Which equation is satisfied by c = 7?
A 9-4+2(10) < c +8
B
18-4xc=6
C
22÷2-c<5
D
3c = 24

The new coordinates of the quadrilateral STUV after a 270-degree rotation about the origin are STUV' = (S', T', U', V') = [(-y₁, x₁), (-y₂, x₂), (-y₃, x₃), (-y₄, x₄)]

To find the new coordinates of the quadrilateral STUV after a 270-degree rotation about the origin, we can apply the rotation matrix formula.

The rotation matrix for a 270-degree rotation is:

R = [ cos(270) -sin(270) ]

[ sin(270) cos(270) ]

which simplifies to:

R = [ 0 -1 ]

[ 1 0 ]

We can then multiply this matrix by each of the four vertices of the quadrilateral in order to obtain their new coordinates. Let the original coordinates of the vertices be:

S = (x₁, y₁)

T = (x₂, y₂)

U = (x₃, y₃)

V = (x₄, y₄)

Then the new coordinates of the vertices after the 270-degree rotation about the origin are:

S' = RS = (0x₁ - y₁, 1x₁ + 0y₁) = (-y₁, x₁)

T' = RT = (0x₂ - y₂, 1x₂ + 0y₂) = (-y₂, x₂)

U' = RU = (0x₃ - y₃, 1x₃ + 0y₃) = (-y₃, x₃)

V' = RV = (0x₄ - y₄, 1x₄ + 0y₄) = (-y₄, x₄)

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The 43-inch TV will fit in Susan's entertainment center.

To determine if the 43-inch TV will fit in Susan's entertainment center, we need to make sure that the height, width, and diagonal of the TV are all smaller than or equal to the corresponding measurements of the entertainment center.

Since the entertainment center has a height of 19.87 inches, the 43-inch TV will fit in terms of height if its height is 19.87 inches or smaller.

Similarly, since the entertainment center has a length of 42 inches, the 43-inch TV will fit in terms of length if its length is 42 inches or smaller. Since the length of the TV is 37.41 inches, it will fit.

Finally, we need to check the diagonal. The diagonal of a rectangle can be found using the Pythagorean theorem. If we let a be the height and b be the length, then the diagonal d is given by:

d = sqrt(a² + b²)

For the entertainment center, this gives a diagonal of approximately 45.53 inches. Since the diagonal of the TV is 43 inches, it will also fit.

Therefore, the 43-inch TV will fit in Susan's entertainment center.

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The direction and the angle of rotation if polygon ABCD is rotated to get polygon A′B′C′D′ is 270° counterclockwise rotation.

Given are graphs of polygon ABCD and A′B′C′D′.

The points of ABCD are,

A(-7, 5), B(-2, 8), C(-2, 4) and D(-4, 3).

The points of A′B′C′D′ are,

A'(5, 7), B'(8, 2), C'(4, 2) and D'(3, 4).

A point (x, y) is changed to the point (y, -x).

This transformation is done if the angle of rotation is 270 degrees counterclockwise or 90 degrees clockwise.

Hence the correct option is 270° counterclockwise rotation.

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A. rolling a 1,3,4,5,6

B. The probability of the complement event is 5/6.

An experiment's probability of an event occurring is measured by its probability of occurring. When there are only two outcomes, or complement, we can say that it is the complete opposite of an event.

11(A ) Rolling any number other than 2 on the number cube is the complement of rolling a 2. Therefore, the complement's outcomes are as follows: rolling a one, a three, a four, a five, and a six

So, the correct answers are:

☐ rolling a 1

☐ rolling a 3

☐ rolling a 4

☐ rolling a 5

☐ rolling a 6

11B) Since there is only one favorable outcome (rolling a 2) out of six possible outcomes, the probability of rolling a 2 is 1/6. By deducting the probability of rolling a 2 from 1, the probability of the complement event (rolling any number other than 2) can be determined:

P(complement) = 1 - P(rolling a 2) = 1 - 1/6 = 5/6

Therefore, the probability of the complement event is 5/6.

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The experimental probability of making both free throws is given as follows:

0.4.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

For an experimental probability, the outcomes are considered from previous trials.

From the table, we have that out of 10 sets of free throws, 4 are (Y,Y), representing both made, hence the probability is given as follows:

p = 4/10 = 0.4.

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The result, when rounded to two decimal places, is 23.87%.

In algebra, a decimals is one of the number types that has a full integer and a fractional component divided by a point that is decimal. 34.5 is an illustration of a decimal number.

The formula A = Ao * (1/2)(t/30) can be used to determine how much cesium-137 is still present after t years, where Ao is the initial amount and t is the amount of time in years.

After simplifying and replacing t=37, we obtain:

A = Ao * (1/2)^(37/30)

A = Ao * (1/2)^(37/30)

After 37 years, there is a proportion of cesium-137 left, which is:

% is equal to (A/Ao) * 100 = (Ao * (1/2)(37/30)/Ao) * 100 = (1/2)(37/30) * 100.

Calculating (1/2)(37/30) yields the result: (1/2)(37/30) 0.2387

Consequently, the percentage of cesium-137 still present in the area now is about equal to: percentage 0.2387 * 100 23.87%

The result, when rounded to two decimal places, is 23.87%.

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About 21.44% of cesium-137 is still near the disaster site today.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

The amount of cesium-137 present near the disaster site at the time of the explosion is Ao.

The half-life of cesium-137 is 30 years. This means that after 30 years, half of the initial amount will have decayed, leaving us with 1/2 of the initial amount. After another 30 years, half of the remaining amount will have decayed, leaving us with 1/4 of the initial amount.

Since it is almost 37 years since the Chernobyl disaster, we can calculate the percentage of cesium-137 that is still near the disaster site today as follows:

Amount of cesium-137 present today = Ao * (1/2)^(37/30)

Percentage of cesium-137 present today = (Amount of cesium-137 present today / Ao) * 100

= (Ao * [tex](1/2)^{(37/30)}[/tex] / Ao) * 100

= [tex](1/2)^{(37/30)}[/tex]) * 100

= [tex](1/2)^{(37/30)}[/tex]) * 100%

≈ 21.44%

Therefore, about 21.44% of cesium-137 is still near the disaster site today.

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Answer:

  2 ft·lb

Step-by-step explanation:

You want the work done on a particle moving it from 0 to 9 ft using a force that is 8/(3+x)² pounds at each point.

The incremental work is the product of the force and the incremental distance:

  dW = 8/(3+x)²·dx

The work done over the distance of interest is the integral of this incremental work over that distance.

 [tex]\displaystyle W=\int_0^9{\dfrac{8}{(x+3)^2}}\,dx=(-8(x+3)^{-1})_0^9=-8\left(\dfrac{1}{12}-\dfrac{1}{3}\right)=2[/tex]

The work done on the particle is 2 ft·lb.

There are an infinite number of ordered pairs that satisfy the equation -2x + y = 85. Some are  (0, 85),(-10, 65)

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.

To find the ordered pairs for the equation -2x + y = 85, we can assign a value to one variable and solve for the other. Here are a few ordered pairs that satisfy the equation:

When x = 0, y = 85:

(0, 85)

When x = -10, y = 65:

(-10, 65)

When x = 20, y = 45:

(20, 45)

When x = -42.5, y = -8:

(-42.5, -8)

And so on. There are an infinite number of ordered pairs that satisfy the equation -2x + y = 85.

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Using the histogram, we can see that the upper-class limit of the second class is given to be 80.5.

A collection of rectangles with bases and the spaces between class boundaries can be referred to as a histogram. Each rectangular bar represents some type of data, and every rectangle is next to another. Rectangle heights are inversely correlated with matching frequencies for both similar and dissimilar groups.

A bar graph is used to represent data in a histogram. It is a visualisation of several outcomes organised into columns along the x-axis. The y-axis of the same histogram represents the number count or multiple occurrences in the data for each column. It is the simplest method for visualising data distributions.

Using the histogram, we can see that the upper-class limit of the second class is given to be 80.5.

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The value of the missing side is 23. 5. Option A

To determine the value of the missing length, we have to note that the trigonometric identities are;

Using the cosine identity, we have;

cos θ = adjacent/hypotenuse

Substitute the values, we get;

cos36 = 19/x

Cross multiply the values

x = 19/cos 36

Divide the values

x =19/0. 8090

x = 23. 5

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Answer:

Step-by-step explanation:

Since there are 16 tablespoons in 1 cup, we can convert the original 3 tablespoons of seasoning to cups by dividing by 16:

3 tablespoons / 16 = 0.1875 cups

After Ricky doubles the amount of seasoning, he will have:

2 * 3 tablespoons = 6 tablespoons

Converting to cups:

6 tablespoons / 16 = 0.375 cups

Therefore, the ratio of cups to tablespoons of seasoning after Ricky doubles the amount is:

0.375 cups / 1 tablespoon = 0.375 : 1

Answer: The ratio of cups to tablespoons of seasoning after Ricky doubles the amount is 0.375 : 1

Answer:

To write an exponential regression equation for this set of data, we can use the formula y = ab^x, where y is the value of the car in dollars, x is the number of years since purchase, a is the initial value of the car, and b is the rate of depreciation.

To find the values of a and b, we can use the first two data points:

y = ab^x

14220 = ab^1

Solving for a, we get:

a = 14220 / b

Now, we can substitute this expression for a into the first data point:

y = ab^x

15700 = (14220 / b) * b^0

Simplifying, we get:

15700 = 14220

This is not a valid equation, so we need to adjust our estimate for the rate of depreciation, b. One way to do this is to take the average of the depreciation rates between each pair of consecutive data points:

b = (14220/15700)^(1/6)

b = 0.9497

Now, we can use this value of b to find the value of a:

a = 14220 / b

a = 14955.15

Therefore, the exponential regression equation for this set of data is:

y = 14955.15 * 0.9497^x

To find the value of the car after 9 years, we can substitute x = 9 into the equation:

y = 14955.15 * 0.9497^9

y = 7327.78

Therefore, the value of the car, to the nearest cent, after 9 years is $7327.78.

The minimum amount of wrapping paper Sarah will need to cover the present is; 351.68 square inches and one gallon of filtered water is not enough because the capacity of fish tank will be 2.17 gallons.

WE are Given that, the dimensions of cylindrical fish tank are height=10 inches and radius = 8/2 = 4 inches.

Now the total surface area of a cylinder is 2πr(r + h).

Here, the required wrapping paper = 2×3.14 ×4(4+10)

= 2×3.14×4×14

= 351.68 square inches

We know that, the volume of cylinder = πr²h

= 3.14 × 4² × 10

= 502.4 cubic inches

Thus, 1 gallon is equal to 231 cubic inches

Number of gallons of filtered water required = 502.4/231

= 2.17 gallons

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The surface area of solid B is 3,750 square meters.

Since the solids are similar with a scale factor k from solid A to solid B, the ratio of their surface areas is k². Therefore, the surface area of solid B is:

Surface area of solid B = Surface area of solid A * k²

Substituting the given values, we get:

Surface area of solid B = 72 * 12²

Surface area of solid B = 10368 square centimeters.

Therefore, the surface area of solid B is 10,368 square centimeters.

Following the same approach as above:

Surface area of solid B = Surface area of solid A * k²

Substituting the given values:

Surface area of solid B = 150 * 5²

Surface area of solid B = 3750 square meters

Therefore, the surface area of solid B is 3,750 square meters.

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Using inequalities, we can find that x - 4 < 9 is an inequality.

Option B is correct.

The two sides of a mathematical equation having an inequality must be equal. We compare two values via inequality rather than equations. The equal-sign is replaced by the signs less than (or less than or equal to), greater than (or greater than or equal to), or not equal to.

Here in the question,

A) 9 less than the product of 4 and y is given.

Let the number be x.

So,

x = 4y - 9

So, this is not an inequality.

B) x decreased by 4 is less than 9 is given.

So,

x - 4 < 9

This is an inequality.

C)  x is decreased by the product of 4 and y is given.

So,

x - 4y.

This is not an inequality.

Hence, x - 4 < 9 is an inequality.

Option B is correct.

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The times the 7 in the Susan's scores is greater than Sarah's score is 100 times

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

Susan = 87, 325

Sarah = 46, 175

The values of the 7's in their scores are

Susan = 7, 000

Sarah = 70

So, we have

Number of times = 7000/70

Evaluate

Number of times = 100

Hence, the number of times is 100

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Keith's subsidized monthly payment upon graduation would be approximately $135.65.

Keith took out a student loan for $14,342 with an annual interest rate of 2.7%. He had 5 years left in college before he began repaying the loan. To find his subsidized monthly payment, we need to first calculate the total amount he owes after 5 years and then divide that by the number of months in the repayment period.

1. Convert the annual interest rate to a decimal: 2.7% ÷ 100 = 0.027
2. Calculate the interest for one year: $14,342 × 0.027 = $387.234
3. Calculate the total interest for 5 years: $387.234 × 5 = $1,936.17
4. Add the interest to the principal amount: $14,342 + $1,936.17 = $16,278.17
5. Assume a standard repayment period of 10 years (120 months) after graduation.
6. Divide the total amount owed by the number of months in the repayment period: $16,278.17 ÷ 120 = $135.65

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Step-by-step explanation:

To solve for the zeros of a quadratic function, we need to find the values of x where f(x) equals zero. This means that we need to set the quadratic function equal to zero and solve for x.

In this case, our quadratic function is f(x) = 9x² + 6x + 1. To set it equal to zero, we write:

9x² + 6x + 1 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± √b² - 4ac) / 2a

In this equation, a, b, and c are the coefficients of the quadratic function. In our case, a = 9, b = 6, and c = 1. Substituting these values into the equation, we get:

x = (-6 ± √36 - 4(9)(1)) / 2(9)

Simplifying, we get:

x = (-6 ± √0) / 18

Since the square root of 0 is 0, we have:

x = -6/18 and x = -6/18

Reducing the fractions, we get:

x = -1/3 and x = -1/3

Therefore, the zeros of the quadratic function f(x) = 9x² + 6x + 1 are x = -1/3 and x = -1/3.

The quintic equation has integer coefficients for x = - 5 / 3.

In this question we need to determine the missing coefficients of a quintic equations, that is, a polynomial of grade 5, on the basis that the coefficients are integers.

First, we evaluate on each case:

x = - 5 / 3

12 · (- 5 / 3)⁵ + a · (- 5 / 3)³ + b · (- 5 / 3)² - 3 · (- 5 / 3) + 15 = 0

- 12500 / 81 - (125 / 27) · a + (25 / 9) · b + 5 + 15 = 0

- (125 / 27) · a + (25 / 9) · b = 10880 / 81

- (5 / 3) · a + b = 2176 / 45

b = (5 / 3) · a + 2176 / 45

x = - 4 / 3

12 · (- 4 / 3)⁵ + a · (- 4 / 3)³ + b · (- 4 / 3)² - 3 · (- 4 / 3) + 15 = 0

- 4096 / 81 - (64 / 27) · a + (16 / 9) · b + 4 + 15 = 0

- (64 / 27) · a + (16 / 9) · b = 2557 / 81

- (4 / 3) · a + b = 2557 / 144

b = (4 / 3) · a + 2557 / 144

x = 3 / 5

12 · (3 / 5)⁵ + a · (3 / 5)³ + b · (3 / 5)² - 3 · (3 / 5) + 15 = 0

2916 / 3125 + (27 / 125) · a + (9 / 25) · b - 9 / 5 + 15 = 0

(27 / 125) · a + (9 / 25) · b - 2709 / 3125 + 46875 / 3125 = 0

(27 / 125) · a + (9 / 25) · b + 44166 / 3125 = 0

(27 / 125) · a + (9 / 25) · b = - 44166 / 3125

(3 / 5) · a + b = - 14722 / 375

b = - (3 / 5) · a - 14722 / 375

x = 6 / 5

12 · (6 / 5)⁵ + a · (6 / 5)³ + b · (6 / 5)² - 3 · (6 / 5) + 15 = 0

12 · (7776 / 3125) + (216 / 125) · a + (36 / 25) · b - 18 / 5 + 15 = 0

93312 / 3125 + (216 / 125) · a + (36 / 25) · b - 18 / 5 + 15 = 0

82062 / 3125 + (216 / 125) · a + (36 / 25) · b + 15 = 0

(216 / 125) · a + (36 / 25) · b = - 128937 / 3125

(6 / 5) · a + b = - 3223425 / 112500

(6 / 5) · a + b = - 644685 / 22500

(6 / 5) · a + b = - 128937 / 4500

b = - (6 / 5) · a - 128937 / 4500

After using a graphing tool, we conclude that x = - 5 / 3 can be found by using the following integers:

(a₁, b₁) = (19, 80), (a₂, b₂) = (31, 100), (a₃, b₃) = (79, 180)

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Answer:Percent distribution is:Apple: 25%

Cherry: 30%

Chocolate Cream: 15%

Pecan: 17.5%

Peach: 12.5%

Step-by-step explanation:

Given,

Appple=20  

Cherry=24

Chochlate cream=12

Pecan=14

Peach=10

Step 1: To find the total number of pie slices=

20  + 24  + 12 + 14 + 10  = 80

Step 2: Calculate the percentage for each type of pie slice.

Divide the number of pie slices for each type by the total number of pie slices, and then multiply by 100 to get the percentage.

For apple pie slices:

20  / 80  = 0.25 or 25%

For cherry pie slices:

24 / 80  = 0.3 or 30%

For chocolate cream pie slices:

12 / 80  = 0.15 or 15%

For pecan pie slices:

14  / 80 = 0.175 or 17.5%

For peach pie slices:

10  / 80 = 0.125 or 12.5%

So, the percent distribution is:

Apple: 25%

Cherry: 30%

Chocolate Cream: 15%

Pecan: 17.5%

Peach: 12.5%

If 453 teenagers were surveyed, the number of teenagers who would receive a weekly allowance is approximately 263.

Given that,

According to a survey,

Percent of teenagers who will receive a weekly allowance for doing household chores = 58%

So, if the number of teenagers surveyed is 453,

Number of teenagers who will receive a weekly allowance for doing household chores = 58% × 453

                              = (58/100) × 453

                              = 0.58 × 453

                              = 262.74 ≈ 263

Hence the number of teenagers who will receive a weekly allowance for doing household chores is approximately 263.

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The arc DEB is major arc.

The arcs, arc EA, arc CB, arc DC and arc AB are minor arcs.

The arc CDA is semicircle.

An arc which has a measure of less than 180° is called minor arc.

An arc whose measure is more than 180° is major arc.

Measure of arc EA = 180° - (30° + 100°) = 50°

[Since AC is a diameter CD + DE + EA = 180°]

Measure of arc CB = 50°

Measure of arc DC = 100°

Measure of arc DEB = 360° - (100° + 50°) = 210°

[ Whole circle = 360°]

Measure of arc AB = DEB - (DE + EA) = 210° - (30° + 50°) = 130°

Measure of arc CDA = 180° [Since AC is a diameter.]

Hence the Major arcs are arc DEB, minor arcs are arc EA, arc CB, arc DC and arc AB. Semicircle is arc CDA.

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The figure is given below.

__________________________________

_________________________________

Answer: e, f, c, a

Step-by-step explanation:

1.   If you follow the chart, students that didn't get hired and CS major was 102 and total applicants were 234. so your percent comes from 102/234=.4358  move decimal over 2 places or multiply by 100

=e. 43.5%

2.  74/234 = .3162

=f. 31.6

3.  58/160 =.3625

=c. 36.2

4. 36/74=.4864

=a. 48.6

If a cylindrical can of vegetables has a label wrapped around the outside, touching end to end.  The height of the can is: A. 22 inches.

How to find the height?

Let's call the height of the can "h". The total surface area of the cylinder is given by 2πr² + 2πrh

where:

r = radius of the cylinder.

The label covers all of the cylinder except for the top and bottom circles, which have a combined area of 4πr². So the area of the label is equal to 2πr² + 2πrh - 4πr² = 2πrh.

Set up the equation to solve for h:

2π × 2 ×h = 88π

Dividing both sides by 2π× 2:

h = 44/2

Therefore  the height of the can is 22 inches.

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If all of the points on the scatter plot are directly on a straight line with a negative slope, the product-moment correlation coefficient is a negative one.

A scatter chart, also known as a scatter plot, is a graph that shows the relationship between two variables. They are a powerful chart type that allows readers to see a relationship or trend that would be impossible to see in almost any other format.

Accordingly, when all of the points on a scatter plot fall on a straight line, the connection between the two variables is perfect linear. The correlation coefficient (r) will be either +1 or -1 in this scenario.

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Step-by-step explanation:

the fourth one

...

.

.

...

..

Answer:

O.D) The broken plate, the creaming children, and the boiling tea kettle.

The points on the equations intersect at (-7, 4)

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

3x + 7y = 7

5x − 7y = −63

The above equations is an illustration of a system of equations

Next, we plot the graph using a graphing tool

The graph is added as an attachment, where the point of intersection is (-7, 4)

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Answer:

1/3

Step-by-step explanation:

Answer:

Since you have no idea what the right answer is, each choice has a probability of 1/4 of being correct. Let X be the number of points you get.

If you answer correctly, X = 1 with probability 1/4.

If you answer incorrectly, X = -1/3 with probability 3/4.

Thus, the expected value of X is:

E(X) = (1/4)×1 + (3/4)×(-1/3)

E(X) = 1/4 - 1/4

E(X) = 0

Therefore, the expected value of the number of points you get is 0.

Step-by-step explanation:

gg

The chemist will need 273 ml of compound A to make 728 ml of the drug.

It is given that 8 parts of drug are made by using 2 parts of compound A and 5 parts of compound B.

So the proportion (ml of compound A)/(ml of drug) = 3/8

Suppose the chemist needs x ml of compound A to make 728 ml of the drug.

So we have, [tex]\frac{x}{728} = \frac{3} {8}[/tex]

So , [tex]x = \frac{(728)(3)}{8} = 273\,\,ml.[/tex]

How do we solve ratio and proportion questions.

How do we solve ratio and proportion questions.Consider this question?

Suppose every project team will have equal no of boys and girls. Suppose a particular team will have 10 members. How many boys will be in this team. To answer this question we find the the key proportionality or ratio in the problem. it is #boys/#girls = 1/1. So #boys/#team members = 1/(1+1)=1/2. So if the team size is 10. then #boys = (1/2)(10) = 5. This is the way we solve problems in ratio and proportion.

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