A downward opening parabola with vertex (-5,2) and a vertical compression of 0. 5

a) To determine if the treatment has a significant effect, we can perform a hypothesis test using the sample mean. The null hypothesis (H0) states that the treatment has no effect, while the alternative hypothesis (H1) states that the treatment does have an effect. In this case, we are conducting a two-tailed test with α = 0.05, meaning we are looking for extreme values in both tails of the distribution.

b) Using the same approach as in part a, we can calculate the z-score with a population standard deviation of σ = 12. Given M = 54, μ = 50, σ = 12, and n = 16, the z-score is calculated as z = (54 - 50) / (12 / √16) = 1.

To perform the test, we can calculate the z-score using the formula: z = (M - μ) / (σ / √n), where M is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. In this case, M = 54, μ = 50, σ = 8, and n = 16.

Plugging these values into the formula, we get z = (54 - 50) / (8 / √16) = 2. Using a z-table or a statistical calculator, we find that the critical z-value for a two-tailed test with α = 0.05 is approximately ±1.96.

Since our calculated z-value of 2 is greater than the critical value of 1.96, we reject the null hypothesis. This means that the sample mean of 54 is statistically significant and provides evidence that the treatment has a significant effect.

Comparing the calculated z-value of 1 to the critical z-value of 1.96, we see that the calculated value is less than the critical value. Therefore, we fail to reject the null hypothesis.

In other words, the sample mean of 54 is not statistically significant when the population standard deviation is 12, and we do not have sufficient evidence to conclude that the treatment has a significant effect.

The magnitude of the standard deviation (σ) plays a crucial role in hypothesis testing. A larger standard deviation indicates that the data points are more spread out from the mean, resulting in a wider distribution. As a result, it becomes more challenging to detect a significant effect of the treatment, as the variability in the data increases. This is evident when comparing parts a and b of the question.

In part a, where the population standard deviation is σ = 8, the calculated z-value of 2 exceeds the critical value of 1.96. This indicates that the sample mean of 54 is statistically significant, suggesting a significant effect of the treatment.

On the other hand, in part b, where the population standard deviation is larger at σ = 12, the calculated z-value of 1 is smaller than the critical value.

Consequently, we fail to reject the null hypothesis, implying that the sample mean of 54 is not statistically significant, and we cannot conclude that the treatment has a significant effect.

Thus, a larger standard deviation reduces the ability to detect a  significant effect in a hypothesis test.

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Answer: x=12

Step-by-step explanation:

Answer:

  x=1

Step-by-step explanation:

The equation can be simplified and solved using the rules of exponents and the usual inverse operations.

__

Interpreted according to the Order of Operations, your equation is ...

  ((2^2)x)^3 = 64

  (4x)^3 = 64x^3 = 64 . . . . . . use (ab)^c = (a^c)(b^c)

  x^3 = 1 . . . . . . . . . . . . . . divide by 64

  x = ∛1 = 1

__

Perhaps you want x in the exponent:

  (2^(2x))^3 = 64

  2^(6x) = 2^6 . . . . . . . . . use (a^b)^c = a^(bc)

  6x = 6 . . . . . . . . match exponents

  x = 1 . . . . . . divide by 6

_____

Additional comment

Folks are often not careful about identifying exponents. It is helpful if you write the exponent in a way that leaves no ambiguity.

Answer:

Step-by-step explanation:

Initial prediction of sales = 45 automobile

Actual amount sold = 48 automobiles

Absolute error ratio a = actual amount sold - initial prediction/initial prediction

Absolute error ratio a = 48-45/45

Absolute error ratio a = 3/45

%error = actual amount sold - initial prediction/initial prediction * 100%

% absolute error = 48-45/45 * 100

% absolute error = 3/45 * 100

% absolute error b = 6.67%

Answer:

a = Start Fraction 3 over 48 End Fraction; b = 6.25 percent

Step-by-step explanation:

Your Welcome;)

Answer:

four x plus three divided by two

Step-by-step explanation:

2170 toys Jamal assemble altogether during his first 20 days.

What is the arithmetic sequence?

A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.

Here, we have

Given: Jamal got a job working on an assembly line in a toy factory. On the 20th day of work, he assembled 137 toys. He noticed that since he started, every day he assembled 3 more toys than the day before.

We have to find how many toys did Jamal assemble altogether during his first 20 days.

We apply the arithmetic sequence formula and we get

tₙ = t₁ + (n-1)d

137 = t₁ + (20-1)(3)

t₁ = 80

To calculate the total number of toys that Jamal assemble in his first 20 days,

S₂₀ = (20/2)(2×80 + (20-1)(3))

S₂₀ = 2170

Hence, 2170 toys Jamal assemble altogether during his first 20 days.

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The length of the base, AB, can be found to be 12. 49 cm

The base length can be found using the Pythagoras Rule which is:

c ² = a ² + b ²

a = CD which is the height

c = AC

So we can find half od base length when we divide the shape into a right angled triangle :

8 ² = 5 ² + b²

b ² = 64 - 25

b = √ 39

b = 6. 24 cm

Double of this would be:

= 12. 49 cm

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Answer:

57

Step-by-step explanation:

-4x - y + 4

-4(-14) - 3 + 4

56 - 3 + 4

53 + 4

57

Answer:

2

Step-by-step explanation:

The values of x and y are given. So, plug in the given values into the equation.

-4x-y+4

-4(-1/4)-(3)+4=?

1-3+4=?

=2

(I assumed that you wrote -1/4, by the way)

Answer:90

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

i just know

The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

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The value represents the climber's change in elevation during the first minute of the training session is  1/5.

Given,

During the second minute of a two-minute training session, a rock climber completed a 12-meter ascent up the wall. The climber returned to the identical location she had been in at the beginning of the two-minute session.

Let x be the distance climbed by the climber is x m

During the first minutes(60 seconds): distance climbed =\(\frac{x}{60}\)

In the 2nd minute, they climbed 12 m higher than in the 1st minute.

Now, the distance climbed by the climbed in the Second minute = \(\frac{x+12}{60}\)

Now, the change in the elevation during the first minute of the training session= \(\frac{x+12}{60}-\frac{x}{60} = \frac{12}{60}=\frac{2}{10}=\frac{1}{5}\)

Hence, the value represents the climber's change in elevation during the first minute of the training session is \(\frac{1}{5}\)

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Answer:

Physical means the actual wires.  Physical is concerned with how the wires are connected. Logical is concerned with how they transmit.

a. Logical

Step-by-step explanation:

...

The arrangement of network cabling between devices is a physical topology. which is the correct answer would be option (C).

The physical configuration of a network, such as the physical arrangement of wires, media (computers), or cables, is referred to as its topology. A link can connect two or more devices, and when the number of connections reaches two, they constitute a physical topology.

A physical network diagram depicts the connecting of devices via cables or wireless links. A logical network diagram, on the other hand, depicts data and signal transfer throughout a network.

Therefore, the arrangement of network cabling between devices is a physical topology.

Hence, the correct answer would be an option (C).

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Answer:

34

Step-by-step explanation:

Answer:

Step-by-step explanation:

mean µ  =  500

standard deviation  σ  =   100

Required P ( X < µ + σ )

=  P ( X < 500 + 100  )

= P ( X < 600 )

= P [Z < (X - µ) / σ  ]

=  P [Z < (600 - 500) / 100  ]

= P [Z < + 1  ]

= .8413

In terms of percent the probability is 84.13 % .

The number of ways to draw five numbers from a group of twelve numbers without considering the order is 792. This can be calculated using the combination formula nCk = n!/((n-k)!k!).

The number of ways to draw five numbers from a group of twelve numbers without considering the order is given by the combination formula.

The formula is nCk = n!/((n-k)!k!), where n is the total number of items in the group and k is the number of items to be chosen. Applying this formula to the given problem, we get 12C5 = 792.

To understand this formula intuitively, imagine picking a team of five players from a group of twelve players. The number of possible teams is the number of combinations of five players that can be formed from the group of twelve players.

For the first player, we have twelve choices. For the second player, we have eleven choices (since one player has already been chosen). Continuing this process, we have 12111098 ways to choose a team of five players if order matters.

However, since the order does not matter, we need to divide this number by the number of ways the five players can be arranged, which is 54321. Therefore, the number of possible teams is (12111098)/(54321) = 792.

In summary, the number of ways to draw five numbers from a group of twelve numbers without considering the order is 792. This can be calculated using the combination formula nCk = n!/((n-k)!k!), where n is the total number of items in the group and k is the number of items to be chosen.

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Answer:

It would be B

Step-by-step explanation:

24 and 36 greatest common factor is 12 and  its least is 72

Answer: A its B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

if y = 0

0 = -2x + 4 _ eq 1

0 - 4 = -2x

-4 = -2x

divide through by 2

x = -4 ÷ -2

x = 2

if x = 0

y = -2(0) + 4_ eq 2

y = 0 + 4

y = 4

:.(x,y) = (2,4)

Answer:

The answer is 19672212.8cm

Answer:

2 cm^3

Step-by-step explanation:

You have the Volume- 125.6 cm^3

And the height- 10 cm

So you will just do the equation just a different way.

\(V= \pi rx^{2} h\)

125.6 = 3.14·x²·10

Once you solve that you get the radius which is 2

So the answer shall be 2

Answer:

137.5

Step-by-step explanation:

2=25

4=50

6=75

8=100

10=125

11=125+12.5 = 137.5

Answer:

I believe it is 14.

Step-by-step explanation:

Answer: The value of x is 14°

Step-by-step explanation:

Since line m is parallel to n, then then the two given angles will have the same measures. Meaning that 136 degrees has to equation (9x+10).

Set them to equal each other and solve for x.

9x + 10 = 136

    - 10      -10

  9x  = 126

x=  14

Answer:

A. 1&3 are vertical

C. 1&3 are supplementary angles

Answer:

7450

Step-by-step explanation:        

Move the decimal to the right 3 times.

The standard notation is 7450

Standard and scientific notation are the ways to represent numbers mathematically. We write numbers in standard and scientific notations using the rules for respective mathematical concepts. Here, 7.56×1011 7.56 × 10 11 is a scientific notation. 756,000,000,000 756 , 000 , 000 , 000 is standard notation.

Given:

7.45 x 10^3

So, when there is multiplication in decimals then the decimal point would shift to the right side.

Then,

7.45* 1000

=7450

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Answer:

B) 114.511m^3

Step-by-step explanation:

Formula of a cylinder is πr^2 x h

r = radius (half of diameter)

h = height

Since it is 3/4 full you only do 3/4 of the height so- 0.75 x 9.60 which equals 7.2

Half of the diameter is 2.25. 2.25^2 = 5.0625.

The volume of the cylinder = 5.0625π x 7.2

By solving this, you will get approximately 114.511 m^3 as your answer.

Required function is f(x) = 2x-3.

What is function?

In mathematics, a function is a rule or a set of rules that assigns a unique output value to each input value. In other words, it is a way of relating one quantity to another. Functions are used in a variety of fields, such as engineering, physics, economics, and computer science, to describe relationships between variables.

An example of a function is the quadratic function f(x) = x² + 2x + 1. This function takes an input value x and produces an output value that is the result of squaring x, multiplying it by 2, and adding 1. For instance, if we substitute x = 3 in the function, we get:

f(3) = 3² + 2(3) + 1 = 9 + 6 + 1 = 16

To determine which function represents the data in the table, we need to substitute the given values of x into each function and compare the results with the corresponding values of f(x) given in the table.

If we use the function f(x) = 2x-3, we get:

f(0) = -3

f(1) = -1

f(2) = 1

f(3) = 3

f(4) = 5

f(5) = 7

We can see that these values match with the values given in the table, so the function that represents the data in the table is:

f(x) = 2x-3.

Therefore, we can conclude that the function f(x) = 2x-3 represents the data in the table.

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