Pete and his sister, Sophie, play the game Space Mission Commander on their video game
console. Pete has already completed 27 missions. Sophie has only completed 13 missions.
From now on, Pete plans to complete 3 missions per week. Meanwhile, Sophie plans to
complete 5 missions per week.
At some point, Sophie will catch up to Pete. How many weeks will it take? How many
missions each will Pete and Sophie have completed?

4/7

Step-by-step explanation:

[tex] \hookrightarrow \sf \frac{200}{350} [/tex]

[tex]\hookrightarrow \sf \: \frac{ \sout{200}}{ \sout{350}} = \frac{\sout{100}}{\sout{175}} = \frac{4}{7} [/tex]

Therefore, [tex] \rm \frac{200}{350} [/tex] = [tex] \sf \frac{4}{7} [/tex]

Step-by-step explanation:

1) The area of rectangle is ( 30x²y + 20xy ) cm² and its breadth is 10xy cm .Find its length....

= Solution ,

Length ( L ) = ?

breadth ( b ) = 10xy cm

area ( a ) = ( 30x² + 20xy )

Now ,

area ( a ) = l × b

or, ( 30x²y + 20xy ) = L × 10xy cm

[tex]or,\frac{30 {xy + 20xy}^{2} }{10xy} = l \\ [/tex]

[tex]or, \: l = 3 {x}^{2 - 1} + 2cm[/tex]

[tex]\boxed{\sf{l = (3x+2)cm}}[/tex]

2) Subtract the quotient when 20x⁴y² is divided by 5x³y from the product of 2x and 3y.

= Solution,

[tex] = \frac{20 {x}^{4} {y}^{2} }{5 {x}^{3} y} \\ [/tex]

[tex] = 4xy[/tex]

The product of 3x and 4y = 6xy

= 6x - 4xy

[tex] = \boxed{\sf {2xy}}[/tex]

hope it helped !!!!

Answer:

A

Step-by-step explanation:

because that's the answer

The correct graph that includes a function, its inverse, and a dashed line that verifies the relationship is shown in option 1.

Used the concept of function that states,

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.

Ask about the function, its inverse, and a dashed line that verifies the relationship.

Now from the first graph;

The dashed line is y = x.

And the graph shows the functions and their inverse as both graphs are opposite to each other.

Therefore, option 1 is true.

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Answer:

c = sqroot45

Put a 45 in the box under the square root.

Step-by-step explanation:

Use Pythagorean Theorem. See image.

Also, sqroot45 can be simplified. It 3root5, just in case they ask that next.

Answer:

c=√45

Step-by-step explanation:

I'm assuming this question is before Pythagorean theorem so.

Big square area:

[tex](3 + 6) \times (3 + 6) = 81[/tex]

All four right-angled triangles area:

[tex]4( \frac{1}{2} \times 3 \times 6) = 36[/tex]

Smaller square area:

[tex]81 - 36 = 45[/tex]

Value of c:

[tex] {c}^{2} = 45 \\ c = \sqrt{45} [/tex]

Answer:

Step-by-step explanation:

Answer:

2,012 is greater than 30

Step-by-step explanation:

The correct solution for the inequality is k > -9.

Given is an inequality -2k + 12 < 30, we need to solve for k,

To solve the inequality -2k + 12 < 30 for k, follow these steps:

Subtract 12 from both sides of the inequality to isolate the term with 'k':

-2k + 12 - 12 < 30 - 12

-2k < 18

Divide both sides by -2, but remember that when you divide an inequality by a negative number, the direction of the inequality sign flips:

(-2k)/(-2) > 18/(-2)

k > -9

So, the correct solution for the inequality is k > -9.

Among the options you provided, the correct answer is: k > -9.

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Answer:

500(-1/5)^(n-1)

Step-by-step explanation:

Each term after the first is obtained by multiplying by -1/5.

This is a geometric series.

The nth term = a1 r^n-1)

= 500(-1/5)^(n-1)

The number of years the amount has been in the venture account with 12% interest per year is 4.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

A sum of $2,500 was deposited in a venture account, which pays 12% compounded per year and it accumulated to $3,950.

Then the number of the years will be

We know the compound interest formula

[tex]\rm A = P(1+r)^t[/tex]

where

A = Accumulated amount

P = Deposited value

r = rate of interest

t = time

Then we have

[tex]3950 = 2500 (1.12)^t\\\\1.58\ =1.12^t[/tex]

Taking log both sides, then we have

[tex]\rm \ln 1.58 = t \times \ln 1.12\\\\or \ \ \ \ t = 4.036 \approx 4 \ years[/tex]

Then the number of the years is 4.

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Answer:

-2

Step-by-step explanation:

The slope of the function can also be described as its gradient.

To find the gradient of the function you can use:

[tex] \frac{change \: in \: y}{change \: in \: x} [/tex]

This gives us

[tex] \frac{ (- 10) - 10}{8 - ( - 2)} [/tex]

Which equals -2

Just remember that 100% = 1.00 !

y = .78x

y = 108.5x

y = .946x

Answer:

EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answer:

The area enclosed by the given curves is  square units.

Step-by-step explanation:

The given equations are

Draw the graph of the given equations.

From the below graph it is clear that both curves intersect each other at (2,12) and (4,24).

The area of the region enclosed by curves is

Therefore the area enclosed by the given curves is square units.

The spinner game is an illustration of probability, and the spinner game that is fair is (b) If you spin a number greater than 10, you win.

The number of sections in the spinner is given as:

n = 20

There are 10 numbers greater than 10 i.e. 11 to 2.

So, the probability that a number greater than 10 is spun is:

P = 10/20

P = 0.5

The probability that a number that is not greater than 10 is spun is calculated using the following complement rule

q = 1 - p

This gives

q = 1 - 0.5

Evaluate

q = 0.5

Notice that both probabilities are the equal

Hence, the spinner game that is fair is (b) If you spin a number greater than 10, you win.

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Answer:

A, C and D are true statements.

Step-by-step explanation:

Megan constructed triangle ABC.

In Megan’s triangle, m∠A is represented by x°.

Therefore, ∠A = x°

For m∠B is 4 times greater than m∠A

Therefore, ∠B = 4x°

For m∠C is 30° less than 5 times m∠A.

Therefore, ∠C = 5x°-30°

ABC is a triangle.

Sum of all angles of a triangle is 180°. Angle sum property of triangle.

m∠A + m∠B + m∠C = 180°

x° + 4x° + 5x°-30° = 180°

x° = 15°

True Statements are:

A) m∠A = x°

C) m∠B = (4x)°

D) m∠C = (5x – 30)°

Answer:

[tex]55.555...\ (\%)[/tex]

Step-by-step explanation:

What percent of values is between the first and third quartiles

[tex]\text{Quartile 1} =\frac{75+100}{2} =87.5[/tex]

[tex]\text{Quartile 2} =\frac{200+225}{2} =212.5[/tex]

50 < 75 < 87.5 < 100 < 125 < 150 < 175 < 200 < 212.5 < 225 < 250

Then we have 5 values between the first and third quartiles which are :

100, 125, 150, 175, 200

Therefore,

The percent of values between the first and third quartiles is :

[tex]\frac{5}{9} \times 100=55.555...[/tex]

Answer:

Answer is [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

To find the interval of x. Use our equations to equal each other.

[tex]-x^2+2x=y,y=0[/tex]

[tex]-x^2+2x=0\\-x(x-2)=0\\-x=0 , (x-2)=0\\x=0 ,2[/tex]

[tex]\int\limits^2_0 {-x^2+2x} \, dx[/tex]

Integrate.

[tex]\frac{-x^3}{3}+x^2\\(\frac{-2^3}{3}+2^2)-[\frac{-0^3}{3}+0^2]\\-\frac{8}{3} +4-0\\-\frac{8}{3}+\frac{12}{3} =4/3[/tex]

Using Desmos I have Graphs of both of the equations you have provided. The problem asks us to find the shaded region between those curves/equations.

Proof Check your interval of x.

Answer:

$0.68

Step-by-step explanation:

you have to do:

9.95 x .068

or

9.95 x 6.8 ÷ 100

and you would get 0.6766 but rounded to the nearest hundredth would be $0.68

The elements that are in A and B in the Venn diagram that represents the pizza topping preferences are (Maria, Zack, Bo).

A venn diagram represents information in a set using circles. The intersection of both circles represents those that like both pepperoni and olives. This is element A and B.

The names at the intersection of both circles are (Maria, Zack, Bo).

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Step-by-step explanation:

To get the perimeter, add up all of the sides.

So, the playground is a rectangle.

It has two sides measuring 58m, and two measuring 91m.

58+58+91+91=298

For the area, length x width

58x90=5278

Answer:

x = 1

Step-by-step explanation:

Question: 4x - 4 = 8

•shifting the -4 to the right side:

⇒4x = 8 - 4

⇒4x = 4

•shifting the 4 to the right side:

⇒x = 4/4

•by cross cancellation we get:

⇒x = 1 Answer...

hope that helps...

69.12ft

11x2 = 22

C= pi x d

= pi x 22

= 22pi

Or

69.11503838

Hope this helps!

Answer:

25. -7/5 [tex]\leq[/tex] x [tex]\leq[/tex] 1

Step-by-step explanation:

18:

[tex]5-|x|\leq 2\\-|x| \leq -3\\|x|\leq 3\\x\geq -3[/tex]or       [tex]x\leq 3[/tex]

25:

[tex]3|5x+1|-6\geq 12\\3|5x+1|\geq 18\\|5x+1|\geq 6\\x\leq -7/5[/tex]or               [tex]x\geq 1[/tex]

[tex]-7/5\leq x\leq 1[/tex]

I don't think I explained this well let me know if you need more explanation.

Answer:

$30.21

Step-by-step explanation:

A z-table is also known as the standard normal distribution table. The percentage of the population that would fall in the 10 to 22 mm Hg range is 0.9386.

A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.

Given the mean and the standard deviation are 16mmHg and 3.2 mmHg, therefore, the percentage of the population whose blood pressure will fall in the range of 10 to 22 mm Hg are,

[tex]P(10 < x < 22) = P(\dfrac{10-16}{3.2} < Z < \dfrac{22-16}{3.2})[/tex]

[tex]= P(-1.875 < Z < 1.875)\\\\=P(Z < 1.875)-P(Z < -1.875)\\\\= 0.9693-0.0307\\\\= 0.9386[/tex]

Hence, the percentage of the population that would fall in the 10 to 22 mm Hg range is 0.9386.

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Answer:

Part 1: (n÷2)-7 = -12

Part 2: n = -10

Step-by-step explanation:

Part 1:

Let's first write "the quotient of a number and 2" using numbers and variables. Let "n" represent "a number". The key word that we see here is quotient, meaning we have to divide something by something else. "The quotient of a number and 2 means that "a number" is the dividend (number that is divided) and "2" is the divisor (number that divides the dividend). Therefore we obtain:

n÷2

The first part says "seven less than the quotient of a number and 2". The keyword here is less, meaning we have to use subtraction. Therefore:

(n÷2)-7

The last part says "is equal to -12". Therefore the whole expression we just wrote is equivalent to -12:

(n÷2)-7 = -12

Part 2

Remember the Order of Operations:

Parentheses

Exponents

M/D: Multiplication/Division (whichever comes first in the equation)

A/S: Addition/Subtraction (whichever comes first in the equation)

Start by adding 7 to both sides

(n÷2) = -5

Then, multiply both sides by 2

[tex]\frac{n}{2}=-5\\n=-10[/tex]

Note: I used a fraction to display the division because it is easier to see why we have to multiply both sides by 2; to cancel out the denominator.

Using it's concept, it is found that the prevalence of frequent multivitamin use is of 0.4523 = 45.23%.

The prevalence of a sample is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 588 out of 1300 women reported taking a multivitamin at least 4 times a week during the month before pregnant, hence the prevalence is given by:

p = 588/1300 = 0.4523 = 45.23%.

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Answer:

1/2=2/4

Step-by-step explanation:

1/4=4/8 - no, if you multiply 1/4 x 4 to get numerator match = 4/32

1/2=2/4 - YES , 1/2 x 2  = 2/4

3/5=5/10 = no if you multiply 3/5 x 2 to get denominator match = 6/10

2/3=3/6 = no if you multiply 2/3 x 2 to get denominator match = 4/6

Answer:

cos B = 9/41

tan B = 40/9

sin B = 40/41

Step-by-step explanation:

There is no picture, so I am making a few assumptions.

I am assuming that angle C is the right angle and is opposite 41.

I am also assuming that angle B is formed by the sides that measure 9 and 41. The hypotenuse is 41.

For angle B, the adjacent leg is 9, and the opposite leg is 40.

cos B = adj/hyp = 9/41

tan B = opp/adj = 40/9

sin B = opp/hyp = 40/41