determine the interval(s) for which the function shown below is decreasing

Step-by-step explanation:

Jim has 65 coins in his pocket. All of the coins are nickels and dimes. If the total value of his coins is $5.10, how many nickels or dimes does he have?

nickels = n

dimes = d

We use:

d + n = 65

0.10d + 0.05n = 5.10

solve for d:

d + n = 65

d + n - n = 65 - n

d = 65 - n

substitute in for the second equation: d = 65 - n

0.10(65 - n) + 0.05n = 5.10

6.5 - 0.10n + 0.05n = 5.10

6.5 - 0.05n = 5.10

6.5 - 0.05n - 6.5 = 5.10 - 6.5

- 0.05n= -1.4

n = 28

so there are 28 nickels

Now, solve for d: when n = 28

d + n = 65

d + 28 = 65

d = 37

so there are 37 dimes

Jim has 28 nickels and 37 dimes in his pocket. which is determined by the substitution method.

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

Let the number of nickels would be n

Let the number of dimes would be d

As per the given question,

d + n = 65  ....(i)

0.10d + 0.05n = 5.10  ....(ii)

From equation (i),

d + n = 65

d + n - n = 65 - n

d = 65 - n

Substitute in for the equation(ii): d = 65 - n

0.10(65 - n) + 0.05n = 5.10

6.5 - 0.10n + 0.05n = 5.10

6.5 - 0.05n = 5.10

6.5 - 0.05n - 6.5 = 5.10 - 6.5

- 0.05n = -1.4

n = 28

This means there are 28 nickels

Substitute the value of n = 28 in the equation (i),

d + n = 65

d + 28 = 65

d = 37

So there are 37 dimes

Thus, Jim has 28 nickels and 37 dimes in his pocket.

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The number of extra tables that you need to double the original seating capacity will be 7.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The seating capacity y for a banquet hall is represented by y = 8x + 56, where x is the number of extra tables you need.

If the no extra table is there. Then the value of 'y' will be

y = 8 (0) + 56

y = 56

Then the number of extra tables do you need to double the original seating capacity will be

8x + 56 = 2 × 56

8x = 56

x = 7

Then the number of extra tables that you need to double the original seating capacity will be 7.

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Answer:

[tex]16x {}^{3} + 1[/tex]

Step-by-step explanation:

We need to differentiate the following function,

[tex]\longrightarrow f(x) = 4x^4 + x [/tex]

Let ,

[tex]\longrightarrow y = f(x) [/tex]

So that ,

[tex]\longrightarrow y = 4x^4+x [/tex]

Differentiating both sides wrt x ,

[tex]\longrightarrow \dfrac{dy}{dx}= \dfrac{d(4x^4+x)}{dx}\\[/tex]

[tex]\longrightarrow\dfrac{dy}{dx}= \dfrac{d(4x^4)}{dx}+\dfrac{dx}{dx}\\ [/tex]

[tex]\longrightarrow \dfrac{dy}{dx} = 4(4)x^{4-1} + 1 \\ [/tex]

[tex]\longrightarrow \underline{\underline{ \dfrac{dy}{dx}= 16x^3 +1}}[/tex]

A 95% confidence interval for the proportion who believe immigration is a good thing is; CI = (0.4173, 0.7173)

The formula for the confidence interval of proportions is;

CI = p ± z√(p(1 - p)/n)

where;

p is sample proportion

z is z-score at confidence level

n is sample size

We are given;

Number of success; x = 631

Sample size; n = 1095

Thus;

sample proportion; p = x/n = 631/1095 = 0.5763

The z-score at 95% confidence level is 1.96. Thus;

CI = 0.5673 ± 1.96√(0.5673(1 - 0.5673)/1095)

CI = 0.5673 ± 0.015

CI = (0.5673 - 0.15), (0.5673 + 0.15)

CI = (0.4173, 0.7173)

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The partial fraction form of the given fraction [x+5/(x-7)(x-5)] is

[A/(x-7)+B/(x-5)].

So, the fraction is:

We know that:

Use the same identity to get the partial fraction of the given fraction as follows:

Therefore, the partial fraction form of the given fraction [x+5/(x-7)(x-5)] is [A/(x-7) + B/(x-5)].

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The answer will be:

B: 5 percent/ 5%

13 words in length will be 5%

Hope this helped

:)

The solution of the given expression -5ax⁶(2ax⁴ + 7x²) is equal to -10a²x¹⁰-35ax⁸.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is -5ax⁶(2ax⁴ + 7x²). The solution of the expression will be done as,

E =  -5ax⁶(2ax⁴ + 7x²)

E = -10a²x¹⁰-35ax⁸.

Therefore, the solution of the given expression -5ax⁶(2ax⁴ + 7x²) is equal to -10a²x¹⁰-35ax⁸.

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The critical values of the chi statistic are; χ²R = 8.643 and χ²L = 42.796

The confidence interval estimate of σ is; 0.20 < σ < 0.45

We are given the following data;

Sample size; n = 23

Degree of freedom; df = n - 1 = 23 - 1 = 22

Confidence level; α - level = 99%

Sample standard deviation; s = 0.25 mg

For χ²R;

The significance level is; 1 - (1 - 0.99)/2= 0.995

The degree of freedom is; df = 22

From critical value tables, we know that; χ²R = 8.643

For χ²L ;

The significance level is; (1 - 0.99)/2 = 0.005

The degree of freedom is; df = 22

From critical value tables, we know that; χ²L = 42.796

The confidence interval estimate of σ is;

s * √[(n-1)/χ²L] < σ < s * √[(n-1)/χ²R)]

Plugging in the relevant values gives;

0.28 * √(22/42.796) < σ < 0.28 * √(22/8.643)

0.2008 < σ < 0.4467

0.20 < σ < 0.45

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The number of points scored by Tyger will be 132 points.

From the information, Captain scores 120 points on Space Invaders. Tyger scores 10% more points than Captain.

Therefore, the number of points scored by Tyger will be:

= Points scored by Captain + (Percentage × Captain point)

= 120 + (10% × 120)

= 120 + 12

= 132

Tyger scored 132 points.

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The number of points scored by Tyger will be 132 points.

From the information, Captain scores 120 points on Space Invaders. Tyger scores 10% more points than Captain.

Therefore, the number of points scored by Tyger will be:

= Points scored by Captain + (Percentage × Captain point)

= 120 + (10% × 120)

= 120 + 12

= 132

Tyger scored 132 points.

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Answer:

so now i think you can find the slope of the sides.the product of slopes of two perpendicular lines is - so now you can also find the slopes of the altitude. i will do one side for you and you do the remaining the slope of side BC is (2-0)/(9-0) = 2/9 so the slope of the altitude passing through A will be -9/2

Step-by-step explanation:

so i think it would be side AC

Answer:

Side BC

Step-by-step explanation:

Let's calculate the slopes of the sides of triangle ABC:

Slope of side AB = (2 - 0) / (9 - 16) = 2 / (-7) = -2/7

Slope of side BC = (0 - 2) / (2 - 9) = -2 / (-7) = 2/7

Slope of side CA = (0 - 0) / (2 - 16) = 0 / (-14) = 0

Among the three sides, only side BC has a slope of 2/7, which is the negative reciprocal of the given slope of -2/7.

Therefore, side BC represents the altitude of triangle ABC with a slope of -2/7.

The length of the line segment with endpoints at (0, 3) and  (-6, -5) is 10 units

An equation shows the relationship between two or more numbers and variables.

The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is:

[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

The line segment have endpoints at (0, 3) and  (-6, -5). Hence:

Length = √[(-5-3)² + (-6 - 0)²] = √(8² + 6²) = √100 = 10

The length of the line segment is 10 units

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Concurrent lines meet at the point of concurrency.

Answer:

2/3 u need to walk to reach the clothing shop

Answer: 25.949%

Step-by-step explanation:

We have to label a graph with the following points: (1,3), (4,2), (0,5), and (5,1).

All the points (and only those points) which lie on the graph of the function satisfy its equation. Thus, if a point is on te graph of a function, then it must also satisfy the function.

To plot the graph with the points follow all the steps given below;

Points are (1,3) , (4,2) , (0,5),and (5,1).

Step1 The coordinate of the graph are; (1,3) , (4,2) , (0,5),and (5,1).

Step2 Plot the coordinate 1 on the x-axis and 3 on the y-axis.

Step3 Plot coordinate 4 on the x-axis and 2 on the y-axis.

Step4  Plot the coordinate 0 on the x-axis and 5 on the y-axis.

Step5 Plot the coordinate 5 on the x-axis and 1 on the y-axis.

Step6 Then Draw a line with the help of the scale and meet all the points.

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The total amount Jaxon should paid for the apples is 12 dollars which is 1200 cents.

Given,

The quantity of apple bought by Jaxon = 10 2/3 pounds

The cost of one pound of apple = $1.80

We have to find the total amount Jaxon should paid for the apples, in dollars and cents;

Here,

Total amount Jaxon should paid = Quantity of apple bought by Jaxon × Cost of one pound of apple

Total amount Jaxon should paid = 10 2/3 × 1.80

Total amount Jaxon should paid = 12 dollars

1 dollar is equal to 100 cents

Then,

12 dollars = 12 x 100 = 1200 cents.

Therefore,

The total amount Jaxon should paid for the apples is 12 dollars which is 1200 cents.

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Answer: D because 8 1/5 is smaller than 8 1/3

The instantaneous rate of change of monthly output with respect to the number of workers is equal to 184.

The instantaneous rate of change can be defined as a type of function that describes the average rate at which a quantity increases or decreases with respect to another quantity at a particular instant.

In Mathematics, the instantaneous rate of change can be calculated by taking the derivate of the function with respect to an independent variable. This ultimately implies that, the instantaneous rate of change is equivalent to the change in the derivative value at a particular instant.

Taking the derivate of the given function, we have:

Q(x) = 15,000 + 2x²

Q'(x) = d/dx(15,000) + d/dx(2x²)

Q'(x) = 0 + 2x(2)

Q'(x) = 4x.

At x = 46, we have:

Q'(x) = 4(46)

Q'(x) = 184.

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Complete Question:

The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x² units, (40 ≤ x ≤ 60), where x is the number of workers employed at the mill. If there are currently 46 workers, find the instantaneous rate of change of monthly output with respect to the number of workers. That is, find Q'(46).

Q'(46) =

Answer:

Step-by-step explanation:

You subtract 583 from 400 (400-583)

Then you get 183

Step-by-step explanation:

e⁰ = 1

so, we have

(f² / (f³gh⁶))⁸ = f¹⁶ / (f²⁴g⁸h⁴⁸) = 1 / (f⁸g⁸h⁴⁸)

FYI - depending on what your teacher wants to see as simplified answer, it could be also

1 / (fgh⁶)⁸

or

(1 / (fgh⁶))⁸

but normally it should be the first result form above

1 / (f⁸g⁸h⁴⁸)

The probability that the part is between 10.8 and 12.8 cm is 0.0669.

What is a normal distribution?

Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is symmetric around the mean.

Here, we have

Mean = 16.3cm

Standard deviation = 2.5cm

We have to find the probability that the part is between 10.8 and 12.8 cm

Now,

we know that z = (x−μ)/σ

putting values in the normal distribution formula, we get

P( 10.8 < x < 12.8) = P( (10.8 - 16.3)/2.5 < z < (12.8 - 16.3)/2.5)

                            = P ( -2.2 < z < -1.4)

P( 10.8 < x < 12.8) = 0.0669, by normal distribution table

Hence, the probability that the part is between 10.8 and 12.8 cm is 0.0669.

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The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.

Given that,

The equation is 3x-8y=39.

We have to find the x- intercept and y- intercept of the equation.

We know that,

x/a + y/b = 1 is the intercept form of the line's equation. One of the key types of line equations is this one. In this equation, the sign of the intercepts also enables us to determine where the line is in relation to the coordinate axes.

To find the x- intercept of the equation.

We have to take y as 0.

3x-8(0)=39

3x=39

x=39/3

x=13

To find the y- intercept of the equation.

We have to take x as 0.

3(0)-8y=39

-8y=39

x=-39/8

Therefore, The x- intercept of the equation is (13,0) and y-intercept of the equation is (0,-39/8) when the equation is 3x-8y=39.

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Answer:

Step-by-step explanation:

Which graph represents the solution set of - 4x - y ≤ - 6?

According to the solving Probability the value are as follows.

a) P(Blue)= 0/10

b) P(Red)= 5/10

c) P(Red or Yellow)= 9/10

The definition of probability is "How likely something is to happen."

Probability is indeed a number ranging from 0 to 1 that expresses the likelihood that an event will take place as specified.

First, 0 P(E) 1 (where P(E) specifies the probability of an event E) and second, the sum of the probabilities of any collection of mutually and exclusive exhaustive occurrences equals 1 are the two characteristics that define a probability.

We have a Bag of marbles has 4 yellow, 5 red, and 1 purple.

Total balls in a bag= 4+5+1=10 balls.

Something that is IMPOSSIBLE to happen.

P(Blue)= 0/10

Something that is EQUALLY LIKELY to happen.

P(Red)= 5/10

Something that is LIKELY to happen.

P(Red or Yellow)= 9/10

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Answer:

123 423 21 34

Step-by-step explanation:

The standard score (z-score) of the given sample mean is equal to 7.11

A standard score is also referred to as a z-value or z-score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Mathematically, the standard score of a given sample mean can be calculated by using this formula:

[tex]Z=\frac{\bar{x}\;-\;\mu}{ \frac{\delta}{n} }[/tex]

Where:

Where:

Substituting the given parameters into the formula, we have;

Standard score, z = (30 - 31)/(9/64)

Standard score, z = -1/0.140625

Standard score, z = 7.11

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Answer:

  78°

Step-by-step explanation:

You want the measure of base angle x in an isosceles triangle with a.pex angle 24°.

The two base angles of an isosceles triangle are congruent. The sum of all angles is 180°, so we have ...

  24° +2x = 180°

  12° +x = 90° . . . . . . divide by 2

  x = 78° . . . . . . . subtract 12°

The measure of angle x is 78°.

The inequality as per the question is x ≥ 9 and y > 3 and the diagram according to this is attached below.

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.

As per the given information in the question.,

x ≥ 9 and,

y > 3

The equation is,

650 x + 1400 y ≤ 1

[tex]\frac{x/15000}{650}+\frac{y/15000}{1400} \leq 1[/tex]

x/23.07 + y/10.71 ≤ 1

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