Which expressions are equivalent to the given expression?


√252
more than one answer

Case 2

The quadratic equation x² - 14 · x + 48 = 0 have the following roots: x₁ = 6 and x₂ = 8. (Correct choice: B)

Case 3

We need to add + 64 to both sides. (Correct choice: B)

Case 4

We need to add + 16 to both sides. (Correct choice: C)

In this problem we find three cases of quadratic equation that are not perfect square trinomials, these equations can be rewritten partially in that form by algebra properties. Completing the square offers a quick method to determine the roots of quadratic equations with integer coefficients. Now we proceed to determine the solutions corresponding to each case:

Case 2

x² - 14 · x + 48 = 0

x² - 14 · x + 49 = 1

(x - 7)² = 1

x - 7 = ± 1

x = 7 ± 1

The roots of the quadratic equation x² - 14 · x + 48 = 0 are x₁ = 6 and x₂ = 8, respectively.

Case 3

x² - 16 · x = - 21

x² - 16 · x + 64 = 64 - 21

(x + 8)² = 43

The first step consists in adding both sides by + 64.

Case 4

x² - 8 · x = 0

x² - 8 · x + 16 = 16

(x - 4)² = 16

The first step consists in adding both sides by + 16.

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The null hypothesis would state that the population mean number of cups of coffee that women would drink 32% the population mean number cups of coffee than men drink.

The term "percentage" comes from the Latin phrase "per centum," which means "by the hundred." With 100 as the denominator, percentages are fractions. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Percentage is a fraction or a ratio in which the value of whole is always 100. For example, if Sam received 30% on his math test, he received 30 points out of 100. It is expressed as 30/100 in fractional form and 30:100 in ratio form.

A certain number or quantity in every hundred is referred to as a percentage. It is a fraction, and the denominator is 100.

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Answer:

thee ordered pair was both (1,2) and (2,4)

The answer is C. The set of all symmetric 3 × 3 matrices is a subspace of M33.


To determine if a set of matrices is a subspace of M33, we need to check three conditions:
1. The set contains the zero matrix.
2. The set is closed under addition of its elements.
3. The set is closed under multiplication by other matrices in the set.
In this case, the set of all symmetric 3 × 3 matrices does contain the zero matrix (all diagonal entries are zero), and it is also closed under matrix addition (the sum of two symmetric matrices is also symmetric).

To check the third condition, we need to verify that if we multiply any symmetric matrix by another symmetric matrix, the result is also a symmetric matrix. This is indeed true, since the transpose of a product of matrices is the product of their transposes in reverse order: (AB)^T = B^T A^T. For any symmetric matrix A, we have A^T = A, so (AB)^T = B^T A^T = BA, which is also symmetric if B is symmetric.
Therefore, all three conditions are satisfied, and the set of all symmetric 3 × 3 matrices is indeed a subspace of M33.

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Answer:

132

Step-by-step explanation:

C=5

3c - 2 = 13

2c = 10

4c + 1 = 21

4c + 2 = 22

length = (3c- 2) + (4c + 1)

length = 13 + 21

length = 34

width = (4c + 2) + (2c)

width = 22 + 10

width = 32

Perimeter

p = 2l + 2w

p = 2*34 + 2*32

p = 68 + 64

p = 132

Answer:

The radius of sphere with volume 4500 cubic inches is 10.24 inches.

Step-by-step explanation:

Let V be the volume of the sphere

Given

Volume of sphere = V = 4500 cubic inches

Let r be the radius of the sphere

The volume of the sphere is given by the formula

\(V = \frac{4}{3}\pi r^3\)

Putting the known values

\(4500 = \frac{4}{3} * \frac{22}{7} * r^3\\4500 = \frac{88}{21} * r^3\\r^3 = \frac{21}{88} * 4500\\r^3 = 1073.8636\)

Taking cube root on both sides

\(\sqrt[3]{r^3} = \sqrt[3]{1073.8636} \\r = 10.2403\)

Rounding off to nearest hundredth

The radius is: 10.24 inches.

Hence,

The radius of sphere with volume 4500 cubic inches is 10.24 inches.

Answer: 320

Step-by-step explanation: 812 divided by 203 is 4

203 min = 40 bacteria.

203 + 203 = 406

406 min = 80 bacteria because 40 times 2 is 80.

406 + 203 = 609

609 min = 160 bacteria because 80 time 2 is 160.

609 + 203 = 812

812 min = 320 bacteria because 160 time 2 is 320.

Answer:

B

Step-by-step explanation:

bc ik it is

Answer: Person above me is right. It's B.

Step-by-step explanation: Got it right on Edg.

The sale price of the ticket is $57.05

The ticket for the summer concert is $81.50

The ticket will be on sale for 30% off

The sale price can be calculated as follows

81.50 × 30/100

= 81.50 × 0.3

= 24.45

Sale price= 81.50-24.45

= 57.05

Hence the sale price is $57.05

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(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

The result is obtained by using the exponential decay equation.

The exponential decay equation can be used to calculate radioactive decay for the activity, the nuclei, and also the mass. The exponential decay equation for the mass is

\(m = m_{o} e^{-\lambda t}\)

Where

The half-life of radium-226 is 1600 years and the mass of a sample is 27 mg.

(a) What is the remaining mass after 4500 years?

(b) What is the decay time if the remaining mass is 15 mg?

First, let's calculate the decay constant.

λ = 0.693/T½

λ = 0.693/1600

λ = 0,000433

After 4500 years, the remaining mass is

\(m = m_{o} e^{-\lambda t}\)

\(m = 27 e^{-0.000433 \times 4500}\)

m = 27 × 0.142

m = 3.8 mg

If the remaining mass is 15 mg, the decay time is

\(m = m_{o} e^{-\lambda t}\)

\(15 = 27 e^{-0.000433 t}\)

\(ln \frac{15}{27} = ln (e^{-0.000433 t})\)

\(ln \frac{15}{27} = -0.000433 t\)

-0.588 = - 0.000433t

t = 1357.9 years

Hence,

(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

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Answer:

do you have discord?

Step-by-step explanation:

Answer:

Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number.

Step-by-step explanation:

The recurrence relation for the amount of water in the bird bath at the end of day n is W(n) = (2/3) * W(n-1) + 1, where n > 0.

5) Recurrence Relation for Water in the Bird Bath:

Let W(n) represent the amount of water in the bird bath at the end of day n.

At the end of day 0, the bird bath contains 8 gallons of water, so we have W(0) = 8.

Each day, one-third of the water evaporates, and Andrew adds one gallon. This means that the amount of water at the end of day n is equal to two-thirds of the water at the end of the previous day, plus one gallon added.

Therefore, the recurrence relation for W(n) is:

W(n) = (2/3) * W(n-1) + 1, where n > 0.

At the end of day n, the amount of water is obtained by taking two-thirds of the water at the end of the previous day (W(n-1)) and adding one gallon (since Andrew adds one gallon each day).

For example, to find the amount of water at the end of day 1 (W(1)), we substitute n = 1 in the recurrence relation:

W(1) = (2/3) * W(0) + 1

    = (2/3) * 8 + 1

    = 5.33 + 1

    = 6.33 gallons.

This relation allows us to calculate the amount of water in the bird bath for any given day based on the previous day's amount, taking into account evaporation and the addition of one gallon each day.

6) Recurrence Relation for Spread of a Virus:

(a) Recurrence Relation:

Let V(n) represent the number of infected people on day n.

On day 1, one person is infected, so we have V(1) = 1.

On each subsequent day, each infected person gives the cold to two others. This means that the number of infected people on day n is twice the number of infected people on the previous day.

Therefore, the recurrence relation for V(n) is:

V(n) = 2 * V(n-1), where n > 1.

Starting from day 1, the number of infected people doubles each day because each infected person infects two others.

For example, to find the number of infected people on day 3 (V(3)), we substitute n = 3 in the recurrence relation:

V(3) = 2 * V(2)

    = 2 * (2 * V(1))

    = 2 * (2 * 1)

    = 4.

This means that on day 3, there are 4 infected people.

(b) Limitations of the Model:

- This model assumes that each infected person will always infect exactly two others. In reality, the rate of transmission may vary depending on various factors such as social interactions, hygiene practices, and preventive measures.

- The model does not consider factors such as recovery or immunity. It assumes that once a person is infected, they remain infected and continue to spread the virus indefinitely, which is not realistic.

- It assumes a homogeneous population, where every individual has an equal chance of being infected. In reality, the spread of a virus may be influenced by various factors such as age, pre-existing health conditions, and geographical location.

- The model does not consider external factors such as vaccination campaigns, quarantine measures, or changes in behavior due to awareness and education.

The recurrence relation for the spread of the virus is V(n

) = 2 * V(n-1), where n > 1. However, this model has limitations as it oversimplifies the spread of a virus by assuming constant transmission rates, neglecting recovery or immunity, and ignoring other influential factors. Real-world virus spread is much more complex and influenced by various factors that this model does not account for.

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Answer:

7 marbles

Step-by-step explanation:

For every 6 marbles, 2 marbles appear as red.

This pattern would repeat thrice as 6x3 = 18, and then the first 2 marbles (one blue and red) will be counted to make 20 marbles.

So total marbles will be 3x2 in the 18 marble set and 1 in the final 2 marbles.

so 3x2 + 1 = 6+1 = 7

We get 7 marbles as red if we continue in this pattern.

Answer

x=7

Step-by-step explanation:

I honestly forgot how to explain but my logic is that 43+137+137+43=360

so, x would equal 7

Ages (in years) of a sample of retirement home inhabitants is option B. For the lowest wait time, the maximum frequency is anticipated to be right-skewed. A desert cannot have a maximum annual temperature of 60°F, and it is not conceivable to watch 60+ hours of TV in a single day.

Residents of senior living facilities are typically 84 years old. While there are many couples in these communities, the majority of people who live in independent living are women. Some people move in at or near the minimum age (often around 65), but most people do so between the ages of 75 and 84. Residents come from all different backgrounds.

Many people are choosing senior living in a community environment, including teachers, nurses, small business owners, big business CEOs, university professors, housewives, lawyers, engineers, musicians, and more. Current residents will attest that the rich diversity of origins fosters amazing interactions and relationships. And contrary to popular belief, the majority of residents of independent living are quite active.

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Correct Question:

Match the plot with a possible description of the sample.

60 70 80 90 100

Choose the correct answer below

A. Wait time (in minutes) for a sample of doctors offices

B. Ages (in years) of a sample of residents of a retirement home.

C. Highest yearly temperatures (F) for a sample of deserts.

D. Time (in hours_ spent watching TV in a day for a sample of teenagers.

By using combination, it can be obtained that

Number of simple random samples of size 3 that can be selected from a population of size 7 = 35

What is combination?

Combination determines the number of arrangements that can be made from a collection of objects when the order of arrangement is not taken into account.

Here, concept of combination is used

Number of simple random samples of size 3 that can be selected from a population of size 7 = \({7 \choose 3}\) = 35

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Based on the information that the smallest score in a population is x=5, and the largest score is x=10, the conclusion is that the standard  deviation is going to be smaller than the range of scores.

Given that in a population, the smallest score is x=5, and largest score is x=10, the range of scores is:

Range of scores=largest score-lowest score

                          =10-5

                           =5

Here the range of scores is 5, and the mean of the scores is likely to be between 5 and 10

Standard deviation which refers to the average spread of the distribution,  will now be considered to be smaller since the range of scores is low.

Because standard deviation is found from the mean, if the mean is between x=5 and x=10, the standard deviation must be lower than x=5.

Hence, smaller than the range of scores.

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The corresponding p-value for the computed test statistic of z = -1.33, testing the null hypothesis H0: μ1 – μ2 = 0, is greater than 0.10 (or 10%).

To find the corresponding p-value, we look at the standard normal distribution table (z-table) or use statistical software. In this case, the test statistic is z = -1.33, which represents the number of standard deviations the sample mean difference is away from the hypothesized mean difference (0).

Since the test statistic is negative, we find the area to the left of -1.33 in the standard normal distribution table.

This gives us a p-value greater than 0.10, indicating that the observed mean difference is not significantly different from the hypothesized mean difference at the conventional significance level (usually α = 0.05). Therefore, we fail to reject the null hypothesis H0: μ1 – μ2 = 0.

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Answer:

B

Step-by-step explanation:

Just answer it nznnznkskosoaksns

The solutions to the equation 2sin(θ) = 1 on the interval [0, 2π) are:

θ = π/6, 13π/6

To find all solutions to the equation 2sin(θ) = 1 on the interval [0, 2π), we can solve for θ by isolating the sin(θ) term and then using inverse trigonometric functions.

Given: 2sin(θ) = 1

Dividing both sides by 2:

sin(θ) = 1/2

Now, we can use the inverse sine function to find the solutions:

θ = sin^(-1)(1/2)

The inverse sine of 1/2 is π/6. However, we need to consider all solutions on the interval [0, 2π).

Since the sine function has a period of 2π, we can find the other solutions by adding integer multiples of 2π to the principal solution.

The principal solution is θ = π/6. Adding 2π to it, we get:

θ = π/6 + 2π = π/6, 13π/6

So, the solutions to the equation 2sin(θ) = 1 on the interval [0, 2π) are:

θ = π/6, 13π/6

These are the two solutions that satisfy the given equation on the specified interval.

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Answer:

it's 42

Step-by-step explanation:

6 7's

6 12 28 24 30 36 42

The t-test yields the probability (p value) that the null hypothesis is option (B) incorrect

The p-value in a t-test represents the probability of obtaining the observed test statistic (or one more extreme) assuming that the null hypothesis is true. The null hypothesis is typically a statement of "no effect" or "no difference" between two groups being compared in the test.

Therefore, a low p-value (generally less than 0.05) indicates that the observed data is unlikely to have occurred by chance under the null hypothesis and suggests that the null hypothesis is likely to be false.

In other words, a low p-value provides evidence against the null hypothesis and in favor of the alternative hypothesis (which typically represents the hypothesis that the researchers are interested in testing).

Thus, the p-value does not directly tell us whether the null hypothesis is correct or incorrect, but rather whether the evidence supports rejecting it or not.

Therefore, the correct option is (B) incorrect

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The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

A sampling distribution refers to a distribution of statistics, such as the mean or proportion, that is derived from a large number of random samples. It provides valuable insights into the behavior.

A sampling distribution is a distribution of statistics, such as the mean or proportion, that are derived from a large number of random samples. It represents the variability and patterns that arise from taking repeated samples from a population.

In statistical analysis, it is often not feasible or practical to collect data from an entire population. Instead, we rely on taking samples to make inferences about the population. The sampling distribution allows us to understand how the statistics of interest vary from sample to sample and provides valuable information about the accuracy and precision of our estimates.

By analyzing the sampling distribution, we can assess the reliability of our sample statistics and make inferences about the population parameters. It helps us understand the spread and central tendency of the statistics, and it guides us in drawing conclusions and making predictions based on the collected sample data.

In summary, a sampling distribution represents the distribution of statistics derived from multiple random samples and provides insights into the behavior and properties of these statistics in relation to the population.

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A sampling distribution refers to a distribution of statistics, such as the mean, that are derived from a large number of random samples taken from the same population. It represents the possible values that the statistic can take on when the same sampling procedure is used repeatedly.

The sampling distribution allows us to make inferences about the population parameter based on the statistics calculated from the samples. It is not the average deviation from the mean in a data set, a measure of whether or not a sample is truly random, or the process of allowing a few numbers to summarize many numbers. The sampling distribution shows the distribution of these sample means. It helps us understand how the sample means vary from sample to sample and gives us an idea of the range of values the population mean could take on. This information is useful in making inferences and drawing conclusions about the population based on the sample data. Imagine you have a population, let's say all the students in a school, and you want to know the average height of the students. It is practically impossible to measure the height of every student, so instead, you take a random sample of students and calculate the average height of that sample. If you repeat this process many times with different random samples, you will get a collection of sample means.

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Answer:

Step-by-step explanation:

Sum = coefficient of x = -1

Product = constant = -6

Factors = 2 , (-3)          

{2 + (-3) = -1  & 2*(-3) = -6}

x² - x - 6 = 0

x² - 3x  + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x - 3)(x + 2) = 0

x -3 = 0    ;x + 2 = 0

x = 3        ; x = -2

Zeros are  3 , -2

To determine the points that are solutions to the inequality y ≤ -2x - 2, we need to test various points and check if they satisfy the inequality.

Here are some points you can evaluate: (0, -2): Plugging in x = 0 and y = -2 into the inequality: -2 ≤ -2(0) - 2. Simplifying, we get: -2 ≤ -2. This is true, so (0, -2) is a solution. (1, -4): Plugging in x = 1 and y = -4 into the inequality: -4 ≤ -2(1) - 2 . Simplifying, we get: -4 ≤ -4. This is true, so (1, -4) is a solution. (3, 0):  Plugging in x = 3 and y = 0 into the inequality: 0 ≤ -2(3) - 2. Simplifying, we get: 0 ≤ -8. This is false, so (3, 0) is not a solution.

Based on these evaluations, the solutions to the inequality y ≤ -2x - 2 are (0, -2) and (1, -4).

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Answer:

Step-by-step explanation:

you have the expression

y-4=3x-5y

add 5y on both sides , than add 4

y+5y=3x+4

6y=3x+4

y=(3x+4)/6

Answer:

(7,2)

Step-by-step explanation:

10

9

8

7

6

5

4

3

2                                                            x

1

     1        2        3      4      5        6        7          8            9           10

Answer:

Remember, X axis always goes first.

Start from zero and go to seven on the right.

and 2 up

I linked an example