = 5[/tex]

Solving (d): The fourth term

This is calculated as:

[tex]a_n = a_{n-1} + a_{n-2}[/tex]

[tex]a_4 = a_{4-1} +a_{4-2}[/tex]

[tex]a_4 = a_3 +a_2[/tex]

[tex]a_4 = 5+3[/tex]

[tex]a_4 = 8[/tex]

Solving (e): The fifth term

This is calculated as:

[tex]a_n = a_{n-1} + a_{n-2}[/tex]

[tex]a_5 = a_{5-1} +a_{5-2}[/tex]

[tex]a_5 = a_4 +a_3[/tex]

[tex]a_5 = 8+5[/tex]

[tex]a_5 = 13[/tex]

Complete Question:

There are 750 spectator in the stadium of which 420 are women and the rest are men. What percent of the spectators are women?

Answer:

Percentage = 56%

Step-by-step explanation:

Given the following data;

Total number of people = 750

Number of women = 420

To find the percentage of women;

First of all, we would determine the number of male spectators (men);

Number of men = Total number of people - Number of women

Number of men = 750 - 420

Number of men = 330

Next, we find the percentage of women;

[tex] Percentage = \frac {420}{750} * 100 [/tex]

[tex] Percentage = \frac {42}{75} * 100 [/tex]

[tex] Percentage = 0.56 * 100 [/tex]

Percentage = 56%

Therefore, the percentage of the spectators that are women is 56%.

Answer:

You should expect 4 of the next 20 children to enroll to be toddlers.

Step-by-step explanation:

This question is solved by proportions.

So far:

We have that of 2 + 8 = 10 children, 2 are toddlers, so the proportion of toddlers is 2/10 = 0.2.

How many of the next 20 children to enroll should you expect to be toddlers?

0.2 out of 20, so: 0.2*20 = 4

You should expect 4 of the next 20 children to enroll to be toddlers.

Answer:

The work done is 202.50Nm

Step-by-step explanation:

Given

[tex]F =450N[/tex]

[tex]x_1 = 30cm[/tex]

[tex]x_2 = 60cm[/tex]

Required

The work done

First, we calculate the spring constant (k)

[tex]F = kx_1[/tex]

[tex]450N = k *30cm[/tex]

[tex]k = \frac{450N}{30cm}[/tex]

[tex]k =15N/cm[/tex]

So:

[tex]F = kx_1[/tex]

[tex]F(x) = 15x[/tex]

The work done using Hooke's law is:

[tex]W =\int\limits^a_b {F(x)} \, dx[/tex]

This gives:

[tex]W =\int\limits^{60}_{30} {15x} \, dx[/tex]

Rewrite as:

[tex]W =15\int\limits^{60}_{30} {x} \, dx[/tex]

Integrate

[tex]W =15 \frac{x^2}{2}|\limits^{60}_{30}[/tex]

This gives:

[tex]W =15 *\frac{60^2 - 30^2}{2}[/tex]

[tex]W =15 *\frac{2700}{2}[/tex]

[tex]W =15 *1350[/tex]

[tex]W =20250N-cm[/tex]

Convert to Nm

[tex]W =\frac{20250Nm}{100}[/tex]

[tex]W =202.50Nm[/tex]

Answer:

The answer is below

Step-by-step explanation:

The profit equation is given by:

p(t)= -25t³+625t²-2500t

The maximum profit is the maximum profit that can be gotten from selling t trailers. The maximum profit is at point p'(t) = 0. Hence:

p'(t) = -75t² + 1250t - 2500

-75t² + 1250t - 2500 = 0

t = 2.3 and t = 14.3

Therefore t = 3 trailers and t = 15 trailers

p(15) = -25(15³) + 625(15²) - 2500(15) = 18750

Therefore the company makes a maximum profit of approximately $18750 when it sells approximately 15 trailers.

Answer:

See below

Step-by-step explanation:

Since t is number of trailers, the domain includes only those values greater than 0.

On the relevant domain, the graph crosses the x-axis at the points (5,0) and (20,0). Between these points, the value of p(t) is positive. So the company makes a profit when it sells between 5 and 20 trailers.

On the positive interval between these points, the graph reaches a relative maximum when t roughly equals 14 and p(t) roughly equals $19,000.

So the maximum profit of approximately $19,000 occurs when it sells approximately 14 trailers.

Answer:

Step-by-step explanation:

Answer:

It would be the letter B :)

[tex]\sf\purple{A.\:Between \:12\:and\:13.}[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \sqrt{156} \\ = 12.4899 \\ = 12.49[/tex]

Therefore, [tex] \sqrt{156} [/tex] will fall in between 12 and 13.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

The answer is 5 units.

Step-by-step explanation:

I just counted the squares

Answer:

k>1.25

Step-by-step explanation:

The given quadratic equation is :

(k – 1)x² + x + 1 = 0

We need to find all values of k for which the above equation has two real and unequal roots.

For a quadratic equation ax²+bx+c=0, for real and unequal roots,

b²-4ac>0

Here, a = (k-1), b = 1 and c = 1

Put all the values,

1²-4×(k-1)1>0

1-4k+4>0

5-4k>0

k>1.25

S, k can take values more than 1.25. Hence, it can take values 1.5, 1.75.

Answer:

4p² - 9p

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

3p(2p - 9) - 2p(-9 + p)

Step 2: Simplify

Answer:

-25

Step-by-step explanation:

-24×(-25)=600

Hope this helps! :)

Answer: It's -25

edg 2023

Answer:

answer is no. a -1/8 for sure

220 cubic units.

Answer:

Solution given:

for small cylinder

r=1

and for large cylinder

R=5+1=6

height for both [h]=2

Now

Volume of solid=πR²h-πr²h=πh(R²-r²)

=3.14*2(6²-1²)=219.8 =220 units ³.

Small cylinder is r=1

Large cylinder is R= 5+1 =6

Height (h) =2

Volume of solid,

→ πR²h-πr²h

→ πh(R²-r²)

→ 3.14 × 2(6²-1²)

→ 219.8

→ 220 cubic units