a and b are in direct proportion. the equation of proportionality is a=8b. work out the value of a when b=4.

To find the value of F1, we can start by writing out the given equations in a more standard form.

First, we can rewrite the equation "F1 + F2 = 100" as "F1 = 100 - F2".

Then, we can rewrite the equation "F1 - F2 = 20" as "F1 = 20 + F2".

If we set these two equations equal to each other, we get "100 - F2 = 20 + F2".

If we simplify this equation, we get "80 = 2 * F2".

If we divide both sides of the equation by 2, we get "40 = F2".

Substituting this value back into either of the original equations, we can find that "F1 = 100 - F2" or "F1 = 100 - 40" which gives us "F1 = 60".

Therefore, the value of F1 is 60.

Answer:

g=7

Step-by-step explanation:

To solve this equation, we need to isolate the variable g on one side of the equation. We can do this by first dividing both sides of the equation by 2. This gives us:

g - 4 = 3

Next, we can add 4 to both sides of the equation to isolate the variable g on the left side of the equation. This gives us:

g = 7

Therefore, the value of g that satisfies the equation is 7.

Answer:

............................

Answer:

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Bc I have calculator

Answer:

To find the amount that the couple needs to invest now, we can use the following formula:

investment = education cost * (1 + interest rate / number of compounding periods per year) ^ (number of years * number of compounding periods per year)

Plugging in the given values, we get:

investment = $40,000 * (1 + 0.055 / 52) ^ (17 * 52)

Solving this equation, we find that the couple needs to invest $11,226.31 now to have $40,000 for the child's education in 17 years. Rounded to the nearest dollar, this is $11,226.

Step-by-step explanation:

The coordinates of point B are (4, 0)

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

A = (6, 10)

Midpoint = (5, 5)

The midpoint of a line from its endpoints is calculated using the following equation

Midpoint  = (x₂ + x₁)/2 + (y₂ + y₁)/2

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

(5, 5) = (6 + x₁)/2 + (10 + y₁)/2

Multiply by 2

(10, 10) = (6 + x₁) + (10 + y₁)

By comparison, we have

x + 6 = 10

y + 10 = 10

Evaluate

x = 4

y - 0

Hence, the point is (4, 0)

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Answer:

.0800

Step-by-step explanation:

Dividing by ten will just move the decimal point one position further to the left

The area of the remaining paperboard is 246.91 in²

A shape can be cut-out of another shape. For example a circle cut off a rectangle. The area of the remaining part of the shape can be calculated as area of original shape - area of cut-out shape

The area of a rectangle = l×w

= 20×21 = 420in²

a semi circle is the shape cut-out, therefore the area of the semi circle= ½πr²

= ½×3.14× 10.5²= 173.09in²

Therefore the area of the remaining part of the paperboard is 420-173.09= 246.91 in²

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The z-score for Johnny’s grade is 1.92.

Johny's score falls into the 97.28 percentile

What is a normal distribution?

The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical representation of data around its mean value. It is represented graphically as the "bell curve."

Here, we have

mean = 69.5, std. deviation = 6.5 , x = 82

A. By normal distribution formula,

  z = ( x - mean) / std. deviation

  z = (82 - 69.5) / 6.5

 = 1.92

Hence, the z-score for Johnny’s grade is 1.92.

B. P(z<1.92) = 0.9728

Hence, Johny's score fall into 97.28 percentile.

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Therefore you can use midpoint to find the other endpoint  (x2,y2), then by rewriting the (x2,y2)= (2a-x1,2b-y1) .

The exact midpoint between two other plane points needs to be found on occasion. For example, you might seek out a line that splits a particular line segment into two equal halves. This central region is known as the "halfway."

Here,

If you are aware of one endpoint (x1, y1) and the midpoint (a, b), but are unaware of the second endpoint (x2, y 2), you can solve the problem by rewriting the

=> a=[tex]\frac{x1+x2}{2}[/tex]

=> 2a=x1+x2

=>2a-x1=x2

=> b=[tex]\frac{y1+y2}{2}[/tex]

=>2b=y1+y2

=> 2b-y1=y2

So, the unknown endpoint can be found by

(x2,y2)=(2a-x1,2b-y1)

Therefore you can use midpoint to find the other endpoint  (x2,y2), then by rewriting the (x2,y2)= (2a-x1,2b-y1) .

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The final balance after 10 years is $33257.92.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

The expression for the amount for compound interest is given as,

A = P(1 + r/100)ⁿ

After 6 years the amount can be calculated as,

A =  10000(1 + 10/100)⁶

  =  10000 × (11/10)⁶

  =  0.01 × 11⁶

  = 17715.61
As per the question $ 5000 is added at the end of 6 years.

So, the principal becomes 17715.61 + 5000 = 22715.61.

And, the remaining time is 10 - 6 = 4 years.
Now, the amount obtained after 10 years can be calculated as,

A = 22715.61(1 + 10/100)⁴

   = 22715.61 × 1.1⁴

   = 33257.92

Hence, the end of 10 years, the balance in Jarad's account is given as $33257.92.

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The area on the graph that is not shaded is the region of feasibility. The shape is a triangle and the vertices of the feasible region are: (5,1.5), (.75,.75), (1.5,.5)

The system of inequalities below, We need to determine the shape of the feasible region and find the vertices of the feasible region

x+y<=2

3x+y>=3

x+3y>=3

x>=0

y>=0

Now, we would graph with the following inequalities

x+y>=2

3x+y<=3

x+3y<=3

x<=0

y<=0

Therefore, the area on the graph that is not shaded is the region of feasibility and the shape is a triangle, the vertices of the feasible region are: (5,1.5) (0.75, 0.75), (1.5,.5).

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The value for p is 9 and the equation is y = 9x.

What is the proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.

We have,

x        y

4        36

8        72

12        108

A proportional relationship between x and y is p,

y = px

p = 36/4 = 9

p = 72/8 = 9

p = 108/12 = 9

Hence, the value for p is 9 and the equation is y = 9x.

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The range is the set of all possible y-values that could come from the equation y = |x|.

Since the absolute value only results in 0 or positive numbers, the range cannot include any negative real numbers.  

    |3| = 3

    |0| = 0

    |-3| = 3

Therefore the range is not all real numbers, since all negative real numbers are excluded from the range.

The range is y ≥ 0.

The equation illustrates that the variable that represents the greatest number is E. This cannot be determined with the given information.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

From the information, the variable is given as 1/2m = 1/3n = 1/4p = 1/5q.

It should be noted that the greatest variable cannot be determined based on the information. In conclusion, the correct option is E.

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Answer:

Step-by-step explanation:

Since we know the general circle equation is in the form

x^2 + y^2 = r^2, where r is radius

Now we are given the information that circle has the origin (0,0) and pass through point (-11,0), which mean the radius is 11 units.

Now we can write the circle equation as

x^2 + y^2 = 11^2

Answer:

the equation for the circle is:

X² +Y² = 11² = 121

The volume of the solid obtained by rotating the region bounded by the given curves about the X-axis is 340978 vu.

Given curve is,

y = [tex]x^{3}[/tex] , y = 8, x = 0 about x = 7

we know the formula for cylindrical shell is

V = πR²h

where R² = f(x)₂-f(x)₁ ,

            h = dx

here f(x)₂ = 8 and f(x)₁ = x³

⇒ V = π(8 - x³)²h

    V = π(64 - 16x³+x⁶)dx

integrating on both sides,

[tex]\int dV[/tex] =π [tex]\int ({64 - 16 x^{2} + x^{6} }) \, dx[/tex]

        = [tex]64 \int dx - 16 \int {x^{3} } \, dx + \int\ {x^{6} } \, dx[/tex]

    V = π(64x - 4x⁴+[tex]\frac{x^{7} }{7}[/tex])

    V = π(64 × 7 - 4(7)⁴ + [tex]\frac{7^{7} }{7}[/tex])

        = π(448 - 9604 + 117649 )

        = [tex]\frac{22}{7}[/tex](108493)

   V = 340978 vu

Therefore volume of the cylindrical shells to the region y = x³, y = 8, x = 0 about x = 7 is 340978 vu.

Cylindrical shells are essential structural elements in offshore structures, submarines, and airspace crafts. They are often subjected to combined compressive stress and external pressure, and therefore must be designed to meet strength requirements.

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The coefficient of x1 = 0.03 and the coefficient of  x2 = - 0.02.

The coefficient of x1 is  positive we can say there is a positive relationship  between x1 and y as the x1  value increases, the y value also increases

If the x1 value increases as 1 unit then the y  value increases as 0.03 unit while x2 keeps constant.

The coefficient of x2 is negative we can say there is a negative relationship between x2 and y as the x2 value increases y  value decreases.

If the x2 value increases as 1 unit then the y value decreases as 0.02 unit while x1 keeps constant.

A dichotomous variable is one that takes on one of just two potential qualities when noticed or estimated. The worth is most frequently a portrayal of a deliberate variable (e.g., mature: under 65/65 and over) or a quality (e.g., orientation: male/female).

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Answer:

15, 6

Step-by-step explanation:

x = large number

y = small number

1) x + y = 21

2) x = 21 - y

3) 2x - 2y = 18

substitute equation 2 into equation 3 so you have an expression all in terms of y, then you can solve for y.

2(21-y) - 2y = 18

42 - 2y - 2y = 18

-4y = -24

y = -24/-4 = 6

Now you can solve for x, plug y=6 into equation 1 :

x + 6 = 21

x = 21 - 6 = 15

6/8 is an equivalent fraction to 3/4; 2/6 is equivalent to 1/3; 6/9 is equivalent to 2/3; 10/25 is equivalent to 2/5; 4/16 is equivalent to 1/4; the fraction of 1/3 is equivalent to 2/6; 8/16 is an equivalent fraction to 2/4.

A fraction can be referred to or considered as a divisional representation of a whole number or a percentage, usually represented as a bigger numerical. A fraction denotes the representation of a number in such a way that the meaning or the accuracy of the number is not disturbed, but is shown differently. The fractions equivalent to each other have been mentioned above.

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a. The equation is, P = 15m + 10

b. The graph of P = 15m + 10 can be seen in the image attached below.

c. The total number of pages written in 5 months, is, 85.

A linear equation is a straight line graph, which can be expressed in slope-intercept form as y = kx + b, where;

a. To write the equation for the total number of pages P written after any number of months m, we have the following defined variables:

Unit rate or slope (k) = 15

Initial value or y-intercept (b) = 10

Number of pages, y = P

Number of months, m = x.

Substitute k = 15 and b = 10 into P = km + b:

P = 15m + 10

b. The graph of the P = 15m + 10 is shown below.

c. Substitute m = 5 into the equation, P = 15m + 10:

P = 15(5) + 10

P = 85

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Answer:

[tex]\dfrac{2}{3}x \geq 250[/tex]

Step-by-step explanation:

Let x be the number of students in the senior class.

If two-thirds of the seniors bought prom tickets and a minimum number of 250 tickets needs to be sold, the inequality that models this scenario is:

[tex]\boxed{\dfrac{2}{3}x \geq 250}[/tex]

Solving the inequality:

[tex]\implies \dfrac{2}{3}x \geq 250[/tex]

[tex]\implies 2x \geq 250 \cdot 3[/tex]

[tex]\implies 2x \geq 750[/tex]

[tex]\implies x \geq 750 \div 2[/tex]

[tex]\implies x \geq 375[/tex]

Therefore, there must be at least 375 students in the senior class to ensure they sold enough tickets to keep the venue.

If alpha specialize in growing apples beta specialize in growing oranges the both could gain profit by the trade is true for the statement

Comparative advantage describes a situation in which a person or a country involved in trade processes may not have an absolute advantage, but can still benefit from trade on a comparative basis.

The nations frequently trade goods based on their comparative advantages so that both parties can benefit from trade.

According to the stated information,

Alpha can produce either 18 oranges or 9 apples per hour, while beta can only produce 16 oranges or 4 apples per hour, it is stated.

so ,If alpha specialize in growing apples and beta specialize in growing oranges the both could gain profit by the trade

Hence, option C is true

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Answer:

Step-by-step explanation:

The given question is incomplete as the graph is missing.

But, considering a line graph, the following parameters can be represented on the x-axis and y-axis:

X-Axis                                                     Y-Axis

Year                                                         Population

Time                                                         Number of employees hired

Identical items purchased                      Total cost in dollars    

What does the blank observed line represent in each graph?  

The blank observed line represents the time. A line graph is basically used to connect the quantitative values over the different time intervals. The change in values over time is easier to estimate, by the help of the line graph. For example: in a graph showing the year on the x-axis and the population on the y-axis, the blank line represents the change in population over the years, the increase or decrease or the rate of change.  

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The expected value means what we expect to lose -$1.05 if the 1st is correct and lose -$.63 for the 2nd if that is correct.

Alright so we need to know the equation for expected value. So this turns our to be a pretty simple equation being:

E(X)=ΣxP(X=x)

So since we have all of our information we just need to use the equation. So:

E(X)= -$5*125/216+ $5*75/216+$10*15/216+$24*1/216 = -$1.045

I did notice however that there might be a mistake on this question since you have the win if 2 dice are correct as only being $10 instead of what i would think of being 16. If that is the case then the expected value is below

E(X)= -$5*125/216+ $5*75/216+$16*15/216+$24*1/216 = -$.6300

So the expected value means what we expect to lose -$1.05 if the 1st is correct and lose -$.63 for the 2nd if that is correct.

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Answer:One fourth

Step-by-step explanation:

In Experiment 1 the probability of each outcome is always the same. The probability of landing on each color of the spinner is always one fourth.

Answer:

Step-by-step explanation:

The correct answer is  People in Canada who are happier are less likely to suffer cardiac problems.

We have been given four options from which we have to select the correct one.

a. Happiness causes better heart health for all people.

b. Happiness causes better heart health for Canadians.

c. Happiness causes better heart health for the people in the study.

d. Happier people in Canada are less likely to have heart problems.

e. Happier people in the study were less likely to have heart problems.

The researchers followed up with each person 10 times later and discovered that those who had been deemed pleased at the start were no longer so. People in Canada who are happier are less likely to suffer cardiac problems.

Therefore, the conclusion is people in Canada who are happier are less likely to suffer cardiac problems.

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As the cube size increases, the surface -area - to - volume ratio decreases .

Given :

as the cubes increased in size, describe what happened to the surface area to volume ratio, mathematically why this happened in terms of the formula for each.

Volume :

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Volume of cube = a^3

Surface area :

Surface area is the amount of space covering the outside of a three - dimensional shape.

Surface area of cube = 6a^2

suppose side length = 1

1^3 : 6 * 1^2

= 6 * 1 : 1

= 6 : 1

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10% trimmed mean of the given data is xbar20 = 0.3269

In between the mean and the median, the trimmed means have some of the advantages of both without some of the disadvantages.

The 10% trimmed mean is the mean computed by excluding the 10% largest and 10% smallest values from the sample and taking the arithmetic mean of the remaining 80% of the sample (other trimmed means are possible: 5%, 20%, etc.

The 10% trimmed means omits 0.278 and 0.326 and yields

xbar10 =  0.278+ 0.285+0.299 + 0.304 + 0.306+ 0.306+ 0.306+ 0.308 +0.309 +0.310+ 0.313+ 0.313+ 0.315+ 0.317+ 0.317 +0.318+ 0.322+ 0.322+ 0.324+ 0.326 / 20

= 5.885 / 20

= 0.29

xbar = 1.29 and xbar = 1

Trimmed means are examples of robust statistics (resistant to gross error).

The 20% trimmed mean excludes the 2 smallest and 2 largest values in the sample above, and

xbar20 = 0.278+ 0.285+0.299 + 0.304 + 0.306+ 0.306+ 0.306+ 0.308 +0.309 +0.310+ 0.313+ 0.313+ 0.315+ 0.317+ 0.317 +0.318+ 0.322+ 0.322+ 0.324+ 0.326 / 18

xbar20 = 0.3269

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