Question 23 of 41
Which of the following is equivalent to the product below?
√9.√5√2
OA. 18√5
OB. 10√3
OC. 3√10
OD. 5√18

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \implies y +7= -\cfrac{4}{3} (x -3) \\\\\\ y+7=-\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x-3 \end{array}}[/tex]

The work done by stretching the spring to the given distance is:

[tex]W=\frac{kx_{0} }{3}[/tex]

The given parameters:

Applied force on the spring = F

Extension of the spring, = x₀

The work done by stretching the spring to the given distance is calculated as follows:

[tex]W=\int\limits^b_a {F} \, dx[/tex]

Where:

F - Force.

W- Work.

x- Distance.

If we know that F=k.x², then the work of the nonlinear spring is:

[tex]W=\int\limits^b_a {F} \, dx \\W=\int\limits^b_a {kx^2} \, dx \\W=k\int\limits^b_a {x^2} \, dx \\\\W=k[\frac{x^3}{3}]\\\\W=k[\frac{x_b-x_a}{3} ]\\\\W=k[\frac{x_o-0}{3} ][/tex]      

W=kx₀/3

Thus, the work done by stretching the spring to the given distance is: W=kx₀/3

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If the Colossus Ferris wheel debuted at the 1984 New Orleans World's Fair and the ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The period of the sine function model is: 2/3 minutes.

Given equation:

h=-82.5 cos 3pi(t)+97.5

Where:

h= height of the passenger above the ground measured in feet

t = time of operation of the ride in minutes

So,

h=-82.5× cos  [2 × π ×t /T) +97.5

2 ×π / T = 3 × π

T = 2/3 minutes

Therefore the period of the sine function model is: 2/3 minutes.

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To reach the speed of light, the spaceship will take 3.1 × 10⁷ seconds. The result is obtained by using the formula for acceleration.

Acceleration is the rate of change in velocity of an object with respect to time. It can be expressed as

[tex]a = \frac{\Delta v}{\Delta t}[/tex]

Where

If we were in a spaceship with an acceleration of g, determine the time we reach the speed of light!

We have

To find the time so that we can reach the speed of light, we use the formula for acceleration.

[tex]a = \frac{\Delta v}{\Delta t}[/tex]

[tex]g = \frac{c - 0}{\Delta t}[/tex]

[tex]9.8 = \frac{3 \times 10^{8}}{\Delta t}[/tex]

[tex]\Delta t = \frac{3 \times 10^{8}}{9.8}[/tex]

Δt = 0.306 × 10⁸

Δt = 3.1 × 10⁷ s

Hence, the spaceship will take 3.1 × 10⁷ seconds to reach the speed of light.

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Integration techniques from chapter 6, such as the power rule, substitution rule, and integration by parts, can be used to solve real-world problems involving calculus.

For example, the power rule can be used to calculate the area of an object by integrating its equation. The substitution rule can be used to calculate the volume of a solid by substituting the equation of its surface. Finally, integration by parts can be used to calculate the arc length of a function given its equation. All these techniques provide a way to calculate the area, volume, and arc length of various objects given their equations, allowing us to apply calculus to real-world situations. Integration techniques from chapter 6, such as the power rule, substitution rule, and integration by parts, can be used to solve real-world problems involving calculus.

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Answer:

To find the ordered pairs that are solutions to the equation X+2y=8, we need to isolate the variable y on one side of the equation.

We can start by subtracting X from both sides:

X+2y = 8

X+2y-X = 8-X

2y = 8-X

Now we can divide both sides by 2:

y = (8-X)/2

So the ordered pairs (X, y) that are solutions to the equation X+2y=8 are the ones that satisfy the equation y = (8-X)/2.

We can substitute any value of x into the equation and find the corresponding y value.

For example, if we take X= 4, we can find the corresponding y value:

y = (8-4)/2 = 4/2 = 2.

so (4,2) is a solution to the equation X+2y=8.

We can also plot the equation on a Cartesian plane and find the points where the equation is true, those are the solutions.

Alternatively, we can solve the equation for X and find the solutions for y.

X = 8-2y

So the ordered pairs (X, y) that are solutions to the equation X+2y=8 are the ones that satisfy the equation X = 8-2y

We can substitute any value of y into the equation and find the corresponding X value.

For example, if we take y= 2, we can find the corresponding X value:

X = 8-2(2) = 8-4 = 4.

so (4,2) is a solution to the equation X+2y=8.

In this case, any value of X and y that satisfies the equations y = (8-X)/2 or X = 8-2y are solutions to the equation X+2y=8

the simplified expression is 2x9/4.19, which can be written as A/B, where A = 2x9 and B = 4.19. Therefore, the value of A is 18 and the value of B is 4.

To simplify the expression V4219, first divide it into two separate terms by breaking the number 4219 into 4 and 2119.

Now, we need to simplify the terms 4 and 2119 separately.

To simplify the term 4, we need to divide it by 4, which gives us 1.

To simplify the term 2119, we need to divide it by 19, which gives us 2x9.

Hence, the simplified expression is 2x9/4.19, which can be written as A/B, where A = 2x9 and B = 4.19. Therefore, the value of A is 18 and the value of B is 4.

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The reversal of the statement would give the converse statement and this is done in option A.

We know that in logic a statement would need to have a premise and a conclusion. The premise is what would naturally lead to the conclusion. The statement is true when the premise does lead to the conclusion.

We know that the converse of a statement can be said to be obtained when we switch the positions of the premise and the conclusion in the statement. The conclusion becomes  the premise and the premise becomes the conclusion.

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: Pretty Sure u need the question to number 4-

Step-by-step explanation:

Answer:

If the sum of the two numbers is 25, we can represent the larger number as x + (smaller number)

The difference between four more than the larger number and twice the smaller number is:

(x + 4) - 2(x) = x + 4 - 2x = -x + 4

Now we can simplify the expression:

-x + 4

That is the variable expression for the difference between four more than the larger number and twice the smaller number.

Step-by-step explanation:

Answer:

307,8

Step-by-step explanation:

The area of a circle is 3.14 times the radius squared, and the radius is the diameter divided by 2. Hence the area is 307.8

Answer: <3, 1>

Step-by-step explanation: A translation of a vector is simply moving it a certain distance in a certain direction. In this case, the first translation of  <6, -4> moves the vector 6 units to the right and 4 units down. The second translation of <-3, -5> then moves the vector an additional 3 units left and 5 units down. The net result of these two translations is to move the vector 3 units to the right and 1 unit up, which is equivalent to a single translation of <3, 1>.

Answer:

I tink D?

Step-by-step explanation:

The function after the reflection over y-axis is f' ( x ) = √( -x )

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = √x

Now , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)

So , the reflected function is f' ( x ) = √( -x ) and the graph is plotted

Hence , the reflected function is f' ( x ) = √( -x )

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The following congruence theorems can be applied to every triangle in the provided pair:

1) SSS

2) SAS

3)SAS

4) SSS

5) SAS

6) SAS

1) We can observe from the that;

FY ≅ CW

FP ≅ CM

YP ≅ MW

This proves the Side-Side-Side (SSS) congruency theorem, which states that the three corresponding sides of the two triangles are congruent.

2) We can observe from the picture that;

CBD and BCA are congruent because they both have alternate interior angles. Thus;

CBD and BCA

We can also see that

EB ≅ EC

DB ≅ CA

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

Using the Side-Angle-Side (SAS) congruency theorem, construct BED and AEC.

3) The image demonstrates that;

SVU and SVT

The shared sides provide using the reflexive property;

SV ≅ SV

VT ≅ VU

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

Side-Angle-Side (SAS) congruency theory is used by VSU and VST.

4) The picture shows what;

MN ≅ QP

MQ ≅ NP

The shared sides provide using the reflexive property;

NQ ≅ NQ

This implies that the three corresponding sides of the two triangles are congruent, which, according to the Side-Side-Side (SSS) congruency theorem, means that QNM QNP.

5) The image demonstrates that;

GL ≅ HL

GJ ≅ HK

JLG and HLK are incongruent angles in the vertical direction;

JLG and HLK

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

employing the Side-Angle-Side (SAS) congruency theorem, QNM and QNP.

6) From the triangles provided, we note that;

XZY and XZW (They both form a straight angle of 90 degrees.)

The shared side is congruent to itself using reflexive property, therefore;

XZ ≅ XZ

Also;

ZW ≅ ZY

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

Using the Side-Angle-Side (SAS) congruency theorem, XYZ = XWZ.

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Complete question:

p/q = (2x^3+1)/2x^3, which implies that p = 2x^3+1 and q = 2x^3.  p + q = 2x^3+1 + 2x^3 = 3x^3.

Let a and b be positive integers satisfying (ab+1)/(a+b) < 3/2. The maximum possible value of (a^3b^3+1)/(a^3+b^3) is given by the equation p/q, where p and q are relatively prime positive integers. We can expand the numerator and denominator as follows: a^3b^3+1 = a^3b^3 + a^3 + b^3 and a^3+b^3 = a^3 + a^2b + ab^2 + b^3. Therefore, the expression is equal to (a^2b^2+a^2+ab+1)/(a^2b+ab^2+1). Since (ab+1)/(a+b) < 3/2, we have (ab+1)/(a+b) < 5/3 and (a^2b^2+a^2+ab+1)/(a^2b+ab^2+1) < 5/3.To find the sum of p and q, we can use the fact that the maximum value occurs when a and b are equal. Thus, setting a = b = x, we have (x^3x^3+1)/(x^3+x^3) = (x^6+1)/2x^3 = (2x^3+1)/2x^3. Thus, p/q = (2x^3+1)/2x^3, which implies that p = 2x^3+1 and q = 2x^3. Therefore, p + q = 2x^3+1 + 2x^3 = 3x^3.

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Answer:

6 votes

Step-by-step explanation:

The correlation coefficient for this data-set is given as follows:

r = 0.43.

The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.

The points for the data-set in this problem are given as follows:

(1,2), (4,3), (3,4), (1,1), (4,2), (6,2), (2,1), (6,2), (2,1).

Inserting these points into a correlation coefficient calculator, the correlation coefficient for this data-set is given as follows:

r = 0.43.

Meaning that the correct option is given by the third option.

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Answer:

5 (less than sign) 2

Step-by-step explanation:

Answer:

5n-20

Step-by-step explanation:

Product means multiply and so the product of 5 and n is 5n. To decrease this value by 20 , means to subtract 20 from it hence: 5n - 20 is algebraic expression for the statement

The correct option D) 811,501, is the calculated number the numbers below, if rounded to the thousandths place, equal 812,000.

Rounding Decimal Numbers:

Choose the final digit you want to keep.

Decimal rounding:

Determine the number that will remain after we are done.

For the stated question:

To get the number 812,000 when rounded to the thousands place,

number used is 811,501, as all other number are either larger than or smaller than 812,000.

Thus, option D) 811,501, is the calculated number the numbers below, if rounded to the thousandths place, equal 812,000.

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The margin of error, given the percentage who replied that Newton ate the apple, is 3.5%.

The margin of error is a measure of how much the sample results are likely to vary from the true population value.

To calculate the margin of error, you need to know the sample size, the proportion of the sample that gave a particular response, and the level of confidence.

The formula for the margin of error is:

Margin of Error = z x √(p x ( 1 - p) / n)

where:

z = the critical value from the standard normal distribution table

p = the proportion of the sample that gave a particular response

n = the sample size

The margin of error for Newton eating the apple is therefore:

Margin of Error = 1.96 x √(0.28 x (1 - 0.28) / 581)

Margin of Error = 1.96 * √(0.00035)

Margin of Error = 1.96 * 0.018

Margin of Error = 0.035

The margin of error is therefore 3.5%.

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Mario can mail the books in the box, as the weight of the books is less than the weight of the box.

The total weight is obtained applying proportions, converting the fractions to decimal, dividing the numerator by the denominator.

The weights of each book are given as follows:

Hence the total weight for the books is given as follows:

0.625 + 0.4375 + 0.75 = 1.8125 pounds.

The weight of the box is given as follows:

2 + 0.5 = 2.5 pounds.

Hence Mario can mail the books in the box, as the weight of the books is less than the weight of the box.

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The average income per household that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.

The correlation of variables is the statistical relationship between two variables.

A correlation is positive if both variables move in the same direction and negative if the variables move in different directions - as one variable increases, the other decreases.

Correlation does not imply causation: This means that one can not legitimately associate a cause-and-effect relationship between the two variables.

In this example, it cannot be legitimately shown that increasing the number of cars per household would cause members of the community members to purchase health insurance, but when we bring in the lurking variable.

which is the increase in average income per household, we can see that this possibility might cause more people to buy more health insurance even after they have purchased cars, because they have more money to spend.

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50 breaks do they make.

An equation is a mathematical statement that shows the relationship between two values, or variables. It is formed by using an equal sign between two expressions that have the same value. Equations are used to solve for unknown values, or to describe a relationship between two or more variables. Equations can be used to solve for a single variable or multiple variables, and can be used to solve problems in both mathematics and science.
To find the answer to this question we must use the formula V = L x W x H. In this case, V = 10 x 9 x 4 = 360. We now know that there is 360 cubic inches in each brick. To find the total number of bricks that can be made from 18,000 cubic inches of concrete, we must divide 18,000 by 360. The answer is 50, which means that the company can make 50 concrete bricks from 18,000 cubic inches of concrete.

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Using simultaneous equations, the number of pounds of Type B coffee that Joe used for the blend was 94 pounds.

Simultaneous equations are two or more equations solved concurrently or simultaneously.

Simultaneous equations are also known as a system of equations.

Cost per pound of Type A coffee blend = $4.65

Cost per pound of Type B coffee blend = $5.95

The total pounds of the blend made for the month = 150 pounds

The total cost of 150 pounds = $819.70

Let the number of Type A coffee pounds = a and Type B coffee pounds = b.

4.65a + 5.95b = 819.7 ... Equation 1

a + b = 150  ... Equation 2

Multiply Equation 2 by 5.95:

5.95a + 5.95b = 892.5  ... Equation 3

Subtract Equation 1 from Equation 3:

5.95a + 5.95b = 892.5

-

4.65a + 5.95b = 819.7

1.3a = 72.8

a = 56 pounds

b = 150 - a

= 150 - 56

= 94 pounds

Thus, we can conclude that Joe's Coffee Shop used 94 pounds of Type B coffee this month.

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This month Joe made 150 pounds of the blend for a total cost of $819.70 how many pounds of type B coffee did he use?

Answer:

A

Step-by-step Explanation:

Every $1 decrease in price corresponds to a 0.8 increase in the number of pairs of jeans sold.

So, if [tex]x[/tex] pairs of jeans are sold, the revenue in dollars is [tex](175-x)(40+0.8x)[/tex].

The roots of this function are [tex]x=175[/tex] and [tex]x=-50[/tex]. The maximum is achieved halfway between these roots at [tex]x=62.5[/tex].

When 62.5 pairs of jeans are sold, the price is $112.50.

The store should discount the price to $112.50 to maximize its revenue

Discount is a deduction from the usual cost of something, typically given for prompt or advance payment or to a special category of buyers.

From the above question, every $1 decrease in price corresponds to a 0.8 increase in the number of pairs of jeans sold.

So, if  pairs of jeans are sold, the revenue in dollars is (175 - x)(40 + 0.8x)

The roots of this function are x = 175 and x = -50. The maximum is achieved halfway between these roots at x = 62.50.

Therefore, When 62.5 pairs of jeans are sold, the price is $112.50.

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The coordinate of the point that partitions the given line in the ratio 2:1 is; (-8, 0)

If the coordinates are given as;

P (x₁ , y₁) and Q (x₂ , y₂) and the partition of the line segment is divided internally in the ratio m : n, then its coordinate ( x, y) given by :

( x ,y ) = [(mx₂ + nx₁)/ ( m + n), (my₂ + ny₁)/ ( m + n)]

We are given the coordinates as  ( − 8 , 10 )to ( − 8 , − 5 ) and if it is partitioned in the ratio 2: 1, the coordinates of the points of partition are;

(x, y) =  [(2(-8) + 1(-8))/ (2 + 1), (2(-5) + 1(10))/ (2 + 1)]

(x, y) = (-24/3), (0/3)

(x, y) = (-8, 0)

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The simple random sample of 200 eggs

Statistic=Proportion of eggs in the sample that contain salmonella.

p = 0.045

The population is the individuals that are being studied.

population=All eggs in one day

A sample is the part of the population of which information was actually collected.

Sample=The simple random sample of 200 eggs

A parameter is a descriptive measure for a population.

Parameter=Proportion of eggs shipped that day that contain salmonella.

p = 0.1 % =0.001

A statistic is a descriptive measure for a sample.

STATISTIC=Proportion of eggs in the sample that contain salmonella.

p=9÷200 = 0.045

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G(:,:) returns the matrix G in its original form. This command takes all elements of G and reshapes them into a single row vector. This means that all elements of G are included in the output, and the output is in the same shape as the original matrix.

G(:) reshapes all elements of G into a single column vector. This command takes all elements of G and places them into a single column. This means that all elements of G are included in the output, and the output is in a column vector.

G(7,6) returns an indexing error. This command attempts to access an element outside of the range of the matrix G. Since G is a 6 x 6 matrix, there is no element at the index (7,6).

max(G) returns the maximum entry in each column of G. This command takes the maximum value from each column and returns them as a single row vector. This means that the output contains the maximum value from each column and the output is in a single row vector.

sum(G) returns the sum of the entries in each column of G. This command takes the sum of all entries in each column and returns them as a single row.

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True, a survey of high school students was conducted to see if students who take advanced classes are offered more scholarship money than students who do not take advanced classes.

Science is used in statistics to gather and arrange data into patterns or trends. A statistical research collects data about a population or group of people and attempts to generalize the findings for use by different people.

The observational study is one type of statistical study. These studies frequently occur early in a given area of health study since they may swiftly and affordably gather a lot of general information about a community.

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Answer:

y = 5.25 [tex](8)^{x}[/tex]

Step-by-step explanation:

the general form of an exponential function is

y = a [tex](b)^{x}[/tex]

to find a and b , substitute the coordinates of the given points into the equation.

using (2, 336 )

336 = a b² → (1)

using (3, 2688 )

2688 = a b³ → (2)

divide (2) by (1)

[tex]\frac{ab^3}{ab^2}[/tex] = [tex]\frac{2688}{336}[/tex] ( cancel ab on numerator/denominator of left side )

b = 8

substitute b = 8 into (1) and solve for a

336 = a × 8² = 64a ( divide both sides by 64 )

5.25 = a

then exponential function is

y = 5.25 [tex](8)^{x}[/tex]