you have a gift card worth 90$ you want to buy several movies that costs 12$ each. Write and solve an inequality that represents the number of movies you can buy and still have at least 30$ on the gift card

Answer:

The value of x is [tex]\frac{7}{4}[/tex].

Step-by-step explanation:

It is given that the inverse variation equation is

[tex]xy=k[/tex]                  ..... (1)

The value of y is 4 and the value of k is 7.

Substitute y=4 and k=7 in equation (1).

[tex]x\times 4=7[/tex]

Divide both sides by 4.

[tex]\frac{x\times 4}{4}=\frac{7}{4}[/tex]

[tex]x=\frac{7}{4}[/tex]

Therefore the value of x is [tex]\frac{7}{4}[/tex].

The two function types where f(x) tends to 0 as x approaches negative infinity are the reciprocal function (y=1/x) and the root function (y=√^n x) where n is even and greater than zero.

The question asks which function types have the end behavior f(x) → 0 as x → -∞ (negative infinity). To answer this, we consider the given functions:

Of these functions, the ones that exhibit the end behavior of f(x) heading towards zero as x heads towards negative infinity are:

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Answer:

-24

Step-by-step explanation:

We are given that

[tex]b(n)=-8-2(n-1)[/tex]

We have to find the 9th term in the sequence.

Substitute n=1

Then, we get

[tex]b(1)=-8[/tex]

Substitute n=2

Then,we get

b(2)=-8-2(2-1)=-8-2=-10

n=3

b(3)=-8-2(3-1)=-8-4=-12

[tex]d_1=b(2)-b(1)=-10-(-8)=-2[/tex]

[tex]d_2=b(3)-b(2)=-12-(-10)=-2[/tex]

[tex]d_1=d_2=d=-2[/tex]

When the difference  between two consecutive terms is constant then, the sequence is called arithmetic sequence.

Therefore, the given sequence is in A.P

The nth term of A.P is given by

[tex]a_n=a+(n-1)d[/tex]

We have, [tex]a=b(1)=-8[/tex]

[tex]d=-2[/tex]

n=9

Substitute the values in the formula

[tex]a_9=-8+(9-1)(-2)=-8-16=-24[/tex]

[tex]a_9=b(9)=-24[/tex]

Answer:

[tex]P=12n+8[/tex]

Step-by-step explanation:

A square is a geometric figure that is made up of four equal and parallel sides.

The perimeter is the contour of a surface or figure.  In other words, in a figure, the perimeter is the sum of all its sides.

In this sense, since in a square all its sides are equal, the perimeter of a square is given by:

[tex]Perimeter=P=l+l+l+l=4l\\\\Where:\\\\l=Length \hspace{3}of \hspace{3}one\hspace{3} of\hspace{3} its\hspace{3} sides[/tex]

So, in this case:

[tex]l=3n+2[/tex]

Therefore the perimeter is:

[tex]P=3n+2+3n+2+3n+2+3n+2[/tex]

Adding like terms:

[tex]P=(3n+3n+3n+3n)+(2+2+2+2)=12n+8[/tex]

The probability that a randomly selected marble is either large or green is approximately 0.6333 or you can express it as a fraction: 19/30.

Consider the total number of marbles that satisfy either of these conditions.

Total large marbles: 19

Total green marbles: 5

However, the large marbles include the green marbles, so we need to subtract the overlap:

Number of large green marbles: 5

Total marbles that are either large or green = Total large marbles + Total green marbles - Number of large green marbles

Total marbles that are either large or green = 19 + 5 - 5

= 19

Now, we'll find the probability by dividing the total marbles that are either large or green by the total number of marbles:

Probability = (Total marbles that are either large or green) / (Total number of marbles)

Probability = 19 / (19 + 11)

Probability ≈ 0.6333 (rounded to four decimal places)

Therefore, the probability that a randomly selected marble is either large or green is approximately 0.6333 or you can express it as a fraction: 19/30.

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The probability that randomly selected marble from the box is large or green is 0.7667.

The probability of selecting a large or green marble from a box can be found by analysing the given information. We have 19 large marbles, out of which 5 are green. We also have 11 small marbles, out of which 6 are small and green since small marbles cannot be large. This means there are a total of 30 marbles (19 large and 11 small), and 9 of them are green. To calculate the probability that a marble is large or green, we need to include all large marbles (since they meet one condition) and add the small green marbles (since they meet the other condition, but aren't already counted with the large marbles).

The number of favorable outcomes is therefore 19 (large marbles) plus 4 (small green marbles), since 5 large marbles have already been counted as green, we don't count them again. That makes a total of 23 favorable outcomes. The probability is the number of favorable outcomes divided by the total number of marbles:

Probability = 23 / 30. As a decimal rounded to four places, this is approximately 0.7667.

Answer:

The museum is 1 block west and 3 blocks north from the hotel.

Step-by-step explanation:

First of all, Ruby goes Northeast to a coffe shop, walking 4 blocks to the east and 2 blocks to the north. Then, she goes 5 blocks to the west, and 1 block to the north.

Therefore, she walks:

-3 blocks north

-4 blocks east

-5 blocks west

As east and west are contrary, we have to substract the lower number to the higher one in order to know the difference between both directions (5 W - 4 E = 1 W). As a result, Ruby finally moved west by 1 block.

Finally, we know that the museum is 1 block west and 3 blocks north from the hotel.

Answer:

D. Multiply equation A by −3.

Step-by-step explanation:

We have been given a system of equations.

Equation A: [tex]x + z = 6[/tex]

Equation B: [tex]2x + 3z = 1[/tex]

We are asked to determine the possible step used in eliminating the z-term.

We can see that coefficient of z term is  equation B is 3, so eliminate z term from the both equations the coefficient of z term is equation A should be [tex]-3[/tex].

We can make coefficient of z term to [tex]-3[/tex] in equation A by multiplying equation A by [tex]-3[/tex] that will give us:

[tex]-3\cdot x + -3\cdot z =-3\cdot 6[/tex]

[tex]-3x-3z =-18[/tex]

Now, adding equation A and equation B the z term will get eliminated.

Therefore, option D is the correct choice.

Final answer:

To find the total number of cars sold in Chicago, we can use percentages and proportions. We can set up a proportion and solve for the unknown variable. The total number of cars sold in Chicago is 1700.

Explanation:

To solve this problem, we can use the concept of percentages and proportions. We are given that 85% of all cars sold in Chicago are some color other than black, and we also know that 300 black cars were sold. We need to find the total number of cars sold in Chicago.

First, let's find the ratio of black cars to colored cars. Since the percentage of colored cars is 85%, the percentage of black cars would be 100% - 85% = 15%. We can express this as a ratio by writing it as 15/100.

Now, let's set up a proportion:

x/300 = 85/15

Next, we can cross-multiply and solve for x:

15x = 300 * 85

x = (300 * 85) / 15

x = 1700

Therefore, the total number of cars sold in Chicago is 1700.

Answer:

Clockwise vertices of q' ( -3 ,4) →→ q( 4 , 3 ).

Counter clock wise rule : q' (-3 ,4 ) →→ q( -4 , -3 ).

Step-by-step explanation:

Given  : rectangle has vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4)

To find :  transformed according to the rule 90º , what is the location of q?

Solution : we have given that

vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4).

By the rule of 90º rotation clock wise rule : (x ,y ) →→ ( y , -x )

90º rotation counter clock wise rule : (x ,y ) →→ ( -y , x ).

Then   Clockwise vertices of q' ( -3 ,4) →→ q( 4 , 3 ).

counter clock wise rule : q' (-3 ,4 ) →→ q( -4 , -3 ).

Therefore, Clockwise vertices of q' ( -3 ,4) →→ q( 4 , 3 ).

counter clock wise rule : q' (-3 ,4 ) →→ q( -4 , -3 ).

Answer: A is the right answer. The probability of the alarm code beginning with a number greater than 7 =[tex]\frac{^2P_1\times\ ^9P_3}{^{10}P_4}[/tex].

Step-by-step explanation:

Given:A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated.  

there is only 2 numbers which are greater than 7 i.e. 8 and 9. ∴ there is 2 possibility for first place.

For the remaining 3 digits there is 9 possibilities (including 1 which would left after choosing 1 from first place )

No of ways for the alarm code beginning with a number greater than 7=[tex]^2P_1\times\ ^9P_3[/tex]

Total ways of code with 4 digits=[tex]^{10}P_4[/tex]

Therefore the probability of the alarm code beginning with a number greater than 7 =[tex]\frac{^2P_1\times\ ^9P_3}{^{10}P_4}[/tex].

Answer:

y =7x , follows the direct variation.

Step-by-step explanation:

Direct variation states that a relationship between two variables in which one is a constant multiple of the other. In other words,  when one variable changes the other changes in proportion to the first.

If y is directly proportional to x i.e, [tex]y \propto x[/tex] or

y = kx              .....[1]  where k is the constant variation

Given : y = 7x

On comparing this with equation [1] we get;

k(constant of variation) = 7

therefore,

it follows the direct variation as [tex]y \propto x[/tex]  or

y = 7x where k =7 is the constant of variation.

Therefore, y =7x follows the direct variation.

Answer:

The expresion for the phrase is:

[tex]\frac{2x}{8}[/tex]

Step-by-step explanation:

In order to get the expression for the phrase, we have to understand the described operations in it.

The phrase starts with "the quotient of...", therefore the expression must be a fraction:

[tex]\frac{A}{B}[/tex]

To get what is the numerator (A) and the denominator (B), we have to analyze carefully the rest of the phrase: "...2 times a number and 8"

In this case, the word "and" separates the numerator from the denominator:

Numerator: "2 times a number"

This unknown number is called x

Therefore, numerator of the fraction (A) is:

[tex]A = 2x[/tex]

And the Denominator: "8"

Therefore: [tex]B=8[/tex]

Finally, replacing values:

[tex]\frac{A}{B} = \frac{2x}{8}[/tex]

The way it changes the graph is  that the parabola shifts 3 units down.

Graph of a quadratic function are parabolic in nature. The parent function is given as:

f(x) = x²

If the graph of the function is changed to y= x^2 - 3, this shows that the parent function was shifted down by 3 units.

Hence we can conclude that the way it changes the graph is  that the parabola shifts 3 units down.

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The volume of the solid is found by integrating the area of circular cross-sections of the cylinder across its height affected by the plane z = y + 8. The integration from y = 0 to y = 8 and then doubling the result gives a volume of 12288π cubic units.

To find the volume of the solid bounded above by the plane z = y + 8, below by the xy-plane, and on the sides by the circular cylinder x2 + y2 = 64, we can use the method of cross-sectional areas.

The equation x2 + y2 = 64 represents a circle with radius 8 in the xy-plane. The cross-sectional area of the cylinder at any height y is a circle's area, which is πr2. Since the radius r is 8, the area A is 64π.

The solid is bounded above by the plane, which means the height of this solid at any point (x, y) on the xy-plane is z = y + 8. To find the volume, we integrate the area over the range of y values within the cylinder, which are from -8 to 8. Keeping the symmetry in mind, we can double the integral from 0 to 8 to account for the full height.

So, the volume V is calculated as:

V = 2 × ∫0864π(y+8) dy

When you integrate, you get:

V = 2 × 64π[½ y2 + 8y]08

V = 2 × 64π[32 + 64]

Finally, simplifying the expression:

V = 2 × 64π(96)

V = 12288π cubic units.

This is the volume of the solid.

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The lines through points P and Q and points R and S are not perpendicular.

To determine if the line through points P(-8, -10) and Q(-5, -12) is perpendicular to the line through points R(9, -6) and S(17, -5), we need to calculate the slopes of both lines and check if they are negative reciprocals of each other. The slope of a line (m) through two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1).

For line PQ:

mPQ = (-12 + 10) / (-5 + 8) = -2 / 3

For line RS:

mRS = (-5 + 6) / (17 - 9) = 1 / 8

Now, the product of the slopes of two perpendicular lines is -1. Let's check if the product of mPQ and mRS is -1:

mPQ * mRS = (-2 / 3) * (1 / 8) = -2 / 24 = -1 / 12

Since -1 / 12 is not equal to -1, the lines are not perpendicular. Therefore, the line through points P and Q is not perpendicular to the line through points R and S.