Select all of the following functions that are quadratic. □ y=2x² 3=2x²-8 y=-2+2x-8 y + 3x = 2x² - 8 Oy+3x²= 2x + 3x²-8​

For the given equation 3x -9y =36 the x-intercept is equal to (12 ,0) and y-intercept is equal to (0,-4).

As given in the question,

Given equation is equal to

3x -9y =36

For the x-intercept of the equation value of y is equal to 0

Substitute y = 0 in the given equation we get,

3x -9(0) = 36

⇒ 3x -0 = 36

⇒ 3x = 36

Divide both the side by 3 we get,

3x/3 = 36/3

⇒ x = 12

x-intercept = ( 12,0)

For the y-intercept of the equation value of x is equal to 0

Substitute x = 0 in the given equation we get,

3(0) -9y = 36

⇒ 0 -9y = 36

⇒ -9y = 36

Divide both the side by -9 we get,

-9y/-9 = 36/-9

⇒ y = -4

y-intercept = ( 0,-4)

Therefore, for the given equation 3x -9y =36 the x-intercept is equal to (12 ,0) and y-intercept is equal to (0,-4).

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Answer:

40kg and 20kg

Step-by-step explanation:

Answer:tana is 40 , Vara is 20

Step-by-step explanation:let x be tana, y be Vara.

x + y = 60

x - y = 20

Eliminate x by subtracting both equations.

Y -(-y) = 40

2y = 40

Y =20

Sub y=20 into x+y =60

X + 20 =60

X = 40

Answer:

92

Step-by-step explanation:

12 + [20(5 - k)]

Substitute the value.

12 + [20(5 - 1)]

Evaluate inside the parenthesis.

12 + [20(4)]

Multiply.

12 + 80

Add.

92

Answer:

56.52 km

Step-by-step explanation:

You can use this formula to find the circumference.

\(C =\pi \:d\)

Here,

C = circumference

d =  diameter

Let us solve now.

\(C =\pi \:d\)

C = 3.14 × 18 km

C = 56.52 km

Hope this helps you.

Let me know if you have any other questions :-)

The bounds for a 95% confidence interval could be option (B) 72 and 79

We know that the 98% confidence interval has bounds of 73 and 80. This means that if we were to repeat the same experiment many times, we would expect that 98% of the time, the true population mean would fall within this range.

To find the bounds for a 95% confidence interval, we can use the fact that a higher confidence level corresponds to a wider interval, and a lower confidence level corresponds to a narrower interval.

Since we want a narrower interval for a 95% confidence level, we can expect the bounds to be closer to the sample mean. We can calculate the sample mean as the midpoint of the 98% confidence interval

(sample mean) = (lower bound + upper bound) / 2 = (73 + 80) / 2 = 76.5

Next, we can use the formula for a confidence interval:

(sample mean) ± (z-score) × (standard error)

where the z-score depends on the desired confidence level, and the standard error depends on the sample size and sample standard deviation. Since we don't have this information, we can assume that the sample size is large enough (i.e., greater than 30) for the central limit theorem to apply, and we can use the formula

standard error = (width of 98% CI) / (2 × z-score)

For a 98% confidence interval, the z-score is 2.33 (found using a standard normal distribution table or calculator). Plugging in the values, we get

standard error = (80 - 73) / (2 × 2.33) = 1.70

Now, we can use this standard error to calculate the bounds for a 95% confidence interval

(sample mean) ± (z-score) × (standard error) = 76.5 ± 1.96 × 1.70

Simplifying, we get

(lower bound) = 76.5 - 3.33 = 73.17

(upper bound) = 76.5 + 3.33 = 79.83

Therefore, the correct option is (B) 72 and 79

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350 cheerleaders. the rate 5:7 is how many do a back tuck. soo the rate 5:7 is the same as 350:490 simplify is 35:49 simplifyed by 7 to 5:7 a

Step-by-step explanation:

the ratio is 5:7 for how many do a back tuck.

soo the rate 5:7 is the same as 350:490 // 35:49 // 5:7. hope that helps!!

Answer:

rational

Step-by-step explanation:

Answer:

1. Do past papers

2. spend your time looking threw questions and understanding them

3. Look at past tests you done before and look into the questions you do not understand

4.ask your teachers to give you some time to help

5. flash cards really help with memorizing!

6. Ask your teacher for work sheets and ask what things you need to revise on, for future tests.

7. if so, you can ask friends to help you

8. go and videos on the topics you don't understand (it really helps)

9. Writing notes are quite helpful

But make sure you uderstand what your write then just copying it down

10. Don't revise for so many hours for all the subjects. Just take your time and understanding is important.

Complete statement : Two events are said to be mutually exclusive if they can not occur at the same time. Two events are said to be Independent  if the occurrence of one does not influence the probability of occurrence for the other.

What are Independent events?

Independent events are events for which the occurrence (or non-occurrence) of one event does not affect the probability of the other event occurring.

Two events are said to be mutually exclusive (or disjoint) if they cannot occur at the same time. In other words, if one event occurs, the other event cannot occur simultaneously.

For example, if we toss a coin, the events "getting a heads" and "getting a tails" are mutually exclusive. If we get a heads, we cannot get a tails at the same time.

Two events are said to be independent if the occurrence of one event does not influence the probability of occurrence of the other event. In other words, the probability of both events occurring together is equal to the product of their individual probabilities.

For example, if we roll a dice twice, the events "getting a 2 on the first roll" and "getting a 4 on the second roll" are independent. The probability of getting a 2 on the first roll is 1/6, and the probability of getting a 4 on the second roll is also 1/6. The probability of getting a 2 on the first roll and a 4 on the second roll is (1/6) x (1/6) = 1/36.

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Answer:

144

Step-by-step explanation:

Multiply each option together 9X4X4=144

Answer: 20°

Step-by-step explanation:

Let's call angle 1 x and angle 2 y

We know that x is three times greater than y, and that means that we can write it like this:

3y = x         pls let me know if this part is confusing

Then we can write this entire equation:

3y + y = 80       remember, x = 3y

4y = 80

y = 20

1/5 (x+0.5) +5.24 = 3/2x + 7/10 (x+2.2)

First, apply the distributive property to solve the parentheses

1/5(x)+ 1/5 (0.5) +5.24 = 3/2x + 7/10(x) + 7/10 (2.2)

1/5x +0.1 +5.24 = 3/2x + 7/10 x + 1.54

Combine like terms

1/5x +5.34 = 11/5x +1.54

Move the x terms to the left side of the equation:

1/5x-11/5x = 1.54-5.34

-2x = -3.8

Divide both sides by -2

-2x/-2 = -3.8/-2

x = 1.9

By using normal distribution of probability, it can be calculated that-

a) When x = 142, z = 1.4

b) When x = 130, z = 0.6

c) When x = 103, z = -1.2

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by

f(x) = \(\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}}\)

Where z = \(\frac{x - \mu}{\sigma}\) , \(\mu\) is the mean and \(\sigma\) is the standard deviation

Here Systolic blood pressure is normally distributed

Mean = 121

Standard deviation = 15

a) x = 142

z = \(\frac{142 - 121}{15}\) = 1.4

b) x = 130

z = \(\frac{130 - 121}{15}\\\) = 0.6

c) x = 103

z = \(\frac{103 - 121}{15}\) = -1.2

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1. 5/6

2. 7/8

3. 1/2

4. 5/4

5. 4/5

6. 5/4

7. 11/12

8. 5/4

9. 11/12

10. 2/3

11. 13/20

12. 1/12

13. 7/22

14. 7/18

15. 2/3

16. 5/12

17. 5/12

18. 3/8

The solution to the initial value problem y'-4y=f(x), y(0)=0 for 0<=x<4 is given by:

y(x) = F(-4)e^(-4x)

The Laplace transform of the differential equation y'-4y=f(x) is given by:

sY(s) - y(0) - 4Y(s) = F(s)

where Y(s) and F(s) are the Laplace transforms of y(x) and f(x), respectively.

Substituting the initial condition y(0)=0 and rearranging, we get:

Y(s) = F(s)/(s+4)

Now we need to find the inverse Laplace transform of Y(s) to obtain the solution y(x). Using the partial fraction decomposition method, we can write:

Y(s) = A/(s+4) + B

where A and B are constants to be determined.

Multiplying both sides by (s+4), we get:

F(s) = A + B(s+4)

Setting s=-4, we get:

A = F(-4)

Setting s=0, we get:

B = Y(0) = y(0) = 0

Therefore, the partial fraction decomposition of Y(s) is given by:

Y(s) = F(-4)/(s+4)

Taking the inverse Laplace transform of Y(s), we get:

y(x) = L^-1{F(-4)/(s+4)} = F(-4)L^-1{1/(s+4)}

Using the table of Laplace transforms, we find that the inverse Laplace transform of 1/(s+4) is e^(-4x). Therefore, the solution to the initial value problem is given by:

y(x) = F(-4)e^(-4x)

where F(-4) is the value of the Laplace transform of f(x) evaluated at s=-4.

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The expected number of empty bins when tossing n balls into n bins, with each toss being independent and equally likely, can be determined using the concept of probability.

Let's define the probability that a specific bin remains empty after n tosses as P(empty). Since each ball has n choices, there are n^n possible ways to distribute the balls. To find the probability that a specific bin is empty, we can consider the situation where balls can be tossed into the remaining n-1 bins, resulting in (n-1)^n possible distributions. Therefore, P(empty) = ((n-1)^n) / (n^n).

Now, to calculate the expected number of empty bins, we can use the concept of linearity of expectation. The expected value of the sum of random variables is equal to the sum of the expected values of the individual random variables. In this case, the random variables represent the empty status of each bin (1 if empty, 0 if not).

The expected number of empty bins is the sum of the probabilities of each bin being empty, which is n * P(empty). So, the expected number of empty bins = n * (((n-1)^n) / (n^n)).

Using this formula, you can determine the expected number of empty bins when n balls are tossed into n bins independently and with equal likelihood.

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The Coase theorem is an economic theory that states that in the absence of transaction costs, the allocation of resources and the distribution of wealth will be efficient regardless of how property rights are assigned.

In this context, the theorem reminds us that efficiency is all about maximizing total welfare, rather than focusing solely on the allocation of resources or the distribution of wealth. When transaction costs are low or non-existent, parties can negotiate with each other to reach mutually beneficial agreements that maximize their combined welfare. This means that ownership of property or resources is less important than the ability of parties to freely negotiate with one another.

For example, imagine two neighboring farms: one produces apples and the other produces honey. If the apple farmer's use of pesticides harms the bee population and reduces the honey farmer's production, the honey farmer could demand compensation from the apple farmer. If transaction costs are low, the two farmers could negotiate a solution that is mutually beneficial, such as the apple farmer paying for the honey farmer to relocate their bees to a safer area. In this scenario, the assignment of property rights is not as important as the ability of the two parties to negotiate and reach an agreement that maximizes their total welfare.

Overall, the Coase theorem highlights the importance of considering the broader impacts of economic decisions and recognizing that efficiency depends on maximizing the overall benefits to all parties involved, rather than just focusing on individual outcomes.

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The value of x when f=-3 is -1 as stated.

Given:

We are given with a table with 2 column and 7 rows.

First column represents different values of  'x'

The second column represents the corresponding f(x)  values.

Observing f(x) = -3

we see that -3 is the 4th value in f(x) - column.

Therefore the corresponding 4th value of 'x' in x-column would be the required x.

Each element of a non-empty set A is associated with at least one element of another non-empty set B by a process or relation known as a function. In mathematics, a relation f is referred to as a function when it connects two sets, A and B, respectively. When a = A and b = B, f = (a,b)|

We observe that the 4th value in x column is -1.

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Answer:

x = 12 units

Step-by-step explanation:

In the picture attached,

Since, DE and BC are the parallel lines,AC and AB are the transverse.

Therefore, ∠AED ≅ ∠ABC [Alternate angles]

∠ADE ≅ ∠ACB [Alternate angles]

ΔADE ~ ΔACB [By AA postulate of similarity]

By the property of similarity,

If two triangles are similar then their corresponding sides will be proportional.

\(\frac{\text{AB}}{\text{AE}}=\frac{\text{AC}}{\text{AD}}\)

\(\frac{(4+8)}{4}=\frac{(6+x)}{6}\)

\(3=1+\frac{x}{6}\)

x = 12

Therefore, length of missing segment is 12 units.

Answer:

son weight = 72

Step-by-step explanation:

D + S = 180

D + 2S = 252

S=252-180

S = 72

D= 108

Approximately 84% (34% + 50%) of the jumpers were in the group jumping below 79.5 inches. This can be answered by the concept of Standard deviation.

In a high school high jump contest, the mean height was 76 inches, and the standard deviation was 3.5 inches. To find the percentage of jumpers below 79.5 inches, we first need to determine how many standard deviations away 79.5 inches is from the mean.

To do this, subtract the mean from 79.5 inches and divide by the standard deviation:
(79.5 - 76) / 3.5 = 3.5 / 3.5 = 1

So, 79.5 inches is 1 standard deviation above the mean. According to the empirical rule, approximately 68% of the data falls within 1 standard deviation of the mean in a normal distribution. Since we are looking for jumpers below 79.5 inches, we need to consider the lower half of this 68%, which is 34%. Additionally, 50% of the data is below the mean.

Therefore, approximately 84% (34% + 50%) of the jumpers were in the group jumping below 79.5 inches.

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Answer: The area is 6.5

A boxplot is a visual display that provides information about the distribution of a dataset. When we want to determine the percentage of data that falls within a certain range, we need to look at the boxplot and find the interquartile range (IQR). The IQR is the difference between the first and third quartiles, which contains the middle 50% of the data. So, approximately 50% of the data lie between 4 and 8 hours.

A boxplot shows the median, quartiles, and possible outliers. To determine the percentage of data that falls between two values, we need to calculate the proportion of the IQR that corresponds to this range. For example, if the IQR is from 2 to 10, and we want to know the percentage of data between 4 and 8, we need to calculate the proportion of the IQR that corresponds to this range. This can be done by subtracting the lower value of the range from the upper value and dividing by the IQR:

Proportion = (8 - 4) / (10 - 2) = 4 / 8 = 0.5

Therefore, approximately 50% of the data lie between 4 and 8 hours. The answer is (C) about 50%.

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Answer:

I'm guessing it's D

Step-by-step explanation:

It says D is the answer

Answer:

Hey there!

Solving for a:

a=x-b

Solving for x:

x=a+b

Solving for b

a+b=x

b=x-a

Let me know if this helps :)

Answer:

12 units

Step-by-step explanation:

area of hexagon = .5*a*p

p = perimeter of hexagon=6s

216√3 = .5*6√3*6s

72= 6s

s=12

1) To find a vector parallel to the line defined by the symmetric equations x + 2y - 4z = -5, -9, 5, we can read the coefficients of x, y, and z as the components of the vector.

Therefore, a vector parallel to the line is <1, 2, -4>.

2) To find a point on the line, we can set one of the variables (x, y, or z) to a specific value and solve for the other variables. Let's set x = 0:

0 + 2y - 4z = -5

Solving this equation, we get:

2y - 4z = -5

2y = 4z - 5

y = 2z - 5/2

Now, we can choose a value for z, plug it into the equation, and solve for y.

Let's set z = 0:

y = 2(0) - 5/2

y = -5/2

Therefore, a point on the line is (0, -5/2, 0).

3) The parametric equations of the line through the point (4, -1, -6) and parallel to the given line with the parametric equations x(t) = 2 + 5t, y(t) = -8 + 6t, z(t) = 8 + 7t, can be obtained by substituting the given point into the parametric equations.

x(t) = 4 + (2 + 5t - 4) = 2 + 5t

y(t) = -1 + (-8 + 6t + 1) = -8 + 6t

z(t) = -6 + (8 + 7t + 6) = 8 + 7t

Therefore, the parametric equations of the line are:

x(t) = 2 + 5t

y(t) = -8 + 6t

z(t) = 8 + 7t

4) Given the lines L₁: x(t) = 6, y(t) = 5 - 3t and L₂: y(s) = 7 + t, z(s) = 3s - 4, we need to find the acute angle between the lines.

First, we need to find the direction vectors of the lines. The direction vector of L₁ is <0, -3, 0> and the direction vector of L₂ is <0, 1, 3>.

To find the acute angle between the lines, we can use the dot product formula:

cosθ = (v₁ · v₂) / (||v₁|| ||v₂||)

Where v₁ and v₂ are the direction vectors of the lines.

The dot product of the direction vectors is:

v₁ · v₂ = (0)(0) + (-3)(1) + (0)(3) = -3

The magnitude (length) of v₁ is:

||v₁|| = √(0² + (-3)² + 0²) = √9 = 3

The magnitude of v₂ is:

||v₂|| = √(0² + 1² + 3²) = √10

Substituting these values into the formula, we get:

cosθ = (-3) / (3 * √10)

Finally, we can calculate the acute angle by taking the inverse cosine (arccos) of the value:

θ = arccos((-3) / (3 * √10))

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Answer:

A=9

Step-by-step explanation:

15÷(3+2)×3

=15÷5×3

=3×3

=9

Hope this helps.