8. What is 3x times (3x² - 5)?
a.3x² + 5x -5
b.9x³-5
c.9x³ - 15x
d.15x³ - 25x

Answer: C) 10n +19

Step-by-step explanation:

Let's simplify the provided expression (3n+13) + (6+7n)

Since this is just addition we can just remove the parenthesis and use the commutative property to make adding easier

3n+13+6+7n

3n+7n+13+6

10n+19

Answer:

D

Step-by-step explanation:

Volume of cylinder = Base x height

Base = πr^2 = 25π

Volume = 25π x 10 = 250π

Volume of cone = 1/3 Base x height

= 1/3 x 25π x 5 = 125π/3

Volume of silo = cylinder + cone + cone

= 250π + 125π/3 + 125π/3

= 785.4 + 130.9 + 130.9

= 1047.2

Answer: GL = \(\sqrt{61}\)

Step-by-step explanation:

     Since this is a right triangle, we can use the Pythagorean theorem. GL is the hypotenuse.

Given:

     a² + b² = c²

Substitue:

     AL² + AG = GL²

Find side lengths (count via the coordinate plane given):

     6² + 5² = GL²

Square:

     36 + 25 = GL²

Add:

     61 = GL²

Square root both sides:

     \(\sqrt{61}\) = GL

Answer:

x = 4

Step-by-step explanation:

Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. For example, m÷(2/3) = m×3/2

Answer:

X=4 I'm not sure what you mean by solve with fractions, but I now the answer is right.

Step-by-step explanation:

3 ÷ 3/4 =4

or

3/4=9/12

3=36/12

36/12÷9/12=4

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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Answer:

x < 6

Step-by-step explanation:

subtract 21 on both sides

-4x > -24

divide both sides by -4 and flip the sign (bc you're dividing by a negative)

x < 6

The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .

Normal distributions are crucial to statistics because they are widely used in the natural and social sciences to represent real-valued covariates whose distributions are unknown.

First we will find the bottom 3% such that P(X ≤ x) = 0.03

⇒ \(P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.03\)

⇒\(P(Z\leq \frac{x-5.48}{0.07} )=0.03\)

Now we will use the normal table to calculate the corresponding z-score.

\(\frac{x-5.48}{0.07} =-1.88\\\\\implies x = 5.348\)

Now we will find the same for the top part of the distribution.

\(P(\frac{X-5.48}{0.07}\leq \frac{x-5.48}{0.07} )=0.97\\\\\implies P(Z\leq \frac{x-5.48}{0.07} )=0.97\)

Now we will use the normal table to calculate the corresponding z-score.

\(\frac{x-5.48}{0.07} =1.88\\\\\implies x = 5.612\)

The two diameters that separate the top 35 from the bottom 35 in the normal distribution are 5.35 mm and 5.61 mm .

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Answer:

go to khan academy on you tube he's really good at explaining stuff also sorry that's all i got...

Step-by-step e

Answer:

  any value less than 10

Step-by-step explanation:

Let x represent the number.

  1.5x < |20 -5|

  1.5x < 15 . . . . simplify

  x < 10 . . . . . . divide by 1.5

The number may be any value less than 10.

The equation of the ellipse is (x - 6)² / 4 + (y - 1)² / (16/9) = 1, the center is (6,1), and the directrices are x = 0 and x = 12.

The center of the ellipse is the midpoint of the major axis. The midpoint of the line segment connecting (4,1) and (8,1) is ((4+8)/2, (1+1)/2) = (6,1). Therefore, the center of the ellipse is (6,1).

The distance between the center and one of the vertices (say, (8,1)) is the length of the semi-major axis, a. This distance is (8-6) = 2. Therefore, the semi-major axis is a = 2.

The eccentricity, e, is given as 1/3.

The distance between the center and one of the foci, c, is related to the semi-major axis and eccentricity by the equation c = ae. Plugging in the values we know, we get c = (1/3)(2) = 2/3.

We can write the equation of the ellipse in standard form:

(x - 6)² / 2² + (y - 1)^2 / b² = 1

where b is the semi-minor axis. We can solve for b using the relationship between the semi-major axis, semi-minor axis, and eccentricity:

So the equation of the ellipse is:

(x - 6)² / 4 + (y - 1)² / (16/9) = 1

The directrices are located a distance of a² / c = (2²) / (2/3) = 6 units away from the center along the major axis. These are the lines x = 6 - 6 = 0 and x = 6 + 6 = 12.

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Answer:

u = 8w-16 /-12        or  =  - 8w-16/12 both mean the same due to the a/-b- = -a/b rule. Then you can factor out the rest. note the fnew subtraction changes mean the same as - (a/b) and should show without brackets as a centre pointing whole fraction subtraction sign.

Step-by-step explanation:

-12u -13 = 8w-3

-12u+13 -13 = 8w-3-13     Eliminate -13 by +13 both sides

-12u = 8w-16                      So you are left with one value left side.

-12u/-12  =  8/-12 - 16/-12   Then divide all values by -12 to find value for u and keep the subtraction as 8 never had subtraction sign and no multiplication .

u = 8w-16 /-12                   Then you can factor out the rest

This has made u the independent variable then you have a choice to continue showing or ignore u; as u =

=       -  8(w-2)/12       Step 1   Factor with subtraction change from -12  to - central fraction

=         - 2(w-2)/3      Step 2   Simplify with new minus sign for central fraction to replace a/-b

Answer:

The answer is W = -3/2u + 2

Step-by-step explanation:

Look at attachment:

Hope this helps! :)

Answer:

6:40

Step-by-step explanation:

6 blue marbles

8 green marbles

9 red marbles

17 yellow marbles

6+8+9+17= 40.

40 is the total amount of marbles.

There are 6 blue marbles.

Comparing the amount of 6 to 40 would be 6:40

Part (a)

The cost is the initial cost plus the cost per slushie multiplied by the number of slushies sold.

\(C(x)=500+1.25x\)

Part (b)

The revenue is the number of slushies sold multiplied by the amount charged per slushie.

\(R(x)=3.50x\)

Both relation (year, percent of men) and (year, percent of women) are functions.

What is a function?

A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

Now,

In given data

For every input (i.e. year) there is a unique output (i.e. percent of men/ percent of women)

Hence, Given relation (year, percent of men) and (year, percent of women) are functions.

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The dot product of vectors a and b is option D. 30.

To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.

Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:

a • b = (5 x 4) + (2 x 5)

= 20 + 10

= 30

Therefore, the dot product of vectors a and b is 30.

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Answer:

-12

Step-by-step explanation:

f (x)=6x – 6

Let x= -1

f(-1) = 6(-1) -6

      = -6-6

     = -12

Answer:

Identify the range of the function shown in the graph.

Answer:

range=(10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10)

Answer:

Part A:

To find the percentage of survey respondents who liked neither hamburgers nor burritos, we need to calculate the frequency in the "Does not like hamburgers" and "Does not like burritos" categories.

Frequency of "Does not like hamburgers" = Total in "Does not like hamburgers" category = 135

Frequency of "Does not like burritos" = Total in "Does not like burritos" category = 54

Total respondents who liked neither hamburgers nor burritos = Frequency of "Does not like hamburgers" + Frequency of "Does not like burritos" = 135 + 54 = 189

Percentage of survey respondents who liked neither hamburgers nor burritos = (Total respondents who liked neither hamburgers nor burritos / Total respondents) x 100

Percentage = (189 / 205) x 100 = 92.2%

Therefore, 92.2% of the survey respondents liked neither hamburgers nor burritos.

Part B:

To find the marginal relative frequency of all customers who like hamburgers, we need to divide the frequency of "Likes hamburgers" by the total number of respondents.

Frequency of "Likes hamburgers" = 110 (given)

Total respondents = 205 (given)

Marginal relative frequency = Frequency of "Likes hamburgers" / Total respondents

Marginal relative frequency = 110 / 205 ≈ 0.5366 or 53.66%

Therefore, the marginal relative frequency of all customers who like hamburgers is approximately 53.66%.

Part C:

To determine if there is an association between liking burritos and liking hamburgers, we can compare the joint and marginal frequencies.

Joint frequency of "Likes hamburgers" and "Likes burritos" = 29 (given)

Marginal frequency of "Likes hamburgers" = 110 (given)

Marginal frequency of "Likes burritos" = 70 (calculated by adding the frequency of "Likes burritos" in the table)

To assess the association, we compare the ratio of the joint frequency to the product of the marginal frequencies:

Ratio = Joint frequency / (Marginal frequency of "Likes hamburgers" x Marginal frequency of "Likes burritos")

Ratio = 29 / (110 x 70)

Ratio ≈ 0.037 (rounded to three decimal places)

Answer:

-0.33333333333 in other word it o.3 with line over 3

Step-by-step explanation:

Answer:

Is 03.841

Step-by-step explanation:

To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.

In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.

To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.

The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.

Therefore, the correct answer is 03.841.

Answer:

We will graph the inequality in simplified form i.e \(y>-3\)

The graph is shown in figure below

Step-by-step explanation:

Which is the graph of the linear inequality \(2y>-6\)

(Note: Considering the inequality is 2y>-6 and x is typing mistake.)

First we will solve the inequality to find value of y

We have inequality:

\(2y>-6\)

For finding y we have to divide both sides of inequality by 2

\(\frac{2y}{2}>\frac{-6}{2} \\y>-3\)

Now, we will graph the inequality in simplified form i.e \(y>-3\)

Inequality can be graphed on number line as well as graph paper.

Graph on number line

Since y is greater than -3, so all values greater than -3 will be included on the number line. An open circle will be drawn on -3, indicating -3 is not included but values greater than -3 are included. The figure A shows the graph

Graph on Graph paper

Since y is greater than -3, so all values greater than -3 will be included on the number line. A dotted line will appear on -3 and the region on right side of -3 (values greater than 3) will be shaded. The figure B shows the graph

The 80% confidence interval for the average water usage of 249 families is (15.42, 16.18) gallons.

To construct an 80% confidence interval for the average water usage of 249 families, we can use the following formula:

CI = X ± t(α/2, df) * (s/√n)

where X is the sample mean (15.8 gallons), t(α/2, df) is the critical t-value from the t-distribution table at the desired confidence level and degrees of freedom (247 in this case), s is the population standard deviation (1.7 gallons), and n is the sample size (249).

At an 80% confidence level and 247 degrees of freedom, the critical t-value is approximately 1.296.

Plugging in the values, we get:

CI = 15.8 ± 1.296 * (1.7/√249)

CI = 15.8 ± 0.38

Therefore, the 80% confidence interval for the average water usage of 249 families is (15.42, 16.18) gallons.

This means that we are 80% confident that the true average water usage of the population lies within this interval.

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Answer:

There are 9 arms.

Step-by-step explanation:

Answer: 1/6

Step-by-step explanation:

There are 6 faces in a dice

The faces are labeled as =

1

2

3

4

5

6

This means, there are 6 different outcomes in a dice

So we have to find out the probability of the dice showing 3

Now, out of 6 different possible outcomes, there is only 1 face labeled as 3.

So there is only 1 possible outcome as "3".

We can simply make it a fraction = 1/6 . 

So the answer is 1/6

Probability is expressed as a fraction, percentage and decimal.

Given:

Required:

To find the probability that the dart land will be in the shaded region.

Explanation:

Area of the circle is given by the formula:

Where r = radius

Thus the area of the circular region

The area of the square is given by the formula:

Thus the area of the given square

The probability of an event is given by the formula:

The probability that the dart land will be in the shaded region

Thus probability

Final answer:

Thus the probability that the dart land will be in the shaded region is 0.349.

Answer:

Step-by-step explanation:

100-65=35%

Therefore, the point (v, w) = (x, y) = (6, 15)

The diagram above has two graphs (ABC and DE) intercepting at a point, (v, w).

To find the interception point (v, w), we need to first find the equations of each graph, with ABC being a parabola and DE, a straight line.

Since ABC is a parabola and the vertex is given, the standard vertex form of a parabola is given by:

y = a(x – h)2 + k ----------- eqn(1)

where (h, k) is the vertex of the parabola (the vertex is the point where the parabola changes direction) and "a" is a constant that tells whether the parabola opens up or down (negative indicates downward and positive indicates upward).

Given vertex (4, 19), eqn(1) becomes:

y = a(x - 4)2 + 19 -------------- eqn(2)

Since the parabola passes through point (0, 3), that is, x = 0 and y = 3,

we substitute the value of x and y into eqn(2) to find the value of "a"

3 = a(0 - 4)2 + 19

3 = a(-4)2 + 19

3 = 16a + 19

16a = 3 - 19

16a = -16

a = -1

Thus, eqn(2) becomes:

y = -(x - 4)2 + 19 ------------- eqn(3)

Next, we find the equation of DE (straight line).

Since DE is a straight line and the general form of straight-line equation is given by:

y = mx + c ------------------ eqn(4)

where m is the slope and c is the point at which the graph intercepts the y-axis.

c = -9

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

At points (0, -9) and (2, -1)

x1 = 0

x2 = 2

y1 = -9

y2 = -1

m = (-1 - (-9)) / (2 - 0)

= (-1 + 9)/2

= 8/2

m = 4

Substitute the values of m and c into eqn(4)

y = 4x - 9 ---------------- eqn(5)

Since point (v, w) is the point where both graphs meet,

eqn(3) = eqn(5)

-(x - 4)2 + 19 = 4x - 9

-[(x - 4)(x - 4)] + 19 = 4x - 9

-(x2 - 8x + 16) + 19 = 4x - 9

-x2 + 8x - 16 + 19 = 4x - 9

-x2 + 8x - 4x - 16 + 19 + 9 = 0

-x2 + 4x + 12 = 0

multiply through with -1

x2 - 4x - 12 = 0 ----------- eqn(6)

The above is a quadratic equation and can be simplified either by factorization, completing the square, or quadratic formula method.

Using the factorization method,

product of roots = -12

sum of roots = -4

Next, find two numbers whose sum is equal to the sum of roots (-4) and whose product is equal to the product of roots (-12)

Let the two numbers be 2 and -6

Replace the sum of roots (-4) in eqn(6) with the two numbers

x2 - 6x + 2x - 12 = 0

Group into two terms

(x2 - 6x) + (2x - 12) = 0

factorize each term

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

Pick and group the two values outside each bracket and inside one of the brackets

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

x + 2 = 0 and x - 6 = 0

x = -2 and x = 6

Since the point, (v, w) is on the right side of the y-axis, it follows that x cannot be –2. Therefore, x = 6.

substitute the value of x into eqn(5)

y = 4(6) - 9

y = 24 - 9

y = 15

Therefore, the point (v, w) = (x, y) = (6, 15)

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