Question 4
If f(x) = 12 - 3| + 7, then which of the following is the value of f(1)?
1)11
2) 13
3)9
4)17

The four basic properties of addition are:

Commutative property.

Associative Property.

Distributive Property.

Additive Identity Property.

When we add two or more numbers, their sum is the same regardless of the order of the addends. We can write this property in the form of A + B = B + A.

When we add three or more numbers, the sum is the same regardless of the grouping of the addends. It also means that when we add three different numbers, the result is not affected by the addition pattern followed.

A +( B+C) = (A + B)+C

On adding zero to any number, the sum remains the original number. Adding 0 to a number does not change the value of the number. It is true for natural numbers, whole numbers, fractions, integers, and decimals.

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately

Hence we get the required answer.

Learn more about Addition here:

brainly.com/question/25421984

#SPJ4

Answer:

i think right 4 up 2!! Sorry if i'm wrong!

a) The solution for b in the equation 2b × 3 = 6 is b = 1.

b) The solution for b in the equation 32 - 3b = 2 is b = 10.

c) The solution for b in the equation 6 + 7b = 41 is b = 5.

d) The solution for b in the equation 100/5b = 2 is b = 10.

a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.

2b × 3 = 6

(2b × 3) / 2 = 6 / 2

3b = 3

b = 3/3

b = 1

Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.

c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.

6 + 7b - 6 = 41 - 6

7b = 35

b = 35/7

b = 5

Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.

b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.

32 - 3b - 32 = 2 - 32

-3b = -30

b = (-30)/(-3)

b = 10

Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.

d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.

(100/5b) × 5b = 2 × 5b

100 = 10b

b = 100/10

b = 10.

Therefore, the solution for b in the equation 100/5b = 2 is b = 10.

In summary, the solutions for b in the given equations are:

a) b = 1

c) b = 5

b) b = 10

d) b = 10

For similar question on equation.

https://brainly.com/question/30451972  

#SPJ8

L/W = 3/1 or L = 3*W

A = L*W = (3*W)*W = 3*W^2 = 675 m^2

W^2 = (675 m^2)/3 = 225 m^2

W = sqrt(225 m^2) = 15 m

L = 3*W = 3*(15 m) = 45 m

The answer to the given linear programming problem, which is solved using the simplex method, is as follows:

The optimal solution to minimize the objective function Z = X1 + 2X2 is X1 = 20 and X2 = 0, with the objective function value Z = -100.

To solve the problem, we'll first convert the inequalities to equations by introducing slack and surplus variables. Then we'll set up the initial simplex tableau and iterate through the simplex algorithm until we reach an optimal solution.

⇒ Convert the inequalities to equations:

A. X1 + 3X2 + S1 = 90 (where S1 is the slack variable)

B. 8X1 + 2X2 + S2 = 160 (where S2 is the slack variable)

C. 3X1 + 2X2 + S3 = 120 (where S3 is the slack variable)

D. X2 + S4 = 70 (where S4 is the surplus variable)

⇒ Set up the initial simplex tableau:

        | X1 | X2 | S1 | S2 | S3 | S4 | RHS |

----------------------------------------------

Z       | -1 | -2 |  0 |  0 |  0 |  0 |  0  |

----------------------------------------------

S1      |  1 |  3 |  1 |  0 |  0 |  0 | 90  |

S2      |  8 |  2 |  0 |  1 |  0 |  0 | 160 |

S3      |  3 |   2 |  0 |  0 |  1 |  0 | 120 |

S4      |  0 |   1 |  0 |  0 |  0 | -1 | 70  |

⇒ a) Select the most negative coefficient in the Z row, which is -2. Choose the corresponding column as the pivot column (X2 column).

b) Find the pivot row by selecting the minimum ratio of the RHS value to the positive values in the pivot column. The minimum ratio is 70/1 = 70. Thus, the pivot row is S4.

c) Perform row operations to make the pivot element (1 in S4 row) equal to 1 and eliminate other elements in the pivot column:

  - Divide the pivot row by the pivot element (1/1 = 1).

  - Replace other elements in the pivot column using row operations:

    - S1 row: S1 = S1 - (1 * S4) = 90 - 70 = 20

    - Z row: Z = Z - (2 * S4) = 0 - 2 * 70 = -140

    - S2 row: S2 = S2 - (0 * S4) = 160

    - S3 row: S3 = S3 - (0 * S4) = 120

d) Update the tableau with the new values:

        | X1 | X2 | S1 | S2 | S3 | S4 | RHS |

----------------------------------------------

Z       | -1 |  0 |  0 |  0 |  2 | -2 | -140|

----------------------------------------------

S1      |  1 |  3 |  1 |  0 |  

0 |  0 | 20  |

S2      |  8 |  2 |  0 |  1 |   0 |  0 | 160 |

S3      |  3 |  2 |  0 |  0 |   1 |  0 | 120 |

S4      |  0 |  1 |  0 |  0 |   0 | -1 | 70  |

e) Repeat steps a to d until all coefficients in the Z row are non-negative.

  - Select the most negative coefficient in the Z row, which is -1. Choose the corresponding column as the pivot column (X1 column).

  - Find the pivot row by selecting the minimum ratio of the RHS value to the positive values in the pivot column. The minimum ratio is 20/1 = 20. Thus, the pivot row is S1.

  - Perform row operations to make the pivot element (1 in S1 row) equal to 1 and eliminate other elements in the pivot column.

  - Update the tableau with the new values.

f) The final simplex tableau is:

        | X1 | X2 | S1 | S2 | S3 | S4 | RHS |

----------------------------------------------

Z       |  0 |  0 |  0 |  0 |  1 | -3 | -100|

----------------------------------------------

X1      |  1 |  3 |  1 |  0 |  0 |  0 | 20  |

S2      |  0 | -22 | -8 |  1 |  0 |  0 | 140 |

S3      |  0 | -7 | -3 |  0 |  1 |  0 | 60  |

S4      |  0 |  1 |  0 |  0 |  0 | -1 | 70  |

⇒ Read the solution from the final tableau:

The optimal solution is X1 = 20 and X2 = 0, with the objective function value Z = -100.

To know more about the simplex method, refer here:

https://brainly.com/question/30387091#

#SPJ11

The standard deviation used to calculate the test statistic for the one-sample z-test is option c, i.e. √(22(78)/200).

Let’s take p as the proportion of students from high school Y who watched the movie on opening night.

Then the sample proportion, ˆp = 22/200 = 0.11

We need to find out whether the proportion of all students in high school Y who saw the movie on opening night is greater than that of high school X. The sample proportion for high school X is 0.09.

We can use a one-sample z-test with the following hypotheses.

H₀: p ≤ 0.09

Hₐ: p > 0.09

The null hypothesis represents the assumption that the proportion of students in high school Y who watched the movie on opening night is less than or equal to that of high school X.

The alternative hypothesis represents the assumption that the proportion of students in high school Y who watched the movie on opening night is greater than that of high school X.We calculate the test statistic, z, as follows:

z = (ˆp - p₀) / σ

Where p₀ = 0.09 and σ is the standard deviation of the sample proportion.

We know that

σ = √[(p₀(1 - p₀)) / n]

Where n = 200.

σ = √[(0.09 x 0.91) / 200]

σ = 0.0274

Therefore,

z = (0.11 - 0.09) / 0.0274 = 0.7299

The p-value for this test is P(Z > 0.7299) = 0.2333

At the 5% level of significance, we fail to reject the null hypothesis since the p-value is greater than 0.05. Thus, we do not have sufficient evidence to conclude that the proportion of all students in high school Y who saw the movie on opening night is greater than that of high school X.

Hence option c is correct.

To know more about the "standard deviation": https://brainly.com/question/24298037

#SPJ11

90% confidence interval would be less than a 95% confidence interval.

Given,

A random sample has been taken from a population. A statistician, using this sample, needs to decide whether to construct a 90 percent confidence interval for the population mean or a 95 percent confidence interval for the population mean;

We have to find the difference between the intervals;

Here,

Confidence intervals are a range that depict the accuracy of the measurement. If a statistician chooses to use a 90% C I instead of a 95% C I, it informs you that you have a 10% probability of being incorrect as opposed to a 5% possibility when using the 95%.

That is, a 90% confidence interval would be less than a 95% confidence interval.

Learn more about confidence intervals here;

https://brainly.com/question/14702610

#SPJ4

The total angle that a point on the edge of the CD player spin in one minute is 72,000°

We know that a CD player spins at about 200 revolutions per minute, where a revolution means a complete rotation.

A complete rotation is equivalent to a rotation of 360°, then in 200 revolutions we have a total rotation of:

200*360° = 72,000°

Then the total angle that a point on the edge of the CD player spin in one minute is 72,000°

If you want to learn more about rotations, you can read:

https://brainly.com/question/9408577

Answer: \((-\infty, 0]\)

Step-by-step explanation:

This is a parabola that opens down (because of the negative leading coefficient).

So, the average rate of change (i.e., the slope of the secant) is negative when the function is decreasing.

The function is decreasing to the left of the vertex, which is at (0, 7).

So, the function has a negative average rate of change for \((-\infty, 0]\).

Answer:

19

Step-by-step explanation:

From 8-->0 =8

+ from 0--->-11=11

11+8

Answer:

15 blue cars

Step-by-step explanation:

multiply

4 x 5 = 20

3 x 5= 15

Answer: 37.50

Step-by-step explanation:

I = $ 37.50

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 1.5%/100 = 0.015 per year,

then, solving our equation

I = 500 × 0.015 × 5 = 37.5

I = $ 37.50

The simple interest accumulated

on a principal of $ 500.00

at a rate of 1.5% per year

for 5 years is $ 37.50.

Explanation

Step 1

Let x represents the number of hours

Let y represents the rate of the company

and

cost per hour = $3

so, the total cost per time is

cost per time= 3* number of hours

cost per time==3x

now, the company charges a $5 boarding rate

so, the rate is

I hope this helps you

Explanatory variables in a regression model are typically considered to be random when they are subject to variability or uncertainty. There are several reasons why explanatory variables may be treated as random:

Measurement error: Explanatory variables may be measured with some degree of error or imprecision. This measurement error introduces randomness into the values of the variables. Accounting for this randomness is important to obtain unbiased and accurate estimates of the regression coefficients.

Sampling variability: In many cases, the data used to estimate the regression model are obtained through sampling. The values of the explanatory variables in the sample may differ from the true population values due to random sampling variability. Treating the explanatory variables as random helps capture this uncertainty and provides more robust inference.

Random assignment in experiments: In experimental studies, researchers often manipulate or assign values to the explanatory variables randomly. This random assignment ensures that the variables are not influenced by any underlying factors or confounders. Treating the explanatory variables as random reflects the randomization process used in the experiment.

By considering the explanatory variables as random, we acknowledge and account for the inherent variability and uncertainty associated with them. This allows for a more comprehensive and accurate modeling of the relationships between the explanatory variables and the response variable in regression analysis.

Learn more about regression here:

https://brainly.com/question/31602708

#SPJ11

True. The correlation coefficient (r) must also be positive, indicating a strong positive linear relationship between the two variables.

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where a value of -1 indicates a perfectly negative linear relationship, a value of 1 indicates a perfectly positive linear relationship, and a value of 0 indicates no linear relationship.  If the slope (b) of ŷ is positive, it means that as the independent variable increases, the dependent variable also increases.

In addition to the above explanation, it is important to note that while a positive slope (b) of ŷ indicates a positive linear relationship between two variables, it does not necessarily mean that the correlation coefficient (r) will always be positive. For example, if there is a weak positive linear relationship between two variables, the correlation coefficient (r) may still be positive but not as strong as if there was a strong positive linear relationship. Similarly, there may be situations where the correlation coefficient (r) is positive but the slope (b) of ŷ is not positive, such as in a curvilinear relationship where the relationship between the two variables is not linear.

To know more about correlation coefficient visit :-

https://brainly.com/question/29978658

#SPJ11

Answer:

900

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

exponential;increase

Step-by-step explanation:

answer is C

To multiply radical expressions with the same index, we use the product rule for radicals. \(\sqrt[n]{A}.\sqrt[n]{B} = \sqrt[n]{A.B}\)

To divide radical expressions with the same index, we use the quotient rule for radicals. \(\frac{\sqrt[n]{A} }{\sqrt[n]{B} } =\sqrt[n]{\frac{A}{B} }\)

Multiplying Radical Expressions :

Example,

given:  Multiply: \(\sqrt[3]{12} .\sqrt[3]{6}\)

Apply the product rule for radicals, and then simplify.

\(\sqrt[3]{12}.\sqrt[3]{6}=\sqrt[3]{12.6}\)

            \(=\sqrt[3]{72}\\=\sqrt[3]{2^{3} .3^{2} } \\=2\sqrt[3]{3^{2} } \\=2\sqrt[3]{9}\)

Dividing Radical Expressions

Example,

given: Divide: \(\frac{\sqrt[3]{96} }{\sqrt[3]{6} }\)

In this case, we can see that 6 and 96 have common factors. If we apply the quotient rule for radicals and write it as a single cube root, we will be able to reduce the fractional radicand.

\(\frac{\sqrt[3]{96} }{\sqrt[3]{6} } =\sqrt[3]{\frac{96}{6} }\)

      \(=\sqrt[3]{16} \\=\sqrt[3]{8.2} \\=2\sqrt[3]{2}\)

To learn more about fractional radicand, visit

brainly.com/question/1542580

#SPJ4

With the given compound interests, Investment B results in greatest total amount.

What exactly is compound interest?

Compound interest is interest charged on a loan or deposit. It is the most widely utilised idea in our everyday lives. The compound interest for an amount is determined by both the principal and the interest earned over time. This is the primary distinction between compound and simple interest.

Compound interest calculation formula:

A=P(1+r/n)ⁿˣ

Where,

A Equals Amount

P stands for principal.

r = interest rate

n is the number of times interest is compounded each year.

x = time (in years)

Alternatively, the formula may be written as follows:

CI = A – P

Where CI stands for Compound Interest.

Now,

For A

principal = $3000, Rate = 7% compounded semiannualy and time = 7 years

amount=3000(1+7/200)¹⁴

A=3000*1.61

=$4856

For B

 principal = $5000, Rate = 3.2% compounded quaterly and time = 4 years

amount = 5000(1+3.2/400)¹⁶

A=5000*1.13

=$5680

hence,

           Investment B results in greatest total amount.

To know more about Compound Interest visit the link

https://brainly.com/question/14295570?referrer=searchResults

#SPJ1

Answer:

  1856 ft²

Step-by-step explanation:

You want the surface area of an isosceles triangular prism 23 ft long with a triangle base of 24 ft and a height of 16 ft.

The area of the two triangles is ...

  A = 2 × 1/2bh = bh

  A = (24 ft)(16 ft) = 384 ft²

The area of the three rectangular sides is ...

  A = LW

  A = (24 ft + 20 ft + 20 ft)(23 ft) = 64·23 ft² = 1472 ft²

The surface area of the prism is the sum of the base area and the lateral area:

  A = 384 ft² +1472 ft² = 1856 ft²

The surface area of the prism is 1856 square feet.

__

Additional comment

We recognize each of the smaller right triangles that make up one base is a 3-4-5 right triangle with a scale factor of 4 ft. That makes the hypotenuse exactly 20 ft, as shown in the diagram.

The lateral area is effectively the product of the prism length (23 ft) and the perimeter of the triangular base.

<95141404393>

Answer:

4/15

Step-by-step explanation:

Sample Space (List of possible outcomes)

Conditions

Space for Listed Outcomes (with conditions applied)

Probability

After 1 hour, 360 g decays to 180 g.

After another hour (total 2 hours), 180 g decays to 90 g.

After another hour (total 3), 90 g decays to 45 g.

After one more (total 4), 45 g decays to 22.5 g.

More quickly, with a half-life of 1 hour, the 360 g of starting material decays to

(360 g) / 2⁴ = 22.5 g

In general, if the half-life is 1 hour, then after n hours, an initial amount A of this substance decays according to

A / 2ⁿ

The equation of a line perpendicular to  y = x - 9 and passes through (-7, 1) is y = - x - 6

The equation of a line can be represented in a point slope form as follows:

y - y₁ = m(x - x₁)

where

Therefore, the line is perpendicular to  y = x - 9 and passes through (-7, 1).

Perpendicular lines follows the rule:

m₁ m₂ = -1

1m₂ = -1

m₂ = -1

Hence, let's find the y-intercept of the equation of the lines using (-7, 1)

y = - x + b

1 = - (-7) + b

1 = 7 + b

1 - 7 = b

b = -6

Therefore, the equation of the line is y = - x - 6

learn more on equation of a line here: https://brainly.com/question/14946832

#SPJ1

Answer:

Step-by-step explanation:

1 = 1/16 (one chance on 16

2 = 7/16 (the non shaded parts are 7, while the total parts are 16)

3 = 11/16 ( 11 is unshaded + even)

4 = 4/16 = 1/4 (the favourable possibilities are: 13, 14, 15, 16)

Based on the given data, the probability of a room being occupied on any particular weekend night is 0.75. To calculate the probability that at least 4 out of the 7 rooms are occupied on a weekend night, we can use the binomial probability formula. By summing up the probabilities for 4, 5, 6, and 7 occupied rooms, we find that the probability is approximately 0.923.

To calculate the probability, we can use the binomial probability formula, which states that the probability of getting exactly k successes in n independent Bernoulli trials, each with a probability p of success, is given by the formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

In this case, we want to find the probability of at least 4 out of 7 rooms being occupied on a weekend night. We can calculate this by summing up the probabilities of getting 4, 5, 6, and 7 occupied rooms.

For 4 occupied rooms:
P(X = 4) = (7 choose 4) * 0.75^4 * (1 - 0.75)^(7 - 4) = 0.339

For 5 occupied rooms:
P(X = 5) = (7 choose 5) * 0.75^5 * (1 - 0.75)^(7 - 5) = 0.395

For 6 occupied rooms:
P(X = 6) = (7 choose 6) * 0.75^6 * (1 - 0.75)^(7 - 6) = 0.266

For 7 occupied rooms:
P(X = 7) = (7 choose 7) * 0.75^7 * (1 - 0.75)^(7 - 7) = 0.122

To find the probability of at least 4 occupied rooms, we sum up the probabilities for 4, 5, 6, and 7 occupied rooms:

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.339 + 0.395 + 0.266 + 0.122 = 0.923

Therefore, the probability that at least 4 out of the 7 hotel rooms are occupied on any weekend night is approximately 0.923, or 92.3% when rounded to three decimal places.

Learn more about probability here: brainly.com/question/32117953

#SPJ11

Based on the given data, the probability of a room being occupied on any particular weekend night is 0.75.

To calculate the probability that at least 4 out of the 7 rooms are occupied on a weekend night, we can use the binomial probability formula. By summing up the probabilities for 4, 5, 6, and 7 occupied rooms, we find that the probability is approximately 0.923.

To calculate the probability, we can use the binomial probability formula, which states that the probability of getting exactly k successes in n independent Bernoulli trials, each with a probability p of success, is given by the formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

In this case, we want to find the probability of at least 4 out of 7 rooms being occupied on a weekend night. We can calculate this by summing up the probabilities of getting 4, 5, 6, and 7 occupied rooms. For 4 occupied rooms:
P(X = 4) = (7 choose 4) * 0.75^4 * (1 - 0.75)^(7 - 4) = 0.339

For 5 occupied rooms:
P(X = 5) = (7 choose 5) * 0.75^5 * (1 - 0.75)^(7 - 5) = 0.395
For 6 occupied rooms:
P(X = 6) = (7 choose 6) * 0.75^6 * (1 - 0.75)^(7 - 6) = 0.266
For 7 occupied rooms:
P(X = 7) = (7 choose 7) * 0.75^7 * (1 - 0.75)^(7 - 7) = 0.122
To find the probability of at least 4 occupied rooms, we sum up the probabilities for 4, 5, 6, and 7 occupied rooms:

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.339 + 0.395 + 0.266 + 0.122 = 0.923. Therefore, the probability that at least 4 out of the 7 hotel rooms are occupied on any weekend night is approximately 0.923, or 92.3% when rounded to three decimal places.

Learn more about probability here: brainly.com/question/32117953
#SPJ11

Answer:

-1

Step-by-step explanation:

I'm pretty sure this is right

We have shown that for every whole number n, there exists a value of x in the interval (2n−1)π/2 < x < (2n+1)π/2 such that tan(x) = x.

To prove that there exists a value of x such that tan(x) = x for each whole number n, we can use the Intermediate Value Theorem.

The Intermediate Value Theorem states that if a continuous function takes on two different values at two different points in an interval, then it must also take on every value between those two points at some point within the interval.

In this case, we consider the function f(x) = tan(x) - x. We want to show that there exists a value of x in the [(2n-1)π/2, (2n+1)π/2] where f(x) = 0, which means tan(x) = x.

First, we note that f(x) is continuous within the given interval since both tan(x) and x are continuous functions.

Next, we evaluate f((2n-1)π/2) and f((2n+1)π/2):
f((2n-1)π/2) = tan((2n-1)π/2) - (2n-1)π/2 = -∞ - (2n-1)π/2 < 0
f((2n+1)π/2) = tan((2n+1)π/2) - (2n+1)π/2 = ∞ - (2n+1)π/2 > 0

Since f((2n-1)π/2) < 0 and f((2n+1)π/2) > 0, by the Intermediate Value Theorem, there must exist a value of x in the integral  [(2n-1)π/2, (2n+1)π/2] such that f(x) = 0. This means there exists an x such that tan(x) = x for each whole number n.

Therefore, we have shown that for every whole number n, there exists a value of x in the interval (2n−1)π/2 < x < (2n+1)π/2 such that tan(x) = x.

learn more about integral here: brainly.com/question/31059545
#SPJ11