7) The senior classes at High School A and High School B planned separate trips to
Yellowstone National Park. The senior class at High School A rented and filled 2 vans
and 7 buses with 407 students. High School B rented and filled 1 van and 7 buses with
389 students. Every van had the same number of students in it as did the buses. How
many students can a van carry? How many students can a bus carry?

Answer:

x-intercepts = (8, 0) and (-4, 0)

y- intercept = (0, 8)

vertex = (2, 9)

Step-by-step explanation:

Sorry if its wrong but I think it's where the coordinates are according to the graph. The x-int would hit at the x-axis, y-int would hit the y-axis, and the vertex would be where it's highest point is

Answer:

$27,444.80

Step-by-step explanation:

12% of 22,540 is 2,704.8

add the amount she made

add the weekly salary (550 × 4)

Answer:

x=-1

Step-by-step explanation:

Step 1- Add 9 to both sides of the equation.

New equation:

3x=-12

Step 2- divide by 3 on both sides of the equal sign to get your answer.

x=-1

Answer:

x = 1

Step-by-step explanation:

This is the answer because:

1) If x equals 1, then -3 x 1 equals -3

2) -3 - 9 = -12 (this is the answer because whenever there are two of the same signs, - and -, you have to multiply the signs, so - times - is equal to a +, therefore the equation will change into 3+9 which equals 12. Once you have 12, put the sign that the bigger number has. 9 has a minus sign in front of it which makes the +12 turn into -12)

Hope this helps! :D

FYI - the length of the mid-segment of a trapezoid is equal to half the sum of the lengths of its bases.

the equation:

18 + 6x - 12 = 2(2x + 10)

18 + 6x - 12 = 4x + 20

6 + 6x = 4x + 20

6x = 4x + 14

2x = 14

x = 7

After making the deposits, your new balance will be $12

Answer:

The coordinates of C" are (-7, 4)

Step-by-step explanation:

From the given figure

∵ ABCD is a trapezoid

∵ The coordinates of the ponit C are (4, 1)

∴ x = 4 and y = 1

∵ The trapezoid is rotated 90 degrees counterclockwise about the origin

→ By using the 1st rule above, change the sigh of y and switch them

∴ C' = (-y, x)

∴ C' = (-1, 4)

∵ The resulting image is translated 6 units left

→ By using the 2nd rule above subtract the x-coordinate by 6

∴ C" = (x - h, y)

∵ h = 6

∵ x = -1 and y = 4

∴ C" = (-1 - 6, 4)

∴ C" = (-7, 4)

∴ The coordinates of C" are (-7, 4)

y^2 - 3y + 12 is a trinomial with a degree of 2, also known as a quadratic trinomial.

The given polynomial y^2 - 3y + 12 is a trinomial with a degree of 2. A polynomial is a mathematical expression that contains one or more terms involving variables and coefficients. In this case, there are three terms: y^2, -3y, and 12. A binomial is a polynomial consisting of two terms, while a trinomial has three terms. Therefore, y^2 - 3y + 12 is a trinomial.

The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the highest exponent of y is 2, so the degree of the polynomial is 2. This degree is also known as the quadratic degree.

It is important to identify the number of terms and degree of a polynomial when solving equations or simplifying expressions involving polynomials. Additionally, the properties of polynomials, such as factoring and graphing, are also influenced by these characteristics.

In summary, y^2 - 3y + 12 is a trinomial with a degree of 2, also known as a quadratic trinomial.

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Answer:

B. The horizontal cross-sections of the prisms at the same height have the same area.

Step-by-step explanation:

Notice that the cone and the pyramid have the same volume. This is important.

This follows the Cavalieri's principle that, for the case of 3 dimensions, as the present case, it states, roughly, that if we have two bodies like the cone and the pyramid, and if we have parallel planes crossing each section, and we always have the same area, these two bodies have the same volume.

In this case, both, cone and pyramid have the same volume, then (reciprocally):

B. The horizontal cross-sections of the prisms at the same height have the same area.

Answer:

B. The horizontal cross-sections of the prisms at the same height have the same area.

Step-by-step explanation:

ap333x

Answer:

yes -2 is the correct answer

Step-by-step explanation:

7x+3=-17-3x

7x+3x=-17-3

10x=-20

x=-20/10

x=-2

Answer:

\(\boxed{\bold{\huge{\boxed{\sf Yes.}}}}\)

Step-by-step explanation:

=> \(\sf 7x+ 3 = -17-3x\)

Combining like terms

=> \(\sf 7x+ 3x = -17-3\)

=> \(\sf 10x = -20\)

Dividing both sides by 10

=> \(\sf x = -2\)

So, -2 is a solution of the given equation.

40% of Damien’s marbles are 6/5 or 1.2.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Damien has three marbles.

40% of Damien’s marbles are blue.

That means,

40% of 3 blue marbles.

So, using the percentage formula,

40% of 3,

= 40 x 3/100

= 120/100

= 12/10

= 6/5

= 1.2

Therefore, 1.2 marbles are blue.

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The answer is (a) no; y does not vary directly with x.

To determine whether y varies directly with x, we need to check if the ratio of y to x is constant. That is, if we divide any y value by its corresponding x value, we should get the same result for all pairs of values. Let's calculate these ratios for the given data:

For x = 18, y/x = 36/18 = 2

For x = 54, y/x = a/54

For x = 2, y/x = 6/2 = 3

Since the ratio of y to x is not constant, we can conclude that y does not vary directly with x. Therefore, the answer is (a) no; y does not vary directly with x.

Note that if y did vary directly with x, we would expect the ratio of y to x to be constant for all pairs of values. In that case, we could write an equation of the form y = kx, where k is the constant of variation. However, since the ratio of y to x is not constant in this case, we cannot write such an equation.

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Answer:

7/280 = 1/40 = .025 = 2.5%

Answer:

They are not similar.

Step-by-step explanation:

The angles of a triangle add up to be 180°. If they were similar, the triangle angles would have to be 60°, 40°, and 80°. Because one of the angles is 81°, the triangles cannot be similar.

81° + 40° + 60° does not equal 180.

Answer:

60 miles

Step-by-step explanation:

Distance travelled :

Answer:

2x-8

Step-by-step explanation:

Answer:

2x-8

Step-by-step explanation:

If your doing distributive property then you multiply the 2 by the x and the 8 which will give you

2x-8

Answer:

Step-by-step explanation:

Answer:

the second one

Step-by-step explanation:

05) is called alpha (α). If the probability (i.e., p-value) is less than alpha that we would obtain a sample mean this large or larger from the null population, we reject the null hypothesis and conclude that our sample was drawn from a different population with a sample mean larger than the null mean.

The correct response is option 3 i.e n = 6.

What is a Sequence?

A sequence is a list of items arranged in a stepwise order, with members coming either before or after.

We know that,

aₙ = a₁ + (n-1)×d     .............................(Arithmetic sequence formulae)

here,

aₙ = -13

a₁ = 7

d = -4

Substituting the values we get,

-13 = 7 + (n-1)×(-4)

∵ (-4)×(n-1) = -20

=> n-1 = 5

=> n = 6

Thus, the final value of n is 6.

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Answer:

To calculate how many standard deviations away from the mean an ACT score of 31 is, we need to use the formula:

z = (x - μ) / σ

Where:

x = ACT score of 31

μ = mean of ACT scores (28)

σ = standard deviation of ACT scores (2)

z = number of standard deviations away from the mean

Substituting the values, we get:

z = (31 - 28) / 2

z = 1.5

Therefore, an ACT score of 31 is 1.5 standard deviations away from the mean.

The parent function of g(x) = |x - 7| +6 is f(x) = |x|

The function is given as:

g(x) = |x - 7| +6

The above function is an absolute function, and the parent function is f(x) = |x|

Hence, the parent function of g(x) = |x - 7| +6 is f(x) = |x|

When f(x) is reflected across the x-axis, we have:

f'(x) = -|x|

When f(x) is reflected across the y-axis, we have:

f'(x) = |x|

When f(x) is stretched horizontally by a factor k

g'(x) = |kx|

When f(x) is stretched vertically by a factor k

g'(x) = k|x|

When f(x) is shifted horizontally by k units

f'(x) = |x ± k|

When f(x) is shifted vertical by k units

f'(x) = |x| ± k

See attachment for the graph of g(x)

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The value of the function (f ∘ g)' at x = 7 is approximately -0.656.

Option C is the correct answer.

We have,

To find the value of the derivative of the composite function (f ∘ g)' at

x = 7, we need to evaluate the derivative of f(g(x)) and then

substitute x = 7.

Given:

f(u) = -u

g(x) = -cos(x)

First, we find the derivative of f(g(x)):

(f ∘ g)'(x) = f'(g(x)) * g'(x)

Since f(u) = -u, the derivative of f(u) is f'(u) = -1.

The derivative of g(x) = -cos(x) is g'(x) = sin(x) (using the chain rule).

Now, we can evaluate the derivative at x = 7:

(f ∘ g)'(7) = f'(g(7)) x g'(7)

= f'(-cos(7)) x sin(7)

= -1 x sin(7)

= -sin(7)

Therefore,

The value of the function (f ∘ g)' at x = 7 is approximately -0.656.

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The complete question:

Find the value of the derivative of the composite function (f ∘ g)' at x = 7, where f(u) = -u and g(x) = -cos(x).

A) 7π

B) -7π

C)  -0.656.

D) 4π

Answer:

I belive it is the second one

Step-by-step explanation:

Answer:

B. The second box plot

Step-by-step explanation:

Answer:

The \(y\)-intercept is \(\boxed{3}\)

Step-by-step explanation:

The \(y\)-intercept of line is just the point where the \(y\)-axis and the line. From the given line, we can see that the \(y\)-axis and the line that models the temperature on a certain winter day since sunrise \((0,3)\). Also, the question just asked us for the \(y\)-coordinate of the \(y\)-intercept so \(3\)

The function f(x) = x² - 1/x + 1, with domain [0, ∞), does not have an absolute maximum on its domain, but this does not contradict the extreme value theorem.

The extreme value theorem states that if a real-valued function f is continuous on a closed interval [a, b], then f must have both an absolute maximum and an absolute minimum on that interval.

However, the theorem does not apply to functions that have an open interval as their domain, such as f(x) = x² - 1/x + 1 with a domain of [0, ∞).

In this case, f(x) approaches infinity as x approaches 0, but it does not have a maximum value within the given domain. The lack of an absolute maximum for f(x) on [0, ∞) is consistent with the behavior of the function, and it does not violate the extreme value theorem since the domain is not a closed interval.

Therefore, the function f(x) = x² - 1/x + 1, defined on [0, ∞), lacks an absolute maximum, but this does not violate the extreme value theorem.

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The probability that you do not roll doubles on the first toss, but you do on the second toss  = 13.89%.

Chance is the study of numerical representations of the probability that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, with 1 generally signifying certainty and 0 generally signifying impossibility.

The chances of rolling doubles are 6 out of 36.

The probability is equal to the number of likely outcomes divided by the total number of outcomes:

According to complement rule:

P( not A)=1−P(A)

Then we obtain:

P( not doubles) = 1 - (1/6)

                          = (5/6)

Using Multiplication rule:

P(A∩B)=P(A)×P(B)

Then we obtain:

P(Doubles on second toss) = P( not doubles)×P( doubles)

                                             = (5/6) * (1/6)

                                              = \(\frac{5}{36}\)

                                               = 13.89%

The probability that you do not roll doubles on the first toss, but you do on the second toss  = 13.89%.

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I understand that the question you are looking for is:

You are tossing a pair of fair, six-sided dice in a board game. Tosses are independent. You land in a danger zone that requires you to roll doubles (both faces showing the same number of spots) before you are allowed to play again. How long will you wait to play again? What is the probability that you do not roll doubles on the first toss, but you do on the second toss?

Answer:

65

Step-by-step explanation:

Present value of the amount she will earn while on sabbatical if the interest rate is 6% is $126,964.34

The value of money reduces as time passes, this is due to the interest factor. $1 is worth more today than tomorrow this is because of the time value of money. The present value of cash flows is discounted value of future cash flows. Discount factors at a given rate of interest are used to find out the present value of cash flows.

Here, the professor will receive $70,000 every 7 years for 42 years.

Hence he will receive $70,000 sabbatical in the 7th, 14th,21st,28th,35th, and 42nd years.

We will find the present value of such receipts and add them.

R=0.06

F=$70,000

\(Present~Value = \displaystyle\frac{FV}{(1+r)^7}+\frac{FV}{(1+r)^{14}}+\frac{FV}{(1+r)^{21}}+\frac{FV}{(1+r)^{28}}+\frac{FV}{(1+r)^{35}}+\frac{FV}{(1+r)^{42}}\)

\(Present~Value = \displaystyle\frac{70,000}{(1.06)^7}+\frac{70,000}{(1.06)^{14}}+\frac{70,000}{(1.06)^{21}}+\frac{70,000}{(1.06)^{28}}+\frac{70,000}{(1.06)^{35}}+\frac{70,000}{(1.06)^{42}}\)

=$126,964.34

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The 60th term in the arithmetic sequence when a of n = -4 + 12(n - 1) is 704.

Arithmetic progression-

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount.

Its alternate name is Arithmetic Sequence.

\(a_{n}\) = -4+12(n-1)

a₁ = -4 + 12(1 - 1)

a₁ = -4

a₂ = -4 + 12(2 - 1)

a₂ = -4 + 12(1)

a₂ = -4 + 12

a₂ = 8

common difference ,d is calculated as

d = a₂ - a₁

d = 8 - (- 4 )

d = 8 = 4

d = 12

the 60th term in the sequence is :

a₆₀ = a₁ + (60- 1)d

a₆₀ = -4 + 59 x 12

a₆₀ = -4 + 708

a₆₀ = 704.

The 60th term in the arithmetic sequence when a of n = -4 + 12(n - 1) is 704.

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Answer:100

Step-by-step explanation:

Answer:

100

Step-by-step explanation: