State all integer values of in the interval - 1 <= x <= 5 that satisfy the following inequality: - 3x + 7 < 6

After answering the presented question, we can conclude that As a equation result, in 2011, the cost of a residence utilising 0 kWh of power would be zero dollars.

In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.

y = x/10 is the provided equation.

If a residence uses 0 kWh of power (x=0), the cost of electricity is as follows:

y = x/10 = 0/10 = $0 per kWh.

As a result, in 2011, the cost of a residence utilising 0 kWh of power would be zero dollars.

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The given conditions to write an equation for the line passing through (−9,2) and parallel to the line whose equation is y = −3x+ 2.

There are many different methods to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically include one or more variables.

More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

\($$We have the equation of a parallel line and a point which it passes through. To write the equation of the line in point-slope form, we will use the following formula:y−y1=m(x−x1)We know that the slope of parallel lines are same and we are given the equation for parallel line, y=−3x+2$$\)

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The probability that the employee is a member of the hourly staff, given that the employee is female is 0.2 or 1/5.

We need to calculate the conditional probability of an employee being a member of the hourly staff given that the employee is female and all the employees of a local university have been classified according to gender and job type.

The given table is:

Job Male Female

Faculty Member 55 5

Salaried Staff 15 25

Hourly Staff 30 20

The total number of female employees is 5+25+20 = 50.

We are to find the probability of an employee being a member of the hourly staff given that the employee is female.

Mathematically, we can represent the above statement as:

P(Hourly staff | Female) = P(Hourly staff and Female) / P(Female)

Now,P(Hourly staff and Female) = 20/100 * 50 = 10P(Female) = 50/100

Therefore,P(Hourly staff | Female) = P(Hourly staff and Female) / P(Female)= 10 / 50= 1/5 = 0.2

Therefore, the probability that the employee is a member of the hourly staff, given that the employee is female is 0.2 or 1/5.

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The interval of convergence for the given power series is (2, 8).

To find the interval of convergence for the given power series. We have the power series:

∑(n=2 to ∞) ((x-5)ⁿ)/(3ⁿ)

To find the interval of convergence, we'll use the Ratio Test. For the Ratio Test, we need to compute the limit:

L = lim (n → ∞) |(a_(n+1)/a_n)|

For our series, a_n = ((x-5)ⁿ)/(3ⁿ). Therefore, a_(n+1) = ((x-5)(n+1))/(3(n+1)). Now, let's compute the ratio:

|(a_(n+1)/a_n)| = |(((x-5)(n+1))/(3(n+1))) / (((x-5)ⁿ)/(3ⁿ))|

Simplify the expression:

|(a_(n+1)/a_n)| = |(x-5)/3|

The series converges if L < 1. So we have:

|(x-5)/3| < 1

Now, we'll solve for x to find the interval of convergence:

-1 < (x-5)/3 < 1

Multiply each term by 3:

-3 < x-5 < 3

Add 5 to each term:

2 < x < 8

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Answer the question 1st:

1-corresponding angles=180

then,90+90=180

2-not parallel

3-not parallel

4-corresponding angles=180

          x+x=180

          2x=180

          x=180/2

          x=90degree

5-suppose x for two angles

then, same as 4 no. x + x=180

6= alternate angles are always equal.

The interquartile range of the set of values given is: 11 - 4 =7

To find the interquartile range, you first begin by defining the lower half, the median, and the upper half. The median of the set of figures given is 8. Then the upper half begins at 11 while the lower half begins and ends at 4.

So, to define the interquartile range, we would subtract 7 from 11 to get 4. So, the interquartile range of the values in the dataset is 4.

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Complete Question:

A data set is made up of these values 3,4,5,8,9,11,12 Find the interquartile range

To obtain a point estimate for the population proportion of adults in the country age 18 and older who have donated blood in the past two years, we can use the formula; P-hat = Number of adults who have donated blood / Total number of adults surveyed Substituting the values we have.

P-hat = 419 / 2298= 0.182 (rounded to three decimal places) Therefore, the point estimate for the population proportion of adults in the country age 18 and older who have donated blood in the past two years is 0.182.B) The requirements for constructing a confidence interval about P are satisfied if; np ≥ 10 and nq ≥ 10where p and q are the sample proportions, and n is the sample size. Substituting the values from the question ;

np = 2298(0.182) = 418.836

nq = 2298(0.818)

= 1879.164 Since np ≥ 10 and nq ≥ 10, the requirements for constructing a confidence interval about P are satisfied.

It was a definite and specific offer that could be accepted by anyone who met the requirements. It is an example of a unilateral offer since it was an open offer, anyone who agreed to the terms of the contract could have accepted it. Furthermore, it was a clear and unambiguous offer since it did not require any more clarification. Shawna and Beatrice, by virtue of their status as the offerees, had the option of accepting or rejecting the offer. The acceptance must meet the requirements of a valid contract. The acceptance must be communicated clearly and immediately. In addition, the acceptance must conform to the offer's terms. In Hyde v Wrench (1840), the court held that an acceptance must be unconditional and absolute and that if the acceptance is not in line with the terms of the offer, it is a counteroffer that terminates the original offer. Since Shawna and Beatrice had not yet responded to the offer, there was no acceptance of the contract. Therefore, there was no legal agreement between the parties as a contract must have both an offer and an acceptance in order to be considered valid.

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The solution to the system of equations using the elimination method is option (a) (2,0).

To solve the system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate the variable "y" by multiplying the second equation by 2 and adding it to the first equation.

Multiplying the second equation by 2, we get:

4x - 20y = 8

Adding the modified second equation to the first equation, we have:

7x + 20y + 4x - 20y = 14 + 8
11x = 22
x = 2

Substituting the value of x into one of the original equations, let's use the second equation:

2(2) - 10y = 4
4 - 10y = 4
-10y = 0
y = 0

Therefore, the solution to the system of equations is x = 2 and y = 0, which corresponds to option (a) (2,0).

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Answer:

Step-by-step explanation:

b-78

Answer: 95/3 gallon of paint

Step-by-step explanation:

I guess you mean each requires 5/3 gallon of paint

If so, we take 5/3 times 19 = 95/3 gallon of paint

95/3 = 31 2/3

Answer:

4 miles

Step-by-step explanation:

In 7 minutes he runs 1 mile

So in 28 minutes he runs 4 miles

How did I get this answer?

7×4=28

So 1×4=4

In ratios, when you times anything by something, you must do the same to the other part of the ratio.

Answer:

Hello there! The answer to this problem is that Bobby can run 4 miles in 28 minutes. If Bobby runs 1 mile in 7 minutes, we will have a table with two columns. On the left, we will have the number of miles, and on the right we will have the number of minutes.

miles - minutes

1 - 7

2 - 14

3 - 21

4 - 28

As the number of miles increases by 1, the number of minutes increases by 7. This is a ratio of 1:7. If it takes Bobby 7 minutes to run a mile, it makes sense that it will take him 28 minutes to run 4 miles because 28/7 = 4.

Hope this helps! Have a great day - Mani :)

Answer:

r=d/t

Step-by-step explanation:

just divide by t to isolate r

Answer:

d/t = r

Step-by-step explanation:

Step 1: Write formula

d = rt

Step 2: Divide both sides by t

d/t = r

To find the value of y'' at the point where x=0, we need to take the second derivative of y with respect to x. First, let's find the first derivative of y: xy = e^y .

Differentiating both sides with respect to x: y + xy' = e^y * y', Simplifying: y' (1 - e^y) = -y, y' = -y / (1 - e^y)
Now, let's find the second derivative of y:
Using the quotient rule,
y'' = [(1 - e^y) (-y') - (-y)(e^y * y')] / (1 - e^y)^2

Substituting y' = -y / (1 - e^y)
y'' = [(1 - e^y) (-(-y / (1 - e^y))) - (-y)(e^y * (-y / (1 - e^y)))] / (1 - e^y)^2
y'' = [(y / (1 - e^y)) + (y * e^y) / (1 - e^y))] / (1 - e^y)^2
y'' = [y + y * e^y] / (1 - e^y)^3

Now we can find the value of y'' at x=0:
Since xy = e^y, when x=0,
0y = e^y, This is only true when y=-infinity, so the point where x=0 is not defined, Therefore, we cannot find the value of y'' at the point where x=0.

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Using the concept of probability, the probability of rolling 2 sixes would be 1/25

From the tree diagram given :

The probability of rolling 2 sixes can be defined thus :

Hence,

P(2 6's) = 1/5 × 1/5 = 1/25

Hence, the probability of rolling 2 sixes is 1/25.

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The price of an adult ticket is $10 and the price of a student ticket is $9.

An equation is a mathematical statement that shows that two expressions are equal. It usually contains variables, constants, and mathematical operations. The equal sign (=) is used to indicate that the expressions on both sides of the equation are equal.

Let "a" be the price of an adult ticket and "s" be the price of a student ticket. We can set up two equations based on the given information:

Equation 1: \(10a + 2s = 118\) (from the first day of ticket sales)

Equation 2: \(6a + 12s = 168\)(from the second day of ticket sales)

We can use the elimination method to solve for one of the variables. Let's multiply Equation 1 by -6 and add it to Equation 2:

\(-60a - 12s = -708\) (multiplying Equation 1 by -6)

\(6a + 12s = 168\)(Equation 2)

\(-54a = -540\)

Dividing both sides by -54 gives us:

a = 10

Now we can substitute a = 10 into either Equation 1 or Equation 2 to solve for s. Let's use Equation 1:

\(10a + 2s = 118\\10(10) + 2s = 118\\100 + 2s = 118\\2s = 18s = 9\)

Therefore, the price of an adult ticket is $10 and the price of a student ticket is $9.

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Answer:

12

Step-by-step explanation:

15/10=1.5

8 times 1.5=12

Answer:

x = 60°

Step-by-step explanation:

Angles FGD and CGE are veritical angles and therefore congruent.

And because ∠CGE + ∠EGB = 90°  we can substitute the values and solve

30 + x = 90               x = 60°

-30        -30        

Answer:  \(f^{-1}(\text{x}) = (\text{x}-9)^2+4\) when \(\text{x} \ge 9\)

=================================================

Work Shown:

\(f(\text{x}) = 9 + \sqrt{\text{x} - 4}\\\\\text{y} = 9 + \sqrt{\text{x} - 4}\\\\\text{x} = 9 + \sqrt{\text{y} - 4}\\\\\text{x}-9 = \sqrt{\text{y} - 4}\\\\(\text{x}-9)^2 = (\sqrt{\text{y} - 4})^2\\\\(\text{x}-9)^2 = \text{y}-4\\\\(\text{x}-9)^2+4 = \text{y}\\\\f^{-1}(x) = (\text{x} - 9)^2+4\)

Explanation:

I replaced f(x) with y. After that I swapped x and y, then solved for y to get the inverse.

The smallest that \(\sqrt{\text{x}-4}\) can get is 0, which means the smallest f(x) can get is 9+0 = 9. The range for f(x) is \(\text{y} \ge 9\)

Since x and y swap to determine the inverse, the domain and range swap roles. Therefore, the domain of the inverse \(f^{-1}(\text{x})\) is \(\text{x} \ge 9\)

So we will only consider the right half portion of the parabola.

The graph is below. The red curve mirrors over the black dashed line to get the blue curve, and vice versa.

Answer:

\(f^-^1(x)=(x-9)^2+4\)   OR \(x^2-18x+85\) if you simplify it

Step-by-step explanation:

to find the inverse function you have to switch x and y with each other and solve for y.

\(y=9+\sqrt{x-4}\\x=9+\sqrt{y-4}\)           step 1: switch x and y with each other

\(x-9=\sqrt{y-4}\)           step 2: subtract 9 from both sides

\((x-9)^2=\sqrt{y-4}^2\)     step 3: square both sides to get rid of the square root

\((x-9)^2=y-4\\(x-9)^2+4=y\\\)         step 4: add 4 to both sides

you could leave the answer like this or you can simplify to get \(x^2-18x+85\)

a) 49 square tiles are needed to make pattern number 7.

b) 84 circular tiles are needed to make pattern number 20.

c) When the pattern number is odd, the total number of tiles (square

and circular) needed to make the pattern will always be odd.

What is a number pattern?

A pattern or sequence in a series of numbers is called a number pattern. Generally speaking, this pattern builds a connection between all integers.

a) The pattern shown for square tiles is as follows -

Pattern 1 - 1 square tile = (1)^2

Pattern 2 - 4 square tiles = (2)^2

Pattern 3 - 9 square tiles = (3)^2

Similarly, for pattern 7, the number of tiles needed is -

Pattern 7 - (7)^2 = 49 square tiles

Therefore, the number of square tiles needed is 49.

b) The pattern shown for circular tiles is as follows -

Pattern 1 - 8 circular tiles = 2(4)

Pattern 2 - 12 square tiles = 3(4)

Pattern 3 - 16 square tiles = 4(4)

Similarly, for pattern 20, the number of tiles needed is -

Pattern 20 - 21(4) = 84 circular tiles

Therefore, the number of circular tiles needed is 80.

c) In Pattern 1 the total number of square and circular tiles is -

Total tiles = Square tiles + Circular tiles

1 +  8 = 9 tiles

In Pattern 3 the total number of square and circular tiles is -

Total tiles = Square tiles + Circular tiles

9 +  16 = 25 tiles

So, the pattern number matches the Total number of tiles (square and circular) used to make the pattern.

Therefore, the total number of tiles will always be odd.

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Answer:

\( \sin( \alpha ) = \frac{8}{14} = \frac{4}{7} \\ \\ \alpha = 34.84 \: degee\)

Answer:

The answer is A.

Answer:

b + c = 7

8 b + 15 c = 70

Or A

Step-by-step explanation:

And I have proof for those with trust issues ;'D

The total cost of the hire purchase for the bicycle is  $19,145.

The difference between the hire purchase price and the cost price for the bicycle is  $2,825.50

The difference as a percentage of cash price 17.31%.

The total cost of the hire purchase is the sum of the deposit and the total monthly instalment.

Total cost of the hire purchase = amount deposited + total instalment paid

Total instalment paid = number of month x payment per month

$1224.50 x 10 = $12,245

Total cost of the hire purchase = $6,900 +  $12,245 = $19,145

The difference = cost of hire purchase + cash price

$19,145 - $16 319.50 = $2,825.50

The difference as a percentage of cash price = (2,825.50 / $16,319.50) x 100 = 17.31%

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The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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Answer:

Step-by-step explanation:

a^6(a + b^6)

Answer:

I am not sure but i will say C.

Step-by-step explanation:

Answer:

The real question is why do the people in math problems have an unnecessary amount of objects? also the answer is capricorn

Step-by-step explanation:

Answer:

110000=p(1+0.019)^168

23.62p=110000

p=4660

credit: sqdancefan

Answer:

84330

Step-by-step explanation:

The compound interest formula gives the value of an investment.

 A = P(1 +r/n)^(nt)

where principal P is invested at annual rate r compounded n times per year for t years. Using your given values, we can solve for P.

 110,000 = P(1 +0.019/12)^(12·14)

 P = 110,000/(1 +0.019/12)^(12·14) ≈ 110,000/1.00158333...^168

 P ≈ 110,000/1.30446

 P ≈ 84326.04 ≈ 84,330 . . . . dollars

The degrees of freedom for a data table can be calculated using the formula:

Degrees of Freedom = (Number of Rows - 1) * (Number of Columns - 1)

In this case, the data table has 10 rows and 11 columns. Plugging these values into the formula:

Degrees of Freedom = (10 - 1) * (11 - 1) = 9 * 10 = 90

Therefore, the degrees of freedom for the given data table is 90.

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Answer:

I think -3x-17 sorry if wrong

Step-by-step explanation:

8x+ 32= 5x+15

-3x-17

Answer:

\(8(x + 4) = 5(x + 3) \\ 8x + 32 = 5x + 15 \\ 32 - 15 = 8x - 5x \\ \)

-3x-17

The measure of the angle is 39°.

Complementary angles are angles whose sum is equivalent to 90°. On the other hand, supplementary angles are angles whose sum is equivalent to 180°.

Let x be the measure of the angle.

90° - x = complement angle of x

180° - x = supplement angle of x

If the measure of its supplement is 39 more than twice the measure of its complement, then

180° - x = 39 + 2(90° - x)

Simplify and solve for x.

180° - x = 39 + 2(90° - x)

180° - x = 39 + 180° - 2x

x = 39°

Hence, the measure of the angle is 39°.

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