Solve the inequality.
-4x-5 <3
Graph the solution on the number line.
Use the tools to enter your answer.

Answer:

A certain shade of pink us created by adding 3 cups of red paint to 7 cups of white paint

Step-by-step explanation:

Constant of proportionality is the constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the factor of proportionality.

To make color pink,

for every 3 cups of red , we need 7 cups of white.

Let 'r' be the cups of red required

let 'w' be the cups of white required

so , as per the question

for 3 r we need = 7 w

r = 7/3 w

so, 7/3 is constant of proportionality

Answer: 3/5 (0.6 decimal form)

Step-by-step explanation:

Answer:

384

Step-by-step explanation:

480x20%=96

480-96=384

Answer:

B

Step-by-step explanation:

We can substitute the x value given, -3, into our equation, y = x^2, to get what the y would be:

y = x^2

y = (-3)^2

When a negative number is squared, it is positive, so (-3)^2 = 9, and:

y = 9

This is option b

Answer:

B) 9

Step-by-step explanation:

We are given the equation y = x^2 for the table, and a x value.

To find the y value that corresponds to that x value, we must plug the x value in the equation.

Y =x^2

Y= -3^2

Y=9

The simplified expression of x(3x + 5)-5(2x - 1) is 3x² - 5x + 5

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

x(3x + 5)-5(2x - 1)

Open the brackets

So, we have

3x² + 5x - 10x + 5

Evaluate the like terms

So, we have

3x² - 5x + 5

Hence, the simplified expression is 3x² - 5x + 5

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Answer: f(3) = g(6)

Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer

By definition of f(x),

f(k) = 1 - 2k + k = 1 - k

Then

f(f(k)) = f(1 - k) = 1 - 2 (1 - k) + k = 3k - 1 = 13

Solve for k :

3k - 1 = 13

3k = 14

k = 14/3

Find f(-1) :

f(-1) = 1 - 2 (-1) + 14/3 = 1 + 2 + 14/3 = 23/3

Answer:

Step-by-step explanation:

Let the number of representatives be r and senators be s

The we have system of equations:

Substitute r in the first equation:

Solving for s:

Answer:  4 boxes.

Step-by-step explanation:

We know that each box has 18 ounces of cereal.

We know that:

1 lb = 16 oz

Then:

1 = (1lb/16oz)

Then we can write:

18 oz = 18oz*(1lb/16oz) = (18/16) lb

This means that each box has (18/16) pounds of cereal.

Now, how many boxes we need to buy if we want to have at least 4 pounds of cereal?

If we buy N boxes, we will have N*(18/16) lb boxes of cereal.

Let's find N such that:

N*(18/16) lb = 4lb

N = 4*(16/18) = 3.56

But you can not have a 0.56 of a box, so we should round our number up to the next whole number, then we get:

N = 4.

She should buy 4 boxes.

Answer:

4 Boxes

Step-by-step explanation:

Given: We know that each box has 18 ounces of cereal.

Note: 1 lb = 16 oz

Solution:

18 oz = 18oz*(1lb/16oz) = (18/16) lb

→ Each box has (18/16) pounds of cereal.

Question → How many boxes we need to buy if we want to have at least 4 pounds of cereal?

If we buy x boxes, we will have x*(18/16) lb boxes of cereal.

Find x :

x*(18/16) lb = 4lb

x= 4*(16/18) = 3.56

Can't have a 0.56 of a box, thus we should round our number up to the next whole number, then we get:

x = 4

Hence, Lily should buy 4 boxes.

[RevyBreeze]

Using the combination formula, it is found that you can draw 10 different combinations of three letters.

The order in which the letters are drawn is not important, as stated in the problem, ACE and CAE are counted as the same combination, hence the combination formula is used instead of the permutation formula.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

For this problem, three balls are taken from a urn with five balls(labeled A, B, C, D and E), hence n = 5, x = 3 and:

\(C_{5,3} = \frac{5!}{3!2!} = 10\)

You can draw 10 different combinations of three letters.

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Answer:

$200 is not part of the confidence interval, which means that this is not a reasonable conclusion, at the 100 - 95 = 5% level of significance.

Step-by-step explanation:

95% confidence interval: $72 to $198.

This means that we are 95% sure that the true mean spending is between $72 and $198.

From this confidence interval the assistant concluded that people spend an average of $200 a month on entertainment. Is this a reasonable conclusion and why?

$200 is not part of the confidence interval, which means that this is not a reasonable conclusion, at the 100 - 95 = 5% level of significance.

The situation can be sketched in the following diagram.

The angles are in the following order

68 > 67 > 45.

Here are some facts about the relationship between angles and triangles:

The shortest side is always opposite the smallest angle.

The longest side is always opposite the largest angle.

Hence, the smallest side is that of the Clarinet and the longest side is that of the trumpet; therefore, the sides ordered from least to greatest are

Clarinet, Flute, Trumpet.

Part A (Domain and Range)

Domain

The domain is the set of all the values of x for which the function represented by the graph is defined. From the graph:

(A)The domain of the function is:

The range is the set of all the values of y for which the function represented by the graph is defined. From the graph:

(A)The range of the function is:

(A)The x-intercepts of the function are:

(A)The y-intercept of the function is:

Part C

The horizontal asymptote is at:

Part D

The vertical asymptotes are at:

Part E

The oblique asymptote is usually slant.

From the graph, there are no obliques asymptotes.

Option B is correct here.

Answer:

0.125b

Since 1 headphone would be 1/8=0.125, 0.125 x b would be the equation

Answer:

im thinking either b or c im leaning towards b

Step-by-step explanation:

The volume of the solid of revolution formed by revolving the region bounded by f(x) = -3x² + 8 and g(x) = 3x² + 2 about the x-axis is 16π cubic units.

To find the volume of the solid of revolution formed by revolving the region bounded by the curves f(x) = -3x² + 8 and g(x) = 3x² + 2 about the x-axis, we can use the method of cylindrical shells and integrate.

First, let's find the points of intersection between the two curves by setting them equal to each other:

-3x² + 8 = 3x² + 2

Rearranging the equation, we get:

6x² = 6

x² = 1

x = ±1

So, the curves intersect at x = -1 and x = 1.

To calculate the volume, we'll integrate along the x-axis from x = -1 to x = 1. The volume of each cylindrical shell can be determined by multiplying the circumference (2πy) by the height (dx), where y represents the distance from the axis of revolution to the curve at a given x-value.

The radius of the cylindrical shell, y, can be obtained by subtracting the lower curve (f(x)) from the upper curve (g(x)). Therefore, y = (3x² + 2) - (-3x² + 8) = 6x² - 6.

The integral to compute the volume of the solid can be expressed as:

V = ∫[from -1 to 1] 2π(6x² - 6) dx

V = 2π ∫[from -1 to 1] (6x² - 6) dx

Simplifying and evaluating the integral, we get:

V = 2π [2x³ - 6x] [from -1 to 1]

V = 2π [(2(1)³ - 6(1)) - (2(-1)³ - 6(-1))]

V = 2π [2 - 6 - (-2 + 6)]

V = 2π [8]

V = 16π

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Answer:

x = 3

y = -5

Step-by-step explanation:

       4x + y = 7 -------------------(I)

       5x - y = 20 -----------------(II)

Add both the equations. Now, y will be eliminated, and we can find the value of 'x'.

       (I)           4x + y = 7

      (II)           5x - y = 20       {Add the equations}

                    9x       = 27

Divide both sides by 9,

                            x = 27 ÷ 9

                            \(\boxed{\bf x = 3}\)

Now, Plugin the value of 'x' in equation (I)

          4*3 + y = 7

           12 +  y = 7

Subtract 12 from both sides,

                    y = 7 - 12

                    \(\boxed{\bf y = -5}\)

Answer:

Step-by-step explanation:

394 subscribers are represented in the venn diagram.

Venn diagrams are charts that are used to visually represent relationships between sets, operations on those relationships, and set relationships. The Venn diagram, which uses circles that are overlapped, intersected, and not intersected to depict the relationship between sets, was created by John Venn. A set diagram or a logic diagram is another name for a Venn diagram, which shows a variety of set operations such the intersection, union, and difference of sets.

Additionally, it can be used to set items. a depiction of each relationship between several sets. Any closed figure, such as a circle or a polygon (square, hexagon, etc.), can be used to represent a Venn diagram. However, each group is typically represented as a circle.

according to the venn diagram

196+41+21+52+84 = 394

There are 394 subscribers

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Answer:

issolat variable

subtract constant

individualize variable

divide by coeficient

answer

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

We have the inequality:

\(-5(r+3)<12-10r+3r\)

Step 1: Combining Like Terms:

\(-5(r+3)<12-7r\)

Step 2: Distribute Property (on the left):

\(-5r-15<12-7r\)

Step 3: Addition Property of Equality (Add 7r to both sides):

\(2r-15<12\)

Step 4: Addition Property of Equality (Add 15 to both sides):

\(2r<27\)

Step 5: Division Property of Equality (Divide both sides by 2):

\(r<27/2=13.5\)

And we're done!

The calculated period of the function is 12

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

The graph

By definition, the period of the function is calculated as

Period = Difference between cycles or the length of one complete cycle

Using the above as a guide, we have the following:

Period = 13 - 1

Evaluate

Period = 12

Hence, the period of the function is 12

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Answer:

y = x + 5

Step-by-step explanation:

We can take away the absolute value signs (as the equation does not differ with or without them).

To graph, one must remember slope-intercept form (y = mx + b)

M is the slope. When a clear "m" is not present, then one must assume that it is one, as the product of one and x is x.

B is where the y-axis intercepts the line (when x equals zero, y equals b). This is called the y-intercept. In this equation, b is five, so one point on the line is (0, 5). Then, following the slope (which is rise over run, or y over x), one must go up one, over one, up one, over one (up one unit, then to the right one unit (then mark your spot as a point)), then, draw a straight line connecting the two or more points. And there you have it!

Answer:

510 minutes.

Step-by-step explanation:

i hope this helped you! :)

510 MINUTES!! :)

Hope this helped!

By using a statistical calculator, the actual sample mean and sample standard deviation are:

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:

Mean = ∑x/(n - 1)

In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:

Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)

By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

x = 2.4

Step-by-step explanation:

4x + 5 / x + 7
combine like terms

X + 4x = 5x

5 + 7= 12

12/ 5x

Divide

12 /5= 2.4

X= 2.4

Answer:

Yes because 44% of people surveyed liked the new ingredient

Step-by-step explanation:

473/1075=.44

.44x100=44

therefore, 44% of people like the new ingredient

n⁵ + (n+1)⁵ + (n+2)⁵ + (n+3)⁵ + (n+4) is not divisible by 25.

Mathematical Induction is a technique of proving a statement, theorem or formula which is thought to be true, for each and every natural number n.

Given expression,

n⁵ + (n+1)⁵ + (n+2)⁵ + (n+3)⁵ + (n+4)

To prove: above expression is divisible by 25.

Putting n = 1 in the expression

1⁵ + (1+1)⁵ + (1+2)⁵ + (1+3)⁵ + (1+4)

= 1 + 2⁵ + 3⁵ + 4⁵ + 5

= 1 + 32 + 243 + 1024 + 5

= 1305

which is not divisible by 25.

Hence, 25 is not divisor of  n⁵ + (n+1)⁵ + (n+2)⁵ + (n+3)⁵ + (n+4)

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Answer:

r = 8  2/3

Step-by-step explanation:

3/5 (r-7)=1

3/5 * (r-7)=1

5/3 * 3/5 * (r-7)=1 * 5/3 ==> multiply both sides by 5/3 to remove the 3/5

                                        from the left side of the equation and isolate r

1 * (r-7) = 5/3

r - 7 = 5/3  ==> simplify

r = 7 + 5/3 ==> add 7 on both sides to isolate r

r = 7 + 3/3 + 2/3  ==> simplify

r = 7 + 1 + 2/3

r = 8 + 2/3

r = 8  2/3