The value of $y$ varies inversely as $\sqrt x$ and when $x=2$, $y=4$. What is $x$ when $y=1$?

What we do is simply replace every n with k+1. So (3n)^2 turns into (3(k+1))^2

We see that only choice A has the correct term mentioned on the left hand side, so this must be the answer.

The right hand side is treated the same way. We plug in n = k+1. Your teacher did a bit of algebraic manipulation to get what is shown for choice A.

Answer:

  (c)  the converse of the original conditional statement

Step-by-step explanation:

If a conditional statement is described by p→q, you want to know what is represented by q→p.

For the conditional p→q, the variations are ...

As you can see from this list, ...

  the converse of the original conditional statement is represented by q→p, matching choice C.

__

Additional comment

If the conditional statement is true, the contrapositive is always true. The inverse and converse may or may not be true.

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Answer:

11

Step-by-step explanation:

\( \mathcal{SOLUTION}\begin{cases} \rm \mapsto \: \dfrac{3}{4} (x + 1) + 1 = \dfrac{1}{2} (x - 2) + 5 \\ \rm \mapsto \: \dfrac{3(x + 1)}{4} + 1 = \dfrac{1(x - 2)}{2} + 5 \\ \rm \mapsto \: \dfrac{3x + 1}{4} + 1 = \dfrac{x - 2}{2} + 5 \\ \rm \mapsto \: \dfrac{3x + 1}{4} - \dfrac{x - 2}{2} = 5 - 1 \\ \rm \mapsto \: \dfrac{3x + 1 -(2 x - 4)}{4} = 4 \\ \rm \mapsto \: \dfrac{3x + 1 - 2x + 4}{4} = 4 \\ \rm \mapsto \: x + 5 = 16 \\ \rm \mapsto \: x = 16 - 5 \\ \rm \mapsto \: x = 11\end{cases}\)

Answer:

64:125

Step-by-step explanation:

When you go from a length ratio to an area ratio you need to square the numbers involved: \(4^{2} :5^{2}\) = 16 : 25

By the same logic, if you want to go from length to volume you need to cube the numbers involved: \(4^{3} :5^{3}\) = 64 : 125

Answer:

Can confirm, it’s a=16.23 and b=17.99

The exponential function shown in the table has the equation y = 3 * 4x.

The general form of an exponential function is y = \(ab^x\), where "a" is the initial value of y when x = 0 and "b" is the common ratio.

Using the given table, we can find "a" by looking at the value of y when x = 0, which is 3. So, a = 3.

To find "b", we can use the ratio of consecutive outputs:

b = y2 / y1 = 48 / 12 = 4

We can verify this ratio by also checking the ratio of y3 to y2:

b = y3 / y2 = 192 / 48 = 4

Therefore, the equation of the exponential function represented by the table is:

y = 3 * 4^x

where x is the input (the value of x in the table) and y is the output (the corresponding value of y in the table).

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The given function f(x)=-2(3+x)²+2x² , is a linear function.

Where:

 A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.

   A function can be linear or quadratic, this is evidenced by the higher exponential degree, in our case we have the following function:

f(x) = -2(3+x)²+2x² we solve the function that seems to be quadratic because it has the highest degree the number "2" in the variable, however we will solve its reduction.

We solve the trinomial and substitute

(3+x)² = (9 + 6x + x²)

-2(9 + 6x + x²) + 2x²

-18 - 12x - 2x² + 2x² + 2x²

0x² - 12x - 18 is a linear function

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Answer: 0.75

Step-by-step explanation:

100/4=25

25*3 = 75

0.75

Answer:

3/4 in decimal form is 0.72

Step-by-step explanation:

To find the answer we just divide 3 by 4 and we get 0.72.  Therefore, 0.72 is our answer.

The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

To determine the critical path of the project, we need to find the longest path of activities that must be completed in order to finish the project on time. This is done by calculating the earliest start time (ES) and earliest finish time (EF) for each activity.

Starting with activity A, ES = 0 and EF = 4. Activity B can start immediately after A is complete, so ES = 4 and EF = 7. Activity C can start after A is complete, so ES = 4 and EF = 6. Activity D can start after B is complete, so ES = 7 and EF = 9. Finally, activity E can start after C and D are complete, so ES = 9 and EF = 11.

The variance for each activity is also given, which allows us to calculate the standard deviation and determine the probability of completing the project on time. The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

Using the expected durations and variances, we can calculate the standard deviation of the critical path. This information can be used to determine the probability of completing the project on time.

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The equation to plot in the complex Cartesian plane is 2Re(z) - |z²| ≥ -3Im(iz).

To plot the equation 2Re(z) - |z²| ≥ -3Im(iz) graphically, you can follow these steps:

1. Represent the complex number z in terms of its real and imaginary parts, z = x + yi, where x is the real part and y is the imaginary part.

2. Substitute the values of x and y into the equation and simplify it.

3. Separate the equation into real and imaginary parts.

4. For each part, plot the corresponding inequality on the Cartesian plane.

- For the real part, plot the inequality 2x - |(x + yi)²| ≥ -3y.

- For the imaginary part, plot the inequality 0 ≥ 0 (as -3Im(iz) = 0 for all values of x and y).

5. Determine the common region that satisfies both inequalities. This region represents the solution to the original equation.

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Answer:

above sea level

Step-by-step explanation:

The value of the algebraic expression 11.5x + 10.9y  at x = 6 and y = 7 is 145.3

What is an algebraic expression?

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division

The given algebraic expression is 11.5x + 10.9y

We have to find the value of the algebraic expression at x = 6 and y = 7

Putting x = 6 and y = 7 in the algebraic expression,

\(11.5 \times 6 + 10.9 \times 7\)

69 + 76.3

145.3

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We can learn a lot about a population if we select a sample of it.

Selecting a representative sample is an important aspect of conducting research or making inferences about a population. Here's more information about the concept of a representative sample and its significance:

Definition: A representative sample is a subset of individuals or elements from a larger population that accurately reflects the characteristics, diversity, and distribution of the population. The goal is to obtain a sample that closely resembles the population in terms of relevant attributes or variables of interest.

Random sampling: The most common approach to achieving a representative sample is through random sampling. Random sampling involves randomly selecting individuals or elements from the population, ensuring that each member of the population has an equal chance of being included in the sample. This helps minimize bias and increase the likelihood of obtaining a representative sample.

Importance of representativeness: A representative sample is crucial because it allows researchers to generalize their findings from the sample to the larger population. When the sample is representative, the results obtained from studying the sample are likely to be applicable and valid for the population as a whole.

Avoiding sampling bias: Sampling bias occurs when the selected sample is not representative of the population, leading to inaccurate or skewed results. Various types of bias, such as selection bias or non-response bias, can compromise the representativeness of the sample. Efforts must be made to minimize or address these biases to ensure the sample accurately represents the population.

Statistical validity: The validity of statistical inferences, such as estimating population parameters or testing hypotheses, relies on the representativeness of the sample. A representative sample helps ensure that the results obtained from the sample accurately reflect the characteristics and behavior of the larger population, increasing the statistical validity of the findings.

Generalizability: The ultimate goal of using a representative sample is to make valid inferences and generalizations about the population. By studying the sample, researchers can gain insights, make predictions, and draw conclusions that can be applied to the broader population with a certain level of confidence.

In summary, selecting a representative sample is vital for accurate research and drawing valid conclusions about a population. It helps minimize bias, ensures statistical validity, and allows for generalizing findings to the larger population with greater confidence.

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9514 1404 393

Answer:

  $100

Step-by-step explanation:

The amount of simple interest earned is given by the formula ...

   I = Prt

where P is the amount investe, r is the annual rate, and t is the number of years.

Solving for P, we find ...

  P = I/(rt) = $5.00/(0.005·10) = $100

Susan deposited $100.

Answer:

The domain is the set of real numbers. In interval form, the domain of f is (-00,000)

Step-by-step explanation:

Answer:

(3, -2)

Step-by-step explanation:

I attached a picture of the work

hope this helps

Answer:

(3,-2)

Step-by-step explanation:

use m a t h w a y! its free and amazing

Answer:

3?

Step-by-step explanation:

It depends on the price of the bottle, for example if the bottle is $1 then you can buy 3 but if it's 50¢ then you can buy 6. If there is tax then the amount of bottles you buy will be less than what it be without tax

Answer:

A

Step-by-step explanation:

Answer:

the answer is A your welcome

The value of the net force acting on the block will be equal to 79N.

Force may be defined as the product of mass and acceleration, and it acts on the body in order to move the body. Since, the external force is acting on the block there will be a frictional force which opposes the block to move. The frictional force may be represented by f(k) and is given by

f(k) = external force - (ma)

f(k) = 40N - (5×6)

f(k) = 40N - 30N

f(k) = 10N and since it opposes the external force then the sign will be negative that is f(k) = -10N.

Also, there is a force of gravity acting on the body which will be equal to mg where 'g' is the acceleration due to gravity.

Now, force of gravity = mg

= 5×9.8 = 49N

Now, net force acting on the block = 40N - 10N + 49N

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According to the information the correct match would be: 3 1/2 - This is a rational number, but not an integer, 0.56 - This is a rational number, but not an integer, 5 - This is an integer, Square root of 11 - This is an irrational number, -3 1/2 - This is a rational number, but not an integer.

To determine the type of number, we need to understand the properties of each number.

3 1/2 can be expressed as the fraction 7/2, which is a rational number (a number that can be expressed as a fraction), but not an integer (a whole number without a fractional or decimal part).

0.56 is a rational number as it can be expressed as the fraction 28/50, but it is not an integer as it has a decimal part.

5 is an integer because it is a whole number without any fractional or decimal part.

The square root of 11 is an irrational number since it cannot be expressed as a fraction or a terminating or repeating decimal.

-3 1/2 can be expressed as the fraction -7/2, which is a rational number (a number that can be expressed as a fraction), but it is not an integer (a whole number without a fractional or decimal part).

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Then the probability of randomly choosing a student with one sibling is:

P =  0.42

To get this probability, we need to take the quotient between the number of students that have a sibling and the total number of students.

On the table we can see that there are:

2 + 7 + 4 + 13 = 26 students in total.

And of these, the ones that have one sibling are:

7 students with only one sister

+

4 students with only one brother.

7 + 4 = 11

Then the probability of having one sibling is:

P = 11/26 = 0.42

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1. The test statistic falls outside the critical t-values therefore we reject the null hypothesis

2. The confidence interval is constructed as CI = x ± (t_(α/2, df) * (σ / √n))

3. The conclusion is there is sufficient evidence to suggest that the mean inside bearing diameter is different from 8.25 cm

1. Hypothesis Testing:

Null hypothesis (H₀): The mean inside bearing diameter is 8.25 cm.

Alternative hypothesis (H₁): The mean inside bearing diameter is not equal to 8.25 cm.

We will conduct a two-sided hypothesis test using a significance level (alpha) of 0.05.

Given:

Sample size (n) = 15

Sample mean (x) = 8.2535 cm

Standard deviation (σ) = 0.002 cm

To test the hypothesis, we will use a t-test since the population standard deviation is unknown and the sample size is small.

Calculate the test statistic (t-value):

t = (x - μ) / (σ / √n)

where μ is the hypothesized mean under the null hypothesis.

t = (8.2535 - 8.25) / (0.002 / √15)

t = 6.77

Calculate the critical t-values for a two-sided test at a 95% confidence level (alpha = 0.05):

Since the sample size is small (n = 15), we will use the t-distribution and degrees of freedom (df = n - 1 = 14) to find the critical t-values.

t_critical = ± t_(α/2, df)

If you look up the critical t-value for alpha/2 = 0.025 and df = 14 in the t-table or use a statistical calculator, we have 2.51

t_critical = 2.51

Compare the test statistic to the critical t-values:

Since the test statistic falls outside the critical t-values, we reject the null hypothesis.

2. Confidence Interval:

To construct a 95% confidence interval, we will use the formula:

CI = x ± (t_(α/2, df) * (σ / √n))

3. Conclusion:

Since the test statistic falls outside the critical t-values, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean inside bearing diameter is different from 8.25 cm.

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The mean (µx) and standard deviation (σx) of a sample can be determined using the given parameters of the population mean (µ), population standard deviation (σ), and sample size (n).

In this case, since we are given the population mean (µ = 84), the mean of the sample (µx) will be the same as the population mean.

µx = 84 (same as the population mean)

σx = 18 / √36 = 3 (the population standard deviation divided by the square root of the sample size)

To determine the standard deviation of the sample (σx), we divide the population standard deviation (σ = 18) by the square root of the sample size (n = 36). This is based on the principle that the standard deviation of the sample is expected to be smaller than the standard deviation of the population, and it decreases as the sample size increases.

Therefore, in this scenario, the mean of the sample (µx) is 84, and the standard deviation of the sample (σx) is 3. These values represent the central tendency and variability of the sample data.

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Answer:

iwiwkkskskhsdvhsishvsuavuiisvys

Answer:

Step-by-step explanation:

I'm assuming that the triangle legs are the same length. if that's the case, set 10 equal to the triangle are formula.

A = 1/2 * b * h

10 = 1/2 * 2b (since both legs are same length assuming)

20 = 2b

b = 10 square units

Hope this helps

Answer:

slope is 1/2

Step-by-step explanation:

rise is 1 and run is 2

Answer:

A

Step-by-step explanation:

P = 4 pi I r^2    solve for I      Divide both sides by 4 pi r^2

to get

I = P / (4 pi r^2)

Natural numbers are strictly only plain numbers like no percents or integers, such as 1, 2, 3, 4, 5, 6 etc. Natural numbers are whole numbers and positive, so 0 would not be considered natural since it is not positive or negative

Rational numbers are numbers like 1, -100, .33, -10000, 2.4, etc it can be ALMOST anything, rational numbers fit every category but one IRRATIONAL

Irrational numbers are numbers like pie (3.145.......) it goes on forever and ever if the number never stops and repeats its called a repeating decimal, (HUGE TIP, IF YOU CAN MAKE IT A FRACTION IS IS ALMOST ALWAYS RATIONAL)

The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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