Quiz 8-1 Graphing Quadratic Equations answers

Step-by-step explanation:

At least twice means it could be   2  3  4  5  6  7  or  8 heads

 there is 8 chances of having only one TAIL

there are   2^8 outcomes = 256 outcomes possible

     take away the EIGHT with one tail

                  248 out of 256 have at least 2 heads

248/256 = 31/32

( Let me know if this is incorrect and I will re-evaluate !)

Answer:

[tex]\frac{247}{256}[/tex]

Pre-requisite Knowledge:

Permutations and Combinations

Elementary Probability

Step-by-step explanation:

Total number of outcomes (Cardinality of the sample space) = [tex]2^{8}[/tex]  

P(at least 2 heads show up) = 1 - [ P(no Head) + P(exactly 1 Head) ]

[tex]= 1-\frac{C(8,0)+C(8,1)}{2^8}\\\\=1-\frac{1+8}{256}\\\\ =1-\frac{9}{256}\\\\= \frac{247}{256}[/tex]

Answer:

The correct answer is: OA(3, -4.5), B(1.5, -1.5), C(-3, 1.5), D'(-3,-3).

To dilate a point using a scale factor of 4, we multiply each coordinate of the original point by 4.

Thus, the coordinates of A' are (-4 * 4, 6 * 4) = (-16, 24)

The coordinates of B' are (-2 * 4, 2 * 4) = (-8, 8)

The coordinates of C' are (4 * 4, -2 * 4) = (16, -8)

The coordinates of D' are (4 * 4, 4 * 4) = (16, 16)

To check our work, we can plot these points on a graph and compare with the original polygon:

Original Polygon:

A(-4, 6) B(-2, 2)

* *

\ /

\ /

\ /

\ /

\ /

* *

C(4,-2) D(4,4)

Dilated Polygon:

A'(-16, 24) B'(-8, 8)

* *

\ /

\ /

\ /

*

C'(16,-8) D'(16,16)

If we divide the coordinates of the dilated polygon by 4, we get the answer:

A'(-16/4, 24/4) = (-4, 6)

B'(-8/4, 8/4) = (-2, 2)

C'(16/4, -8/4) = (4, -2)

D'(16/4, 16/4) = (4, 4)

So the vertices of polygon A'B'C'D' are OA (3, -4.5), B(1.5, -1.5), C(-3, 1.5), and D'(-3,-3).

Answer:

Correct equation:

x + 22 + x + 22 + 10 = 48

Answer:

251.327 km² (nearest thousandth)

Step-by-step explanation:

The formula for the surface area of a cylinder is:

[tex]\boxed{S.A. = 2\pi r^2 + 2\pi rh}[/tex]

where r is the radius and h is the height of the cylinder.

Substitute the given values of r = 4 km and h = 6 km into the formula and solve:

[tex]\begin{aligned}S.A. &= 2\pi (4)^2 + 2\pi (4)(6)\\&=2\pi (16)+2 \pi (24)\\&=32 \pi+ 48 \pi\\&=80 \pi\\&=251.327412...\\&=251.327\; \sf km^2 \end{aligned}[/tex]

Therefore, the surface area of the cylinder with height 6 km and radius 4 km is 251.327 square kilometers, rounded to the nearest thousandth.

Answer:

-------------------------

Curved surface area of a cylinder:

Substitute 6 for h and 4 for r:

Total surface area adds top and bottom faces:

The statement "Each additional serving will require 1 additional can of beans" is not correct.

It should be noted that to make more than 3 servings, Robert will need to increase the amount of both beans and ground turkey used in the recipe.

Assuming that the recipe calls for one 18-ounce can of beans for 3 servings, Robert will need to use 6 cans of beans for 12 servings.

This is because each serving requires 6 ounces of beans (18 ounces ÷ 3 servings), and 12 servings would require a total of 72 ounces of beans (12 servings × 6 ounces per serving).

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Using Pythagorean trigonometric identity, the value of cosθ is √2/2

To find the value of cosθ, we can use Pythagorean identity to do this. However, we are also told that θ terminates in the the first quadrant.

sinθ = √2/2

sin²θ + cos²θ = 1

Substituting the value of sin θ into the formula above

cos²θ + (√2/2)² = 1

cos²θ + 1/2 = 1

collect like terms

cos²θ = 1 - 1/2

cos²θ = 1/2

cosθ = √(1/2)

cosθ = √2/2

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The volume of air of a sphere with diameter 9 centimeters is 381.51 cubic centimeters

The formula for the volume of a sphere is:

V = (4/3)πr³

where r is the radius of the sphere.

The diameter of the sphere is 9 cm, which means the radius is half of that:

r = 9/2 = 4.5 cm

Substituting this value into the formula, we get:

Volume = (4/3)π(4.5)³

Volume = (4/3)×3.14 × 91.125

Volume = 381.51 cubic centimeters

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The variable t becomes the subject of the equation c=t³ - 8v by adding 8v to both sides and taking the cube root, giving t = ∛(c + 8v).

We need to make t the subject of the equation c=t³ - 8v. To do this, we first add 8v to both sides of the equation to isolate t³ on one side, giving us t³ = c + 8v. We then need to take the cube root of both sides to solve for t. Hence, t = ∛(c + 8v). Now, t is the subject of the equation.

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The complete factorization of the original expression is:

4x² (x + 1)²

We have,

First, we can factor out 4x².

4x² (x² + 2x + 1)

Next, we can see that the expression inside the parentheses is a perfect square trinomial, which means it can be factored as:

4x² (x + 1)²

Thus,

The complete factorization of the original expression is:

4x² (x + 1)²

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Answer:

66 inches

Step-by-step explanation:

Every foot is twelve inches

Answer: 66 inch is in 5 1/2 feet

Step-by-step explanation: there is 12 inches in 1 foot so you do 12 x 5= 60 then there is 6 inches in a half of a foot so you add 60 and 6 and you get 66 inches

Answer:

The answer is C) 2.

Step-by-step explanation:

Since g(x) is the inverse of f(x), we know that f(g(x)) = x for all x in the domain of g.

Therefore, f(g(2)) = 2.

The answer is C) 2.

Answer:

∠x = 38°

Step-by-step explanation:

∠x + ∠y = 180°

∠x + 142° = 180°

∠x = 180° - 142

∠x = 38°

Step-by-step explanation:

'Find the product...'   just means multiply the two numbers together:

(use your calculator)    5602 x 17 =   95,234

Product means multiply them together. Please see image showing multiplication. You could also break this up into (5602 x 7) + (5602 x 10), which is basically what I did vertically.

The rational numbers are solved and the incorrect number is A = 3/0

Given data ,

Let the rational number be represented as A

Now , the value of A is

A)

The division 0/3 will be a rational number because any number divided by 0 is undefined, but in this case, the division is defined and the result is 0, which is a rational number.

B)

The division 3/0 will not be a rational number because any number divided by 0 is undefined, and therefore, the division is not defined.

C)

The division -3/8 will be a rational number because it can be expressed as a ratio of two integers (-3 and 8) and can be written in the form of a fraction -3/8

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According to the given sample data, and assuming a sample standard deviation of 5 hours, the results of the hypothesis test suggest that there is substantial evidence to support the assertion that the average time spent using the internet by Canadians exceeds 12.5 hours.

To conduct the hypothesis test, we first set the null and alternative hypotheses. The null hypothesis (H0) states that the mean time spent by Canadians on the internet is equal to or less than 12.5 hours. The alternative hypothesis (Ha) states that the mean time spent by Canadians on the internet is greater than 12.5 hours.

Using the given sample data, and assuming a sample standard deviation of 5 hours, we calculate the test statistic and the p-value. To calculate the test statistic, we use the formula t = (x - μ) / (s / √n), where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

We find that the test statistic is 1.78 (rounded to two decimal places). If the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is strong evidence that the mean time spent using the internet by Canadians is greater than 12.5 hours.

If the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean time spent using the internet by Canadians is greater than 12.5 hours.

In this case, assuming a significance level of 0.05, we calculate the p-value to be 0.0397 (rounded to four decimal places). Since the p-value is less than the significance level, we reject the null hypothesis and conclude that there is substantial evidence that the mean time spent using the internet by Canadians is greater than 12.5 hours.

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The mean and standard deviation is x ~ N(76,3).

Given that a population has a mean = 76 and a standard deviation o = 24

We need to find the standard deviation of a sampling distribution of sample means with sample, n = 64.

The mean of the sampling distribution of sample means is =

x = μ

x = 76

Now,

SD = σ/√n

= 24/√64

= 24/8

= 3

Hence, x ~ N(76,3).

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The total amount of paper required is 3π(3+√71)unit²

The equation for the surface area of a cone is given as follows:

A = πr²+πrs.

Height of the cone, h = 8 & radius of the cone = 3, the slant height s is given as: s = √(r²+h²)

Substituting the values of r & h to determine s

s = √(8²+3²)

s = √71

Substituting the values to get Area,

A=π*3²+π*3*√71.

A=3π(3+√71)

Hence, the required paper will be A=3π(3+√71)unit²

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Answer:

58 nickels; 234 dimes; 20 quarters

Step-by-step explanation:

number of dimes = d

number of nickels = n

number of quarters = q

n + d + q = 312

d = 3(n + q)

0.05n + 0.1d + 0.25q = 31.3

n + d + q = 312

d = 3n + 3q

5n + 10d + 25q = 3130

n + 3n + 3q + q = 312

5n + 30n + 30q + 25q = 3130

4n + 4q = 312

35n + 55q = 3130

n + q = 78

7n + 11q = 626

n = 78 - q

7(78 - q) + 11q = 626

546 - 7q + 11q = 626

4q = 80

q = 20

n = 78 - 20 = 58

d = 3(58 + 20) = 3(78) = 234

Answer: 58 nickels; 234 dimes; 20 quarters

The equation of the new line will be y = -9x + 4. Then the correct option is B.

Given that:

Linear equation, y = x + 2

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 y-value of the y-intercept will be raised by 2 units, and the slope will be multiplied by -9.

Then the slope of the equation will be given as,

m = -9 x 1

m = - 9

The y-intercept of the equation is given as,

c = 2 + 2

c = 4

The equation of the new line will be y = -9x + 4. Then the correct option is B.

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In the function y = x + 2, the slope will be multiplied by -9, and the y-value of the y-intercept will be increased by 2 units. Which of the following graphs best represents the new function

The exact value of sin θ, given that cosθ = 1/2 and θ terminates in Quadrant IV, is -√(3)/2.

The Pythagorean Identity states that sin²θ + cos²θ = 1. This identity can be used to find the value of sinθ, given the value of cosθ, and vice versa.

In Quadrant IV, the cosine function is positive, and the sine function is negative. This is because in Quadrant IV, the x-coordinate is positive, and the y-coordinate is negative.

Given that cosθ=1/2, we can use the Pythagorean Identity to find the value of sin²θ.

sin²θ + cos²θ = 1

sin²θ + (1/2)² = 1

sin²θ + 1/4 = 1

sin²θ = 1 - 1/4

sin²θ = 3/4

To find the value of sinθ, we take the square root of both sides of the equation:

sinθ = ±√(3/4)

However, since θ terminates in Quadrant IV, sinθ is negative. Therefore, we take the negative square root of 3/4:

sinθ = -√(3/4)

We can simplify this expression by writing 3/4 as a fraction in terms of its square roots:

sinθ = -√(3/4)

sinθ = -√(3)/√(4)

sinθ = -√(3)/2

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The hypothesis are

Null Hypothesis: The proportion of time the penny lands on heads 0.5

Alternative Hypothesis: The proportion of times the penny lands on heads in not 0.5.

We can denote the proportion of times the penny lands on heads as p.

If the null hypothesis is true, then p = 0.5. If the alternative hypothesis is true, then p is not equal to 0.5.

We can use a hypothesis test to determine if the sample data provides evidence to reject the null hypothesis in favor of the alternative hypothesis. One possible hypothesis test is the two-tailed z-test for proportions.

To perform this test, we would calculate the test statistic :

z = (p' - p) / √(p x (1-p) / n)

where p' is the sample proportion, p is the null hypothesis proportion (0.5), and n is the sample size.

In this case, we have a sample size of n = 50 and a sample proportion of p' = 30/50 = 0.6. We can calculate the test statistic:

z = (0.6 - 0.5) / √(0.5 x 0.5 / 50)

z ≈ 2.24

To determine if this test statistic is significant at the 5% level, we would compare it to the critical values from the standard normal distribution. For a two-tailed test at α = 0.05, the critical values are -1.96 and 1.96.

Since 2.24 falls outside of this range, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the proportion of times the penny lands on heads is not 0.5.

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There are 10 bundles and 1 sticks in the Popsicle sticks

Given that  Sasha has 47 Popsicle sticks (4 bundles of 10 and 7 sticks)

4B+7S=47

Jose has 62 (6 bundles of 10 and 2 sticks).

6B+2S=62

We have to find B and S values

12B+21S=141

12B+4S=124

Subtract both the equations

21S-4S=141-124

17S=17

Divide both sides by 17

S=1

Now let us plug in the value of S

4B+7=47

4B=40

B=10

Hence, there are 10 bundles and 1 sticks in the Popsicle sticks

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Answer:

the absolute value of 6 is just 6

Answer: 638

Step-by-step explanation:1

2

3

4

5

7

6

7

8

9

3/8 x ?/? > 1

3/8 x ?/? = 1

An equation to represent A, the area in square feet, as a function of w, the width in feet will be; A = 120W -2W²

Here, the perimeter of the rectangle will give:

120 = L + 2W

Area = LW

We know that the area of a rectangle is l × w

When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000

When w = 20, length = 120 - 40 = 80,  area =  80 x 20  = 1600

When w = 40, length = 120 - 80 = 40.  area = 40 x 40 = 1600.

So, the completed table will be

Width            Length          Area

10                    100              1000

20                    80              1600

40                    40              1600  

w                  120 - 2w        (120 - 2w) w

To maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60

On substituting, we have,

A = LW = (120 - 2W) W

L = 120 - 2W,

On simplification, we have

A = 120W -2W²

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The expressions that shows a correct way to set up the slope formula for the line that passes through the points (3,6) and (-7,-4) is (-4-6) / (-7 - 3) (option c).

To find the slope of a line that passes through two points, we can use the slope formula, which is:

slope = (change in y) / (change in x)

This formula tells us how much the y-coordinate changes (rise) for every one unit of change in the x-coordinate (run).

Now let's use the given points (3,6) and (-7,-4) to set up the slope formula. We'll call the first point (x₁, y₁) and the second point (x₂, y₂). Then we can plug these values into the slope formula:

slope = (y₂ - y₁) / (x₂ - x₁)

Plugging in the coordinates of the two given points, we get:

slope = (-4 - 6) / (-7 - 3)

We simplify this expression to get:

slope = (-10) / (-10)

Which simplifies further to:

slope = 1

So the correct way to set up the slope formula for the line that passes through the points (3,6) and (-7,-4) is:

slope = (y₂ - y₁) / (x₂ - x₁)

= (-4 - 6) / (-7 - 3)

= 1

Therefore, the slope of the line passing through these two points is 1.

Hence the correct option is (c).

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The probability that a student is chosen randomly from the class has a cat or a dog is 15/20.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

The class has a cat and a dog = 9

Has a dog and does not have a cat = 2

Does not have a dog and has a cat = 4

Does not have dog and cat = 5

The total strength of the class is 20

The probability that a student is chosen randomly from the class has a cat or a dog =  Number of favorable outcomes / total number of outcomes

P(E) = 15 /20

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Answer:

Step-by-step explanation:

its 11/28

The water evaporated.

Option B is the correct answer.

We have,

When a liquid is left open in a container, it can undergo a phase change to become a gas or vapor, which is known as evaporation.

In this case,

The water in the beaker would have evaporated, leaving behind the salt. The water did not disappear forever but instead changed state to become a gas in the air.

Thus,

The water evaporated.

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Answer:

the answer is C!