1a. If an escape room party

has 16 participants and 4

escape puzzles:

• How many staff are

needed?

• Write an expression to

solve how many staff

are needed.

Answer:

\(m = \frac{1}{18}\)

Step-by-step explanation:

The slope formula:  \(\frac{y2-y1}{x2-x1}\)

The two coordinates: (9,8) and (−9,7)

-

Now let's substitute:

1) \(m =\frac{7-8}{-9-9}\)

2) \(m = \frac{1}{18}\)

Answer:

y= (5/2)x+2

Step-by-step explanation:

Using the binomial distribution, it is found that there is a 0.0555 = 5.55% probability that more than 3 of these selected children have three siblings.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem, for the parameters, we consider that:

The probability that more than 3 of these selected children have three siblings is given by:

\(P(X > 3) = 1 - P(X \leq 3)\)

In which:

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)

Then:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{15,0}.(0.1)^{0}.(0.9)^{15} = 0.2059\)

\(P(X = 1) = C_{15,1}.(0.1)^{1}.(0.9)^{14} = 0.3432\)

\(P(X = 2) = C_{15,2}.(0.1)^{2}.(0.9)^{13} = 0.2669\)

\(P(X = 3) = C_{15,3}.(0.1)^{3}.(0.9)^{12} = 0.1285\)

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.2059 + 0.3432 + 0.2669 + 0.1285 = 0.9445\)

P(X > 3) = 1 - 0.9445 = 0.0555

0.0555 = 5.55% probability that more than 3 of these selected children have three siblings.

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By using the points (0, -7)and (2, 0), the graph of 7x - 2y = 14 is attached below.

A graph is a pictorial representation of a diagram that represents data or values in an organized way.

A graph consists of data whose input maps to which output. Analysis of this leads to the relations which were used to make it

We need to find two points by giving x and y values and solving the equation as;

7x - 2y = 14.

-2y = 14 - 7x

y = -7 + 7/2x

y = -7, x =0

The first point is (0, -7)

The second point is (2, 0)

Now we have to plot those two points on the graph and draw a line through them.

The graph has given in the attachment below.

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The left-hand side of the equation represents the logarithm of 64 with base x, and it is not possible to find a real value of x that satisfies the equation.

solve the equation logₓ(64) + 5 = 2, we can follow these steps:

Step 1: Move the constant term to the other side of the equation:

logₓ(64) = 2 - 5

logₓ(64) = -3

Step 2: Rewrite the equation in exponential form:

x^(-3) = 64

Step 3: Rewrite 64 as a power of x:

x^(-3) = x^6

Step 4: Set the exponents equal to each other:

-3 = 6

The equation -3 = 6 is not true, which means there is no real solution to the given equation.

Therefore, the equation logₓ(64) + 5 = 2 has no solution in the real number system.

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Answer:

23x+250 and that would equal your total cost

The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.

To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.

We are given that the area of the square is 25, so we can find the side length of the square:

Area of square = \(s^2 = 25\)

Taking the square root of both sides, we get:

s = √25 = 5

Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:

Diagonal = Diameter = s√2 = 5√2

The radius of the circle is half the diameter, so:

Radius = 5√2 / 2 = (5√2)/2

Now, we can calculate the area of the circle using the formula:

Area of circle = \(\pi r^2\)

Substituting the value of the radius, we get:

Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2

Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.

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Answer:

A population can be a group of objects or events.

A population must be the target of the survey question.

Step-by-step explanation:

I had the same question.

Answer:

386.75

Step-by-step explanation:

added in the picture

The cost of joining the gym for 6 months is 386.75.

Given,

The function G(m) = 49.5m + 89.75 represents the cost of joining the gym in addition to the one-time membership fee.

The cost, G, is measured in dollars for m months.

We need to find the value of G(6).​

Here,

The one-time membership = 89.75.

Now,

Putting m = 6 months in:

G(m) = 49.5m + 89.75

G(6) = 49.5 x 6 + 89.75

       = 297 + 89.75

       = 386.75

Thus the cost of joining the gym for 6 months is G(6) = 386.75.

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Answer:

6854 do not have a tablet

2163 have a mobile computing device

Step-by-step explanation:

You just have to read it.

Given,

Inequality : y-5>2x-10

To find,

Draw the graph.

Solution,

We have,

y-5>2x-10

First we simplify the above inequality.

Taking variables to LHS and constant to RHS.

y-2x>5-10

y-2x>-5

The points are (0,-5) and (3,1).

The attached figure shows the graph for the above equation. So, the correct graph is in option (2).

Step-by-step explanation:

If the discriminant of the Quadratic formula is > 0  it will have two 'solutions' or  'zeroes'.    If = 0   it will have one 'double root'  .   If <0 it will have only imaginary roots.

b^2 - 4ac

1)  1^2 - 4 (-3)(12)    = 145       two roots

2) (-6)^2 - 4(2)(5)   = -4          no real roots

3)  7^2 - 4(1)(-11)    =  93         two roots

4)  (-8)^2 - 4(1)(-16) =       <======what do you think?

The number of real solutions for each equation can be determined using the discriminant. If the discriminant is positive, there are two real solutions.

To determine the number of real solutions for each equation, we can use the discriminant. The discriminant is found using the formula b²-4ac.

For the equation y=-3x²+x+12, the discriminant is (-1)²-4(-3)(12) = 145. Since the discriminant is positive, there are two real solutions.

For the equation y=2x²-6x+5, the discriminant is (-6)²-4(2)(5) = 16. Since the discriminant is positive, there are two real solutions.

For the equation y=x²+7x-11, the discriminant is 7²-4(1)(-11) = 105. Since the discriminant is positive, there are two real solutions.

For the equation y=-x²-8x-16, the discriminant is (-8)²-4(-1)(-16) = 128. Since the discriminant is positive, there are two real solutions.

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Answer:

1.32x10^-3

Step-by-step explanation:

hope it helps

\((x - 9)\)

Hope it helps you

Answer:

x-1

Step-by-step explanation:

from the graph, we can easily identify the 2 roots are x=-3 and x=1

linear factors include (x+3) and (x-1)

check: w(x) = (x-1)(x+3)(x²+3x+3)

EXPLANATION:

Given;

We are given a table of x and y values in order to calculate the correlation coefficient.

Required;

We are required to calculate and populate the tables for the values;

The variables here are;

With the use of a calculator the mean and standrd deeviations are as follows;

The values that goes in the column;

For the next column;

For the last column;

Let numerator of the fraction be 'n' then denominator 'd' equals (3 + 2n)

What is a fraction?

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction is made up of a numerator shown above a line and a non-zero denominator shown below that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.

Let numerator of the fraction be 'n' then denominator equals '3 + 2n'

Then, according to problem

   \(\frac{n-5}{3+2n-5} = 922\)

\(or, \frac{n-5}{2n-2} = 922\)

\(or,n-5=922(2n-2)\)

\(or,n-5=1844n-1844\)

\(or, n-1844n=-1844+5\)

\(or,-1843n=-1839\)

\(or, n=\frac{1839}{1843}=0.997\)

\(so, d =3+2(0.997)\)

       \(=3+1.994=4.994\)

Thus, the fraction is \(\frac{0.997}{4.994}\)

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Answer:

93.6

Step-by-step explanation:

The easiest way for me to complete this was to break it up into parts. I Separated the small triangle and the big triangle. I turned them both into squares and multiplied the dimensions. I then divided those by two and added them together.

Answer: Answer is 15 hours

Step-by-step explanation:Given 6 men dig 5 holes in 25 hours

Therefore 10 men will take to dig 5 holes is

workers(1) × time(1) = workers(2)×time(2)

(This formula is used when Total work is same)

where workers(1)= 6 men

Time (1) = 25 hours

workers (2) = 10 men

We have find out Time(2)=T(2)

by applying above formula

6×25=10×T2

after simplify

T2= 15 hours

Rounding 6.78 to the nearest hundredth, we get 6.79.Therefore, the missing number in the green box is 6.79

To determine the missing number that belongs in the green box, we need to round 6.78 to the nearest hundredth.

The hundredth place is the second decimal place after the decimal point. In this case, the number in the hundredth place is 8. To round 6.78 to the nearest hundredth, we need to look at the number to the right of the hundredth place, which is 9.

According to the rounding rule, if the number in the next decimal place (in this case, the thousandth place) is 5 or greater, we round up the number in the hundredth place. If it is less than 5, we round down.

In this case, the number in the thousandth place (9) is greater than 5. Therefore, we round up the number in the hundredth place.

So, rounding 6.78 to the nearest hundredth, we get 6.79.

Therefore, the missing number in the green box is 6.79.

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Answer:

$2768.83

Step-by-step explanation:

(22+22+32+32)x 4= 432 in

(92+92+48)x 2=464 in

464+432= 898

898/12= 74.8

74.8 x 37= $2768.83

i feel this may be wrong, but this is what i got

Answer:

$295

Step-by-step explanation:

2950 · 0.10 =  295

The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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Answer:

20\(c^{6}\)

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

given

(- 4c³)(- 5c³) ← remove parenthesis

= - 4 × c³ × - 5 × c³

= - 4 × - 5 × c³ × c³

= 20 × \(c^{(3+3)}\)

= 20\(c^{6}\)

Using the scale drawing, we can see that dimensions of the room are 17 feet by 14 feet.

So the correct option is A.

We know that each inch in the scale drawing is equal to 5 feet in the real room, in this case we know that the length of the drawing is 3.4 inches, then the real length is:

L = 3.4*5 ft = 17ft

And the width in the drawing is 2.8 inches, then the real width is:

W = 2.8*5 ft = 14ft

Then the dimensions of the room are 17 feet by 14 feet.

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Answer:

-287.66

Step-by-step explanation:

9514 1404 393

Answer:

  3x^4 +x^3 +3x^2 -18x +4

Step-by-step explanation:

The multiplication is done the same way as "long multiplication" with numbers. Each partial product is placed in the column corresponding to its "place value" (the degree of the variable). The only difference from numerical multiplication is that the sums of the partial products have no carry into any column with a different "place value".

The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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