The volume of gas a balloon can hold varies directly as the cube of its radius. Imagine a balloon with a radius of 4 inches can hold 192 cubic inches of gas. How many cubic inches of gas must be released to reduce the radius down to 3 inches?

Answer:

1-0.89=0.11

0.11*100=11%

Answer:

3.  x^10

4.  648

Step-by-step explanation:

See the attached worksheet

Stem-and-leaf plots contain original data values where histograms do not. Therefore, option B is the correct answer.

The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values.

The "stem" is used to group the scores and each "leaf" shows the individual scores within each group.

The advantage of a stem leaf diagram is it gives a concise representation of data. The advantage of a frequency histogram is, that it is visually strong. Histograms are usually preferable to stem and leaf diagrams in large data sets. The disadvantage of a stem leaf diagram is not visual.

Therefore, option B is the correct answer.

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Answer: Solution = (- 3, 2)

Explanation:

The system of equations is

6x + 8y = -2

-5x - 7y = 1

We would eliminate x. The first step is to multiply equation 1 by 5 and equation 2 by 6. We have

30x + 40y = - 10

- 30x - 42y = 6

By adding both equations, we have

30x + - 30x + 40y + - 42y = - 10 + 6

30x - 30x + 40y - 42y = - 4

- 2y = - 4

Dividing both sides by - 2,

- 2y/- 2 = - 4/- 2

y = 2

Substitu4ing y = 2 into equation 1, we hav

6x + 8 * 2 = -2

6x + 16 = - 2

Subtracting 16 from bth sides,

6x + 16 - 16 = - 2 - 16

6x = - 18

Dividing both sides by 6,

6x/6 = - 18/6

x = - 3

Solution = (- 3, 2)

Probability that 79 or more seeds germinate is 0.138, or about 13.8%.

To approximate the probability that 79 or more seeds germinate, we can use a normal approximation to the binomial distribution. First, we need to find the mean and standard deviation of the number of seeds that germinate.

The mean is the expected value of a binomial distribution, which is equal to the product of the number of trials (90) and the probability of success (0.84):

mean = 90 x 0.84 = 75.6

The standard deviation of a binomial distribution is equal to the square root of the product of the number of trials, the probability of success, and the probability of failure (1 minus the probability of success):

standard deviation = sqrt(90 x 0.84 x 0.16) = 3.11

Next, we can use the normal distribution to approximate the probability that 79 or more seeds germinate. We need to standardize the value of 79 using the mean and standard deviation we just calculated:

z = (79 - 75.6) / 3.11 = 1.09

Using a standard normal distribution table (or calculator), we can find the probability that a standard normal variable is greater than 1.09:

P(Z > 1.09) = 0.138

This means that the approximate probability that 79 or more seeds germinate is 0.138, or about 13.8%.

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1 )Note that based on the depreciation, at the end of the 3rd year, the worth of the automobile was $20,900.

2) With regard   to the speakers,there are 6 various ways to select speakers .

3) there are 15 rungs in the whole ladder.

1) Given -

Initial value of the automobile(at year 0) = $35,000

Value of the automobile   after 7 years = $2,100

Depreciation rate per year = (Initial value - Final value) / Number of years

Depreciation rate per year = ($35,000 - $2,100) / 7

= $32,900 / 7

≈ $4,700

Now we can   calculate the value of the automobile at the end of the third year  -

Value   at the end of the third year = Initial value - (Depreciation rate per year x Number of years)

Value at the end of the third year= $35,000 - ($4,700 x  3)

= $35,000 - $14,100

= $20,900

Hence, the automobile was worth $20,900 at the end of the 3rd year.

2)

Number of combinations = nCr = n!   / (r! (n-r)!)

Where n is the total number of choices and r is the number of speakers to be selected.

In this case, n = 4 (choices of Ben, Will, Stewart, and Hilary) and r = 2 (two speakers to be selected).

Number of combinations = 4! / (2!(4-2)!)

= 4! / (2! x 2!)

= (4 x  3x 2 x 1) / ((2 x  1) x (2  x 1))

= 24 / (2 x2)

= 24 / 4

= 6

Thus, there are 6 different ways to select two speakers from the choices of Ben, Will, Stewart, and Hilary.

3)

Given that

Rungs climbed up = 3 + 5 + 3 = 11

Rungs moved down = 4

Total rungs on the ladder = Rungs climbed up + Rungs moved down

r = 11 + 4

= 15

This means that  there are 15 rungs in the whole ladder.

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The mean of the number of drivers expected not to be wearing seatbelts is approximately 4.35, the variance is approximately 15.62, and the standard deviation is approximately 3.95 and they expect to stop approximately 4.35 cars before finding a driver whose seatbelt is not buckled.

a. To find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts, we can model the situation using a geometric distribution.

Let's define a random variable X that represents the number of cars stopped until the first driver without a seatbelt is found. The probability of a driver not wearing a seatbelt is given as p = 0.23.

The mean (μ) of a geometric distribution is given by μ = 1/p.
μ = 1/0.23 ≈ 4.35

The variance (σ^2) of a geometric distribution is given by σ^2 = q/p^2, where q = 1 - p.
σ^2 = (0.77)/(0.23^2) ≈ 15.62

The standard deviation (σ) is the square root of the variance.
σ = √(15.62) ≈ 3.95


b. The expected number of cars they expect to stop before finding a driver whose seatbelt is not buckled is equal to the reciprocal of the probability of success (finding a driver without a seatbelt) in one trial. In this case, the probability of success is p = 0.23.

Expected number of cars = 1/p = 1/0.23 ≈ 4.35

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Answer:

7

Step-by-step explanation:

as it does that F thing where its equal to it....

Answer:

I wont answer for you, but ill guide you in the right direction

Step-by-step explanation:

Answer:

fourth option

Step-by-step explanation:

Given

3x < - 9 ( divide both sides by 3 )

x < - 3

solution set is { x | x < - 3 }

\( \large \purple {\sf { {16x}^{2} + 8x + 1}} \)

\( \large \pink {\sf { = {(4x)}^{2} + 2(4x)(1) + {(1)}^{2}}} \)

\( \large \orange {\sf { = {(4x + 1)}^{2} }}\)

\( \large \green {\sf {{16x}^{2} + 8x + 1 = {(4x + 1)}^{2}}} \)

Answer:

B, C, D

Step-by-step explanation:

In this problem, the range is what the output, or y, can be. The origin, or the middie of the graph, is when x=0 and y=0. From the 10s on the screen, we can gather that 5 lines = a distance of 10 on the graph. Using this information, we can say

5 lines = distance of 10

divide both sides by 5 to find the distance for each line

1 line = distance of 2

The function goes from y=0 to three lines down, for a distance of 6. The range is therefore [-6,0] as all values from -6 to 0 on the y axis are included on the graph, including 0 and -6. In this range, -6, -2, and -1 are all included.

Answer:

Step-by-step explanation:

One that has the next least in common with the rest.

Answer:

root 194=13.928 inches

The given question is incomplete. The complete question is:

Omar rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 98 cents for each mile driven. Omar had to pay $23 when he returned the truck. For how many mile did he drive the truck?

Answer: Omar drove the truck for 5.15 miles

Step-by-step explanation:

Base fee = 17.95 $

Additional charge per mile = 98 cents = 0.98 $     ( 100cents = 1$)

Now Omar payed = 22 $

Let the miles he travelled = x

Now , \(17.95+0.98\times x=23\)

Solvimg for x :

\(x=5.15miles\)

Thus Omar drove the truck for 5.15 miles

Answer:

see explanation

Step-by-step explanation:

cos F = \(\frac{adjacent}{hypotenuse}\) = \(\frac{FD}{EF}\) = \(\frac{5}{13}\)

sin F = \(\frac{opposite}{hypotenuse}\) = \(\frac{ED}{EF}\) = \(\frac{12}{13}\)

tan F = \(\frac{opposite}{adjacent}\) = \(\frac{ED}{FD}\) = \(\frac{12}{5}\)

Thus, the number line which shows the graph of Negative 2.75 less-than x is given by option second.

A number line is a visual depiction of numbers on either a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction.

All sets of numbers, including natural and whole numbers, are included in the numbers on a number line. The natural number ranges from 1 to 6 while a group of whole numbers is represented by (0, 1, 2, 3,4,5,6).

There are three main components to a number line. The origin is typically plotted with zero in the centre. The mnemonic "The origin like most things is nothing" can help you recall that the origin is zero.

The expression for Negative 2.75 less-than x is:

-2.75 < x

So, x > -2.75 in which, -2.75 is not included.

Thus, the number line which shows the graph of Negative 2.75 less-than x is given by option second.

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Answer:

Our problem is \(x^2-2x+6=0\), but as we can see, we are unable to factor. We have to use the quadratic equation to solve.

\(x^2-2x+6=0\)

\(\frac{-b+-\sqrt{b^2-4ac}}{2a}\)

Positive Quadratic Formula:

\(\frac{-(-2)+\sqrt{(-2)^2-4(1)(6)}}{2(1)}\)

\(=\frac{2+\sqrt{4-24}}{2}\\=1+\frac{\sqrt{-20}}{2}\)

Negative Quadratic Formula:

\(\frac{-(-2)-\sqrt{(-2)^2-4(1)(6)}}{2(1)}\)

\(=\frac{2-\sqrt{4-24}}{2}\\=1-\frac{\sqrt{-20}}{2}\)

Since both of our answers are the square root of a negative number, we know that the quadratic equation has no real solution.

*We could have also used the Discriminant Test to determine whether the quadratic equation has real roots or not. However, for our means, the quadratic equation seems enough.

Answer:

D. No real Solution

Step-by-step explanation:

Hello!

Let's use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

In our equation:

This comes from the standard form of a quadratic: \(ax^2 + bx + c\)

Now, solve:

Since the radicand (-5) is negative, there are no real solutions. The correct answer is Option D.

To find the position vector of point C on AB such that AC:CB = 3:4, we can use the section formula. According to the section formula, the position vector of C can be expressed as: C = (4b + 3a) / 7

Here, we are multiplying the position vector of B by 4 and the position vector of A by 3, then adding them together and dividing by the sum of the coefficients (in this case, 3 + 4 = 7).

So, if the position vector of A is a = (x1, y1, z1) and the position vector of B is b = (x2, y2, z2), then the position vector of C can be calculated as:

C = (4b + 3a) / 7 = [(4x2 + 3x1) / 7, (4y2 + 3y1) / 7, (4z2 + 3z1) / 7]

Therefore, the position vector of C on AB such that AC:CB = 3:4 is (4b + 3a) / 7, where a and b are the position vectors of A and B, respectively.

In summary, the section formula helps us find a point on a line segment given the position vectors of its endpoints and the ratio in which it divides the segment. The resulting position vector can be expressed as a combination of the position vectors of the endpoints, weighted by the corresponding ratio coefficients. This method works for lines and segments in any number of dimensions, not just in 3D space.

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Answer:

the answer is 3rd option.

X=5.961 cm

Possible values for the discriminant of the quadratic function are given as follows:

A. -7.

B. -25.

The numeric value of the coefficient and the number of solutions of the quadratic equation are related as follows:

The function in this problem has no x-intercepts, hence it has complex solutions, meaning that the discriminant is negative.

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This means that the value of x should not exceed 2.5, as Leanna needs no more than 2.5 hours to complete her homework.

The inequality that represents the number of hours, x, Leanna needs to finish her homework is: x ≤ 2.5.

The inequality x ≤ 2.5 means that the value of x should not exceed 2.5. Since Leanna needs no more than 2.5 hours to finish her homework, we can use this inequality to represent the possible values of x. If x is greater than 2.5, then Leanna would take more than 2.5 hours to finish her homework, which contradicts the given condition. Therefore, the inequality x ≤ 2.5 is the correct representation of the number of hours Leanna needs to finish her homework.

In conclusion, the inequality x ≤ 2.5 represents the number of hours, x, Leanna needs to finish her homework. This means that the value of x should not exceed 2.5, as Leanna needs no more than 2.5 hours to complete her homework.

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Answer:

2 (3 y - 4) <- Complete answer, but since you only have those choices it's

6 y - 8

Step-by-step explanation:

Simplify the following:

8 y - 2 (y + 4)

Hint: | Distribute -2 over y + 4.

-2 (y + 4) = -2 y - 8:

8 y + -2 y - 8

Hint: | Group like terms in 8 y - 2 y - 8.

Grouping like terms, 8 y - 2 y - 8 = (8 y - 2 y) - 8:

(8 y - 2 y) - 8

Hint: | Combine like terms in 8 y - 2 y.

8 y - 2 y = 6 y:

6 y - 8

Hint: | Factor out the greatest common divisor of the coefficients of 6 y - 8.

Factor 2 out of 6 y - 8:

Answer: 2 (3 y - 4)

Answer:

(2m^2-3)(m-1)

Step-by-step explanation:

2m^3-2m^2+3-3m

2m^3-2m^2-3m+3

2m^2(m-1)-3(m-1)

(2m^2-3)(m-1)

Answer:

(2m^2-3)(m-1)

Step-by-step explanation:

2m^3-2m^2+3-3m

=(2m^3-2m^2)+(3-3m)

=2m^2(m-1)+3(1-m)

=(m-1)(2m^2-3)

=(2m^2-3)(m-1)

Answer:

The Muffin Recipe calls for 3 more cups of Milk than the Bread Recipe.

Step-by-step explanation:

11/3=

3\(\frac{2}{3}\)

2/3

We can see that the difference is GREAT. So, now, let's subtract.

\(3\frac{2}{3} -\frac{2}{3} =3\)

So hence, the Muffin Recipe calls for 3 more cups of Milk than the Bread Recipe!

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:D

The muffin recipe requires 2/3 cup more milk than the bread recipe.

Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.

To find out how much more milk is needed for the muffin recipe than the bread recipe,

we need to calculate the difference between the amount of milk required for each recipe.

The muffin recipe calls for 1 1/3 cups of milk, which is equivalent to 4/3 cups of milk.

The bread recipe calls for 2/3 cup of milk.

To find the difference between the two amounts of milk, we can subtract the milk required for the bread recipe from the milk required for the muffin recipe:

4/3 - 2/3 = 2/3

Therefore, 2/3 is the required fraction.

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It will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

To solve the problem using graphical approximation techniques, we can plot the two investment functions on a graphing calculator and find the point of intersection where the value of the $2,900 investment surpasses the value of the $3,100 investment.

Let's use the formula \(A = P(1 + i)^n\),

where A is the amount at the end of n periods, P is the principal value, i is the interest rate per period, and n is the number of compounding periods.

For the $2,900 investment at 15% compounded quarterly:

P = $2,900

i = 15% = 0.15/4

= 0.0375 (interest rate per quarter)

For the $3,100 investment at 9% compounded quarterly:

P = $3,100

i = 9% = 0.09/4

= 0.0225 (interest rate per quarter)

Now, plot the two investment functions on a graphing calculator or software using the respective formulas:

Function 1:\(A = 2900(1 + 0.0375)^n\)

Function 2:\(A = 3100(1 + 0.0225)^n\)

Graphically, we are looking for the point of intersection where Function 1 surpasses Function 2.

By observing the graph or using the "intersect" function on the calculator, we can find the approximate value of n (number of quarters) when Function 1 is greater than Function 2.

Let's assume the graph shows the intersection point at n = 15.6 quarters. Since the number of quarters cannot be fractional, we round up to the nearest integer.

Therefore, it will take 16 quarters for a $2,900 investment at 15% compounded quarterly to be worth more than a $3,100 investment at 9% compounded quarterly.

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Answer:

D.

Step-by-step explanation:

The whole point of a line graph is keep track of data that is always changing. For example, a line graph would be used to track the change in weather.

The equation lim(x→1) [x^2/(x-2)] / (x-1) = lim(x→1) (x^2) is correct due to the cancellation of the common factor of (x-1) in both the numerator and denominator. This cancellation allows us to simplify the expression and evaluate the limit.

In the given equation, we have the limit of the expression [x^2/(x-2)] / (x-1) as x approaches 1. We can rewrite this expression as (x^2) / [(x-2)(x-1)]. By factoring out the common factor of (x-1) in the numerator and denominator, we obtain [(x-1)(x+1)] / [(x-2)(x-1)].

Since the factor (x-1) is common in both the numerator and denominator, it cancels out, resulting in the simplified expression of (x+1) / (x-2).

Now, as x approaches 1, we can substitute the value into the simplified expression to evaluate the limit, giving us (1+1) / (1-2) = 2 / -1 = -2.

Therefore, the equation lim(x→1) [x^2/(x-2)] / (x-1) = lim(x→1) (x^2) is correct, and the value of the limit is -2.

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If the circumference of a dinner plate is 19.4 cm, so according to the formula 2πr radius would be 3 cm approx.

We know that Plate is in circular shape and the circumference is 19.4 cm.

We know that Circumference of circles = 2πr

Thus, 2πr = 19.4

         r = 19.4/2π

         r = 3.08 cm

Therefore the radius of the plate is 3 cm approx.

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more generally referred to as the perimeter.

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The number of people that speak only spanish = 6

We are given;

Total number of people surveyed = 50

31 speak French 2 speak French, German and Spanish.

4 speak French and Spanish but not German.

7 speak German and Spanish.

8 do not speak any of the languages.

All 10 people who speak German speak at least one other language.

Thus;

From the Venn diagram;

Number of people that speak only French and German = 10 - 5 - 2 - 0 = 3

Number that speak only spanish = 50 - 22 - 3 - 2 - 4 - 5 = 6

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