A blimp is fully expanded when it contains 35,000 cubic feet of gas. If the blimp is inflated with 28,700
cubic feet of gas, what percent full is it?

Initial value of the linear function through A and B is 3.

The starting output value, or the y-value when x = 0, is the initial value. The rate of change is the rate at which the input or, in the case of a graph, the rate at which y changes in relation to x. A function's starting value in mathematics denotes the function's y-intercept. The constant in an equation can also be used to determine initial values. In graph functions, understanding the y-intercept is beneficial. By substituting 0 0 for x x and finding y y, you may verify the starting value.

Given,

Points

A (1,3)

B (6,13)

Linear function,

f(x) = ax + b

Equating,

f(x) = x + 3

Let x = 0

f(x) = 3

As we know,

The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.

Initial value of the linear function through A and B is 3.

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The value of the larger of the two numbers is 5.73.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Two numbers = M and N

M + N = 8 _____(1)

M = 8 - N _____(2)

MN = 13 _____(3)

Putting (2) in (3) we get,

(8 - N)N = 13

8N - N² = 13

N² - 8N + 13 = 0

This is in the form of ax² + bx + c = 0

a = 1, b = -8 and c = 13

Using the determinant we have,

N = -b ± √(b² - 4ac) / 2a

N = 8 ± √(64 - 52) / 2

N = 8 ± √12 / 2

N = 8 ± 2√3 / 2

N = 4 ± √3

N = 4 + √3 and N = 4 - √3

[√3 = 1.73]

N = 5.73

N = 2.27

Now,

When N = 5.73, M = 8 - 5.73 = 2.27

When N = 2.27, M = 8 - 2.27 = 5.73

Now,

The two numbers are 5.73 and 2.27

Thus,

The larger of the two numbers is 5.73.

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Answer: 12 3/5

Step-by-step explanation:

1 3/4 x 7 1/5 = 12.6= 12 3/5

The solution is 16 units

The length of the line segment is 16 units

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:  y=f(x+c) (same output, but c units earlier)

Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the length of the line segment be = A

Now , the initial length of the line segment = 16 units

The line is reflected across the y-axis

So , 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)

And , the resulting line is translated 5 units down

But , the line segment does not change in dimension at all

So , the reflection and a translation does not affect the length of the line segment

Hence , the length of the line segment is 16 units

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Answer:

2

Step-by-step explanation:

A 14 seater matatu makes 1420 = <<1420=280>>280 shillings per trip during normal hours.

It makes 1430 = <<1430=420>>420 shillings per trip during rush hours.

Since the matatu made 10 trips and earned 3540 shillings, then it made 10-3540/280 = <<10-3540/280=12>>12 trips during normal hours.

This means it made 10-12 = <<10-12=2>>2 trips during rush hours. Answer: {2}.

A full size scale is a type of scale in which the representative factor is 1 is to 1

A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size.

To determine the scale factor, first identify the corresponding sides on the two figures.

Then, divide the new figure's measurement by the original figure's measurement. The resulting value is your scale factor, or how many times your new figure is larger or smaller than the original.

A full size scale is a scale in which the length of the drawing is proportional to the actual length of the object.

As a result, its representative fraction is 1:1 by definition. The drawing is drawn in full size scale with the actual measurement

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P(Z3)=0.1170 is the likelihood of earning at least 1 gram of extra cereal.A probability seems to be a number that expresses the possibility or probability that a specific event will take place.

The probability is computed by dividing the total possible outcomes by the number of possible ways the event could occur. Probabilistic and odds are two distinct ideas. Odds are the likelihood that something will occur and the variety of outcomes that can result in success. the overall number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping the coin and getting heads is 1 in 2.

Y=1.8945 grams.

Y = 0.8405 grams.

The z-score is the result of dividing the standard deviation by the value that has been decreased by the mean:

z= σx−μ = 0.85053−1.9845≈1.19

Table A can be used to determine the relevant value:

P(Z≥3)=P(Z>1.19)=1−P(Z<1.19)=1−0.8830=0.1170

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557,568 inch³ of refrigerant can be held by the tubing.

Here we have to find how much a refrigerant can hold.

Data given:

outer diameter (d) = 78inch

outer radius(r) = 39 inch

inner diameter (d') = 34 inch

inner radius (r') = 17inch

Height (h) = 12 feet

= 12 × 12

= 144 inch

the formula to find the volume of the cylinder:

volume= пr²h

So here we get

Refrigerant hold = Volume of the outer cylinder - the volume of the inner cylinder

= πr²h - πr'²h

= πh(r² - r'²)

= π ×144 ( 39² - 17²)

= π × 144 ×56 × 22

= 22/7 × 144 × 56 × 22

= 557,568 inch³

Therefore the refrigerant can hold 557,568 inch³.

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the average rate of change of the function on the interval from x = 0 to x = 5 is 580.8

Average rate of change of a function f(x) between x-values x1 and x2 = (f(x2) -f(x1)/ (x2 -x1)

For this given function f(x)=12(3)x then it will mean that

f(x) = 12.3^x and x-values 0 and 5, the average rate of change is

the average rate of change = (f(5) -f(0))/(5 -0) = (2916 -12)/5 = 580.8

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Synthetic division is a yet another way to divide a polynomial by the factor, where k is a constant.

What is a synthetic division?

Synthetic division is usually used to find factors of polynomials of degree 3 that cannot be factored by grouping the polynomial.

Synthetic division is also used to find factor polynomials of degree 4 or higher.

We use synthetic division if and only if no other methods will work since there is a trial and error aspect to using it.

Taking an example:

We have to find the roots of the polynomial, [tex]f(x)= x^3+3x^2-4[/tex]

Substituting x=1 in the above equation, we get,

f(1)= [tex]1^3+3-4[/tex]=0

Thus, (x-1) is a root of the above polynomial.

Dividing the given function by (x-1)

[tex]x^3+3x^2-4/x-1\\=x^2+4x+4\\=(x+2)^2[/tex]

Thus, the roots of the given polynomial are given as, (x-1) and [tex](x+2)^2[/tex].

Hence, this is the synthetic division to find out the roots of the polynomial.

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Answer: Area=35km^2

Step-by-step explanation:

You need to find the areas of the rectangle and then the triangle.

First, you start with splitting up the figure to a rectangle and a triangle.

Secondly 6*5= 30 so the area of the rectangle is 30 km.

Thirdly, you add that to the area of the triangle, which you figure out because the opposite side of the figure is 6 km so the remaining length is going to be 2km. The area of a triangle is (1/2)(Base)(Height), so (1/2)(5)(2)= 5.

Add the 30 with the 5 and you get a total of 35 km for the area.

Answer:

i think the answer is 240km cuz you multiply 8x5x6. hope this helps, boo!

Step-by-step explanation:

Answer:

You would be saving the same amount of money either way.

Step-by-step explanation:

It's the commutative property.

The average rate of change between x = -3 and x = 1 is; 9/4

The average rate of change is calculated as the slope of the line between the two given points on the graph.

Now, looking at the graph, we can see that the coordinates of the two given points are;

(-3, -6) and (1, 3)

The formula to calculate the average rate of change which is the slope is;

m = (y₂ - y₁)/(x₂ - x₁)

m = (3 - (-6))/(1 - (-3))

m = 9/4

Thus, that is the average rate of change in conclusion

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Answer: 25% i believe

Step-by-step explanation:

The probability that it lands inside the triangle is,

P = 25%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Since, the probability is equal to,

P = size of the event space/size of the sample space

Here, In this problem

size of the sample size = area of the rectangular dartboard = 648 square centimeters

And, size of the event space = area of the triangular part = 162 square centimeters.

Hence, the probability that it lands inside the triangle is,

P = 162 / 648

P = 0.25

P = 25%

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If the sample mean is 12.8, sample standard deviation is 2 and sample size is 20, then the student's t-distribution should be use to perform the hypothesis test

The population mean = 13

The sample mean = 12.8

The standard deviation = 2

The sample size of the population = 20

The given condition is the underlying population is normal.

Here population standard deviation is missing in the given data. So to perform a hypothesis test when the population standard deviation is missing then we have to use the student t-distribution

Therefore, the student's t-distribution should be use to perform the hypothesis test

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Answer:

1503

Step-by-step explanation:

1803 - 300

Answer:

0

Step-by-step explanation:

Slope=(y2-y1)/(x2-x1)

=(4-(-3))/(10-c)=7/10

=7/(10-c)=7/10

c=0

By using the concept of unitary method, ratio and percentage, it can be calculated that-

7) Option D is correct

6) Option C is correct

8) Option D is correct

What is Unitary method, ratio and percentage?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Ratio is used to determine how much one quantity is bigger  as compared to another. The first part of the ratio is called antecedant and the second part of the ratio is called consequent.

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

Here, unitary method, ratio and percentage will be used.
7) The scale on a map reads [tex]\frac{1}{2} \ inch = 30 \ miles\\[/tex]

1 inch = [tex]30 \div \frac{1}{2} \ miles[/tex] = 60  miles

[tex]\frac{23}{4} \ inches[/tex] = [tex]\frac{23}{4} \times 60 \ miles[/tex] = 345 miles

Option D is correct

6) Let the number of empty seats be 3x and the number of full seats be 7x

Total number of seats = 3x + 7x = 10x

By the problem,

7x  = 203

x = [tex]\frac{203}{7}[/tex]

x = 29

Total number of seats = [tex]29 \times 10[/tex] = 290

Option C is correct

8) Let the number of students be x

Percentage of students in the band = [tex]\frac{37.5}{100} \times x[/tex]

By the problem,

[tex]\frac{37.5}{100} \times x =42\\x = \frac{42 \times 100}{37.5}\\x = 112[/tex]

Option D is correct

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To find the slope of a line given an equation in the form of ax + by = c .The slope of 7x + y = -4 is 7.

To find the slope of a line given an equation in the form of ax + by = c, you first need to put the equation into slope-intercept form, which is y = mx + b. To do this, start by subtracting ax from both sides of the equation, leaving you with by = c - ax. Then divide both sides by b, giving you y = (c - ax) / b. This is the equation in slope-intercept form, with m being the slope, which in this case is 7.

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Answer:

150%

Step-by-step explanation:

2 x 2 = 4

Remainder=1

50% OR 0.5 x 2 = 1

Answer:

The average rate of change of a function over an interval is found by taking the difference between the function's values at the endpoints of the interval and dividing by the length of the interval. In this case, we have:

f(1) = -3(1)^3 + 7(1) = -3 + 7 = 4

f(3) = -3(3)^3 + 7(3) = -27 + 21 = -6

The average rate of change over the interval from x=1 to x=3 is therefore (-6 - 4) / (3 - 1) = -10 / 2 = -5.

To label your answer, you could write something like: "The average rate of change of the whale's movement over the interval from x=1 to x=3 seconds is -5 meters/second."

1) The line's equation is y = 4 because it passes through the coordinates (-5,4).

2)  The equation of the line is y= 2x + 4

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

1) A line with a slope of 0 is considered to be horizontal.

The equation is y=4 because along a horizontal line, the y-values remain constant.

The line's equation is y=4 because it passes through the coordinates (-5,4).

2) (x1,y1) = (-2,0) , m=2

y-y1=m(x-x1)

y-0 = 2 (x-(-2))

y=2(x+2)

y= 2x + 4

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The required type ii error probability of the test using is 0.085.

It is determined by duplicating the pretest chances by the probability of a positive or negative test (as we will show). Post-test  probability  is characterized, as the likelihood of the objective problem after a symptomatic experimental outcome is known.

We have,

standard deviation = 7, mean = 6, size of the sample = 23.

P(type II error) = P(Xbar >=8 given mean =6)

=P(Z>(8-6)×√(23)/7) =P(Z>1.37)=1-P(Z<1.37)

=1-0.9147=0.0853 =0.085

Thus, required probability is 0.085

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It is true that a multiple linear regression model interprets the slope differently than a simple linear regression model.

The link between two variables is determined through simple linear regression. The slope of a straight line used to represent linear regression indicates how changing one variable impacts another variable.

For the complex relationships between data, multiple linear regression is used. More than one variable may contribute to the explanation of this relationship.

One y-intercept and numerous slopes (one for each variable) make up a multiple regression formula. The formula is understood in the same way as a simple linear regression formula, however more than one variable influences the relationship's slope.

Therefore, the statement is true.

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Explanation:

Segments JK, KL, and JL are tangent to the circle.

We can break those segments into smaller pieces and notice we have these 3 pairs of congruent tangents:

Let's use the first equation to solve for x.

MJ = NJ

5x-8 = 8x-35

5x-8x = -35+8

-3x = -27

x = -27/(-3)

x = 9

Use the same idea to find y.

KN = KO

7y-9 = 2y+11

7y-2y = 11+9

5y = 20

y = 20/5

y = 4

Now compute the length of segment KO.

KO = 2y+11 = 2*4+11 = 19 units

Subtract this from LK to find LO

LO = LK - KO

LO = 32 - 19

LO = 13

This makes segment LM to be also 13 units long.

Now use the value of x to find sides MJ and NJ

MJ = 5x-8 = 5*9-13 = 32

NJ = 32 as well

--------------------------------------------------------------

We have these pieces:

which give us

Therefore, the perimeter of triangle JLK is:

JK+KL+JL = 51+32+45 = 128 units

The equation relating C and S is given as follows:

C(S) = 5000 + 200S.

The graph of the equation is then given by the image shown at the end of the answer.

The first step in defining the function is verifying the input and the output variables, as follows:

Then from these variables, we identify the type of function, which is linear, as for each additional ton of sugar, the cost increases by a fixed amount.

This fixed amount is of $200, hence it represents the slope of the function. The fixed fee of $5,000 to rent trucks is the intercept, hence the equation is defined as follows:

C(S) = 5000 + 200S.

And then the graph starting at (0,5000) and connecting point (10, 7000) is given at the end of the answer.

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Answer:

3/2*2/3=1

Step-by-step explanation:

3/2*2/3. Everything cancels out, and you are left with 1.

3/2*2/3=6/6=1

Answer:

=1

Using the given fractions,

3/2×2/3

Applying the fractions formula for multiplication,

=3×2/2×3

=6/6

Simplifying 6/6, the answer is

=1

Answer:

x = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 8[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 4[tex]\sqrt{3}[/tex]

Answer: ( -9, -8)

Step-by-step explanation:

When reflected across the y-axis, the y-coordinate will be the opposite!

So the answer is (-9, -8)