Evaluate the expression for the given values. If x=−5 and y=29​, find y−x2.

The Results:

a) Cost of the bouncy castle for 20 children = £149

b) Number of children who went to the party = 14.

a) To find the cost of the bouncy castle for 20 children, we can substitute the number of children, which is 20, into the formula provided:

Cost = £3.65 * number of children + £76

Cost = £3.65 * 20 + £76

Now we can estimate the cost:

Cost = £73 + £76

Cost = £149

Thus, the cost of the bouncy castle for 20 children = £149.

b) To find the number of children who went to the party based on the given cost of £127.10, we can rearrange the formula to solve for the number of children:

Cost = £3.65 * number of children + £76

£127.10 = £3.65 * number of children + £76

Subtracting £76 from both sides of the equation:

£127.10 - £76 = £3.65 * number of children

£51.10 = £3.65 * number of children

Now we can divide both sides of the equation by £3.65 to isolate the variable:

£51.10 / £3.65 = number of children

14 = number of children

Therefore, the number of children who went to the party = 14.

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The image coordinates of M′ are M′(0, 3).

What is translation?

A translation is a geometric transformation when each point in a figure, shape, or space is moved in a specific direction by the same amount. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Here, we have

Given: Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1).

When the shape is moved up by k units, then replace y with y + k.

The translation is as follows:

Here, J(-2, -5) → (-2, -5+4) → J'(-2, -1)

K(-4, 0) → (-4, 0+4) → K'(-4, 4)

L(-1, 2) → (-1, 2+4) → (-1, 6)

M(0, -1) → (0, -1+4) → (0, 3)

Hence, the image coordinates of M′ are M′(0, 3).

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Answer:

C

Step-by-step explanation:

if we have a number line that has fractions listed, it should be C, because if 6/2 makes 3, which would be D, 5/2 should be C.

The payment due is given as Rs 875.94

Interest rate Rs 730.50

The principal is Rs 145.44

The balance is Rs 145954.56

Given:

P = principal, the initial amount of the loan

I = the annual interest rate (from 1 to 100 percent)

L = length, the length (in years) of the loan, or at least the length over which the loan is amortized.

J = monthly interest in decimal form = I / (12 x 100)

N = number of months over which loan is amortized = L x 12

Okay now for the big monthly payment (M) formula, it is:

                             J

        M  =  P  x ------------------------

                     1  - ( 1 + J ) ^ -N

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The statement "color cannot work to bring together parts of a painting" is false. OB. False

what is proportionality ?

The interaction of two variables that changes as a single ratio or proportion is referred to as proportionality.

The use of a cohesive color palette can help to create a sense of unity throughout the painting, tying together disparate elements and creating a harmonious whole. Color can also be used to create visual connections between different parts of the painting, leading the viewer's eye from one area to another and creating a sense of flow and movement within the composition.

So, the statement "color cannot work to bring together parts of a painting" is false.

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The rate at which the infected population is growing after 8 days of the outbreak is approximately 1096.57 people per day, as determined by the derivative of the given function with respect to time.

To find the rate at which the infected population is growing after 8 days, we need to take the derivative of the given function I(t) with respect to t:

[tex]dI/dt = 3900(0.0514)e^(0.0514t)[/tex]

At t=8, the rate at which the infected population is growing is:

[tex]dI/dt = 3900(0.0514)e^(0.0514*8) = 1096.57[/tex]

Therefore, the rate at which the infected population is growing after 8 days is approximately 1096.57 people per day.

It is important to note that this rate of growth is an instantaneous rate at t=8, and it will likely change as time passes and the outbreak progresses. Furthermore, the rate of growth of the infected population depends on various factors such as the transmission rate of the virus, the effectiveness of preventive measures, and the availability of healthcare resources.

In conclusion, the rate at which the infected population is growing after 8 days of the outbreak is approximately 1096.57 people per day, as determined by the derivative of the given function with respect to time. This result provides insight into the early stages of a flu outbreak, but further analysis is required to understand the longer-term dynamics of the outbreak and the factors that affect the spread of the disease.

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To cover the full football pitch, you will want 10 bags of fertiliser, rounded up to the nearest whole number.

The term "area" refers to the volume of space occupied by a two-dimensional (2D) form or surface.

It's represented by squares.

You must multiply the length by the breadth of the football pitch to determine its total area:

field size for football = length x width

field size for football = 360 feet x 160 feet

field size for football = 57,600 square feet

You must now calculate how many thousands of square feet the football pitch has in order to get the total amount of fertiliser required:

the size of a football pitch in square feet = the size of the football pitch overall / 1,000

the size of a football pitch in square feet = 57,600 / 1,000

the size of a football pitch in square feet = 57.6

You must spread 8 pounds of fertiliser per 1,000 square feet of the football pitch because it is 57.6 thousand square feet in size.

Total required fertiliser quantity = 8 pounds per 1,000 square feet x 57.6 thousand square feet

Total required fertiliser quantity = 460.8 pounds

Given that the fertiliser is sold in 50-pound bags, you will require:

number of fertiliser bags = Total amount of fertilizer needed / Weight of each bag

number of fertiliser bags = 460.8 pounds / 50 pounds/bag

number of fertiliser bags = 9.216 bags

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Answer:

x = 19.6

Step-by-step explanation:

The sum of the angles of a triangle is 180.

<A + <B+ < C = 180

x + 5x + 4x - 16 = 180

Combine like terms.

10x-16=180

Add 16 to each side.

10x-16+16 = 180+16

10x = 196

Divide each side by 10.

10x/10 = 196/10

x = 19.6

Answer :

Step-by-step explanation :

According to the question It is given that,

We will apply angle sum property in the question.

Angle sum property states that sum of all the angles of triangle is 180°

[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180

[tex]\: :\implies [/tex] x + 5x + 4x - 16 = 180

[tex]\: :\implies [/tex] 10x - 16 = 180

[tex]\: :\implies [/tex] 10x = 180 + 16

[tex]\: :\implies [/tex] 10x = 196

[tex]\: :\implies [/tex] x = 196/10

[tex]\: :\implies [/tex] x = 19.6

Therefore, The Measure of Angle A is 19.6°

HI THIS IS DREAM AND TO

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The surface area of the triangular prism is 511 in²

An exponential equation is an expression that shows how numbers and variables using mathematical operators.

The surface area of the prism is gotten by summing the individual area of each surface of the prism.

The surface area = (0.5 * 11 in * 7 in) + (0.5 * 11 in * 7 in) + (11 in * 14 in) + (9 in * 14 in) + (8 in * 14 in) = 511 in²

The surface area is 511 in²

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An equation of the regression line is y = 5.98 + 0.39x.

The data has a pattern that is not a straight line.

In this scenario, the x-values (x) would be plotted on the x-axis of the scatter plot while the y-values (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the x-values (x) and y-values (y), the linear regression equation and the correlation coefficient are given by:

y = 5.98 + 0.39x

Correlation coefficient, r = 0.6021345002 ≈ 0.60

In conclusion, we can logically deduce that there is a moderate correlation between the data because the correlation coefficient (r) is is greater than 0.4 but less than 0.7;

0.4＜|r| ≤ 0.7   (strong correlation)

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The right answers  outoff these options are: 3,5,6,8

Length is a measure of the size or distance of an object or space in one dimension, usually referring to the longest dimension of an object. It is typically measured in units such as inches, meters, or feet.

In geometry, a triangle is a closed two-dimensional shape that is formed by connecting three non-collinear points with straight line segments. The line segments are called sides, and the points where they meet are called vertices. A triangle has three angles, which are formed by the intersection of its sides.

To determine the possible length of the third side of a triangle, we need to apply the triangle inequality theorem which states that the sum of the lengths of any two sides is always greater than the third side.

Using this theorem, we can see that the possible lengths for the third side are:

- 3 inches

- 5 inches

- 6 inches

- 8 inches

Therefore, the correct answers are:

3,5,6,8.

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Answer: 12 inches

Step-by-step explanation:

If the dilation is uniform, both height and width will be multiplied by 4.

So the new height = (1 in) × 4 = 4 in

and the new width = (3 in) × 4 = 12 in

Hope it helps!

The function N for d days of both rumors are N(d) = 2 + 5d and N(d) = 2(3)^d

Here, the number of students are the students that start the rumor i.e. Susanna and Liz

So, we have

For the Justin Beiber rumor, the rumor spreads at a linear rate of 5 per day

So, we have

JB day 2 = 2 + 5(2) = 7

For the Rihanna rumor, the rumor spreads at an exponential rate of 3

So, we have

Rihanna day 2 = 2 * (3)^2 = 18

Using the functions, we have

JB

2 + 5x = 32 students

5x = 30

x = 6 days

Rihanna

2(3)^x = 162 students

3^x = 81

x = ln(81)/ln(3)

x = 4 days

JB

N(d) = 2 + 5d

Rihanna

N(d) = 2(3)^d

So, we have

d          JB          Rihanna

0           2           2

1           7           6

2          12           18

3           17           54

4           22           162

5           27           486          

6           32           1458

7           37           4374

8           42           13122

9           47           39366

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Answer:

There are 18 total pieces of vegetables, so there are 18 possible choices for the first piece, 17 possible choices for the second piece, 16 possible choices for the third piece, and so on, until there is only 1 possible choice for the last piece. Therefore, the total number of different orders we could eat all the vegetables is:

18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

which simplifies to:

18! / 0! = 6,402,373,705,728

Therefore, there are 6,402,373,705,728 different orders in which we could eat all the vegetables.

Answer:

There are 6,402,373,705,728 different orders in which we could eat all the vegetables.

Step-by-step explanation:

To find the total number of different orders in which we could eat all the vegetables, we can use the formula for permutations of n objects:

[tex]\sf\qquad\dashrightarrow P(n) = n![/tex]

where:

In this case, we have a total of 18 vegetables (6 carrot sticks + 4 celery sticks + 5 tomatoes + 3 pieces of cauliflower). So we can calculate the permutation of 18 objects:

[tex]\begin{aligned}\sf:\implies P(18)& =\sf 18! \\&=\sf 18 \times 17 \times 16 \times ... \times 3 \times 2 \times 1 \\ &= \boxed{\bold{\:\:6,402,373,705,728\:\:}}\:\:\:\green{\checkmark}\end{aligned}[/tex]

Therefore, there are 6,402,373,705,728 different orders in which we could eat all the vegetables.

We have 24 possible permutations because there are four choices for the first place, three choices for the second place (as two people have already won first and second place), and two choices for the third place (as three people have already won first, second, and third place).

For the 100 m race with Mark Chase and Beatrice, the sample space of all the possible ways in which the three runners can win first, second, and third place is:

{M-C-B, M-B-C, C-M-B, C-B-M, B-M-C, B-C-M}

where M stands for Mark, C stands for Chase, and B stands for Beatrice. We have six possible permutations because there are three choices for the first place, two choices for the second place (as one person has already won first place), and one choice left for the third place.

If there were four runners and three positions to be won, the sample space would be:

{A-B-C-D, A-B-D-C, A-C-B-D, A-C-D-B, A-D-B-C, A-D-C-B, B-A-C-D, B-A-D-C, B-C-A-D, B-C-D-A, B-D-A-C, B-D-C-A, C-A-B-D, C-A-D-B, C-B-A-D, C-B-D-A, C-D-A-B, C-D-B-A, D-A-B-C, D-A-C-B, D-B-A-C, D-B-C-A, D-C-A-B, D-C-B-A}

where A, B, C, and D represent the four runners. We have 24 possible permutations because there are four choices for the first place, three choices for the second place (as two people have already won first and second place), and two choices for the third place (as three people have already won first, second, and third place).

Note that in both cases, we assume that all runners are equally skilled and have an equal chance of winning each position. In reality, there may be differences in skill levels, which would affect the probabilities of each possible outcome.

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Answer:

Area = length * width

Step-by-step explanation:

If all the sides of the room are equal, all you have to do is 20*20 = area

the length of the rope is approximately 11.9 feet.

What is right angle triangle?

The term "right-angled triangle" refers to any triangle with an internal angle that is either a right angle or 90 degrees in value. The right triangle or the 90-degree triangle are other names for this triangle because of this. Right triangles have "opposite" and "adjacent" sides, which refer to the sides that are across from and next to respective angles, respectively. When a right triangle is formed, the hypotenuse is its longest side.

We can consider the flagpole, the ground, and the rope as forming a right triangle. The angle between the flagpole and the rope is 90 degrees, and the angle between the rope and the ground is 35 degrees. Therefore, the angle between the flagpole and the ground is 90 - 35 = 55 degrees.

Let's call the length of the rope "r". We can use the trigonometric function tangent to find r:

tan(35°) = opposite/adjacent = r/20

Multiplying both sides by 20, we get:

r = 20 tan(35°)

Using a calculator, we get:

r ≈ 11.9 feet

Therefore, the length of the rope is approximately 11.9 feet.

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To write the given equation in logarithmic form, we can use the definition of logarithms. The equation 10^m = w can be rewritten as a logarithm with base 10: log10(w) = m

The general relationship between exponents and logarithms is as follows:

base^(exponent) = result

In logarithmic form, it's written as:

log_base(result) = exponent

For our given equation, 10^m = w, we have:

base = 10

exponent = m

result = w

Applying the general logarithmic relationship, we write:

log10(w) = m

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Answer:

[tex]m = \frac{ - 5 - 2}{2 - 4} = \frac{ - 7}{ - 2} = \frac{7}{2} [/tex]

[tex]2 = \frac{7}{2} (4) + b[/tex]

[tex]2 = 14 + b[/tex]

[tex]b = - 12[/tex]

[tex]y = \frac{7}{2} x - 12[/tex]

According to the information, the exact values of sin(2u), cos(2u) and tan(2u) are sin(2u) = -120/169, cos(2u) = -1, and tan(2u) = -120/119.

We can use the double-angle formulas to find the values of sin(2u), cos(2u), and tan(2u) in terms of sin(u) and cos(u).

First, we need to find cos(u) using the Pythagorean identity:

Since pi/2 < u < pi, we know that sin(u) is positive and cos(u) is negative. Therefore:

Now we can substitute sin(u) and cos(u) into the double-angle formulas:

Therefore, sin(2u) = -120/169, cos(2u) = -1, and tan(2u) = -120/119.

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The probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.

1. Let's calculate the probability of selecting a blue disk

We can select a blue disk with number 2, 6 or 8 out of a total of 8 disks, it means that the probability of selecting a blue disk is

3/8

2. Let's calculate the probability of selecting the blue disk labeled with number 2:

We can select the blue disk labeled with number 2 out of three blue disks, it means that the probability of selecting the blue disk labeled with number 2 is  1/3

3. These are dependent events because the fact that we select the disk labeled with number 2, depends on selecting a blue disk before, thus:

Probability of selecting a 2 given that a blue disk is selected =

3/8 * 1/3 = 3/24 = 1/8

So we can state that the probability of selecting a 2 given that a blue disk is selected is 1/8, or 0.125.


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Full Question:

See the attached image.

The ordered pairs that represent points on the graph of y = 2x - 3 are (0,-3), (5,7), (-2,-7), (2,1), and (4,5).

An ordered pair is a pair of numbers written in a specific order (x,y) that represents a point in the coordinate plane.

A graph is a visual representation of data or a mathematical function that is plotted on a coordinate plane, usually with an x and y-axis. It is used to analyze trends and relationships between variables.

According to the given information:

To determine whether a given ordered pair represents a point on the graph of the equation y = 2x - 3, we need to substitute the values of x and y into the equation and see if the equation is true.

a) (3,-3):

y = 2x - 3

-3 = 2(3) - 3

-3 = 3

This is not true, so (3,-3) is not on the graph.

b) (0,-3):

y = 2x - 3

-3 = 2(0) - 3

-3 = -3

This is true, so (0,-3) is on the graph.

c) (5,7):

y = 2x - 3

7 = 2(5) - 3

7 = 7

This is true, so (5,7) is on the graph.

d) (-2,-7):

y = 2x - 3

-7 = 2(-2) - 3

-7 = -7

This is true, so (-2,-7) is on the graph.

e) (2,1):

y = 2x - 3

1 = 2(2) - 3

1 = 1

This is true, so (2,1) is on the graph.

f) (4,5):

y = 2x - 3

5 = 2(4) - 3

5 = 5

This is true, so (4,5) is on the graph.

Therefore, the ordered pairs that represent points on the graph of the equation y = 2x - 3 are: (0,-3), (5,7), (-2,-7), (2,1), and (4,5). Answer: b), c), d), e) and f).

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We can fill in the blanks as "Equations with fractions and/or decimals can be rewritten as equivalent equations without fractions and/or decimals, and then solve in the usual manner."

The process described above is called clearing the equation of fractions and/or decimals. To clear fractions, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators. To clear decimals, you can multiply both sides of the equation by a power of ten that will shift the decimal point to the right until there are no more decimals.

After clearing the equation of fractions and/or decimals, you can simplify and solve the equation using algebraic techniques, such as combining like terms, distributing, and isolating the variable.

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The inequality states that the sum of the number of conference rooms and ballrooms should be greater than the number of guests, so that all the guests can be accommodated. The correct answer is d. 30y + 139x>1640.

It is usually written using symbols such as “<”, “>”, “≤”, and “≥”, where one side of the expression is greater than, less than, or equal to the other side.

This is the appropriate inequality to determine how many of each type of room Amy will need to reserve because it expresses the total number of guests (1,640) that must be accounted for in the total number of conference rooms (30y) and ballrooms (139x).

To solve the inequality, Amy can start by assuming the number of conference rooms (y) she will need to reserve.

If she decides to reserve 10 conference rooms, the inequality will become 30(10) + 139x > 1640.

This can be simplified to 1390x > 1640 - 300, which reduces to x > 7.64. This means that Amy will need to reserve at least 8 ballrooms to accommodate all 1,640 guests.

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Answer:

1100

Step-by-step explanation:

8 = 1000

9 = 1001

10 = 1010

11 = 1011

12 = 1100

hope this helps :)

The probability that exactly 2 students prefer salad is 0.302

From the question, we have the following parameters that can be used in our computation:

n = 10

r = 2

p = 20%

The probability is then calculated as

P(x = 2) = nCr * p^x * (1 - p)^(n - x)

substitute the known values in the above equation, so, we have the following representation

P(x = 2) = 10C2 * (20%)^2 * (1 - 20%)^8

Evaluate

P(x = 2) = 0.302

Hence, the probability is 0.302

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