Mark and Allen were assigned the same book to read for class. Mark started reading on Saturday , and he is reading 40 pages per day. Allen didn't start until Sunday , but he is still reading 45 pages a day.

How many days will it take Allen to catch up to Mark, and how many pages will they each have read?

Let x represent the number of days Allen has been reading.

Answer:

133.33

Step-by-step explanation:

Answer:

133 1/3 or 133.33

Step-by-step explanation:

So first let's turn 15% into a decimal. For me personally, its less intimidating that way.

15%=0.15

now, let's say the number we are trying to find is x.

A trick I use for these questions is to look at the words. "Of" is used when something is multiplied. "Is" is used for equal signs. So if 20 is 0.15 of x, our formula is easy to figure out!

20=0.15x

x=133.33333...

x=133 1/3

Answer:

Step-by-step explanation:

graph b and a is negative because it does not start at point 0 and has a straight line that passes through the origin

Answer:

2 + 5p

Step-by-step explanation:

Hi there!

Let [tex]p[/tex] equal the number of points scored by the red team.

We're given:

The blue team scored two more than five times the number of points scored by the red team.

⇒ blue team points = 2 + (5 × red team points)

⇒ blue team points = 2 + 5p

I hope this helps!

Answer:

(1, - 2 )

Step-by-step explanation:

Given the equations

3x - 4y = 11 → (1)

y + 3x = 1 ( subtract 3x from both sides )

y = 1 - 3x → (2)

Substitute y = 1 - 3x into (1)

3x - 4(1 - 3x) = 11 ( distribute and simplify left side )

3x - 4 + 12x = 11

15x - 4 = 11 ( add 4 to both sides )

15x = 15 ( divide both sides by 15 )

x = 1

Substitute x = 1 into (2) for corresponding value of y

y = 1 - 3(1) = 1 - 3 = - 2

solution is (1, - 2 )

Answer:

1) 11[tex]\sqrt{3}[/tex]

2) 2[tex]\sqrt{2}[/tex]

3) [tex]20\sqrt{3} + 15\sqrt{2}[/tex]

4) [tex]53 + 12\sqrt{10}[/tex]

5) -2

6) [tex]7\sqrt{2} - 5\sqrt{3}[/tex]

Step-by-step explanation:

1) 2[tex]\sqrt{12}[/tex] + 3[tex]\sqrt{48}[/tex] - [tex]\sqrt{75}[/tex]

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

= 4[tex]\sqrt{3}[/tex] + 12[tex]\sqrt{3}[/tex] - 5[tex]\sqrt{3}[/tex]

= 11[tex]\sqrt{3}[/tex]

2) 4[tex]\sqrt{8}[/tex] -2[tex]\sqrt{98}[/tex] + [tex]\sqrt{128}[/tex]

= (4 × 2[tex]\sqrt{2}[/tex]) - (2 × 7[tex]\sqrt{2}[/tex]) + 8[tex]\sqrt{2}[/tex]

= 8[tex]\sqrt{2}[/tex] - 14[tex]\sqrt{2}[/tex] +8[tex]\sqrt{2}[/tex]

= 2[tex]\sqrt{2}[/tex]

3) 5[tex]\sqrt{12\\}[/tex] - 3[tex]\sqrt{18} + 4 \sqrt{72} +2\sqrt{75}[/tex]

= 5× [tex]2\sqrt{3}[/tex] - 3×[tex]3\sqrt{2}[/tex] + 4×[tex]6\sqrt{2}[/tex] + 2×[tex]5\sqrt{3}[/tex]

= [tex]10\sqrt{3} - 9\sqrt{2} +24\sqrt{2} +10\sqrt{3}[/tex]

= [tex]20\sqrt{3} + 15\sqrt{2}[/tex]

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

= [tex]8 + 12\sqrt{10} + 45[/tex]

= [tex]53 + 12\sqrt{10}[/tex]

5) [tex](1+\sqrt{3} ) (1-\sqrt{3} )[/tex]

= [tex]1 - 3[/tex]

= -2

6) [tex](2\sqrt{6} -1) (\sqrt{3} -\sqrt{2} )[/tex]

= [tex]2\sqrt{18}-2\sqrt{12} -\sqrt{3} +\sqrt{2}[/tex]

= 2×[tex]3\sqrt{2}[/tex] - 2×[tex]2\sqrt{3}[/tex] - [tex]\sqrt{3} + \sqrt{2}[/tex]

= [tex]6\sqrt{2} - 4\sqrt{3} -\sqrt{3} +\sqrt{2}[/tex]

= [tex]7\sqrt{2} - 5\sqrt{3}[/tex]

Hope the working out is clear and will help you. :)

Step-by-step explanation:

please I solved the question in the diagram above

[tex]\\ \bull\sf\longmapsto -9+(-4)=-9-4=-13[/tex]

[tex]\\ \bull\sf\longmapsto +3-(-5)=3+5=8[/tex]

[tex]\\ \bull\sf\longmapsto 2\times 2=4[/tex]

[tex]\\ \bull\sf\longmapsto 36+4=40[/tex]

[tex]\\ \bull\sf\longmapsto 5\times 7=35[/tex]

[tex]\\ \bull\sf\longmapsto 8(9)=72[/tex]

[tex]\\ \bull\sf\longmapsto -4+(-2)=-4-2=-6[/tex]

[tex]\\ \bull\sf\longmapsto 3-(-6)=3+6=9[/tex]

[tex]\\ \bull\sf\longmapsto -6(-3)=18[/tex]

[tex]\\ \bull\sf\longmapsto -4+(-4)=-4-4=-8[/tex]

[tex]\\ \bull\sf\longmapsto 5(7)=35[/tex]

[tex]\\ \bull\sf\longmapsto 4-(-5)=4+5=9[/tex]

[tex]\\ \bull\sf\longmapsto 4-3=1[/tex]

[tex]\\ \bull\sf\longmapsto 10+5=15[/tex]

[tex]\\ \bull\sf\longmapsto 3(8)=24[/tex]

Answer:

A

Step-by-step explanation:

Let's say we need x pounds of one-dollar-a-pound coffee . The coffee must average out to 84 cents a pound, and the formula for average is

sum of cost of coffee / number of pounds of coffee, so we have

0.84 = total cost of coffee / (x+80) . The total cost of coffee can be found to be the sum of the cost of $1 coffee and 70 cent coffee, so we have

0.84 = (cost of $1 coffee + cost of 70 cent coffee) / (x+80)

The cost of $1 coffee can be found by adding $1 for each pound of one dollar coffee, or $1 * x. Similarly, the cost of 70 cent coffee is equal to 0.70 * 80, so we have

0.84 = (1*x+0.7*80)/(x+80)

0.84 = (x+56)/(x+80)

multiply both sides by (x+80) to remove a denominator

0.84(x+80) = x+56

0.84x + 67.2 = x+56

subtract both sides by 56 and 0.84x to isolate the x and its coefficients

11.2 = 0.16 x

divide both sides by 0.16 to isolate x

11.2/0.16 = x = 70

The number of pounds of a constituent in a mixture given the cost of the

mixture and the cost and mass of the other constituent can be calculated

by using an equation to model the system

The correct option for the number of pounds of one-dollar- pound coffee needed is option A

(A) 70 pounds

The procedure for arriving at the correct option is as follows:

The given parameters are;

The cost of the the coffee for which the mass in the mixture is to be determined = One-Dollar a pound = 100 ¢ a pound

The mass of the coffee 70¢ a pound coffee to be mixed = 80 pounds

The cost per pound of the mixture = 84 ¢ a pound

The required parameter;

The number of pounds of the one-dollar-a-pound (100 ¢ a pound) coffee in the mixture

Method:

Let x (pound) represent the number of pounds of the one-dollar-a-pound coffee in the mixture, we have;

Mass of mixture = Mass of the one-dollar-a-pound in the mixture, x + Mass of 70 ¢ a pound in the mixture, 80

∴ Mass of mixture in pounds = x + 80

Cost = Cost per pound × Number of pound

Find solution by applying the equation;

Cost of the constituents = Cost of the mixture

Where;

Cost of the constituents = $1 × x + 70 ¢ × 80 = 100 ¢ × x  + 70 ¢ × 80

Cost of the mixture = 84 ¢ × (x + 80)

Therefore;

100 ¢ × x  + 70 ¢ × 80 = 84 ¢ × (x + 80)

The above can be expressed as 100·x + 70×80 = 84 × (x + 80)

Expanding, evaluating and collecting like terms gives;

100·x + 5,600 = 84·x + 6,720

100·x - 84·x = 6,720 - 5,600 = 1,120

16·x = 1,120

x = 1,120/16 = 70

The number of pounds of one-dollar- pound coffee needed, x = 70 pounds

Learn more about equation modelling here;

https://brainly.com/question/14102741

Answer:

-12 =x

Step-by-step explanation:

5 [(x/6)-2] = 2x + 4

Distribute

5/6x - 10 = 2x+4

Subtract 5/6x from each side

5/6x -10 -5/6x = 2x -5/6x +4

-10 =2x -5/6x +4

Subtract 4 from each side

-10-4 = 2x - 5/6x

Get a common denominator for the right side

-14 = 12/6x - 5/6x

-14 = 7/6x

Multiply each side by 6/7

-14 * 6/7 = 7/6 x * 6/7

-12 =x

Answer:

x = -12

Step-by-step explanation

Answer:

5m^2-2m

Step-by-step explanation:

2m^2-2m + 3m^2

5m^2-2m

Answer:

5m² - 2m

Step-by-step explanation:

Given

2m² - 2m + 3m² ← collect like terms

= (2m² + 3m²) - 2m

= 5m² - 2m

Answer:

B

Step-by-step explanation:

this is just common sense. if you would have tried you could have easily answered this yourself.

the sequence starts with 6. that is a1.

so, the formula simply has to add "something" to 6.

therefore, A and D are out.

and then we see immediately that the sequence is built by subtracting 4 (or adding -4) for every step.

so, we need to add multiples of -4.

therefore, only B is correct (C adds multiples of +4).

Answer:

Step-by-step explanation:

Find the equation of the graphed line.

Use 2 points, (0, -6) and (2, 4)

The equation is:

Compare with the given line y = 4x + 2

Correct answer choice is c

Answer:

0.16666...

6/36

2/12

3/18

4/24

5/30

There's a lot of things.

Answer:

C. 36π units²

Step-by-step explanation:

Surface area of a sphere: 4πr²

[tex]4\pi r^2\\4\pi (3)^2\\4\pi (9)\\36\pi[/tex]

Answer:

Sample

Step-by-step explanation:

A sample refers to a small subset of a particular population of study. The sample must be chos n at random in other to ensure that it is representative of the entire population. In the scenario above, all males in the United States aged 18 - 25 years form the population of interest required for the study. However, due to the fact that it is impractical to include all in the study, then a smaller subset is selected form the population, which is referred to as the sample.

[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Volume \: of \: Cone \: = \: \pi \: {r}^{2} \: \frac{h}{3} }}}}}\end{gathered}[/tex]

‌ ⇛76/2 = 38

‌ ⇛radius = 38 cm

[tex]\bf \Large \longrightarrow \:π \: × \: (38 \: cm)² \: × \: \frac{90 }{3} [/tex]

[tex]\bf \Large \longrightarrow \: \pi \: \times \: \:1444 \: {cm}^{2} \: \times \: \cancel\frac{90}{3} \: \: ^{30 \: cm} [/tex]

Option ( B ) is the correct answer

Answer:

-15

Step-by-step explanation:

df(x, y) / dy = lim (f(x, y+h) - f(x, y)) / h =

lim (e^x^2 - 15y - 15h - e^x^2 ‐ 15y) / h = lim -15h / h = -15

so, the first derivative of f(x,y) by y is simply a constant : -15

fy (x, y) = -15 for any and every values of x and y.

the fast track would be derivative calculation :

the derivative by y makes x a constant. and every constant is eliminated for derivation.

so, e^x^2 goes away (= 0 in the derivative).

that leaves -15y = -15×y¹. its derivative simply is

1×-15×y⁰ = -15

Answer:

65

Step-by-step explanation:

because

Answer:

1st coin:  the probability for it to be a nickel is 6/29.

the 2nd coin, the probability for it to be a dime is 8/28.

total probability is 6/29 * 8/28 = 14/203.

Answer:

it's off topic but which grade are you in

Answer:

17.00 and 17,000.00

this is your answer to ur question

Answer:

Irrational

Step-by-step explanation:

If we evaluate the square root, we realize that the number will not be a perfect square.

Since it is not a perfect square, it will be an unending, never-repeating, decimal.

Therefore, it will be irrational.

Answer:

Weak negative correlation

Answer:

See attached image for the sum computed using wolfram alpha, raw value is: 49382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382715160

Answer:

Step-by-step explanation:

First, i divide all terms by 4

sequence is 1,11,111,1111,....,1111...1111 (with 2000 digits)

[tex]u_1=1\\\\u_2=11=10+1=\dfrac{10^2-1}{9}\\\\u_3=111=100+10+1=\dfrac{10^3-1}{9}\\\\u_4=1111=1000+100+10+1=\dfrac{10^4-1}{9}\\....\\u_n=\dfrac{10^n-1}{9}\\\\\\\displaystyle \sum_{i=1}^n\ u_1 =\dfrac{10^1-1}{9}+\dfrac{10^2-1}{9}+\dfrac{10^3-1}{9}+...+\dfrac{10^n-1}{9}\\=\dfrac{1}{9} *(10+10^2+10^3+....+10^n+1-1-(1+1+1+1...+1)\ )\\\\=\dfrac{1}{9}*( \frac{10^{n+1}-1}{9} -(n+1)\ )[/tex]

[tex]\boxed{4+44+444+....+444...4=\dfrac{4}{9}*( \dfrac{10^{2001}-1}{9} -2001\ )}\\\\\\\approx{4,9382716049382716049382716049383*10^{1999} }[/tex]

Answer:

The two functions have the same initial value

Hi there!  

»»————-　★　————-««

I believe your answer is:  

D) 8

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'b'...}}\\\\\sqrt[3]{b} =2\\--------------\\\rightarrow ( \sqrt[3]{b} )^3= 2^3\\\\\boxed{b = 8}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

390 degrees

Step-by-step explanation:

The conversion factor is 180/pi

13 pi /6 * 180/pi

13/6 *180

390

Answer:

0.28

Step-by-step explanation:

Answer:

sqrt(2)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 45 = x/2

2 sin 45 =x

2 (sqrt(2)/2) =x

sqrt(2) =x