sider the following. f(x) = x3 - 108x + 7 (a) Find the intervals on which f is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing (b) Find the local maximum and minimum values of f. (If an answer does not exist, enter DNE.) local minimum value local maximum value (C) Find the intervals of concavity and the inflection points. (Enter your answers using interval notation.) concave up concave down inflection point (x, y) = = dditional Materials

Answer:

$3.45

Step-by-step explanation:

cost of grapes x quantity

Answer:

8.20

Step-by-step explanation:

4x0.75=3

3+4=7

0.6=60%

60% of 0.75= 0.45

0.75+0.45=1.20

7+1.20=8.20

(a) The interval on which f is increasing: (0, ∞)

The interval on which f is decreasing: (0, 1)

(b) Local minimum: At x = 1, f(x) has a local minimum value of -1.

There is no local maximum value.

(c) Inflection point: At x ≈ 0.293, f(x) has an inflection point.

The function f(x) = x^2 - x - ln(x) is a quadratic function combined with a logarithmic function.

To find the interval on which f is increasing, we need to determine where the derivative of f(x) is positive. Taking the derivative of f(x), we get f'(x) = 2x - 1 - 1/x. Setting f'(x) > 0, we solve the inequality 2x - 1 - 1/x > 0. Simplifying it further, we obtain x > 1. Therefore, the interval on which f is increasing is (0, ∞).

To find the interval on which f is decreasing, we need to determine where the derivative of f(x) is negative. Solving the inequality 2x - 1 - 1/x < 0, we get 0 < x < 1. Thus, the interval on which f is decreasing is (0, 1).

The local minimum is found by locating the critical point where f'(x) changes from negative to positive. In this case, it occurs at x = 1. Evaluating f(1), we find that the local minimum value is -1.

There is no local maximum in this function since the derivative does not change from positive to negative.

The inflection point is the point where the concavity of the function changes. To find it, we need to determine where the second derivative of f(x) changes sign. Taking the second derivative, we get f''(x) = 2 + 1/x^2. Setting f''(x) = 0, we find x = 0. Taking the sign of f''(x) for values less than and greater than x = 0, we observe that the concavity changes at x ≈ 0.293. Therefore, this is the inflection point of the function.

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a. The claim that vending machines are causing students to miss school is not necessarily supported by the positive relationship observed in the scatter plot.

b. . A better headline might be "Positive correlation found between number of vending machines in schools and student absenteeism".

Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".

a. The claim that vending machines are causing students to miss school is not necessarily supported by the positive relationship observed in the scatter plot. Correlation does not equal causation, meaning that just because two variables are related, it doesn't necessarily mean that one causes the other. There could be other factors at play, and more research is needed to establish a causal relationship between vending machines and school absences.

b. A better headline might be "Positive correlation found between number of vending machines in schools and student absenteeism". This headline accurately reflects the relationship observed in the scatter plot without making any claims about causation

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Step-by-step explanation:

Difference of some numbers is 66,

Let the number be x,

So, 5x - 2x = 66

=> 3x = 66

=> x = 66/3

=> x = 22

So, for finding the numbers 2x and 5x,

=> 2 * 22 , 5 * 22

=> 44 , 110

So the two numbers are 44 , 110 respectively,

If my answer helped, please mark me the brainliest!

Thank You!

Answer:

The two numbers are 44  and 110.

Step-by-step explanation:

Answer: Random condition

10% condition

Step-by-step explanation:

The conditions for inference that have been satisfied will be:

• Random condition: This has been satisfied since a random sample of 18 adults were taken from 1500 adults.

• 10% condition: Since 25% of those who responded said they were in favor of the change, then the 10% condition is satisfied.

Answer:  \(\log_{4}\left(\frac{m^7}{125b^2}\right)\)

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

Work Shown:

\(7\log_{4}(m)-3\log_{4}(5)-2\log_{4}(b)\\\\\log_{4}(m^7)-\log_{4}(5^3)-\log_{4}(b^2) \ \ \text{... see note1 below}\\\\\log_{4}(m^7)-\log_{4}(125)-\log_{4}(b^2)\\\\\log_{4}(m^7)-\big(\log_{4}(125)+\log_{4}(b^2)\big) \\\\\log_{4}(m^7)-\log_{4}(125b^2)\ \ \text{... see note2}\\\\\log_{4}\left(\frac{m^7}{125b^2}\right) \ \ \text{... see note3}\\\\\)

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

As for the explanation process to your teacher, you can mention each rule verbally or using symbolic notation as I have done above. In my opinion, the steps in the "work shown" section should be sufficient.

Verbally describing the rule in note2 for instance could go something like "the sum of two logs is the same as the log of the product of the arguments". There is probably a more elegant way to state this rule verbally, so feel free to explore various creative options.

Keep in mind that the logs must be the same base for the log rules to apply. Something like \(\log_{2}(A)+\log_{3}(B) = \log_{2}(A*B)\) is NOT valid.

Answer:

874.6

Step-by-step explanation:

total sales = 1045

1045 * .12 = 125.4

fuel = 9 * 5 = 45

1045 - 125.4 - 45 = 874.6

Area of the large semicircle

\( = \pi{r}^{2} \div 2\)

\( = \frac{22}{7} \times 12 {}^{2} \times \frac{1}{2} \)

\( = \frac{11}{7} \times12 \times 12\)

\( = \frac{11}{7} \times 144\)

\( = 226.28\)

Area of the small semicircle

\( = \pi {r}^{2} \div 2\)

\( = \frac{22}{7} \times 6 {}^{2} \times \frac{1}{2} \)

\( = \frac{11}{7} \times 6 \times 6\)

\( = \frac{11}{7} \times 36\)

\( = 56.57\)

Area of the figure

\( = 226.28 - 56.57\)

\( = 169.71 {cm}^{2} \)

The area of the sector created by a central angle of 60° in a circle with a diameter of 6 inches is approximately 4.7124 square inches.

To find the area of a sector of a circle, we need to know the central angle and the radius of the circle. In this case, we are given the central angle of 60° and the diameter of the circle, which we can use to find the radius.

The diameter is given as 6 inches, so the radius is half of that, which is 3 inches.

To calculate the area of the sector, we can use the formula:

Area of Sector = (θ/360°) * π * r²

where θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius.

Plugging in the values:

Area of Sector = (60°/360°) * π * (3)²

Area of Sector = (1/6) * 3.14159 * 9

Area of Sector ≈ 4.7124 square inches

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The Probability that all four of the light bulbs work is 0.004 approx.

The probability that all four light bulbs work can be calculated by taking the product of the probability that each individual light bulb works. If each light bulb works independently of the other light bulbs, then the probability that all four light bulbs work is:

P(all 4 bulbs) = P(bulb 1) * P(bulb 2) * P(bulb 3) * P(bulb 4)

P(all 4 bulbs) = 0.25 * 0.25 * 0.25 * 0.25

P(all 4 bulbs) = 0.25^4

P(all 4 bulbs) = 0.00390625

So, the probability that all four light bulbs work is 0.00390625 or approximately 0.004.

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Decimal degrees 45.5013 converts to 45 degrees, 30 minutes and 4.68 seconds, or 45° 30' 4.68"

Decimal degrees 168.7862 converts to 168 degrees, 47 minutes, 10.32 seconds, or 168° 47' 10.32".

Decimal degrees  87.2530 converts to 87 degrees, 15 minutes, 10.8 seconds, or 87° 15' 10.8".

To translate decimal degrees into DMS, take the following actions:

Converting the following angles from decimal degrees to degrees, minutes, and seconds.

A) 45.5013

The whole number is degrees. So 45.5013 gives you 45degrees.

Multiply the remaining decimal by 60.

0.5013*60 =30.078, so the whole number 30 equals minutes.

Multiply the remaining decimal by 60.

.078*60 = 4.68, so the whole number 4.68 equals seconds.

Decimal degrees 45.5013 converts to 45 degrees, 30 minutes and 4.68 seconds, or 45° 30' 4.68".

B) Similarly for this 168.7862.

Decimal degrees 168.7862 converts to 168 degrees, 47 minutes, 10.32 seconds, or 168° 47' 10.32".

C)Similarly for this  87.2530.

Decimal degrees  87.2530 converts to 87 degrees, 15 minutes, 10.8 seconds, or 87° 15' 10.8".

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The three equations are:

3x = 30.3

30.3 - x = 27.3

3x + 30.3 = 63.6

We have,

Equation 1:

3x = 30.3

Solving for x, we can divide both sides by 3:

x = 10.1

Equation 2:

30.3 - x = 27.3

Solving for x, we can subtract 27.3 from both sides:

x = 3

Equation 3:

3x + 30.3 = 63.6

Solving for x, we can first subtract 30.3 from both sides:

3x = 33.3

Then, we can divide both sides by 3:

x = 11.1

Thus,

The three equations are:

3x = 30.3

30.3 - x = 27.3

3x + 30.3 = 63.6

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Answer:

y = x^2 - 4.

Step-by-step explanation:

This graph is the reslt of translating y = x^2 down by 4 nits

Answer:

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

Recall properties of special right triangles.

45° right triangle has side ratios: 1 : 1 : √2.

It gives us:

30°×60° right triangle has side ratios: 1 : √3 : 2.

It gives us:

No, actually that graph has a global minimun at x = 0

Answer:

A. 3

B. 5

C. 1

D. 2

E. 4

Step-by-step explanation:

one way to quickly check your answers is to check for the number lines with a blank hole and one with a coloured in hole. the one with a coloured in hole should be x=<y. the ones with a blank hole should be x<y. (this trick will not completely check for every mistake.)

The height and radius of the cone that will use the smallest amount of paper are h ≈ 2.45 cm and r ≈ 1.22 cm, respectively.

The minimum paper will be used when the surface area of the cone is minimized. Let the height and radius of the cone be h and r, respectively. Then, using the formula for the volume of a cone, we have:

V = (1/3)πr^2h = 33 cm^3

Solving for h, we get:

h = 99/(πr^2)

Next, we need to express the surface area of the cone in terms of r. The surface area is given by:

A = πr√(r^2 + h^2)

Substituting the expression for h obtained above, we have:

A = πr√(r^2 + (99/πr^2)^2)

To find the value of r that minimizes A, we take the derivative of A with respect to r and set it equal to zero:

dA/dr = π(2r√(r^2 + (99/πr^2)^2) + (r^2 + (99/πr^2)^2)^(-1/2)(2r(99/πr^3)))

Setting dA/dr = 0 and solving for r, we get:

r = (33/(2π))^(1/4) ≈ 1.22 cm

Substituting this value of r back into the equation for h, we obtain:

h ≈ 2.45 cm

Therefore, the height and radius of the cone that will use the smallest amount of paper are h ≈ 2.45 cm and r ≈ 1.22 cm, respectively.

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Answer:

1047.4 cm^3

Step-by-step explanation:

Answer:1047.4

Step-by-step explanation:

.

Therefore , the solution of the given problem of expression comes out to be the coefficient of given expression  XYZ  is 1.

By substituting each variable with a number and conducting mathematical functions, an algebraic formula must be checked. The solution variable in the previous example is identical to 6 since 79 + 8 = 87. To evaluate the expression, we can replace the variables values with ones we are familiar with.

Here,

Given :

XYZ

To find the coefficient of given expression ,

Thus,

From observing we can see XYZ

can be written as

=>1*XYZ

Where 1 is coefficient.

Therefore , the solution of the given problem of expression comes out to be the coefficient of given expression  XYZ  is 1.

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Answer:

15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

The mathematical average of the number of feet in a yard, seconds in a minutes and months in a year is 25.

In Mathematics and Geometry, the arithmetic average for any data set can be calculated by using the following formula:

Arithmetic average = [∑(x)]/n

Generally speaking, we have the following standard parameters;

∑(x) = 3 + 60 + 12

∑(x) = 75

Now, we can determine the arithmetic average as follows;

Arithmetic average = 75/3

Arithmetic average = 25.

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Answer:

The radius is just the diameter split in half, so r = 15 meters.

Explanation:

D = 30

30/2 = 15

r = 15

We substitute z=-7 back into the original equation |4-(-7)|-10=1 simplifies to |11|-10=1. |11|-10=1 simplifies to 1=1. Since the left side equals the right side, our solution is correct.

To solve the equation |4-z|-10=1, we can start by isolating the absolute value term.

Adding 10 to both sides, we get |4-z|=11.
Now, we need to consider two cases:

when 4-z is positive and when it is negative.
When 4-z is positive, we have 4-z=11.

Solving for z, we subtract 4 from both sides and get z=-7.
When 4-z is negative,

we have -(4-z)=11.

Simplifying,

we get z-4=-11.

Solving for z,

we add 4 to both sides and get z=-7.
Therefore, the equation has a solution of z=-7.
To check our answer.

we substitute z=-7 back into the original equation.

|4-(-7)|-10=1

simplifies to |11|-10

=1. |11|-10

=1 simplifies to 1

=1.

Since the left side equals the right side, our solution is correct.

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Both solutions satisfy the original equation,

so z = -7 and z = 15 are the correct answers.

To solve the equation |4-z|-10=1, we will need to consider two cases.

Case 1: (4-z) is positive
In this case, we can remove the absolute value signs and solve for z:
4 - z - 10 = 1
Simplifying this equation, we have:
- z - 6 = 1
To isolate z, we can add 6 to both sides:
- z = 1 + 6
- z = 7
To solve for z, we can multiply both sides by -1:
z = -7

Case 2: (4-z) is negative
In this case, we can rewrite the equation with the absolute value expression as:
-(4 - z) - 10 = 1
Simplifying this equation, we have:
-4 + z - 10 = 1
Combining like terms, we get:
z - 14 = 1
To isolate z, we can add 14 to both sides:
z = 1 + 14
z = 15

So, the two possible solutions for the equation |4-z|-10=1 are z = -7 and z = 15.

To check our solutions, we substitute them back into the original equation:
For z = -7:
|4 - (-7)| - 10 = 1
|4 + 7| - 10 = 1
|11| - 10 = 1
11 - 10 = 1
1 = 1 (True)

For z = 15:
|4 - 15| - 10 = 1
|-11| - 10 = 1
11 - 10 = 1
1 = 1 (True)

Both solutions satisfy the original equation, so z = -7 and z = 15 are the correct answers.

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Answer:

Step-by-step explanation:

a=0.5

The statistical unit for John's study is A. the 35 countries. John is trying to estimate the average literacy rate across all countries, and he randomly selected 35 countries to research their literacy rates. The statistical unit in this case is the individual country, as each country's literacy rate is being used to calculate the average.

The statistical unit for John's study is A. the 35 countries. This is because John's study is based on a sample of 35 countries that he randomly selected. The sample is used to estimate the average literacy rate for all countries. The sample size of 35 countries is large enough to provide a representative sample of the population of countries. If John had selected only a few countries or individuals, his estimate of the average literacy rate would not have been reliable. However, by selecting a sample of 35 countries, John can make a more accurate estimation of the average literacy rate for all countries. In conclusion, the statistical unit for John's study is the sample of 35 countries that he researched to estimate the average literacy rate for all countries.

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The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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If the mpc increases in value, the consumption function will become steeper.

What is MPC ?

MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.

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