If 6x + 7y= 2007 and 7x+6y= 7002, then what is the value of x + y?

The second segment crosses the x-axis at (1.5, 0), and the slope of the segment is -1

The area under any probability density curve is always 1 and it is used for finding out the probabilities for any random variable X taking a certain range of values.

Let the second segment crosses at (a,0) on the X-axis:

The area under the density curve is 1.

the given fig can be divided into a rectangle and a triangle by dropping a line from the point (0.5, 1) in the x-axis.

The coordinate point of the second segment at the x-axis:

Now,

1*0.5+1/2*1*(a-0.5)=1

1+(a-0.5)=2

a-0.5=2-1

a=1+0.5

a=1.5

Thus the second segment crosses the x-axis at (1.5, 0)

The slope of that segment c:

The slope  of that segment=y₂-y₁/x₂-x₁

By considering the points (0.5, 1) and (1.5, 0)

We will have the slope as:

m=0-1/1.5-0.5

m=-1/1

m=-1

the equation of the line containing this segment:

The line passes from the point (0.5, 1)

y=mx+b is used to find the value of the intercept

so, substitute the values in the equation:

1=(-1)*0.5+b

1=-0.5+b

b=1.5

so, the equation for that line segment is

y=-x+1.5

x+y=1.5

To calculate the probability P(X > 1):

[tex]P(X > 1)=\int\limits\limits^1_1 {y} \, dx \\P(X > 1)=\int\limits^1_1 {(-x+1.5)} \, dx[/tex]

[tex]P(X > 1)=[\frac{-x^2}{2}+1.5x]_1^1^.^5\\\\P(X > 1)= (\frac{(-1.5)^2}{2} +1.5*1.5)-(\frac{-1^2}{2}+1.5*1)\\[/tex]

P(X>1)=-1.125+2.25+0.5-1.5

P(X>1)=0.125

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Answer:

Genesis has 126 different outfits to choose from.

Step-by-step explanation:

To calculate the total number of different outfits Genesis can choose, we need to multiply the number of choices available for each article of clothing. So we have:

7 choices for pants

2 choices for t-shirts

3 choices for sweaters or hoodies

3 choices for shoes

To find the total number of outfits, we multiply the number of choices for each category:

7 x 2 x 3 x 3 = 126

Therefore, Genesis has 126 different outfits to choose from.

126 different combination does Genesis have to choose.

We have,

Pants = 7

T shirts = 2

Sweaters or Hoodies = 3

Shoes = 3

So, the number of different combination is

= C(7, 1) x C( 2, 1) x C(3, 1) x C(3, 1)

= 7 x 2 x 3 x 3

= 126 ways

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•Mr Bradford lunged at his wedding ring as it fell into the WHIRLPOOL of the bathtub drain.

•Sarah's morher CALMED her screaming baby by giving her a teddy bear to hold.

Answer: whirlpool, calmed

Step-by-step explanation:

A vortex looks like a whirlpool

Since the baby is scream giving a teddy bear will probably calm it

Answer:

There would be 600 fish after 12 months.

Step-by-step explanation:

The number of fish on the farm increases by 10% each month, so the formula to calculate the number of fish after n months is:

F = 350 * (1 + 0.1)^n

where,

F is the number of fish after n months

We want to find the number of fish after 12 months, so:

F = 350 * (1 + 0.1)^12

F = 350 * 1.719178

F = 603.56 to the nearest 100, which is 600.

To find out how much each ticket costs, we can use this equation:

Total cost ÷ Number of tickets = Price of each ticket

Inserting the numbers into the equation would look like this:

To check our work, we can multiply the number of tickets by the price of each ticket to see if it matches up to the correct total price.

Therefore, each ticket costs $8.

a) 720 ways 3 boys and 3 girls sit in a row.

b) 48 ways boys and the girls are each to sit together.

c) 6 ways boys must sit together.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Given:

Number of girls= 3

Number of boys = 3

a) Using Permutation

⁶P₆ = 6! / (6 - 6)!

⁶P₆ =  6! / (0!)

⁶P₆ = 6!

       = 6 × 5 × 4 × 3 × 2 × 1

        = 30 × 24

        = 720

b) 3 boys and 3 girls sit in a row if the boys and the girls are each to sit together

= 3! x 2³

= 3 x 2 x 2 x 2 x 2

= 48 ways

c) the number of ways boys can sit together

= 3!

= 6 ways

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The possible value for the original number is 30

Represent the number with n

So, we have

Lacey = 10 * (n/10 + 1/2)

Euan = 100 * (n/100 + 1/2).

Also, Lacey's new number is 3/4 of Euan's new number, so we have:

10 * (n/10 + 1/2) = (3/4) * (100 * (n/100 + 1/2))

Solving for n, we have:

100 * (n/100 + 1/2) = (4/3) * (10 * (n/10 + 1/2))

Divide through by 100

n/100 + 1/2 = (4/30) * (n/10 + 1/2)

Evaluate

(n + 50)/100 = 4n/300 + 2/30

So, we have

n + 50 = 4n/3 + 20/3

Multiply through by 3

3n + 50 = 4n + 20

Evaluate the like terms

n = 30

Hence, the original number is 30

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Answer: all points are a solution except for (4, 2) (and (2, 0) i think)

Step-by-step explanation:

The rectangular blocks with the measure of 7 cm by 8 cm by 9 cm will not fit in the smallest cylindrical cup with the radius of 5cm.

Rectangular block with the least dimensions, 7cm by 8cm side.

Circle with radius r is x² + y² = r²

∴ x² + y² = 5² or x² + y² = 25

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

Its observed that the block cannot fit inside the cup. We can confirm this if

y >4 when x = 3.5

3.5² + y² = 25

12.25 + y² = 25

y² = 12.75

taking positive square root, y≈3.57

Since this is <4, the block cannot fit the 5 cm radius cup.

equation for the cup with r = 6cm,

x² + y² = 6² or x² + y² = 36

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

it is observed the block will fit inside the cup as y>4 when x = 3.5

3.5² + y² = 36

12.25 + y² = 36

y² = 23.75

taking positive square roots, y≈4.87

Since this is >4, the block can fit the 6 cm radius cup.

equation for the cup with r = 7cm,

x² + y² = 7² or x² + y² = 49

Draw the area of the block using the coordinates (3.5,4) ; (-3.5,4) ; (-3.5,-4) and (3.5,-4)

it is observed the block will fit inside the cup as y>4 when x = 3.5

3.5² + y² = 49

12.25 + y² = 49

y² = 36.75

taking positive square roots, y≈6.06

Since this is >4, the block can fit the 7 cm radius cup.

∴ the block will not fit the smallest cup

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Answer:

The volume of one marble can be calculated as follows:

V = (4/3) * π * (r^3)

where r = 1.25 cm (diameter of 2.5 cm divided by 2)

V = (4/3) * 3.14 * (1.25^3) = 5.20 cm^3

The mass of one marble is then:

m = V * 2.6 g/cm^3 = 13.52 g

And the total mass of 66 marbles is:

m = 66 * 13.52 g = 888.32 g

Rounding to the nearest gram, the total mass of the marbles in Keisha's pouch is 888 g.

The percentage of expenditure which goes towards salaries is 78%

Company's expenditure:

Salaries: R105 000 000

Equipment: R10 000 000

Marketing: R2 000 000

Other: R8 000 000

Total expenditure= R105 000 000 + R10 000 000 + R2 000 000 + R8 000 000

= R135,000,000

percentage of the expenditure is salary= R105 000 000 / R135,000,000 × 100

= 0.78

= 78%

Therefore, 78% of the company's expenditure goes towards salary.

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Answer:

yes

Step-by-step explanation:

In maths, x and y are variables. common factor is taken only when these variables are repeatedly used.

The Z score associated with our observation is 2.45. This means that our observed value is 2.45 standard deviations away from the expected value.

2.45

Z score = (Observed value - Expected value) / Standard Deviation

Z score = (95 - 85) / √(85*(1-85)/30)

Z score = 2.45

We can calculate the Z score associated with our observation by taking the observed value, 95%, and subtracting the expected value, 85%, and dividing this by the standard deviation. To calculate the standard deviation, we use the formula: √(expected value*(1-expected value)/sample size). In this case, 85*(1-85)/30. The Z score associated with our observation is 2.45. This means that our observed value is 2.45 standard deviations away from the expected value.

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Answer:

The volume of the rectangular prism can be calculated by multiplying its length, width, and height: 8 x 4.12 x 3.12 = 128.064 cubic inches.

Answer:

V=342,784in

Step-by-step explanation:

V=1/3(L×W×H)

where v=volume of rectangular prism,L=length.W=width or breadth,H=height

V=1/3×8×412×312

V=342,784in

The number of terms in the sequence is given as follows:

135 terms.

The general notation of a sequence is given as follows:

[tex]\sum_{m = a}^{k} f(m)[/tex]

The parameters are given as follows:

Hence the number of terms in the sequence is obtained as follows:

n = k - a + 1.

The parameter values for this problem are given as follows:

a = 1, k = 135.

Considering the parameter values above, the number of terms of the sequence is given as follows:

n = 135 - 1 + 1

n = 135.

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Answer:

the answer is c

Step-by-step explanation:

Divide 198.00 by 100, multiply 1.98 by 40, 198.00 minus 79.20, 118.80

Answer:

Step-by-step explanation:

I gotchu.

sin70 = x/3.6

x = 3.6sin70

x = 3.4

Answer:

x = 3.4

Step-by-step explanation:

As the given triangle is a right triangle we can use trigonometric ratios to solve for x.

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the triangle:

As we know the angle and the hypotenuse, and wish to find the side opposite the angle, substitute the values into the sine ratio and solve for x:

[tex]\implies \sin(70^{\circ})=\dfrac{x}{3.6}[/tex]

[tex]\implies x=3.6\sin(70^{\circ})[/tex]

[tex]\implies x=3.382893...[/tex]

[tex]\implies x=3.4\; \sf (nearest\;tenth)[/tex]

Therefore, x = 3.4 to the nearest tenth.

Answer:

angle 1 = 26 degrees angle 2 is 154 degrees

DONT FORGET TO PUT THE DEGREES SIGN IN YOUR ANSWER

Step-by-step explanation:

Since the angles add up to a straight line, or 180 degrees, the equation is

(x+4)+7x=180 degrees

8x+4=180

8x=176

x=22

so, angle 1 is 26, angle 2 is 154 degrees

The scale factor was applied to the first diamond is 2.5

From the question, we have the following parameters that can be used in our computation:

The diamonds

The scale factor is calclated as

scale factor = Diamond 2/Diamond 1

Substitute the known values in the above equation, so, we have the following representation

scale factor = 1.5/0.6

Evaluate

scale factor = 2.5

Hnce, the scale factor is 2.5

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The game with 8 minutes of time-outs is 98 minutes long.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division.

In this case, the algebraic expression that represents the length of the soccer game would be:

m = 90 + x

where m represents the total length of the game in minutes, 90 represents the fixed length of the game, and x represents the variable length of time-outs in minutes.

To find the length of the game with 8 minutes of time-outs, we substitute x = 8 into the expression:

m = 90 + 8 = 98

Therefore, the game with 8 minutes of time-outs is 98 minutes long.

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Answer: 40%

Step-by-step explanation:

Answer:

15

_

2

Step-by-step explanation:

hope you get it since I don't know how to do it under __

He need the 500 gram of ground chicken.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

We are Given that the total kilogram of chicken = 0.5 kilograms

Recall :

1000 grams = 1 kilogram

Hence,

B grams = 0.5 kg

B = (0.5 x  1000) = 500 gram.

Hence,

The 500 gram of ground chicken.

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To find the probability of randomly withdrawing 5 jellybeans such that at least 2 are red, we need to find the total number of ways to select 5 jellybeans from the bag and then find the number of ways to select 2 or more red jellybeans.

Let's first find the total number of ways to select 5 jellybeans from the bag:

Total number of jellybeans = 4 red + 7 green = 11 jellybeans

Number of ways to select 5 jellybeans from 11 = 11 choose 5 = 462

Next, we need to find the number of ways to select 2 or more red jellybeans:

Number of ways to select 2 red jellybeans = 4 choose 2 = 6

Number of ways to select 3 red jellybeans = 4 choose 3 = 4

Number of ways to select 4 red jellybeans = 4 choose 4 = 1

Total number of ways to select 2 or more red jellybeans = 6 + 4 + 1 = 11

The desired probability is the ratio of the number of favorable outcomes (selecting 2 or more red jellybeans) to the total number of possible outcomes (selecting 5 jellybeans):

P(at least 2 red) = 11/462 = 11/462 = 0.0239 or 2.39%

So, the probability of randomly withdrawing 5 jellybeans such that at least 2 are red is 2.39%.

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Marianne's withholding tax if her monthly gross earnings are $3,270 is $305.00.

The correct option is A.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Brittany works as a medical office assistant.

She is married and claims 2 withholding allowances.

Her monthly gross earnings are $3,270.

So, 3270 - 2(666.5) = $1937.3

So,

(1937.3 x 0.15) + 14.49 = $305.00

Therefore, the value is $305.00.

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The dimension of the rectangle is 40 inches by 64 inches. Then the area of the rectangle is 2,560 square inches.

Assume L is the length and W is the width. Then the area is given as,

A = L × W

And the perimeter is given as,

P = 2(L + W)

A rectangle has a width-to-height ratio of 8:5. The perimeter of the rectangle is 208 inches. Then the equations are given as,

208 = 2(W + H)

H + W = 104                ...1

H / W = 8 / 5              ....2

From equations 1 and 2, then we have

(8/5)W + W = 104

(13/5)W = 104

W = 40 inches

Then the height is given as,

H = (8/5) x 40

H = 64 inches

Then the area of the rectangle is given as,

A = 40 x 64

A = 2,560 square inches

The dimension of the rectangle is 40 inches by 64 inches. Then the area of the rectangle is 2,560 square inches.

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The four possible times that car B could take to complete one lap are: 120 seconds, 90 seconds, 60 seconds, and 30 seconds.

The equation used to solve this problem is (150 - 30) = N * B, where N is the number of laps and B is the total number of seconds for car B to complete one lap. Therefore, the four possible times for car B to complete one lap are 120 seconds, 90 seconds, 60 seconds, and 30 seconds.

When solving for the total time, it is important to remember that the two cars start the race together and that their speeds remain constant. This means that the time it takes for car B to complete one lap must be a factor of 150 seconds. If car B takes a time that is not a factor of 150, then it will not be able to finish the race in 150 seconds.

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A bar chart or a histogram might be suitable if all the sample sizes are the same and the team is worried about the amount of flaws.

Consider comparing the quantity of defects across several production lines, departments, or time periods.

The number of faults would be the continuous variable in this instance, and the bars would represent the number of samples that included a particular number of defects.

When illustrating the distribution of a count variable, such as the number of defects, bar charts and histograms can be used to visually spot patterns and trends in the data.

Therefore, the number faults would be the continuous variable in this instance, and the bars would represent the number of samples that included a particular number of defects.

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Step-by-step explanation:

This is a trick question I think.

It says he managed to only travel 3 7/8. So wouldn't that mean the fraction of his planned trip that he travel would be... 3 7/8? Unless they want it as 31/8? Something is odd with the question