2. If x represents a positive integer, find the solutions to the following inequalities. a. x − 15 < 20 b. x + 3 ≤ 15 c. −x > 2 d. x3 < 2 e. 3 − x4>2

Step-by-step explanation:

Greetings !

The arithmetic mean (average) is the sum of the values in the set divided by the number of elements in that set.

If our data set contains the values a₁,.....,an

(n elements) then the mean=

\( \frac{1}{n} summation \frac{n}{i} = 1ai\)

Hope it helps!

Answer:

f(y + 2) = 5y - 10

Step-by-step explanation:

To evaluate f(y + 2), substitute x = y + 2 into f(x), that is

f(y + 2) = 5(y + 2) - 20

           = 5y + 10 - 20

           = 5y - 10

The median daily electricity use is 1 kW-hr than the average (arithmetic mean) daily electricity use.

The median is the middle value of a set of data when the data is arranged in order. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

The data in ascending order is : 19 24 27 29 31

The median of the data is 27.

The mean, or average, is calculated by summing all the values in a set of data and dividing by the total number of observations.

Average of the data is

= ( 19 + 24 + 27 + 29 + 31)/ 5

= 26

The difference is therefore

= 27 - 26

= 1

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Answer:

Step-by-step explanation:

His functions are:

h(x)= $350

s(x)=(1.04))^x-1

To find total amount of money in Tommy's account using the functions above, we substitute the first function x= $350 in the second function

So, we can say that the new function represents the interest received by

Tommy with initial saving $350.

A function is a group of statements that together perform a task.

Given that Tommy got $350 as the gift which he saves.

So, the amount saved is given by the function is \(h(x)=350....(1)\)

Also, the interest by the saving bank account is given by,

\(s(x)=(1.04)^{x-1}....(2)\)

Comparing equations (1) and (2)  we get a new function as,

\(g(x)=350(1.04)^{x-1}\)

The function gives the value \(h(x)=350\) when \(x=0\) and the amount is increasing by the interest.

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The expression is 2 - m/4 + 10, when m = 12, the value is 9. Then the correct option is C.

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

Two less than the quotient of a number and four, increased by ten.

That can be written as in the form of m will be

\(\rm 2 - \dfrac{m}{4} + 10\)

If the value of m is 12, then we have

\(\rm 2 - \dfrac{m}{4} + 10\\\\\rm 2 - \dfrac{12}{4} + 10\\\\2- 3 + 10\\\\12 - 3 \\\\9\)

Thus, the expression is 2 - m/4 + 10, when m = 12, the value is 9. Then the correct option is C.

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Answer:

D

Step-by-step explanation:

The correct equation is n + 2.2 = 5 and the value of n is 2.8.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The sum of two and two tenths and a number is five.

Let the number be n.

Sum means the result of adding two numbers.

Two tenths means 2/10.

The sum of two and two tenths and a number means 2 + (2/10) + n.

So we have,

2 + (2/10) + n = 5

(2 + 2/10) + n = 5

[(2 × 10 + 2) / 10] + n = 5

22/10 + n = 5

2.2 + n = 5

n + 2.2 = 5, which is the required equation.

Solving,

n = 5 - 2.2

n = 2.8

Check the value of n = 2.8 in the equation.

n + 2.2 = 2.8 + 2.2 = 5

Hence the equation is n + 2.2 = 5 and the value of n is 2.8.

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Answer:

0.0285714286

Step-by-step explanation:

1÷35=0.0285714286

0.0285714286×35=1.000000001

The Y-intercept, b₀ = 14, implies that when the value of X is 0, the mean value of Y is 14.

The equation of a straight line can be represented by the equation y=mx+c where m is the slope of the line and c is the y-intercept. y is the dependent variable and x is the independent variable.

The given equation is:

\(Y_i = 14 - 0.2X_i\)

Y-intercept is the value of y when x=0. The y-intercept is 14.

Therefore, option d: The Y-intercept,  b₀ = 14, implies that when the value of X is 0, the mean value of Y is 14 is the correct answer.

Option a: The Y-intercept, b₀ = -0.2, implies that when the value of X is 0, the mean value of Y is -0.2 is wrong because the slope cannot be negative.

Option b: The Y-intercept, b₀ = 14, implies that the average value of Y is 14 is wrong because the y-intercept does not indicate the average value of y. It only represents the value of y when x=0.

Option c: The Y-intercept, b₀ = 14, implies that for each increase of 1 unit in X, the value of Y is expected to increase by 14 units is wrong because the slope is negative (-0.2) and the value of y decreases as the value of x increases.

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Using multiplication we know that Nicole needs to buy a total of 18 cups for 8 people.

In mathematics, multiplying the numbers is used to find the product of two or more numbers.

We carry out one of the basic mathematical operations on a regular basis.

Similar to addition, multiplication is commutative, which means that the product (the solution) is unaffected by the parts' order.

In other words, multiplying two numbers in any sequence will get the same result.

As an illustration, multiplying 8 by 2 will have the same result as multiplying 2 by 8.

So, using multiplication calculate as follows:

= 2 1/4 * 8

= 8+1/4 * 8

= 9/4 * 8

= 9/1 * 2

= 9 * 2

= 18

Therefore, using multiplication we know that Nicole needs to buy a total of 18 cups for 8 people.

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The range of acceptable values for the golf ball diameter is from 42.668 mm to 42.672 mm.

To determine the range of acceptable values for the golf ball diameter, we need to consider the maximum allowable discrepancy from the standard diameter. Given that the standard diameter is 42.67 mm and the inspector decides to stop production if the discrepancy is more than 0.002 mm, we can calculate the range of acceptable values as follows: Upper limit: Standard diameter + Maximum allowable discrepancy. Upper limit = 42.67 mm + 0.002 mm = 42.672 mm. Lower limit: Standard diameter - Maximum allowable discrepancy. Lower limit = 42.67 mm - 0.002 mm = 42.668 mm. Therefore, the range of acceptable values for the golf ball diameter is from 42.668 mm to 42.672 mm.

Any diameter measurement within this range will be considered acceptable, while measurements outside this range would indicate a discrepancy and result in the inspector stopping production.

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Answer:

X=-5

y=5

Step-by-step explanation:

Answer:

The answer is A

-1/2

Step-by-step explanation:

y=sin330

270≤x≥360

cosine=posite

sin=negative

tan=negative

y=sin330°= -1/2

y= -1/2

Note that this prompt deals with unit rate conversion. Thus,

10) Where Speed skiing takes place on a course that is 2/3 mile long. The speed skiing course is 3,520 feet

11) the pumpkin weighed 1000 pounds.

12 Note that in yards, the boat is 13 yards long approximately.

13) Note that the amount of blood in quarts is 17.5 yarts.

14) the Go-Kart's speed was  11.5 miles/h.

Unit rate conversion is the process of converting a quantity from one unit to another.

It involves finding the ratio between the two units, and multiplying or dividing by the appropriate conversion factor to convert the quantity to the desired unit.

9)

There are different ways to approach the problem, but one possible method is:

Recall that 1 mile is equal to 5,280 feet (this is a commonly used conversion factor).

Multiply both sides of this equality by 1/2 (since the course is half a mile long, or 0.5 miles).

The result is:

1/2 mile = 1/2 * 5,280 feet

= 2,640 feet

Therefore, the speed skiing course is 2,640 feet long.

10)
We can start by using the fact that 1 mile is equal to 5,280 feet:

1 mile = 5,280 feet

To convert 2/3 mile to feet, we can multiply both sides of the equation by 2/3:

2/3 mile = 2/3 × 5,280 feet

2/3 mile = 3,520 feet

Therefore, the speed skiing course is 3,520 feet long.

11)
One ton is equal to 2000 pounds. Therefore, half a ton is equal to:

0.5 ton * 2000 pounds/ton = 1000 pounds

So the pumpkin weighed 1000 pounds.


12) There are 3 feet in 1 yard. To find the length of the boat in yards, we can divide 40 by 3:

40 feet ÷ 3 feet/yard = 13.33 yards

To the nearest yard, the boat is about 13 yards long.

13)

There are 2 pints in a quart, so to convert pints to quarts, we need to divide by 2.

35 pints / 2 = 17.5 quarts

Therefore, 35 pints of blood is equivalent to 17.5 quarts of blood.

14)

There are 5,280 feet in a mile. To convert from feet per hour to miles per hour, we need to divide the number of feet per hour by the number of feet per mile.

60,720 feet per hour / 5,280 feet per mile = 11.5 miles per hour (rounded to one decimal place)

Therefore, the go-kart's top speed is 11.5 miles per hour.

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Answer:

2552cm^2

Step-by-step explanation:

C.S.A=1320cm^2 ;r=?

h=15cm.

[C.S.A. = 2πrh]

(r=1320×7/660=14cm)

Now,

TSA of cylinder = 2πr (h + r) sq

TSA=2×22/7(15+14)=2552cm^2

Answer:

find the radius of the base

find the area of the base

find the height of the cone

divide by three at the end

Step-by-step explanation:

this is from the formulae of volume of the cone

1/3πr2h

Answer: there's no orange fish

Answer:

1+1=2

2+2=4

4+4=8

8+8=16

16+16=32

32+32=64

64+64=128

Step-by-step explanation:

Answer:

This equation is one of the most complicated I have EVER seen....

Step-by-step explanation:

Jk, your answer should be 2.

Have a nice day! ♥

( and buddy... Use a calculator) XD

Answer:

6 Terms

Step-by-step explanation:

Terms- Each of the quantities in a ratio, series, or mathematical expression.

14x

-14y

7

-x

z

2x

There are 6 terms in this expression.

Answer:

3 like terms

Step-by-step explanation:

X, Y, and Z

Answer:

D.  40%

Step-by-step explanation:

The are 6 apples out of 15 fruit. To find the percentage, first write it as a fraction.

Answer: 38

Step-by-step explanation:

Subtract 1/8 from 1/2

12 - 18 is 38.

Steps for subtracting fractions

Find the least common denominator or LCM of the two denominators:

LCM of 2 and 8 is 8

Next, find the equivalent fraction of both fractional numbers with denominator 8

For the 1st fraction, since 2 × 4 = 8,

12 = 1 × 42 × 4 = 48

Likewise, for the 2nd fraction, since 8 × 1 = 8,

18 = 1 × 18 × 1 = 18

Subtract the two like fractions:

48 - 18 = 4 - 18 = 38

Answer:

-36,36

Step-by-step explanation:

3x - 6(5x + 3) = 9x + 6

 Distribute:

3x - 30x - 18 = 9x + 6

Combine like terms:

-27x - 18 = 9x + 6

There are two possible ways to isolate x

On the left

Subtract 9x from each side

-27x - 18 -9x = 9x-9x + 6

-36x -18 = 6

On the right

Add 27x from each side

-27x - 18 +27x = 9x+27x + 6

-18 =36x+ 6

The equation of the tangent line to the curve `y = 2ex cos(x)` at the point (0,2) is given by `y = 2ex + 2`.

To find an equation of the tangent line to the curve at the given point (0,2) whose equation is given by `y = 2ex cos(x)`, we need to determine the derivative `y'` of `y = 2ex cos(x)` first. Using the product rule, we have;

`y = 2ex cos(x)`...let `u = 2ex` and `v = cos(x)`, then `u' = 2ex` and `v' = -sin(x)`.`y' = u'v + uv'` `= 2ex cos(x) - 2ex sin(x)` `= 2ex(cos(x) - sin(x))`

Therefore, the derivative of `y = 2ex cos(x)` is `y' = 2ex(cos(x) - sin(x))`.

The equation of the tangent line to the curve at the point (0,2) is obtained by using the point-slope formula, which is given by: `y - y1 = m(x - x1)`where `(x1,y1)` is the point of tangency, `m` is the slope of the tangent line.

Substituting the values of `m`, `x1` and `y1`, we obtain: `m = y' |(0,2)` `= 2e(1 - 0)` `= 2e`Using the point-slope formula with `(x1,y1) = (0,2)` and `m = 2e`, we have: `y - 2 = 2e(x - 0)` `y - 2 = 2ex` `y = 2ex + 2`

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Answer:

Its 67.9 but technically its 67.912 *hope this helps

Step-by-step explanation:

Right scalene triangle.

Sides: a = 66   b = 16   c = 67.912

Area: T = 528

Perimeter: p = 149.912

Semiperimeter: s = 74.956

Angle ∠ A = α = 76.373° = 76°22'23″ = 1.333 rad

Angle ∠ B = β = 13.627° = 13°37'37″ = 0.238 rad

Angle ∠ C = γ = 90° = 1.571 rad

Height: ha = 16

Height: hb = 66

Height: hc = 15.55

Median: ma = 36.674

Median: mb = 66.483

Median: mc = 33.956

Inradius: r = 7.044

Circumradius: R = 33.956

Vertex coordinates: A[67.912; 0] B[0; 0] C[64.142; 15.55]

Centroid: CG[44.018; 5.183]

Coordinates of the circumscribed circle: U[33.956; 0]

Coordinates of the inscribed circle: I[58.956; 7.044]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 103.627° = 103°37'37″ = 1.333 rad

∠ B' = β' = 166.373° = 166°22'23″ = 0.238 rad

∠ C' = γ' = 90° = 1.571 rad

Answer:

Rise/Run = y/x

Step-by-step explanation:

On a number line the X-axis is on the bottom, and the Y-axis is on the Top.

The difference in volume between the two pyramids is 12,371,740 cubic feet.

To find the volume of a square pyramid, you use the formula :

V = (1/3)Bh, where B is the area of the base and h is the height.

Using the dimensions given in the table, we can calculate the volumes of the two pyramids:

- Volume of Bent Pyramid = (1/3)(619 feet * 619 feet)(332 feet) = 26,384,053.33 cubic feet
- Volume of Red Pyramid = (1/3)(722 feet * 722 feet)(341 feet) = 38,755,793.33 cubic feet

To find the difference in volume between the two pyramids, we subtract the smaller volume from the larger volume:

38,755,793.33 - 26,384,053.33 = 12,371,740 cubic feet.

Rounding to the nearest cubic foot, the difference in volume between the two pyramids is 12,371,740 cubic feet.

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You dilate a line segment around a point by following a simple procedure mentioned below that begins with identifying the center of a line segment.

Dilating a line segment around a point is a simple process. First, you need to identify the center of the line segment.

Then, use a ruler or other measuring device to measure the distance from the center of the line segment to each end point.

To dilate the line segment, multiply the measured distance by the desired scale factor. Finally, draw a new line segment connecting the two new end points.

This will give you the dilated line segment around the point you identified at the beginning.

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Yes, f(x)=-5.3x+256 is a function.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

We have the expression,

f(x)=-5.3x+256.

Suppose, the given expression is relation.

To prove that the given relation is a function:

Choose the input values.

We have chosen 1,2,0,-1,-2.

Determine the results.

The results are shown in the table.

Consider the connection to be a function if each input value results in just one output value.

In the table and graph, each input value results in just one output value.

Do not identify the relationship as a function if any input value results in two or more outputs.

Therefore,  f(x)=-5.3x+256 is a function.

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