Exponents and Exponential Functions Unit Test

someone PLEASE oh PLEEEEEAAAASSSSEEEEE explain to me all of the answers cuz i just can't think straight, plus, mathematics are literally making mah brain go "FLOP"

HMMMM -(10)^-1
A. -1/10
B. -1/-1^10
C. 1/10
D. 10

(-7.4)^0

A. -1
B. -7.4
C. 0
D. 1

-1/a^-2
A. -a2
B. -2/a
C. -2a
D. a^2

5^4 x 5^7

A. 125^11
B. 15^11
C. 5^28
D. 5^11

Simplify this expression:

(3)^10 (3)^-9

A. 3
B. 1/3
C. 9^-90
D. 9

(t^8)^2

A. 2t^16
B. t^10
C. t^16
D. t^64

(5t^3)^-4

A. 625/t^12
B. 20/t^7
C. 1/625t^12
D. 1/20t^7

(ok i'm sorry if i don't write the rest of the questions/options, it's just my back is hurting from leaning to long and my fingers hurt for typing to long and my brain is burning up because of how many numbers and letters there are in this test......)

(IF YOU KNOW THE REST OF THE QUESTIONS AND OPTIONS PLEASE WRITE IT ALONG IN YOUR ANSWER!!! I NEED IT ASAP OR ELSE I'M GETTING AN F- IN MY GRADE ._.)

Answer:

126/100

Step-by-step explanation:

126% / 100

= 1.26

Answer:

1.26

Step-by-step explanation:

divide 126 by 100 first

\(\frac{126}{100}\)

you will get

1.26

Answer:

3/5^4

Step-by-step explanation:

(2^5 / 3^2)^4

(32 / 9)^4

= 159.8195

Answer:

option 1

Step-by-step explanation:

y ≤ x - 2

-4 ≤ 2-0

-4 ≤ 2  Satisfies the inequality

y ≥ - x - 4

-4 ≥ - 2- 4

-4 ≥ - 6  (2 , -4) satisfies the inequality

Answer:

Measure of side a: 6

Measure of side b: 8

Measure of side c: 10

Side a/c: 6/10 = 3/5

Side b/c: 8/10 = 4/5

Side a/b: 6/8 = 2/3

Step-by-step explanation:

\(\beta=59\ degrees\)

Step-by-step explanation:

\(< ABC+ < BAC=90\ degrees\\ The\ acute\ angles\ of\ a\ right\ triangle\ are\ complementary.\)

\(\beta+31\ degrees=90\ degrees\\ Substitute\ < ABC=\beta, < BAC=31\ degrees\ into\\ < ABC+ < BAC=90\ degrees\)

\(\beta=59\ degrees\\ Calculate\ \beta+31\ degrees=90\ degrees\)

Answer:

Angle T = Angle Q

Step-by-step explanation:

Logical

The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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A Z-score represents how many standard deviations an individual data point is from the mean of a dataset. The formula for calculating a Z-score is:

Z = (X - μ) / σ

Where:
- Z is the Z-score
- X is the individual data point
- μ (mu) is the mean of the dataset
- σ (sigma) is the standard deviation of the dataset

If you can provide the data or statistics needed, I'd be more than happy to help you calculate the Z-scores for the given problems.

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Answer:

No, all of her work is correct.

Step-by-step explanation:

Answer:

No, all of her work is correct.

Step-by-step explanation:

All of her work is correct.

The first step is showing factorization of √50

The second step is simplifying the factorization

The third step is simplifying the entire radical.

When you take a square root of a square, they cancel out, so:

√5² = 5

We multiply it with our leftover √2 and we get:

5√2

Because of the SSS postulate for proving triangles congruent, you can say that triangles DEG and FEG are congruent. Corresponding parts of congruent triangles are congruent (CPCTC) means that angles DEG and FEG are congruent, which means their measures are equal. So 3y + 4 = 5y - 10.

4 = 2y - 10

14 = 2y

7 = y

The measure of angle DEF is 50 degrees

A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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APA format was developed to create a uniform standard of writing.

APA format, which stands for the American Psychological Association format, was established to provide a standardized structure and style for writing scientific papers in the social sciences. It ensures consistency and uniformity in the presentation of research papers, allowing researchers to communicate their work effectively and facilitate the dissemination of knowledge. APA format includes guidelines for organizing the content, citing sources, formatting references, and presenting data. By following these guidelines, researchers can promote clarity, accuracy, and professionalism in their written work. The adoption of APA format helps maintain a common writing style across various disciplines, enhancing readability, facilitating comprehension, and ensuring that scholarly work adheres to established conventions.

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The inequality "12 ≤ a ≤ 18" represents the age range, "a", of players on a baseball team.

As per the question, it means that the age of each player is either equal to or greater than 12, and at the same time, it is either equal to or less than 18.

The inequality "12 ≤ a ≤ 18" represents the age range, "a", of players on a baseball team. It indicates that the ages of the players fall between 12 and 18, inclusive.

The symbol "≤" represents "less than or equal to."

Thus, any age value between 12 and 18, including 12 and 18 themselves, would satisfy the given inequality and be within the age range of the players on the baseball team.

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The missing figure is as follows:

Answer:

The cubic function f(x) = x3 is symmetric about the origin (it is an odd function). Here are some types of functions that are odd: Lines Through The Origin – any line with a zero y intercept (b = 0) and a nonzero slope (m not zero) will have equation f(x) = mx.

Step-by-step explanation:

Answer: No

f(x) = x³ + 2x − 5

Step-by-step explanation:

No

f(x) = x³ + 2x − 5

Answer:

$28,100

Step-by-step explanation:

I divided 140.50 by 10 to get 14.05

Then, I multiplied 14.05 by 2000.

I believe the answer is $28,100

(I might be wrong. Sorry if I am. Pease don't get mad)

Hope I helped :)

Please consider Brainliest :)

Answer:

(- 1, - 3 )

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

The lines intersect at (- 1, - 3 ) ← solution

Answer:

here is your aneswer

the answer. will be 40

the coordinates of B' after dilating ABCD by a factor of 3 are (3a,3b). we need to first determine the center of dilation and then use the dilation formula to find the new coordinates.

Assuming that ABCD is a rectangle, we can find the center of dilation by finding the midpoint of AC, which is the line connecting the center of the rectangle to its opposite vertex. Let's call this point M.

To find the coordinates of M, we can use the midpoint formula:

M = (A+C)/2

Assuming that A = (-a,b) and C = (a,-b), we get:

M = ((-a,b) + (a,-b))/2 = (0,0)

So the center of dilation is the origin (0,0).

Now, to find the coordinates of B' after dilation, we can use the dilation formula:

B' = k * B

where k is the dilation factor (in this case, k = 3) and B is the original coordinates of point B.

Assuming that B = (a,b), we get:

B' = 3 * (a,b) = (3a,3b)

So thethe coordinates of B' after dilating ABCD by a factor of 3 are (3a,3b).

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Answer:

44,62, and where is E

Step-by-step explanation:

Part (i)

--------

Reason:

Angle CBA is a right angle (thales theorem), so angle DBA must add to DBC to get 90 degrees. In other words, we solve x+46 = 90 to get x = 44.

============================================================

Part (ii)

--------

Reason:

Both inscribed angles DAC and DBC subtend the same arc (minor arc DC), so the inscribed angles are congruent.

============================================================

Part (iii)

--------

Reason:

Angle BDC is 28 degrees since angle BAC is also 28 degrees (similar reasoning as part ii above). Let y = angle BCD

Focus on triangle BCD. The three interior angles add to 180

B+C+D = 180

46+y+28 = 180

y+74 = 180

y = 180-74

y = 106

Then subtract 180 from this to get the exterior angle BCE

angle BCE = 180-(angle BCD)

angle BCE = 180-y

angle BCE = 74

Or as a shortcut, you could use the remote interior angle theorem

angle BCE = (angle BDC) + (angle DBC)

angle BCE = (28) + (46)

angle BCE = 74

Answer:

Below

Step-by-step explanation:

Z score is the ± standard deviations from the mean

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

Answer:

the answer is B

Step-by-step explanation:

Answer:

Answer: The same number of tickets was sold on the fourth day and tenth day.

Answer:

A

Step-by-step explanation:

edge 2021

(a) The potential at x = 0 is = 10.4 V

The potential at x = 3 is = - 9.1 V

The potential at x = 6 is = - 28.6 V

(b) At every value of x =0, 3, 6 the electric field is 6.50 V/m and direction is + X axis.

Given that,

V = a + bx

a = 10.4 V and b = - 6.50 V/m.

(a) The potential at x = 0 is,

V = 10.4 - 6.50 * 0 = 10.4 V

The potential at x = 3.0 m is,

V = 10.4 - 6.50 * 3  = - 9.1 V

The potential at x = 6.0 m is,

V = 10.4 - 6.50 * 6 = - 28.6 V

(b) Electric field E can be written as,

E = - dV/dx

E = -d/dx [10.4 - 6.50 x]

E = 6.50 V/m

The direction of electric field is in the direction in which the electric potential decreases. From previous part if we move along positive X the potential decreases, so the direction of electric field at x = 0 is along + X axis.

The electric field is independent of x. So at every value of x the direction along + X axis and the value is 6.50 V/m.

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a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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This introduces nonresponse bias, as the survey results may not accurately represent the opinions and characteristics of the entire population being surveyed.

Nonresponse bias occurs when individuals who choose not to participate in a survey differ in important ways from those who do participate, leading to potential distortions in the survey results. In this case, the suspicion of the volunteers expressed by some people influences their decision not to participate, resulting in a nonresponse bias.

To determine the extent of nonresponse bias, researchers typically compare the characteristics of the respondents and non-respondents. If the non-respondents significantly differ from the respondents in terms of demographic factors, attitudes, or other relevant variables, it suggests the presence of nonresponse bias.

In this particular scenario, the suspicion expressed by certain individuals towards the volunteers leads them to opt out of participating in the survey. This introduces nonresponse bias, as the survey results may not accurately represent the opinions and characteristics of the entire population being surveyed. To mitigate nonresponse bias, researchers can employ techniques such as follow-up surveys or weighting adjustments to ensure a more representative sample and minimize the potential impact of nonresponse on the survey findings.

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Answer:

150

Step-by-step explanation:

5×10×3=150 I think that's how you do area I could be wrong if I am then oops

Answer:

Step-by-step explanation:

You want values of ∆y and dy for y = x² -6x and x = 5, ∆x = dx = 0.5.

The value of dy is found by differentiating the function.

  y = x² -6x

  dy = (2x -6)dx

For x=5, dx=0.5, this is ...

  dy = (2·5 -6)(0.5) = (4)(0.5)

  dy = 2

The value of ∆y is the function difference ...

  ∆y = f(x +∆x) -f(x) . . . . . . . where y = f(x) = x² -6x

  ∆y = (5.5² -6(5.5)) -(5² -6·5)

  ∆y = (30.25 -33) -(25 -30) = -2.75 +5

  ∆y = 2.25

__

Additional comment

On the attached graph, ∆y is the difference between function values:

  ∆y = -2.75 -(-5) = 2.25

and dy is the difference between the linearized function value and the function value:

  dy = -3 -(-5) = 2.00

<95141404393>

Answer:

Step-by-step explanation:

MULTIPLY BY 442 THEN DIVED 55 FROM YOUR CURRENT AWNSER

There will be $21,935.05 in retirement account on the day of retirement.

To calculate the amount of money you will have in your retirement account on the day you retire:

The annual contribution to your retirement account is $4,500.

The interest rate is 9.5% per year.

You plan to retire in 43 years.

To calculate the amount of money in your retirement account, we can use the following formula:

retirement fund = annual contribution * (1 + interest rate)**number of years

Plugging in the values for the annual contribution, interest rate, and number of years, we get:

retirement fund = 4500 * (1 + 0.095)**43 = 21935.05

Therefore, you will have $21,935.05 in your retirement account on the day you retire.

Correct Question:

You are trying to decide how much to save for retirement. Assume you plan to save $4,500 per year with the first investment made one year from now. You think you can earn 9.5​% per year on your investments and you plan to retire in 43 ​years, immediately after making your last $4,500 investment. How much will you have in your retirement account on the day you​ retire?

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