Suppose there are 10 five and six-year-old attending a birthday party. When a 30 year old mother walks into the room with an infant in her arms, what happens to the mean age in the room? what happens to the standard deviation of ages in the room?

A. The mean and standard deviation of both change.
B. The meaning will change, but the standard deviation will stay approximately the same.
C. I mean will stay approximately the same, but the standard deviation will change.
D. The mean and standard deviation will both stay approximately the same.

The equations are as follows where x represents the number of minutes the cell phone is used.

For plan one: Total cost = $20 + $0.15x

For plan two: Total cost = $35 + $0.10x

For both the costs to be the same, we need to use the cell phone for

300 minutes.

Equations are relations showing the value of one quantity related to another quantity when it can change. The changing value is the variable.

We are informed that one cell phone plan charges $20 per month plus $0.15 per minute used. A second cell phone plan charges $35 per month plus $0.10 per minute used.

We are asked to write and solve an equation to find the number of minutes you must talk to have the same cost for both calling plans.

Let the number of minutes the cell phone is used be x minutes.

Now we solve for equations for both plans in the following way:-

Plan one:

Charges $20 per month plus $0.15 per minute used.

When the use is for x minutes, the additional charge = $0.15*x = $0.15x

∴ Total cost = Fixed cost + Additional cost

or, Total cost = $20 + $0.15x.

Plan two:

Charges $35 per month plus $0.10 per minute used.

When the use is for x minutes, the additional charge = $0.10*x = $0.10x

∴ Total cost = Fixed cost + Additional cost

or, Total cost = $35 + $0.10x.

We are asked to find the number of minutes used so that the costs in both the plans are equal. To find this we equate the equation of total costs in both the cases to get:

$20 + $0.15x = $35 + $0.10x.

Subtracting ($20 + $0.10x) from both sides of the equation, we get

$20 + $0.15x - ($20 + $0.10x) = $35 + $0.10x - ($20 + $0.10x).

or, $20 + $0.15x - $20 - $0.10x = $35 + $0.10x - $20 - $0.10x.

or, $0.05x = $15

Dividing both sides of the equation by $0.05, we get

$0.05x/$0.05 = $10/$0.05

or, x = 300.

∴ We must talk for 300 minutes for both the plans to cost the same to us.

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The steps are shown below. From here, we can write:

[tex]\frac{x^3-2x^2-14x+3}{x+3}=x^2-5x+1+\frac{0}{x+3} \\ \\ \therefore \boxed{\frac{x^3-2x^2-14x+3}{x+3}=x^2-5x+1}[/tex]

Answer:

x^2-5x+1

Step-by-step explanation:

this is correct

bearing in mind that the hypotenuse is never negative, since it's just a distance unit, so if an angle has a sine ratio of -(5/13) the negative must be the numerator, namely -5/13.

[tex]\bf cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{then we can say that}~\hfill }{sin^{-1}\left( -\cfrac{5}{13} \right)\implies \theta }\qquad \qquad \stackrel{\textit{therefore then}~\hfill }{sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}}\impliedby \textit{let's find the \underline{adjacent}}[/tex]

[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12=a \\\\[-0.35em] ~\dotfill\\\\ cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right]\implies cos(\theta )=\cfrac{\stackrel{adjacent}{\pm 12}}{13}[/tex]

le's bear in mind that the sine is negative on both the III and IV Quadrants, so both angles are feasible for this sine and therefore, for the III Quadrant we'd have a negative cosine, and for the IV Quadrant we'd have a positive cosine.

Answer:

-3, -2, -1, 0, 1, 2

Step-by-step explanation:

Note that "integer" means whole numbers, and "consecutive" means continuously following. Also, note that you are starting with -3:

-3 , -2 , -1 , 0 , 1 , 2, is your answer, because you just need to add 1 each time until you have 6 numbers.

~

Answer:

Part 1) The vertex is the point (-83,-9)

Part 2) The focus is the point (-82.75,-9)

Part 3) The directrix is [tex]x=-83.25[/tex]

Step-by-step explanation:

step 1

Find the vertex

we know that

The equation of a horizontal parabola in the standard form is equal to

[tex](y - k)^{2}=4p(x - h)[/tex]

where

p≠ 0.

(h,k) is the vertex

(h + p, k) is the focus

x=h-p is the directrix

In this problem we have

[tex]x=y^{2} +18y-2[/tex]

Convert to standard form

[tex]x+2=y^{2} +18y[/tex]

[tex]x+2+81=y^{2} +18y+81[/tex]

[tex]x+83=(y+9)^{2}[/tex]

so

This is a horizontal parabola open to the right

(h,k) is the point (-83,-9)

so

The vertex is the point (-83,-9)

step 2

we have

[tex]x+83=(y+9)^{2}[/tex]

Find the value of p

[tex]4p=1[/tex]

[tex]p=1/4[/tex]

Find the focus

(h + p, k) is the focus

substitute

(-83+1/4,-9)

The focus is the point (-82.75,-9)

step 3

Find the directrix

The directrix of a horizontal parabola is

[tex]x=h-p[/tex]

substitute

[tex]x=-83-1/4[/tex]

[tex]x=-83.25[/tex]

Answer:

y - 2 = 2(x - 3).

Step-by-step explanation:

The point -slope form of a line is:

y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.

Here m = 2, x1 = 3 and y1 = 2. So we have the equation:

y - 2 = 2(x - 3).

Answer:

[tex]y=2x-4[/tex]

Step-by-step explanation:

Given: The line passes through (3, 2) and has a slope of  2.

To find: Point slope form of the equation.

Solution: We know that the point slope form of the line passing through [tex]\left ( x_{1},y_{1}\right )[/tex] and slope m is [tex]y-y_{1}=m\left ( x-x_{1} \right )[/tex]

Here, [tex]x_{1}=3,\ y_{1}=2, \text{and} \:\:m=2[/tex]  

So we have,

[tex]y-2=2(x-3)[/tex]

[tex]y-2=2x-6[/tex]

[tex]y=2x-4[/tex]

Hence, the point slope form of the line is [tex]y=2x-4[/tex].

For this case we must find the inverse of the following function:

[tex]g (x) = 2x + 4[/tex]

Replace g(x) with y:

[tex]y = 2x + 4[/tex]

We exchange the variables:

[tex]x = 2y + 4[/tex]

We solve for "y":

We subtract 4 on both sides of the equation:

[tex]x-4 = 2y[/tex]

We divide between 2 on both sides of the equation:

[tex]y = \frac {x} {2} -2[/tex]

We change y by [tex]g ^ {-1} (x)[/tex]:

[tex]g ^ {- 1} (x) = \frac {x} {2} -2[/tex]

Answer:

[tex]g ^ {- 1} (x) = \frac {x} {2} -2[/tex]

Answer:

[tex]f^{-1}=\frac{x}{2} -2[/tex]

Step-by-step explanation:

the inverse function of g(x) = 2x + 4

To find the inverse of a function we replace g(x) with y

[tex]y=2x+4[/tex]

Replace x with y and y with x

[tex]x=2y+4[/tex]

Solve the equation for y

Subtract 4 from both sides

[tex]x-4= 2y[/tex]

Divide both sides by 2

[tex]\frac{x}{2} -2=y[/tex]

[tex]y=\frac{x}{2} -2[/tex]

Replace y with f inverse

[tex]f^{-1}=\frac{x}{2} -2[/tex]

Answer:

the one on the bottom left

Step-by-step explanation:

Note that the cube on the bottom left is composed of

4 × 4 × 4 = 64 ← unit cubes

Thus the volume of the cube = 64 units³

The volume of a cube = s³ ← where s is the side length

Thus s³ = 64

To find s given the volume take the cube root of both sides, that is

s = [tex]\sqrt[3]{64}[/tex] = 4

Answer:

B  (the second graph)

Step-by-step explanation:

3.55g<-28.4

Divide each side by 3.55

3.55g/3.55<-28.4/3.55

g < -8

This would be an open circle at 8  (because g is less than not less than or equal to)  and it goes to the left ( since g is less than)

Answer:

C. s= 75

Step-by-step explanation:

One radian is the angle subtended by an arc length equal to the radius of the circle.

∅=s/r where s is the arc length ∅ the angle and r the radius of the circle.

Thus s=∅×r

In the circle provided arc s subtends and angle of 5 radians.

s= 5 radians× 15

=75

Answer:

4 cups of candies and 8 cups of nuts

Step-by-step explanation:

Cost per cup = $1.29

Total number of cups = 12

Total cost of cups = 12 x $1.29

                              = $15.48

Cost of candies = $2.49 per cup

Total number of candies = x

Cost of nuts = $0.69 per cup

Total number of nuts = y

Equations :

x + y = 12 (because total cups of nuts and candies will be equal to 12)

2.49x + 0.69y = 15.48 (Total cost of the 12 cups should be 15.48)

Step 1 : Find x in terms of y

x = 12 - y

Step 2 : substitute x in terms of y from step 1 in the second equation

2.49x + 0.69y = 15.48

2.49 ( 12 - y) + 0.69y = 15.48

29.88 - 2.49y + 0.69y = 15.48

-1.8y = -14.4

y = 14.4/1.8

y = 8

Step 3 : Find x

x + y = 12

x = 12 - y

x = 12- 8

x = 4

Yumi should use 4 cups of candies and 8 cups of nuts.

!!

The number of cups of candies and nuts, Yumi should use is 4 and 8 cups respectively.

Given the following data:

Translating the word problem into an algebraic expression, we have;

For total number of cups:

[tex]C + N = 12[/tex]  .....equation 1

For cost of candies and nuts:

[tex]2.49C + 0.69N = 1.29(12)\\\\2.49C + 0.69N = 15.48[/tex].....equation 2

From equation1:

[tex]C = 12 - N[/tex]   ....equation 3

Substituting eqn 3 into eqn 1, we have:

[tex]2.49(12 - N) + 0.69N = 15.48\\\\29.88 - 2.49N + 0.69N = 15.48\\\\1.8N = 29.88 - 15.48\\\\1.8N = 14.4\\\\N = \frac{14.4}{1.8}[/tex]

Number of nuts, N = 8 cups

For candies:

[tex]C = 12 - N\\\\C = 12 - 8[/tex]

Number of candies, N = 4 cups

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Answer:

maybe

[tex] y = \frac{1}{2} x + 0.5[/tex]

Answer:

x - 2y = - 1

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (3, 2) ← 2 points on the line

m = [tex]\frac{2+1}{3+3}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 2), then

2 = [tex]\frac{3}{2}[/tex] + c ⇒ c = [tex]\frac{1}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{2}[/tex] ← in slope- intercept form

Multiply all terms by 2

2y = x + 1 ( subtract 2y from both sides )

0 = x - 2y + 1 ( subtract 1 from both sides )

- 1 = x - 2y , that is

x - 2y = - 1 ← in standard form

Answer:

Catherine's sister ate 2/15 gallons of the ice cream.

[tex]\displaystyle \frac{2}{15}[/tex].

Step-by-step explanation:

Let [tex]x[/tex] be the amount of ice cream that Catherine's sister ate, in gallons.

Consider the relationship:

[tex]\text{Original amount - What Catherine ate - What Catherine's Sister ate}\\ =\text{ What's left.}[/tex].

That is:

[tex]\displaystyle 1- \frac{1}{5} - x = \frac{2}{3}[/tex].

Add [tex]x[/tex] to both sides of this equation:

[tex]\displaystyle 1 - \frac{1}{5} = \frac{2}{3} +x[/tex]

Substract [tex]\displaystyle \frac{2}{3}[/tex] from both sides:

[tex]\displaystyle 1 - \frac{1}{5} - \frac{2}{3} = x[/tex].

Convert the denominator of all three numbers on the left-hand side to [tex]3 \times 5 = 15[/tex]

[tex]\displaystyle \frac{15}{15} - \frac{3}{15} - \frac{10}{15} = x[/tex].

[tex]\displaystyle x = \frac{2}{15}[/tex].

In other words, Catherine's sister ate [tex]\displaystyle \frac{2}{15}[/tex] gallons of the ice cream.

To solve this, we need to add the 1/5 of the ice cream to the 2/3 left of ice cream to find out how much her sister ate.

First, we need a common denominator. We can multiply 3 by 5 to get a common denominator easiest, since they are both multiples of it.

3*5=15

Now multiply the numerators by the amount the denominators were multiplied by.

1*3=3 so 3/15

2*5=10 so 10/15

Now, add them together.

10/15+3/15= 13/15.

Finally, subtract that amount from the original full amount of ice cream (15/15) to get the amount her sister ate, since that is the only unknown value left.

15/15-13/15=2/15.

Because 15 isn’t divisible by 2, we can’t simplify this fraction anymore.

Her sister ate 2/15 of a gallon of ice cream.

Hope this helps!

Answer:

C

Step-by-step explanation:

Given that the triangles are congruent then corresponding sides are congruent.

YZ = BC = 12 and XZ = AC = 13, thus

cosZ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{YZ}{XZ}[/tex] = [tex]\frac{12}{13}[/tex]

The solution is, the value of cos(z) is C.) 12/13.

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

here, we have,

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

here, we have,

Given that the triangles are congruent then corresponding sides are congruent.

YZ = BC = 12

and XZ = AC = 13,

thus,

we get,

cosZ = base/hypotenuse

        =YZ/XZ  

        = 12/13

Hence, The solution is, the value of cos(z) is C.) 12/13.

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The balance in Josie's account at the beginning of year 3, with a $400 investment at 5% annual compound interest, can be calculated using the compound interest formula A = P(1 + r)^n, which results in $441.

The explicit formula to find the account's balance at the beginning of year 3 for Josie's investment with an annual compound interest rate can be determined using the compound interest formula:

A = P(1 + r)^n

Where:

In Josie's case, she invested $400 at a 5% annual interest rate for 2 years. The formula will look like this:

A = 400(1 + 0.05)^2

Now, calculate the amount:

A = 400(1 + 0.05)^2

A = 400(1.05)^2

A = 400(1.1025)

A = $441

Hence, the balance in Josie's account at the beginning of year 3 would be $441.

Answer:

13 and 14

Step-by-step explanation:

13+ (2*13) +6= 45 which is less than 50

14+ (2*14) +6= 48 which is also less than 50.

When you do the same with 15,16, and 17 the answers all come out to be  51, 54, and 57 which are all greater than 50

Answer:

13 and 14

Step-by-step explanation:

Given : [tex]x + 2x + 6 < 50[/tex]

To Find : From the set {13, 14, 15, 16, 17}, the values of x for which the inequality holds true are .

Solution:

Inequality :  [tex]x + 2x + 6 < 50[/tex]

Substitute x =  13

[tex]13 + 2(13) + 6 < 50[/tex]

[tex]45 < 50[/tex]

Substitute x = 14

[tex]14 + 2(14) + 6 < 50[/tex]

[tex]48 < 50[/tex]

Substitute x = 15

[tex]15 + 2(15) + 6 < 50[/tex]

[tex]51 > 50[/tex]

Substitute x = 16

[tex]16+ 2(16) + 6 < 50[/tex]

[tex]54 > 50[/tex]

Substitute x = 17

[tex]17+ 2(17) + 6 < 50[/tex]

[tex]57 > 50[/tex]

So,  the values of x for which the inequality holds true are 13 and 14.

Answer:

0,-9

Step-by-step explanation:

To solve [tex]x^2[/tex] + 9x = 0, we factor out the common x to get x(x + 9) = 0 and set each factor equal to zero, which gives us the solutions x = 0 and x = -9.

To solve the equation x2 + 9x = 0, we can apply factoring techniques. The first step is to factor out the common factor x from both terms in the equation. This yields:

x(x + 9) = 0

Then you have to realize that a product of two multiplicands is equal to zero if either multiplicand is equal to zero. Setting either multiplicand equal to zero and solving for x yields the solutions. Therefore, we have two multiplicands:

x = 0

x + 9 = 0, which simplifies to x = -9

The solutions to the equation are x = 0 and x = -9. As a check, we can substitute these values back into the original equation and confirm that both satisfy the equation.

Answer:

Look to the attached graph

Step-by-step explanation:

* Lets explain the difference between the graphs of f(x) and g(x)

∵ f(x) = IxI

∵ g(x) = IxI - 4

- If we add are subtract f(x) by k, where k is a constant that means

 we translate f(x) vertically

- If g(x) = f(x) + k

∴ f(x) translated vertically k units up

- If g(x) = f(x) - k

∴ f(x) translated vertically k units down

∵ g(x) = IxI - 4

∵ f(x) = IxI

∴ g(x) = f(x) - 4

∴ f(x) translated vertically 4 units down

∴ The graph of f(x) will translate down 4 units

∵ The origin point (0 , 0) lies on f(x)

∴ The origin point (0 , 0) will translate down by 4 units

∴ Its image will be point (0 , -4)

∴ Point (0 , -4) lies on the graph of g(x)

- So you can translate each point on the graph of f(x) 4 units down to

 graph g(x)

# Two point on the left part

∵ Point (-2 , 2) lies on f(x)

∴ Its image after translation 4 units down will be (-2 , -2)

∴ Point (-2 , 2) lies on g(x)

∵ Point (-7 , 7) lies on f(x)

∴ Its image after translation 4 units down will be (-7 , 3)

∴ Point (-7 , 3) lies on g(x)

# Two point on the right part

∵ Point (3 , 3) lies on f(x)

∴ Its image after translation 4 units down will be (3 , -1)

∴ Point (3 , -1) lies on g(x)

∵ Point (8 , 8) lies on f(x)

∴ Its image after translation 4 units down will be (8 , 4)

∴ Point (8 , 4) lies on g(x)

* Now you can draw the graph with these 5 points

Answer:

1.25

Step-by-step explanation:

Calculate the scale factor as the ratio of the corresponding sides of the image to the original.

here the image is 6.25 and the original is 5

scale factor = [tex]\frac{6.25}{5}[/tex] = 1.25

This represents an enlargement

-4 times -2 equals 8.

8 times -1 equals -8.

Therefore, the point on your number line that is on -8 is your answer!

Answer:

4n+2

Step-by-step explanation:

The common difference between the terms is 4 which means that the sequence is an arithmetic sequence.

The general formula for arithmetic sequence is:

[tex]a_{n}=a_{0}+(n-1)d[/tex]

where a_n is the nth term, a_0 is the first term and d is the common difference between them.

We know that

[tex]a_{0}=6\\d=4[/tex]

Putting the value in general formula:

[tex]a_{n}=6+4(n-1)\\a_{n}=6+4n-4\\a_{n}=4n+6-4\\a_{n}=4n+2\\[/tex]

So the generalized pattern is 4n+2 ..

Answer:

Third Option

Step-by-step explanation:

Given expression is:

[tex]\sqrt{\frac{55x^7y^6}{11x^11y^8}}[/tex]

Simplifying

[tex]=\sqrt{\frac{11*5*x^7*y^6}{11*x^11*y^8}}\\=\sqrt{\frac{5*x^7*y^6}{x^11*y^8}}\\Combining\ exponents\ with\ same\ base\\=\sqrt{\frac{5}{11*x^{(11-7)}*y^{(8-6)}}}\\=\sqrt{\frac{5}{x^{4}*y^{2}}}\\Applying\ radical\\=\frac{5^{\frac{1}{2}}}{x^{(4*\frac{1}{2})}*y^{(2*\frac{1}{2})}}}\\=\frac{\sqrt{5}}{x^2y}[/tex]

As 5 cannot be taken out of the square root, it will remain inside the square root.

Hence, Third option is the correct answer ..

The requried, to make the game fair, the first place prize should be worth 4n - 13 dollars. None of the options are correct.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
The second place prize is worth $8 and the third place prize is worth $5, so the total value of these two prizes is $8 + $5 = $13.

If the game is fair, then the total amount of prize money awarded should be equal to the total amount of entry fees collected. If n players enter the game, then the total entry fees collected will be 4n.

Let x be the value of the first-place prize, which we want to find. The probability of winning any of the three prizes is 1/n, so the total amount of prize money awarded is,

1/n × x + 1/n × $8 + 1/n × $5 = ($4)n
x + 8 + 5 = 4n
x = 4n - 13

Therefore, to make the game fair, the first place prize should be worth 4n - 13 dollars.

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Answer:

D) 5 7/9

Work Shown:

-52/-9 = 5 7/9 = 5.7777777778

The greater common divisor between 10 and 15 is 5, so we can factor it out:

[tex]10x^2-15x = 5(2x^2-3x)[/tex]

The greater common exponent between 1 and 2 is 1, so we can factor x out:

[tex]10x^2-15x = 5x(2x-3)[/tex]

So the x-axis represents the age of the car and the y represents the value of the car

As you can see as the x values increase the y value decreases

This means that the answer is C. As the age of the car increases the value of the car decreases

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

3

Step-by-step explanation:

Answer: 0 is the answer, the 1/7 and -1/7 cancel each other out. Leaving zero as the answer!

Answer:

Step-by-step explanation:

[tex]z-2+8=24\\\\z+(-2+8)=24\\\\z+6=24\qquad\text{subtract 6 from both sides}\\\\z+6-6=24-6\\\\z=18[/tex]

Answer:

Z = 18

Step-by-step explanation:

Z- 2 + 8 = 24

Combine like terms

Z +6 = 24

Subtract 6 from each side

Z+6-6 =24-6

Z = 18

Your answer is the first option, "One is a factor of every whole number since every number is divisible by itself".

This is true because whenever you multiply 1 by anything you always get the thing you multiplied by, which makes it a factor of every number.

You can also find this by eliminating the other options, for example a prime number is any number whose factors are 1 and itself, 2 factors, so since 1 only has 1 factor it is not prime and option 3 is eliminated.

This also eliminates option 4 because 1 cannot be a composite number if it only has 1 factor.

I hope this helps!

The true statement among the given options is that one is a factor of every whole number since every number is divisible by itself.

A prime number is that number that is only fully divisible by 1 and that number itself.

Since we know that every number is divisible by 1. Thus 1 is also a factor of every number.

Thus one is a factor of every number.

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Answer:

last choice

Step-by-step explanation:

sin(theta) is positive

tan(theta)=sin(theta)/cos(theta) is negative

If sin(theta) is positive and tan(theta) is negative, then cos(theta) is negative because +/-=-

So we are looking for the quadrant where sine is positive and cosine is negative or when x is negative and y is positive.

This is in quadrant 2 so our angle theta is between 90 and 180 degrees.