8) What is the area of a polygon with vertices
A(-2,4), B(4,4), C(7,0) and D(-5,0)?
(A) 48
(B) 42.5
(C) 36
(D) 24

To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:

Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190

Number of favorable outcomes:

Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:

Favorable outcomes = C(2, 2) = 1

Probability = Favorable outcomes / Total outcomes = 1/190

Therefore, the correct answer is (G) 1/190.

Answer:

s = 6

Step-by-step explanation:

Goal is to isolate the variable (s)

1/2s = 4s - 21

Subtract 4s from both sides - this cancels out the 4s on the right side and moves it to the left side

1/2s - 4s = -21

To add or subtract fractions, they must have a common denominator

Convert 4s to a fraction over 2

1/2s - 8/2s = -21

Subtract the numerators and keep the denominators

-7/2s = -21

Remember the goal is to isolate the variable

In order to get rid of the -7/2, we multiply by its reciprocal (which is -2/7)

What we do to one side, we must do to the other (this means multiply by -2/7 on both sides

-7/2s × -2/7 = -21 × -2/7

s = -21 × -2/7

Negative × negative = positive

s = 42/7

Divide 42 by 7

s = 6

Answer:

\(\frac{8}{15}\)

Step-by-step explanation:

Therefore, the answer is \(\frac{8}{15}\).

Answer: 13 is in C (the set of complex numbers)

Step-by-step explanation:

13 is in R (the set of real numbers)

13 is in Q (the set of rational number)

13 is in Z (the set of integers)

13 is in N (the set of natural numbers)

Answer:

180°

Step-by-step explanation:

the interior of every single triangle is 180°

if it doesn't add up to 180% something is wrong or it isn't a triangle

hope this helped, good luck

-cheesetoasty

Answer:

are the answers actual people or loyalist and patriots

Answer:

Iv'e checked both of them and they have NO solutions so nyour answer is (None)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

We can use the factored form of the quadratic equation, given by:

\(y=a(x-p)(x-q)\)

Where a is the leading coefficient and p and q are the zeros.

We have zeros x = -2 and x = 3. So, let p = -2 and q = 3:

\(y=a(x+2)(x-3)\)

Next, we are given that our y-intercept is (0, -30).

In other words, when x = 0, y = -30. So:

\(-30=a(0+2)(0-3)\)

Solve for a:

\(-30=-6a\Rightarrow a=5\)

Hence, our factored equation is:

\(\displaystyle y=5(x+2)(x-3)\)

For the standard form, expand:

\(y=5(x^2-3x+2x-6)\)

Simplify:

\(y=5(x^2-x-6)\)

Distribute:

\(y=5x^2-5x-30\)

Our answer is C.

Answer:

5,x6=5

4÷6=6

4=6=8

4=6687554=+÷976555££=6££6/=

Answer and Step-by-step explanation:

Solution:

Given:

V = 2π cm3

We know that:

2π = πr2h

2π / πr2 = h

Which gives: h = 2 / r2

Minimize surface area = 2πrh + 2πr2

S = 2πrh + 2πr2

Put h = 2/ r2 in surface area, we get:

S = 2πr (2/ r2 ) + 2πr2

S = 4 π / r + 2πr2

Therefore, s(r) = 4 π / r + 2πr2

Differentiate concerning r, we have

S’(r) = -4π / r2 + 4πr

Again differentiate concerning r, we have:

S”(r) = 2 x 4 π/ r3 + 4π

For s’(r) = 0

0 = -4π / r2 + 4πr

-4π + 4πr3 = 0

r3 = 1

r = 1 cm

and s”(1) > 0 at r = 1 is point of minima.

So h = 2 π / π x1 x1

  = 2cm

Therefore minimum surface area the can should have a radius of 1cm and height of 2cm.

The number of guests that shared one platter is 10.

A. Since 3 people bring a total of 4 platters each, there are a total of 3 x 4 = 12 platters.

If the 120 guests share the platters equally, then each platter is shared by 120/12 = 10 guests. Therefore, 10 guests share 1 platter.

B. Landon's reasoning is incorrect.

While it is true that 3 people bring 4 platters each, the total number of platters is 3 x 4 = 12, not 7.

Therefore, 7 guests cannot be the correct answer. The correct answer is 10 guests share 1 platter, as explained in part A.

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Three people each bring 4 platters of food to a family reunion. The 120 guests all share the platters equally. A. How many guests share 1 platter? Explain your answer. 3.AR.1.2 B. Landon thinks that the answer is 7 guests. He says, " 3+4=7, and 7 rounds to 10 . Then 10×12=120." Do you agree with his reasoning

Answer:

c is the anser

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

D 1.44

Step-by-step explanation:

the answer is the last one 1.44

Answer:

√17

Step-by-step explanation:

√121 = 11

√25 = 5

√1.44 = 1.2

√17 is an irrational number/

Answer: 2.4

Step-by-step explanation: Given the angles below, the length of EF will be 2.4

Answer:

B) 3.8.

EF = 3.8

Use the law of sines to find the unknown length EF

Answer: 452.16

Step-by-step explanation:

Answer:

its 91

Step-by-step explanation:

Answer:.

Step-by-step explanation im not sure

Answer:

Step-by-step explanation:

47.)  sin20 = 6/b

b = 6(sin20) = 17.5

c = √6²+17.5² = 18.5

48.)  tan61 = y/18

y = 18(tan61) = 32.5

z = √18²+32.5² = 37.1

49.)  r = √25²+23² = 34

50).  d = √30²+7² = 30.8

51.)  sin71 = j/19

j = 19(sin71) = 18

k = √19²-18² = 6.2

52.)  y = √4²-1² = √7 = 2.6

53.)  sin49 = f/26

f = 26(sin49) = 19.6

h = √26²-19.6² = 17

54.)  t = √7²+4² = 8.1

The values of the inverse of the functions are:

g⁻¹(7) = 4

h⁻¹(x) = (x - 13)/8

(h * h⁻¹)(-3) = 22

An inverse function is defined as a function that can be inverted into another function. Simply put, if the function 'f' brings x to y, the inverse of 'f' brings y to x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f^(-1) or F^(-1).  

We are given the one to one function as:

g = {(2, 2), (4, 7), (5, 2), (7, -3), (8, 3)}

h(x) = 8x + 13

g⁻¹(7) will be the value of x when y is 7 and as such we have:

g⁻¹(7) = 4

h⁻¹(x) is:

y = 8x + 13

x = (y - 13)/8

h⁻¹(x) = (x - 13)/8

(h * h⁻¹)(-3) = (8(-3) + 13) * (-3 - 13)/8

= 22

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Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

This equation can be factored as:

(2x + 5)(x - 2) = 0

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

Therefore, the x-intercepts of the graph of f(x) are x = -5/2 and x = 2.

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

x = -(-1) / (2 * 2) = 1/4

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Answer:

If two sides of a triangle are congruent, then the angles opposite to these sides are congruent.

Step-by-step explanation:

Congruent/Congruency: having the same size and shape congruent triangles.

Theorem 1: If a line is drawn parallel to one side of a triangle to intersect the midpoints of the other two sides, then the two sides are divided in the same ratio.

I hope this helped, have a great day <3

Answer:

D. (-2,-5), (0, -7), (1, -4)

Step-by-step explanation:

From Function Theory we must remember that range of a function is the set of images related to elements of the domain. In this case, we must find the image of each of the three elements that forms the domain of \(f(x, y) = (y+2, -x-4)\), which are: \(A(x,y) = (1, -4)\), \(B(x,y) = (3,-2)\) and \(C(x,y) = (0,-1)\).

Then we proceed to find all elements of range:

\(A(x,y) = (1, -4)\)

\(f(1,-4) = (-4+2,-1-4)\)

\(f(1,-4) = (-2,-5)\)

\(B(x,y) = (3,-2)\)

\(f(3,-2) = (-2+2,-3-4)\)

\(f(3,-2) = (0,-7)\)

\(C(x,y) = (0,-1)\)

\(f(0,-1) = (-1+2,0-4)\)

\(f(0,-1) = (1,-4)\)

Which corresponds to option D.

Answer:

C

Step-by-step explanation:

Lorraine is typing at 8 words per minute, while Bea is doing 9 per minute

Answer: B :  Lorraine’s unit rate is 1 more word per minute than Bea’s unit rate.

Step-by-step explanation:

I took the test, B) it said It was correct

Answer:

4

Step-by-step explanation:

I like to use the FOIL method! I've attached a quick picture of how it works below, but basically you multiply the first terms. Next, multiply the outside/outer terms. Then, multiply the inside/inner terms. Lastly, you multiply the last terms.

In this question, the binomial is (x + 2)².

You can expand this to be (x + 2)(x + 2).

When you expand it using the FOIL method, you get x times x, which is x².

Next, the outside/outer terms are x and 2, which is 2x.

Then, you multiply the inside/inner terms 2 and x, which is 2x.

Last, you multiply the last terms, which are 2 and 2, which is 4.

When you put them together, it looks like this:

x² + 2x + 2x + 4.

You can simplify this to x² + 4x + 4.

So your answer is 4.

The number of barrels of crude oil required to run the car for a year is 61.4

The information given is as follows;

Percentage of crude oil processed into gasoline = 45%

The distance achieved per gallon by car = 31 mi/gal

Distance driven per year = 36,000 miles

Hence, the number of Gasoline usage in one year,

\(\text{Gasoline usage in one year} = \dfrac{\text{Distance drievn per year}}{\text{distance achieve per gallon by car}}\)

\(\text{Gasoline usage in one year} = \dfrac{36000 \ \text{miles}}{31\ \text{miles/gallon}}\)

\(\text{Gasoline usage in one year} = 1,161 \ \text{gallons}\)

Here, Percentage of crude oil processed into gasoline = 45%

Hence, where 45% of the crude oil produces 1000, the volume of crude, x, from which the gasoline is sourced becomes;

\(x \times 45\% = 1161\)

\(x \times \dfrac{45}{100} = 1161\)

\(45x = 1161\times 100\)

\(45x = 1,16,100\)

\(x = 2580\) gallons of crude

Since 1 barrel of crude oil is approximately 42 gallons of crude oil.

Hence, we have;

\(2580 \ \text{gallons of crude }\) = \(\dfrac{2580}{42} \text{ barrels of crude}\)

= \(61.4\)  \(\text{ barrels of crude}\)

Hence the number of barrels of crude oil required to run the car for a year = \(61.4\)  \(\text{ barrels of crude}\)

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Approximately 61.44 barrels of crude oil are required to run your car for a year.

To determine the number of barrels of crude oil required to run your car for a year, we'll need to calculate the total amount of gasoline consumed and then convert that into the equivalent volume of crude oil.

Volume of a barrel of crude oil: 42 gallons

Approximately 45% of crude oil is processed into gasoline

Car fuel efficiency: 31 miles per gallon

Distance driven in a year: 36,000 miles

First, let's calculate the total amount of gasoline consumed in a year. We'll divide the total distance driven by the car's fuel efficiency:

Gasoline consumed = Distance driven / Fuel efficiency

Gasoline consumed = 36,000 miles / 31 miles per gallon

Gasoline consumed ≈ 1161.29 gallons

Next, we need to calculate the equivalent volume of crude oil required to produce this amount of gasoline. Since only approximately 45% of crude oil is processed into gasoline, we'll multiply the gasoline consumed by the reciprocal of 45% (or 0.45) to account for this conversion:

Equivalent volume of crude oil = Gasoline consumed / Conversion factor

Equivalent volume of crude oil = 1161.29 gallons / 0.45

Equivalent volume of crude oil ≈ 2580.64 gallons

Finally, to determine the number of barrels of crude oil required, we'll divide the equivalent volume of crude oil by the volume of a barrel (42 gallons):

Number of barrels of crude oil = Equivalent volume of crude oil / Volume of a barrel

Number of barrels of crude oil = 2580.64 gallons / 42 gallons

Number of barrels of crude oil ≈ 61.44 barrels

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The slope of the line will be negative. Then the correct option is B.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation of the line will be

y = -mx + 2

The slope of the line will be negative.

Then the correct option is B.

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Answer:

B. Negative

Step-by-step explanation:

The value of q is 0.35.

The value of p is 0.16.

The value of r is 0.27.

The value of P(A given NOT B) is approximately 0.4211.

To calculate the values of p, q, and r, we can use the information provided in the Venn diagram and the probabilities of events A and B.

Given:

P(A) = 0.43

P(B) = 0.62

P(A∩B) = 0.27

Calculating the value of p:

The value of p represents the probability of event A occurring without event B. In the Venn diagram, p corresponds to the region inside A but outside B.

We can calculate p by subtracting the probability of the intersection of A and B from the probability of A:

p = P(A) - P(A∩B)

= 0.43 - 0.27

= 0.16

Therefore, the value of p is 0.16.

Calculating the value of q:

The value of q represents the probability of event B occurring without event A. In the Venn diagram, q corresponds to the region inside B but outside A.

We can calculate q by subtracting the probability of the intersection of A and B from the probability of B:

q = P(B) - P(A∩B)

= 0.62 - 0.27

= 0.35

Therefore, the value of q is 0.35.

Calculating the value of r:

The value of r represents the probability of both event A and event B occurring. In the Venn diagram, r corresponds to the intersection of A and B.

We are given that P(A∩B) = 0.27, so the value of r is 0.27.

Therefore, the value of r is 0.27.

Finding the value of P(A given NOT B):

P(A given NOT B) represents the probability of event A occurring given that event B does not occur. In other words, it represents the probability of A happening when B is not happening.

To calculate this, we need to find the probability of A without B and divide it by the probability of NOT B.

P(A given NOT B) = P(A∩(NOT B)) / P(NOT B)

We can calculate the value of P(A given NOT B) using the provided probabilities:

P(A given NOT B) = P(A) - P(A∩B) / (1 - P(B))

= 0.43 - 0.27 / (1 - 0.62)

= 0.16 / 0.38

≈ 0.4211

Therefore, the value of P(A given NOT B) is approximately 0.4211.

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Answer:

  41/56

Step-by-step explanation:

The LCD is 7×4 = 28. With that denominator, the two fractions are ...

  5/7 = 20/28

  3/4 = 21/28

The average of the two values will be ...

  (5/7 +3/4)//2 = (20 +21)/28/2 = 41/56

_____

Additional comment

  5/7 ≈ 0.714285... (6-digit repeat)

  3/4 = 0.75

Then numbers like 0.72 = 18/25, or 0.73 = 73/100, or 0.74 = 37/50 will all be between the given fractions.

Of course, any terminating or repeating decimal in that range will also be a rational number. For example, 0.727272727272... = 8/11  will be a rational number in the required range.