If y varies directly with x and y=88 when x=44, find x when y=4.

Answer:

2/3

Step-by-step explanation:

Probability (A) = # of outcomes that satisfy A/ # of total outcomes

There are four numbers on the dice that are strictly less than 5 (not equal to), namely: 1, 2, 3 and 4.

The number of possible outcomes are: 1, 2, 3, 4, 5, 6.

Therefore the probability that Daniel rolls a number less than 5 is:

4/6 = 2/3

2.5% is the time Rachel hits a home run after 200 times at bat

To solve for a percentage, you need to divide the part by the whole and multiply by 100 to get the percentage value.

After 200 times at bat

the percentage of the time that Rachel would have to hit the home run would be:

5 / 200

= 0.025

= 2.5%

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Answer:

A. the moon's mass is only a fraction of Earth's

It takes the object 15 seconds to travel the entire length of the path.

Let's denote the length of the path as "L" and the time it takes for the object to travel the entire length of the path as "t".

We are given that the object travels 1/20 of the length of the path in 3/4 seconds.

This means that its speed is:

(1/20) L ÷ (3/4) s

= (1/20) L × (4/3) s⁻¹

= (1/15) L s⁻¹

Now, we can use the formula:

speed = distance ÷ time

to find the time it takes for the object to travel the entire length of the path:

(1/15) L s⁻¹ = L ÷ t

Solving for "t", we get:

t = (15/1) s = 15 s

Therefore, it takes the object 15 seconds to travel the entire length of the path.

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The 25th percentile is 166 cm. 50th percentile (median) is 172. the 75th percentile is 184 cm.

To find the percentiles for the given data, we first need to put the heights in order from smallest to largest:

137, 148, 155, 158, 165, 166, 166, 166, 166, 171, 171, 173, 175, 180, 184, 184, 186, 186, 186, 186

We can see that there are 20 boys in the class, so we can use the following formulas to find the percentiles:

To find the xth percentile, we need to find the value that separates the x% of the data from the rest. This can be found using the formula: x/100 * (n + 1), where n is the number of data points.

If the result of the formula is a whole number, the percentile is the average of that value and the next value in the data set. If the result is not a whole number, we round up to the nearest whole number and take the value in that position.

Using these formulas, we can find the 25th, 50th, and 75th percentiles:

25th percentile: 25/100 * (20 + 1) = 5.25, so we round up to 6. The 6th value in the data set is 166, so the 25th percentile is 166 cm.

50th percentile (median): 50/100 * (20 + 1) = 10.5, so we take the average of the 10th and 11th values in the data set: (171 + 173) / 2 = 172 cm.

75th percentile: 75/100 * (20 + 1) = 15.75, so we round up to 16. The 16th value in the data set is 184, so the 75th percentile is 184 cm.

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The interquartile range or the standard deviation can be used to measure the spread of data depending on the outlier present.

It is possible to measure spread using the interquartile range or the standard deviation. The presence of extreme outliers should warrant the observer using the interquartile range for the measurement of spread.

However, if there are no extreme outliers in the dataset you are working with, then it is recommended that you use the standard deviation for the purpose of measurement.

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It will take 15 days for the hair to grow from 12mm to 16.5mm

By "average rate" in this context, we mean the typical or usual amount of hair growth per unit of time, which is often measured in millimeters per day. This rate can vary slightly depending on factors such as age, gender, genetics, diet, and overall health.

Let's first find out how much the hair needs to grow by subtracting its initial length (12mm) from its target length (16.5mm):

16.5mm - 12mm = 4.5mm

Now we can divide this growth by the average rate of hair growth to find the number of days it will take to grow this much:

4.5mm ÷ 0.3mm/day = 15 days

Therefore, it will take 15 days for the hair to grow from 12mm to 16.5mm.

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This is rοughly 0.5556 when expressed in decimal fοrm as the number οf favοrable οutcοmes divided by the tοtal number οf pοssible οutcοmes.

Each integer in a divisοr is a pοwer if 10, starting first frοm left οf the decimal pοint. Decimals are based mοstly οn base-10 numbering system. In the number 3.14159, fοr instance, the digit 3 is in the "οnes" place, whereas 1 is in the "tenths," 4 is in the "hundredths," and sο οn.

In science, math, and daily life, decimals are frequently emplοyed. In additiοn tο representing mοnetary values and percentages, they are additiοnally emplοyed tο regs that cannοt be stated as whοle numbers, including measures οf length, weight, and time.

The spinner has the numbers 1 thrοugh 9, therefοre there are nine equally likely events that cοuld οccur. Out οf these nine οutcοmes, 1, 2, 3, 4, and 5 are the οnly οnes that fall belοw the threshοld οf six.

The number οf favοurable οutcοmes divided by the tοtal number οf pοssible οutcοmes gives the likelihοοd οf P(less than 6):

P(less than six) = 5/9

This is rοughly 0.5556 when expressed in decimal fοrm as the number οf favοurable οutcοmes divided by the tοtal number οf pοssible οutcοmes .

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Answer:

6 hours tutoring and 8 hours landscaping.

Step-by-step explanation:

Helping in the name of Jesus.

Answer:

x^2 - 24x + 22  +  (75x - 40)/(x^ +x + 2)

Step-by-step explanation:

There is no term in x^2 so we insert  + 0x^2 into the polynomial:-

x^2 + x + 2 )x^4 -  23x^3 + 0x^2 + 49x + 4(x^2 - 24x + 22 <------Quotient

                   x^4 + x^3     + 2x^2

                          - 24x^3 - 2x^2  + 49x

                          - 24x^3 - 24x^2 - 48x

                                          22x^2 + 97x + 4

                                          22x^2 + 22x + 44      

                                                        75x - 40    <-------- remainder            

The possible solutions of the points are as follows

The solutions are the points that fall in the areas where the shading of the two graphs representing the equation passed

In the attached graph it can be seen that the points shown are within the areas that has the shading of the two equations.

Therefore we can say that the points (-3,1), (-3, -1), and (-4, -5) are the solution.

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The cargo plane flew for 6 hours.

Let's start by calculating the Air Force plane's distance traveled after 11 hours:

distance = speed x time = 240 km/h x 11 h = 2640 km

"t" will stand for the time the cargo plane took off. The Air Force aircraft kept flying for an additional 11 hours throughout this period.

The formula distance = speed x time = 155 km/h x t = 155t km can be used to calculate the distance covered by the cargo plane.

The sum of the lengths traveled by the two planes is the distance between them:

3570 km = 2640 km + 155t km.

2640 km from each side results in 155t km = 930 km.

155 km/h divided by both sides results in t = 6 hours.

Therefore, the cargo plane flew for 6 hours.

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Answer:

The slope and y-intercept values indicate characteristics of the relationship between the two variables x and y.

Step-by-step explanation:

The slope indicates the rate of change in y per unit change in x.

The y-intercept indicates the y-value when the x-value is 0.

The correct option is A. Both the slopes and the y intercepts are same.

Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.

First we will find the equation of the graph of f(x) in slope intercept form.

The line passes through (0, 3) and (1, 1).

So the y intercept is 3, since the line touches the y axis at that point.

Slope = (1 - 3) / (1 - 0) = -2

Equation of the line in slope intercept form is,

f(x) = -2x + 3

The function g(x) = -2x + 3.

Both functions are same.

Hence both slopes and y intercepts are same.

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Answer:

(x+1) (x+6)/(x+7) (x+8)

X+1=0 so x=-1 and -6 respectively on the

x+7=0 so x=-7 and -8 in the

1denominator

Step-by-step explanation:

answer x<-1 and x<-6/

x<-7 x<

Answer:

1/15

Step-by-step explanation:

you write down 1/5÷3= 1/5x1/3= 1/15

Linear would you expect if graphing number of hours worked and money earned. So correct option is B.

Linear association, also known as linear correlation or correlation coefficient, is a statistical measure of the strength and direction of the relationship between two continuous variables. It indicates how closely the data points are clustered around a straight line, and it is measured by a value called the correlation coefficient.

The correlation coefficient, denoted by the symbol "r", ranges from -1 to 1, where a value of -1 indicates a perfect negative correlation, a value of 0 indicates no correlation, and a value of 1 indicates a perfect positive correlation. A negative correlation means that as one variable increases, the other variable decreases, while a positive correlation means that as one variable increases, the other variable also increases.

Linear association is often depicted graphically using a scatter plot, which displays the data points as a set of dots on a two-dimensional plane, with one variable plotted on the horizontal axis and the other variable plotted on the vertical axis.

B. Linear.

As the number of hours worked increases, we would expect the amount of money earned to increase at a constant rate (assuming a fixed hourly wage). This would result in a linear relationship between the two variables, with a positive slope.

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The complete question is:

What association would you expect if graphing numbers of hours worked and money earned?

A. Negative

B. Linear

C. Nonlinear

D. None of the above!

Answer:

$135

Step-by-step explanation:

We Know

A gold chain is sold for $635 at a gain of 27% on the sale price.

Find the profit.

Let's W be wholesale.

W = 635/1.27 = $500

Profit = 635 - 500 = $135

So, the profit is $135

Proportionately, if Tom had already used 15 crayons, which is 10% of his total number of crayons, Tom has 150 in all.

Proportion refers to the ratio, part, or portion of the whole value, quantity, or number.

Proportions are depicted using decimals, fractions, and percentages.

The number of crayons that Tom had already used = 15

The percentage representing the used portion = 10%

Proportionately, since 15 = 10% of the total number of crayons Tom has, the total number will be equal to 150 (15 ÷ 10).

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Step-by-step explanation:

x^3   = volume of smaller cube

(x+2)^3  = volume of larger

(x+2)^3  - x^3 =   152   cm^3            <=======given     Expand

x^3 + 6x^2 + 12x + 8    -  x^3  = 152         simplify

6x^2 + 12x - 144 = 0

6 ( x^2 + 2x - 24) = 0               factor

6 ( x+6)(x-4) = 0                 shows  x = 4    

  the smaller cube is  4 x 4 x 4 cm    ( length = 4cm)

Answer: .6

Step-by-step explanation: Fractions are basically division problems and you can do it like normal division. However, if wanted to you could also notice the 10 is the denominator and figure out that it would be in tenths so 6 tenths or .6.

Answer: 6/10 as a decimal is 0.6!

Step-by-step explanation: 6/10= 6÷10=0.6 using a simple calculator.

Answer:

5(3y^2+4y-5)

Step-by-step explanation:

You do this by finding the common factor and working it out so it works when you multiply to get back to the standard equation.

Step-by-step explanation:

QUESTION 1

Two coins are flipped. Find the probability that the first coin land on heads and the second coin lands on heads.

There are four possible outcomes when two coins are flipped: HH, HT, TH, and TT. Since the coins are fair, each outcome is equally likely.

The probability of the first coin landing on heads is 1/2, and the probability of the second coin landing on heads is also 1/2.

Therefore, the probability of both coins landing on heads is:

P(HH) = P(first coin lands on H) × P(second coin lands on H)

= 1/2 × 1/2

= 1/4

Hence, the probability that the first coin lands on heads and the second coin lands on heads is 1/4.

QUESTION 2

Two cards are drawn from a deck of 52 cards. The first card is replaced before drawing the second card. Find the probability that the first card is black and the second card is an Ace.

There are 26 black cards in a deck of 52 cards, and there are 4 Aces in a deck of 52 cards. Since the first card is replaced before drawing the second card, the two draws are independent.

The probability of drawing a black card on the first draw is 26/52 = 1/2. The probability of drawing an Ace on the second draw is 4/52 = 1/13.

Therefore, the probability of the first card being black and the second card being an Ace is:

P(black and Ace) = P(black on first draw) × P(Ace on second draw)

= 1/2 × 1/13

= 1/26

Hence, the probability that the first card is black and the second card is an Ace is 1/26.

QUESTION 3

A single digit between 0 and 9 is randomly chosen, and a single letter from A to Z is randomly chosen. Find the probability that the number is 6 and the letter is a consonant.

There are 10 possible digits and 21 possible consonants in the English alphabet. Since the choices are independent, the probability of selecting a 6 as the digit and a consonant as the letter is the product of the probabilities of each event occurring separately.

The probability of selecting a 6 is 1/10, and the probability of selecting a consonant is 21/26.

Therefore, the probability of selecting a 6 and a consonant is:

P(6 and consonant) = P(6) × P(consonant)

= 1/10 × 21/26

= 21/260

= 3/40

Hence, the probability that the number is 6 and the letter is a consonant is 3/40.

QUESTION 4

Two dice are rolled. Find the probability that first die lands on an even number and the second die is less than 3.

There are 6 possible outcomes when two dice are rolled: (1,1), (1,2), (1,3), (2,1), (2,2), and so on. Each outcome is equally likely.

The probability of rolling an even number on the first die is 1/2, since there are three even numbers (2, 4, 6) and three odd numbers (1, 3, 5) on a standard six-sided die. The probability of rolling a number less than 3 on the second die is 2/6, since there are two numbers less than 3 (1 and 2) out of six possible outcomes.

Therefore, the probability of the first die landing on

a. To find the additional cost incurred in dollars when production is increased from 2 units to 15 units, we need to integrate the marginal cost function from 2 to 15:

[tex]\implies\texttt\:\int_{2}^{15} C'(x) dx = \int_{2}^{15} (0.12x^2 - 4x + 100) dx[/tex]

$\texttt\:= \left[ 0.04x^3 - 2x^2 + 100x \right]_{2}^{15} \ = (0.04 \cdot 15^3 - 2 \cdot 15^2 + 100 \cdot 15) - (0.04 \cdot 2^3 - 2 \cdot 2^2 + 100 \cdot 2) \ = 1590$

Therefore, the additional cost incurred in dollars when production is increased from 2 units to 15 units is $1590.

b. We can use the information we found in part (a) and the given value of C(2) to find C(15):

[tex]\texttt\:C(15) = C(2) + \int_{2}^{15} C'(x) dx \ = 267 + 1590 \ = 1857[/tex]

Therefore, C(15) is 1857.

After the change where the company starts paying for a driver at a price of 0.25 cents a mile, the cost of operating the truck will increase by 0.25 cents for every mile traveled. This means that the profit for the company will decrease by 0.25 cents for every mile traveled.

After the change where the company starts paying for a driver at a price of 0.25 cents a mile, the cost of operating the truck will increase by 0.25 cents for every mile traveled. This means that the profit for the company will decrease by 0.25 cents for every mile traveled.

Therefore, the slope of the line will change because the profit is decreasing at a faster rate for every mile traveled. The slope will become steeper, which means that the value of X will be less. This is because the decrease in profit for every mile traveled will happen at a faster rate, causing the line to slope downward at a steeper angle.

The Y-intercept of the line represents the profit made by the company when the truck has not yet traveled any miles. Since the cost of operating the truck has increased, the profit will be lower even when the truck has not yet traveled any miles. Therefore, the Y-intercept will be less, which means that option A, "Y-intercept will be less and X will be less," is the correct answer.

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Gaussian Elimination and Gauss-Jordon Elimination are two methods of solving linear systems of equations.
A-x=3, y=2, z=-2,B-x=4, y=-2, z=15 C-x=2, y=-2, z=2.

An equation is a mathematical statement that states two expressions are equal. It consists of two expressions separated by an equals sign (=) and can use any of the operations of arithmetic such as addition, subtraction, multiplication, division and exponents. An equation can be solved to find the value of one or more variables that make the equation true.

Question 1:

Using Gaussian Elimination:

2x+y + 2z = 1

4x + 3z = -5

5y + 4z = 13

Step 1: Subtract 2 times the first equation from the second equation.

0x+3y+z=-6

Step 2: Subtract 5 times the first equation from the third equation.

0x+2y+3z=10

Step 3: Subtract 2 times the second equation from the third equation.

x+y=4

Step 4: Subtract 4 times the second equation from the first equation.

x=3

Step 5: Substitute x = 3 in the second equation.

3+2y+z=-6

Step 6: Subtract 3 times the fifth equation from the fourth equation.

y=2

Step 7: Substitute y = 2 in the fifth equation.

3+4+z=-6

Step 8: Solve for z.

z=-2

Answer: x=3, y=2, z=-2

Question 2:

Using Gauss-Jordan Elimination:

2x+y+z=13

x+2y+z= 11

x + 3y + 3z = 19

Step 1: Subtract 2 times the first equation from the second equation.

-x+3y=2

Step 2: Subtract x times the first equation from the third equation.

2y+2z=6

Step 3: Subtract 3 times the second equation from the third equation.

x=4

Step 4: Substitute x=4 in the second equation.

4+3y=2

Step 5: Solve for y.

y=-2

Step 6: Substitute y=-2 in the first equation.

2x+(-2)+z=13

Step 7: Solve for z.

z=15

Answer: x=4, y=-2, z=15

Question 3:

Using Gaussian Elimination:

-3x+2y-6z = 6

5x + 7y - 5z = 6

x + 4y = 2z = 8

Step 1: Subtract 5 times the first equation from the second equation.

2x+9y-z=0

Step 2: Subtract 2 times the third equation from the first equation.

-5x+2y-2z=-2

Step 3: Subtract 2 times the first equation from the third equation.

3x+7y=2

Step 4: Subtract 3 times the second equation from the third equation.

x=2

Step 5: Substitute x=2 in the second equation.

4+9y-z=0

Step 6: Solve for y.

y=-2

Step 7: Substitute y=-2 in the fifth equation.

2+(-2)-z=0

Step 8: Solve for z.

z=2

Answer: x=2, y=-2, z=2

Conclusion:

Gaussian Elimination and Gauss-Jordon Elimination are two methods of solving linear systems of equations. Both methods rely on manipulating the equations to create a triangular form, which allows for the easier determination of the variables. By using both methods, we were able to solve each of the three linear systems of equations given in the question.

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The differential of the given function will be equal to -8cot(3t).

What is Differential Equation?

Any equation that contains one or more functions with its derivative is called the differential equations. Studying the solutions that will satisfy the equation and properties of the solution is the main purpose of the differential equations. Solving the equations using explicit formulas is one of the easiest way of solving any differential equation. It is denoted as [tex]\frac{dy}{dx} = f(x)[/tex], where 'x' is the independent variable and 'y' is the dependent variable. The derivatives which are present in the differential equations are either partial or ordinary derivatives.

Here in this question the given differential equation is: e-8xcos(3t)

By the Sum Rule, the derivative of e−8xcos(3t) with respect to x is

  [tex]\frac{d}{dx}[e] + \frac{d}{dx}[-8xcos(3t)].[/tex]

Since e is constant with respect to x, the derivative of e w.r.t x will be 0.

Thus we have to evaluate: [tex]\frac{d}{dx} [-8xcos(3t)][/tex]

Since -8cos(3t) is constant w.r.t x, the derivative of -8xcos(3t) with respect to x is -8cot(3t) is  [tex]-8cot(3t)\frac{d}{dt}[x][/tex].

or, [tex]0-8cot (3t)\frac{d}{dx}[x][/tex]

Now, differentiating using power rule;

0-8cot(3t). 1

Multiplying -8 by 1

0-8cot (3t)

Thus the final answer is, -8cot(3t)

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To find the point-slope form of the line satisfying the given conditions, we can start by using the intercepts to find two points on the line: (-1/2, 0) and (0, 1). Then, we can use the point-slope formula to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line. The slope of the line can be found using the two points we found:

m = (y2 - y1)/(x2 - x1) = (1 - 0)/(0 - (-1/2)) = 2

Now we can choose one of the points we found and use it in the point-slope formula:

y - 1 = 2(x - 0)

Simplifying this equation gives:

y - 1 = 2x

This is the point-slope form of the line satisfying the given conditions.

negative one half times vector v can be represented as  [tex]< 10, -4 > ,[/tex] which is equivalent to the option: open angled bracket negative [tex]10[/tex] comma 4 close angled bracket. Thus, option B is correct.

To obtain the negative one half times vector v, we need to multiply each component of vector v by  [tex]-1/2[/tex] . Given that vector v has an initial point at [tex](5, 2)[/tex]  and a terminal point at [tex](-15, 10)[/tex]   , we can calculate the components of vector v as follows:

x-component of vector v = terminal x-coordinate - initial x-coordinate

[tex]= -15 - 5[/tex]

[tex]= -20[/tex]

y-component of vector v = terminal y-coordinate - initial y-coordinate

[tex]= 10 - 2[/tex]

[tex]= 8[/tex]

So, vector v can be represented as  [tex]< -20, 8 > .[/tex]

To find negative one half times vector v, we need to multiply each component by [tex]-1/2[/tex]  :

x-component of negative one half times vector   [tex]v = -1/2 \times -20= 10[/tex]

y-component of negative one half times vector  [tex]v = -1/2 \times 8= -4[/tex]

Therefore, negative one half times vector v can be represented as < 10, -4 >, which is equivalent to the option: open angled bracket negative 10 comma 4 close angled bracket.

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