For which points is the y-coordinate greater than -3

Answer:

At age 82.5 the person that started taking benefits at age 70 would have more in total benefits.

Step-by-step explanation:

2000 x 12 = 24,000  This is how much you would make for one year.

If you took that for the years 66, 67, 68 ,69, the total would be

24000 x 4 = 96000

The equation for how much money you would make starting at age 70 would be

y = 2000x + 96000

The equation if you stated taking money at 70 would be

y = 2640x

If we set these equations equal to each other we found find at what month the incomes would be equal.

2000x + 96000 = 2640x  Subtract 2000x from those sides

96000 = 640x  Divide both sides by 640

x = 150

150 months after 70 the amounts would be equal.  this would be 12.5 years.

70 + 12.5 = 82.5

Answer:

82 years and 7 months.

(They will have the same total at 82.5 years)

Step-by-step explanation:

Define the variables:

Given that $2,000 monthly social security benefit is paid at a full retirement age of 66, the amount paid from the age of 66 until the age of 70 is:

\(\implies \$2,000 \times 12 \times 4 = \$96,000\)

Therefore, from the age of 70, the equation for the total pay of a person who retired at the age of 66 is:

And from the age of 70, the equation for the total pay of a person who retired at the age of 70 is:

To find the age at which the person who started taking benefits at age 70 will have more in total than if they had started taking benefits at age 66, set the equation for the person who started taking benefits at age 70 more than the equation for the person who started taking benefits at age 66 and solve for x:

\(\implies 2640x > 2000x+96000\)

\(\implies 640x > 96000\)

\(\implies x > 150\)

150 months equals 12.5 years.

70 years + 12.5 years = 82.5 years

Therefore, at the age of 82.5 years, the person who started taking benefits at the age of 70 will have the same in total benefits paid as the person who started taking benefits at the age of 65.

Therefore, the age at which the person who started taking benefits at the age of 70 will have more in total benefits paid than if they had started taking benefits at age 66 is after 82.5 years.  So 82 years and 7 months.

Answer:

0

Step-by-step explanation: 2x+8=2x+6 --> 8=6

8 cant be equal to 6 so this equation is wrong and has no solution.

option A and D

We need to check the options:

Answer:

650

Step-by-step explanation:

195

_. of 30

100

and these 30 zero cut and 100 zero also cut and 3 * 195= 65 and 65 x 10 =650

Answer:

Find below the answer :)

Step-by-step explanation:

1. Move the constant to the left.

2. Eliminate the opposites.

x-intercept = 0

y-intercept = 0

domain = (-∞, 6)

Range = (8, +∞)

Here, we want to graph the given piecewise equation

From the question, we have two equations

There is a quadratic equation and a linear equation

For values of x less than 2, we make use of the quadratic equation

For vaules between 2 and 6, we make use of values between 2 and 6

Now, when we talk of the x-intercept, we simply mean the positions on the graph on which y = 0

From the range we have, the value of x at which y is 0 is the point where x = 0 which corresponds to the origin

For the y-intercept, we can only have the value of f(x) as 0 when x is 10

For the quadratic equation, the y-intercept is at x = 0, so 0 is the y-intercept

The domain refers to the values on the x-axis

The domain in this case is (-∞, 6)

The range refers to the value on the y-axis

In this case, that will be (8, ∞)

8 is obtained by substituting the value of x = 2 into the equation

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:63M N 56

Step-by-step explanation:

To begin, let's find how much the book is including tax and the student discount.  Once we find this, we can see if Lara or Alex is correct and if they can afford it.

First, we want to compute the student discount. The student discount is 35%. Thus, we can do 0.65 x 28.50 = 18.525. With 10% tax, we have 18.525 x 1.1 = 20.3775. Which will round up to $20.38.

Now, lets see what Alex did and if he got the same answer. First he takes 35% of $28.50 and subtracts it from the normal price.

.35 x 28.50 = 9.975

28.50 - 9.975 = 18.525

Then he takes 10% of this number and adds it back.

.10 x 18.525 = 1.8525

18.525 + 1.8525 = 20.3775

Alex has the correct answer.

Next, we will see if Lara computed it correctly.

First she takes 65% of the normal price.

0.65 x 28.50 = 18.525

Then she computes 110% of the reduced price.

18.525 x 1.10 = 20.3775

Lara also gets the correct answer.

So, do they have enough money to purchase the book?

YES:

$20.38 < $21

Is Alex correct?

YES

Is Lara correct?

YES

Although they used different methods to get the answer, they both got the right one!

Answer:

The correct answer is: u = 10,500. When the value of the alternative hypothesis is greater than that of the null hypothesis, the power of the test will be increased, so a value of u = 10,500 would yield the greatest power to reject the null hypothesis.

The absolute minimum of the function is f ( -10 ) = -1

Given data ,

Let the function be represented as f ( x )

Now , the function f ( x ) is plotted on the graph

where the minimum of a function is the smallest value that the function takes on over its entire domain.

It is the point on the graph of the function that is the lowest possible point

So , the function has the minimum value of - 1 at the point x = -10

Hence , the minimum of function is f ( -10 ) = -1

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Answer:

The answer is : x > 2

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:

c) 33%

Step-by-step explanation:

In a  standard deck of cards, there are 52 cards total and of those 52, there are 12 face cards. One-third of those face cards are queens, (because there are 4 queens in a deck of cards, and \(\frac{4}{12}=\frac{1}{3}\)). Therefore, there is a 33% chance that the card Luke holds is a queen.

Answer:

33%

Step-by-step explanation:

Got it right on the test.

Answer:

c

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

sin(α + β) = sin α cos β + sin β cos α

sin(α - β) = sin α cos β - sin β cos α

\(\frac{1}{2}\)[ sin(α + β) + sin(α - β)] = \(\frac{1}{2}\)[sin α cos β + sin β cos α + sin α cos β - sin β cos α]

                               = \(\frac{1}{2}\)[2 sinα cos β]

                               = sin α cos β = \(\frac{1}{2}\)[ sin(α + β) + sin(α - β)]

The speed limit for the highway in rounded to the nearest whole is 33 mi/h.

The speed is the ratio of the distance in a given time interval. The distance is represented by a unit of length and the time is represented by a unit of time.

There are different units for the length or distance. In the International System Units (SI), the standard unit of distance is the meter (m) and the standard unit of time is the second (s). Nonetheless, there are others units, for example: inches (in), miles (mi) and  yards (yd).

For solving this exercise, you need to know the relation between the given units for distance and time.

The question gives - 100 km/h. The kilometer (km) is a multiple of the  standard unit of distance -  the meter (m) and the hour is a submultiple of the  standard unit of time  - the second (s)

For solving this question, it is necessary that you know the relation between km/h and mi/h. See  below.

\(\text{1 km/h}= 0.6213712 \ \text{mi/h}\)

Now you can solve the question from a math tool - Rule of three. Thus,

\(\text{1 km/h}= 0.6213712 \ \text{mi/h}\)

\(100 \ \text{km/h}= \text{x mi/h}\)

\(\text{x}= 100 \times 0.6\)

\(\text{x}=33 \ \text{mi/h}\)

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After answering the presented question, we can conclude that This is equation true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3): a = 30.8/(11n+3)

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

We are given that the factored form of 30.8n+8.4 is a(11n+3).

To find the value of a, we can expand the product a(11n+3) and equate it to the given expression 30.8n+8.4.

Expanding a(11n+3), we get:

a(11n+3) = 11an + 3a

Equating this to 30.8n+8.4, we have:

11an + 3a = 30.8n + 8.4

We can factor out an "a" from the left-hand side:

a(11n + 3) = 30.8n + 8.4

Now we can see that this is the same as the given factored form, so we can equate the two expressions:

a(11n + 3) = a(11n + 3)

This is true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3):

a = 30.8/(11n+3)

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\(\boxed{\sf I=\dfrac{PRT}{100}}\)

\(\\ \sf\longmapsto I=\dfrac{2000(12)(2.5)}{100}\)

\(\\ \sf\longmapsto I=\dfrac{24000(2.5)}{100}\)

\(\\ \sf\longmapsto I=\dfrac{60000}{100}\)

\(\\ \sf\longmapsto I=600\)

\( \large\begin{gathered} {\underline{\boxed{ \rm {\red{S.I \: = \: \frac{P × R × T}{100} }}}}}\end{gathered} \)

As we know that , first we need to convert 2 years 6 months into years.

\( \sf \ \implies \: 1 \: \: year \: = \: 12 \: \: months\)

\( \sf \implies \: 2 \: \: years \: \: and \: \: 6 \: \: months \: = \: 30 \: \:months\)

\( \sf \implies \: \:\frac{ \cancel{30} \: \: ^{2.5 \: \: years} }{ \cancel{12 \: }} \\ \)

\(\bf{\blue{ Time \: = \: 2.5 \: \: years}}\)

\(\Large\rm{\orange{ \begin{cases} \large\begin{gathered} {\underline{\boxed{ \rm {\purple{S.I \: = \: \frac{P × R × T}{100} }}}}}\end{gathered} \end{cases}}}\)

\( \tt \large \longrightarrow \: \: S.I \: = \: \frac{2000 \: × \: 12 × \: 2.5}{100} \\ \)

\( \tt \large \longrightarrow \: \: S.I \: = \frac{60000}{100} \\ \)

\(\tt \large \longrightarrow \: \: S.I \: = \frac{600 \cancel0 \cancel0}{1 \cancel0 \cancel0} \\ \)

\(\tt \large \longrightarrow \: \: S.I \: = \: 600\)

\(\large \underbrace{\textrm {{{\color{navy}{Simple Interest \: = \: 600}}}}}\)

Answer:

I

Step-by-step explanation:

9514 1404 393

Answer:

  a)  CD = 5.7

  b)  ED = 3.05

Step-by-step explanation:

Triangle ABE is similar to triangle ACD by AA similarity. This means we can write the proportions ...

a) CD/BE = AC/AB

  CD = BE(AC/AB) = 3.8(12.3/8.2)

  CD = 5.7

__

b) ED/AD = BC/AC

  ED = AD((AC -AB)/AC) = 9.15(12.3 -8.2)/12.3

  ED = 3.05

Answer:

Step-by-step explanation:

Answer:

a = b = 3√2

Step-by-step explanation:

Use trigonometry:

\( \sin(45°) = \frac{a}{6} \)

Cross-multiply to find a:

\(a = 6 \times \sin(45°) = 6 \times \frac{ \sqrt{2} }{2} = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2} \)

Use the Pythagorean theorem to find b:

\( {b}^{2} = {6}^{2} - {a}^{2} \)

\( {b}^{2} = {6}^{2} - ( {3 \sqrt{2}) }^{2} = 36 - 9 \times 2 = 36 - 18 = 18\)

\(b > 0\)

\(b = \sqrt{18} = 3 \sqrt{2} \)

There was 4 dollar of discount on the total amount.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that Adrian bought a jacket that costs 11 dollars and a scarf that costs 15 dollars.

At the counter, he received a discount. If he only paid 22 dollars total, then

Total cost 11 + 15 = 26

But 26 - 22 = 4

Therefore, the discount was 4 dollar.

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The critical value is 9.925, rounded to three decimal places.

To calculate the critical value for a 99.9% confidence level with a sample size of 4, we will use the t-distribution, since the population standard deviation is unknown.

The t-distribution is used when the sample size is small (usually n < 30) and the population standard deviation is unknown.

First, find the degrees of freedom (df) for the t-distribution, which is equal to the sample size (n) minus 1:

Next, we need to find the critical value (t) that corresponds to a 99.9% confidence level (or a 0.999 probability) and 3 degrees of freedom. We will look this up in a t-distribution table or use a t-distribution calculator.

Using a t-distribution calculator or table, the t-score corresponding to a 99.9% confidence level (two-tailed) and 3 degrees of freedom is approximately 9.925.

So, the critical value is 9.925, rounded to three decimal places.

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The radius is the center of circle to its edge or half of a diameter so half of 4/5 is 0.4 since 0.8 / 2 = 0.4.

To find the volume we need to do the equation π r² h.

So, π x 0.4^2 x 10 = 5.02654825.

Round 5.02654825 to the nearest hundredth and it is 5.03.

Volume is 5.03.

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Answer:

Because besides for the principal amount, it has a steady growth. In simple interest, it is a linear equation.

Step-by-step explanation:

Answer:

Explanation:

Given the expression:

When w=3

The value of the given expression when w=

Answer:

C

Step-by-step explanation:

just look at point A and the difference to A'.

A was moved 2 units to the left and 4 units up to get A'.

and the same happened, of course, to all other points of the triangle.

so, C is correct.