Identify the number of solutions or zeros:
f(3) = 23 – 3.75 +27 – 9
3
1
5
7

Answer:

6,3

Step-by-step explanation:

Answer:

13 P

Step-by-step explanation:

Answer: 13p

Step-by-step explanation:

All three terms have the same variable. Therefore, you can add all three terms together into a singular term (below).

5p + 2p + 6p = 13p

g(x) is shifted 8 units to the right and 3 units up is the correct answer.

Given the graph of a function expressed as:

g(x) = (x - 8)^3 + 3

The graph of g(x) = (x - 8)^3 + 3 is obtained by taking the graph of the parent function f(x) = x^3 and performing two transformations:

A horizontal shift of 8 units to the right. This means that the graph of g(x) will be shifted to the right by 8 units compared to the graph of f(x).

A vertical shift of 3 units up. This means that the graph of g(x) will be shifted upwards by 3 units compared to the graph of f(x).

Therefore, the correct answer is: g(x) is shifted 8 units to the right and 3 units up.

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The point on the line y = 2x + 3 which is closest to origin is (-6/5, 3/5).

In order to find the point on line y = 2x + 3 that is closest to the origin, we  minimize the distance between the origin (0, 0) and a point (x, y) on the line.

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula : d = √(x₂ - x₁)² + (y₂ - y₁)²,

In this case, one point is the origin (0, 0) and other point is (x, 2x + 3) on the line y = 2x + 3.

We can write , d = √(x - 0)² + ((2x + 3) - 0)²,

= √(x² + (2x + 3)²)

= √(x² + 4x² + 12x + 9)

= √(5x² + 12x + 9)

To minimize the distance, we minimize square of distance, which is equivalent. So, we minimize the square of distance,

d² = 5x² + 12x + 9

To find the minimum-point, we take derivative of d² with respect to x and equate to 0,

d²/dx = 10x + 12 = 0

Solving this equation,

We get,

10x + 12 = 0

10x = -12

x = -12/10

x = -6/5

Now, we substitute value of "x" in equation y = 2x + 3 to find the corresponding y-coordinate,

y = 2(-6/5) + 3

y = -12/5 + 15/5

y = 3/5.

Therefore, the closest point is (-6/5, 3/5).

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The given question is incomplete, the complete question is

Find the point on the line y = 2x + 3 that is closest to the origin.

Answer: He run 7 high-speed intervals and 8 low-speed intervals.

Step-by-step explanation:

Let x = Number of high-speed intervals.

y= Number of low-speed intervals .

He runs high-speed intervals in 16 seconds, and low-speed intervals in 23 seconds, and he runs a combined total of 15 intervals in 4 minutes and 56 seconds.

4 min 56 sec = (4(60)+56) sec = 296  sec   [ 1 minute = 60 seconds]

According to the question , we have the following linear equations :

\(x+y=15\ ...(i)\\\\ 16x+23y=296\ ...(ii)\)

Multiply (i)by 16 , we get

\(16x+16y=240\ ...(iii)\)

Subtract (iii) from (ii)

\(7y=56\\\\\Rightarrow\ y=8\)

Put value of y in (i) , we get

\(x+8=15\Rightarrow\ x=7\)

Hence, he run 7 high-speed intervals and 8 low-speed intervals.

Answer:

(5w-1) (w-1)

Steps:

5w^2-w-5w+1

w(5w-1)-(5w-1)

(5w-1) (w-1)

(5w-1) (w-1)

Answer

the answer is 200

taking the test . hope this helps!!!!

Step-by-step explanation:

Answer: $200

Explanation: Find the total amount of money the Federal Income taxed Yarin. Then, find the difference with what Yarin believes he owes ($115).

Step 1.) Find the actual tax amount in dollars. To find how much money is 9% of $3,500, you will convert the percentage (9%) to a decimal, then multiple the gross pay by the decimal.

1.) 9% -> .09

2.) 3,500 x .09 = 315

Step 2.) Find Refund. To find the refund, we simply find the difference between the Federal Income tax ($315) and what Yarin believes he owes ($115).

1.) 315-115 = 200

Result: Yarin can expect a $200 refund if he actually owes $115, since the Federal Income tax withdrew 9% of his gross pay which added up to $315.

Your Welcome, Let me know if you have any questions.

The inequality which represents all the possible values for x is (2x/3) - 6 ≥ 24.

It is given in the question that the difference of two-thirds of a number x and 6 is at least -24.

We have to find the inequality which represents all the possible values for x.

In mathematics, Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Hence, according to the data given in the question, we can write,

(2x/3) - 6 ≥ 24

Here, we can also find the possible values of x.

(2x/3) - 6 ≥ 24

2x/3  ≥ 24 + 6

2x/3  ≥ 30

x  ≥ 30*3/2

x  ≥ 45

Hence, every number greater than or equal to 45 will be a possible value of x.

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Answer:

$71.00 - $20 = $51

51 divided by 6 = 8.5!

Step-by-step explanation:

-1/28 is the average rate of change of f(x) from 8 to 64. Thus, option A is correct.

The f(x) function of the  

f(x)=−\(\sqrt[3]{x}\)

the range is provided to lie between 8 and 64.

The function for 8 will be:

f(8)  =−\(\sqrt[3]{8\\}\)

= -2

The function for 64 will be:

f (64)  =−\(\sqrt[3]{64\\}\)

= - 4

The average is usually determined with the help of the intervals that are given:

The average function of (64,f(64)) and (8,f(8)); will be calculated as:

f = \(\frac{-4 - (-2)}{64 - 8}\)

= -2 / 56

= -1 / 28

Therefore, option A is correct.

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The question is incomplete, Complete question probably will be  is:

Let f(x)=−x√3.

What is the average rate of change of f(x) from 8 to 64?

−1/28

1/28

−28

28

The most precise classification of the quadrilateral with opposite sides having the same slopes and consecutive sides having slopes that are reciprocals is a Rectangle.

1. Opposite sides with the same slopes imply that these sides are parallel.
2. Consecutive sides with slopes that are reciprocals mean that they are perpendicular.
3. Parallel opposite sides make the quadrilateral a parallelogram.
4. Perpendicular consecutive sides make it a rectangle, as all angles are 90 degrees.

So, the quadrilateral is a Rectangle.

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X is a connected set but not a path-connected set. X={x,0xe[0,1}U{1/nyneN,ye{0,1]}U{0,1}.

To prove that X is connected, let us assume that X can be divided into two disjoint non-empty open sets A and B. Since X is the union of different points, any point in X will be in either A or B. Let us take an arbitrary point p in A. Since A is open, there is an open ball centered at p that is contained in A. Because B is disjoint from A, it follows that every point in this ball is also in A. By a similar argument, any point in B must have a ball centered at that point that is entirely contained in B. Thus, X must be either in A or B and hence, cannot be divided into two disjoint non-empty open sets. However, X is not path-connected since there is no path between points in [0,1] x {0} and {1} x {1}. Thus, it is connected but not path-connected.

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Answer:

1 acre is equal to 43,560 square feet.

Step-by-step explanation:

Hope it helped!

if it includes some but not all of its limit points, it is not closed and not open.(i) ∩ n∈N(0, n1)Firstly, let's find the intersection of all the sets:  

∩ n∈N(0, n1)= {x∈X|∀n∈N, x∈(0,n1)}= {x∈X| 0

(i) ∩ n∈N(0, n1) is closed and not open and convex.

(ii) ∩ n∈N(0,1+ n1) is closed and not open and not convex.

(iii) ∩ n∈1k(0,1+ n1) for some k∈N is both closed and open and convex.

(iv) (0, n1) for some n∈N is open and not closed and convex.

Discussion:Let X be a set, and d be a distance function on X.

Then,

(X, d) is called a metric space if it fulfills the following conditions:∙For each x, y∈X, d(x, y)≥0, and d(x, y)=0 if and only if x=y.

For each x, y∈X, d(x, y)=d(y, x).∙For each x, y, z∈X, d(x, y)≤d(x, z)+d(z, y).Thus, let X=[0,1] with Euclidean metric d(x,y)=|x−y| for x,y∈X.

Then, the distance between two points on a line is calculated using the Euclidean distance. For example, the distance between 0 and 1 on [0, 1] is 1.

The distance between 1/2 and 3/4 on [0, 1] is 1/4.Convex: If two points lie within the same set, then a set is known to be convex.Closed and open:

If the set includes its limit points, the set is closed. If a set includes none of its limit points, it is open.

Therefore, if it includes some but not all of its limit points, it is not closed and not open.(i) ∩ n∈N(0, n1)Firstly, let's find the intersection of all the sets:  

∩ n∈N(0, n1)= {x∈X|∀n∈N, x∈(0,n1)}= {x∈X| 0

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answer: they spend $27.92 on goodie bags

the hourly rate is $37.5

they spend $177.92 in total

The value of x in the given equation  \(3\sqrt[6]{x} +7=10\) is 1.

Two or more expressions with an Equal sign is called as Equation.

The given equation is \(3\sqrt[6]{x} +7=10\)

In the given equation x is the variable and plus is the operator.

Subtract 7 from both the sides to eliminate 7 in the left side and to isolate the variable x.

\(3\sqrt[6]{x} =10-7\)

When seven is subtracted from 10 we get 3.

\(3\sqrt[6]{x} =3\)

Divide both sides by 3

\(\sqrt[6]{x} =1\)

x³=1

Take cube root on both sides

x=1

the value of x in the given equation  \(3\sqrt[6]{x} +7=10\) is 1.

Hence, the value of x in the given equation  \(3\sqrt[6]{x} +7=10\) is 1.

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Answer:

Therefore the largest number that these fractions can be divided by to give them a whole number is

a) 8/15 = The largest number is 8/15

b) 18/35 = The largest number is 18/35

Step-by-step explanation:

A quotient is the result obtained by dividing two numbers.

So that the quotient obtained is a whole number we have to find out, what number they can be divided by to give them that.

Let's assume the whole number is 1

a. 8/15

8/15 ÷ x = 1

8/15 × 1/x = 1

8/15x = 1

We would cross multiply

8 = 15x

We would divide both sides by 15

8/ 15 = x

Hence the largest number that would divide 8/15 and give it a whole number = 8/15

b) 18/35

18/35÷ x = 1

18/35 × 1/x = 1

18/35x = 1

We would cross multiply

18 = 35x

We would divide both sides by 35

18/ 315 = x

Hence the largest number that would divide 18/35 and give it a whole number = 18/35

Answer:

The answer is 2/105

Step-by-step explanation:

first we have to find the LCM of both denominators. IN this case, the LCM of 15 and 35 is 105. Then we have to find the GCF of these numerators. IN this case, the GCF of 8 and 18 is 2.

Now, put the GCF you found over the LCM.

ANSWER: 2/105

This fraction is the largest number you can divide both numbers by to get a whole number.

Answer:

-3/19

Step-by-step explanation:

slope = rise/run = (y1 - y2) / (x1 - x2)

s = (19 - 16) / (-9 -10)

s = 3/-19 = -3/19

The correct answer is (D) AB is 4 x 4, BA is 2 x 2.

What is order of a matrix?

The order of a matrix refers to the number of rows and columns in the matrix. If a matrix has m rows and n columns, we say that it is an m x n matrix. The order of the matrix is written as "m x n".

In general, if A is an m x n matrix and B is an n x p matrix, then the product AB is an m x p matrix and the product BA is an n x n matrix.

In this case, A is a 4 x 2 matrix and B is a 2 x 4 matrix. Therefore, the product AB is a 4 x 4 matrix, and the product BA is a 2 x 2 matrix.

So the answer is (D) AB is 4 x 4, BA is 2 x 2.

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Answer:

y is x because if x+y is 2x then y must equal x

The sum of x and y is twice x. Then the value of y will be equal to x.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

It is given that sum of x and y is twice x. Then the value of y will be calculated as below:-

x + y = 2x

y = 2x - x

y = x

Therefore, the sum of x and y is twice x. Then the value of y will be equal to x.

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Answer:  3/4

Step-by-step explanation:

The slope = (y2-y1)/(x2-x1) for two points (x1,y1) and (x2,y2).

In this image, the two points are (-3,-2) and (1,1)

We can plug this into the equation.

Slope = (1-(-2))/(1-(-3))

Slope = 3/4

Answer:

slope = \(\frac{3}{4}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, - 2) and (x₂, y₂ ) = (1, 1) ← 2 points on the line

m = \(\frac{1-(-2)}{1-(-3)}\) = \(\frac{1+2}{1+3}\) = \(\frac{3}{4}\)

The incidence rate of HIV infection among prisoners in Nevada prisons is 4.17 cases per 1000 person-years.

The prevalence of HIV infection among incoming prisoners in Nevada before the study was not given in the provided question. However, the prevalence of HIV infection after the study can be calculated as 35/1100 = 0.0318 or 3.18%.The incidence rate of HIV infection among prisoners in Nevada prisons is 5 per 1200 person-years. This can be calculated using the formula: incidence rate = (number of new cases of HIV / total person-years of observation) x 1000.

Therefore, the incidence rate of HIV infection among prisoners in Nevada prisons is (5/1200) x 1000 = 4.17 cases per 1000 person-years. The study published in 1990 (Amer J. Pub Health 80:pp 209-210) investigated the occurrence of HIV infection among prisoners in Nevada. Out of 1100 prison inmates who were tested for HIV upon admission to the prison system, 35 were found to be infected. The prevalence of HIV infection among incoming prisoners in Nevada after the study can be calculated as 35/1100 = 0.0318 or 3.18%.

All uninfected prisoners were followed for a total of 1200 person-years and retested for HIV upon release from prison. Five of the uninfected inmates demonstrated evidence of new HIV infection. The incidence rate of HIV infection among prisoners in Nevada prisons is 5 per 1200 person-years. This can be calculated using the formula: incidence rate = (number of new cases of HIV / total person-years of observation) x 1000. Therefore, the incidence rate of HIV infection among prisoners in Nevada prisons is (5/1200) x 1000 = 4.17 cases per 1000 person-years.

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The length of a standard basketball court is 94 feet (28.65 meters), and the width is 50 feet (15.24 meters).

A standard basketball court is rectangular in shape and follows certain dimensions specified by the International Basketball Federation (FIBA) and the National Basketball Association (NBA). The length and width of a basketball court may vary slightly depending on the governing body and the level of play, but the most commonly used dimensions are as follows:

The length of a basketball court is typically 94 feet (28.65 meters) in professional settings. This length is measured from baseline to baseline, parallel to the sidelines.

The width of a basketball court is usually 50 feet (15.24 meters). This width is measured from sideline to sideline, perpendicular to the baselines.

These dimensions provide a standardized playing area for basketball games, ensuring consistency across different courts and facilitating fair play. It's important to note that while these measurements represent the standard dimensions, there can be slight variations in court size depending on factors such as the venue, league, or specific regulations in different countries.

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Answer:

Step-by-step explanation:

All of the answer choices are wrong lol. The answer choice is supposed to be (173+124) divided by 3. Total students divided by student per seat. Your closest answer choice is going to be (175+125) divided by 3. Hope this helped!

Step-by-step explanation:

10 + 3x = 30 + 7x

collect terms that look alike on one side.

we can see that 3x & 7x have something in common which is x.

so move one of these to either of the equality's sides.

0 = 30 + 7x -10 - 3x

i changed the sign of 3x to -3x & 10 to -10 because we'll have to subtract 3x or 10 from the left side inorder for them to vanish & appear on the right hand side.

collect like terms.

0 = 30 - 10 + 7x - 3x

0 = 20 + 4x

take 20 to the left side to find x by dividing by 4.

20 = 4x

20 / 4 = x

5 = x

The exact length of the curve for the function y = ln(1 - x²) is log(5/4) - 1/9

The general formula for the arc length of the curve y on the interval [a, b] is written as,

\(s=\int\limits^a_b {\sqrt{1+(\frac{dy}{dx})^2 } } \, dx\)

Here we have given that the function is y = ln(1 - x²)

And the limit is 0 ≤ x ≤ 1/9

When we differentiate the function, then we get the value of y' as,

y' =  1/(1 - x²) × (-2x) = -2x/(1 - x²)

Now, we have to apply the values on the arc length formula, then we get,

\(s=\int\limits^{1/9}_0 {\sqrt{1+(\frac{-2x}{1-x^2} )^2 } } \, dx\)

When we simplify this one then we get,

\(s=\int\limits^{1/9}_0 {\sqrt{\frac{1+x^4-2x^2+4x^2}{(1-x^2)^2} } } \, dx\)

Now, we have to divide numerator by denominator and expressing using

the rule Dividend/Divisor = Quotient + (Remainder/Divisor)

Then we get the resulting equation as,

\(s=\int\limits^{1/9}_0 {-1 + \frac{2}{1-x^2} } \, dx\)

When we apply the limit value, then we get

s = −1/9 + log∣10/8∣−log(1)

When we simplify this one then we get,

s = log(5/4) - 1/9

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Option B provides the best approximation of the instantaneous velocity at t=75 seconds by considering a time interval that is infinitesimally close to the desired point in time.

To obtain the best approximation of the instantaneous velocity of the automobile at time t=75 seconds, we need to consider a time interval that is as close to t=75 as possible. The concept of instantaneous velocity involves calculating the velocity at a specific point in time, which requires considering an infinitesimally small time interval.

Option B, which suggests calculating the average velocity from t=74.99 to t=75 seconds, is the most appropriate choice. By choosing a time interval that is extremely close to t=75, we minimize the effect of any fluctuations in velocity within that interval and obtain a better approximation of the instantaneous velocity.

Option A, the average velocity from t=70 to t=80 seconds, encompasses a larger time interval and may include significant variations in velocity over that period. Option C, the average velocity from t=75 to t=75.1 seconds, introduces a small time interval, but it is still not as precise as option B.

Thus, option B provides the best approximation of the instantaneous velocity at t=75 seconds by considering a time interval that is infinitesimally close to the desired point in time.

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Answer:

\(13.\overline 3\)

Step-by-step explanation:

We can use proportions to find the amount of water needed

Let \(x\) be the amount of water needed

\(\frac{3}{2} = \frac{20}{x}\) (with the ratio being 3 powder to 2 water)

Now we can cross multiply and solve for \(x\)

\(3(x) = 20(2)\\3x = 40\\x = \frac{40}{3}\\ x = \boxed{13.\overline3}\)

You will need \(13.\overline3\) grams of water to make the flavored drink.