Please help me.
Prove that if a + b > 100, a, b, or both must be greater than 50

Answers

Answer 1

Answer:

Step-by-step explanation:

To prove this statement, we can use the contrapositive. The contrapositive of the statement "If a + b > 100, then a, b, or both must be greater than 50" is "If a and b are both less than or equal to 50, then a + b is less than or equal to 100."

To prove the contrapositive, we must show that if a and b are both less than or equal to 50, then a + b is indeed less than or equal to 100. This is easy to do, because if a and b are both less than or equal to 50, then the largest possible value for a is 50 and the largest possible value for b is 50. Therefore, the largest possible value for a + b is 50 + 50, which is equal to 100.

Since the contrapositive is true, it follows that the original statement must also be true. Therefore, we have proven that if a + b > 100, then a, b, or both must be greater than 50.


Related Questions

evaluate the expreshion
-8+-14/2+5

Answers

Answer:

Maybe -10

Hope this helps :)

what is the answer
2y+5x

Answers

Answer:

5x + 2y

Step-by-step explanation:

Given the polynomial function below, find F(-1).

Given the polynomial function below, find F(-1).

Answers

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\(f(x) = - {x}^{3} - {x}^{2} + 1\)

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\(f( - 1) = - ({ - 1})^{3} - ({ - 1})^{2} + 1 \\ \)

\(f( - 1) = - ( - 1) - (1) + 1\)

\(f( - 1) = 1 - 1 + 1\)

\(f( - 1) = 2 - 1\)

\(f( - 1) = 1\)

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The correct answer is (( D )) .

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HELPP. In words, write the meaning of: √a+3

Answers

Answer:

square root of a plus 3

Step-by-step explanation:

What is the length of AB?

What is the length of AB?

Answers

Answer:

C=10

Step-by-step explanation:

A^2 + B^2 = C^2

A=6

B=8

C=?

A^2=36

B^2=64

C^2=100

can someone tell me to stop slacking off school please LOL

Answers

stop slacking off and be a bad a

Giovanna has been named valedictorian for having straight As, which means that her GPA is at least

1.0.
2.5.
3.5.
4.0.

Answers

Answer:

D.  4.0

Step-by-step explanation:

D. 4.0
step- by- step explanation:::

Part of a table showing the amount of money in Joseph's bank account is given below. The account pays simple interest.
He deposited an amount of money at the start and hasn't added or removed since.
Work out the annual interest rate on this account.
Give answer as a percentage to 1 d.p.
After 5 years £1433.50
After 6 years £1476.20

Answers

The annual interest rate is 0.035, οr 3.5% (tο 1 decimal place).

What is the simple interest?

Simple interest is a type οf interest that is calculated as a fixed percentage οf the principal amοunt οver a specific periοd οf time.

Tο find the annual interest rate, we can use the simple interest fοrmula:

I = Prt

Where:

I is the interest earnedP is the principal (initial amοunt depοsited)r is the annual interest rate (as a decimal)t is the time (in years)

Let's start by finding the interest earned frοm year 5 tο year 6:

I = £1476.20 - £1433.50

I = £42.70

We knοw that Jοseph hasn't added οr remοved any mοney frοm the accοunt, sο the interest earned in each year is the same. Therefοre, the interest earned frοm year 1 tο year 5 is alsο £42.70.

Let's use this infοrmatiοn tο find the annual interest rate:

£42.70 = P × r × 1

£42.70 = P × r

£1433.50 = P + £42.70 × 5

£1433.50 = P + £213.50

P = £1220.00

Nοw we can substitute P intο the equatiοn we derived earlier:

£42.70 = £1220.00 × r

r = £42.70 ÷ £1220.00

r = 0.035

Hence, The annual interest rate is 0.035, οr 3.5% (tο 1 decimal place).

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What is the additive inverse of x=-1317, and verify -(-x) = x ?

Answers

Answer:

1317 is the additive inverse of x = -1317.

Step-by-step explanation:

Additive inverse of a number which when added to the original number gives zero as the result.

Additive inverse of x = -1317

-1317 + 1317 = 0

1317 is the additive inverse of x = -1317.

Verification of -(-x) = x

L. H. S

-(-x) = -{-(-1317)}

= - 1317

R. H. S

x = -1317

Thus, L.H.S. = R.H.S

-(-x) = x

Verified

Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of bottles she needs to sell to earn $100.
1.25x + 1.49 = 100

What error did Barbara make in writing the equation?
Barbara’s equation did not consider the number of bottles of water.
Barbara’s equation did not consider the number of bottles of iced tea.
Barbara’s equation did not use the correct price for the bottles of iced tea.
Barbara's equation did not use the correct total for sa

Answers

Answer:

B

Step-by-step explanation:

edge 2020

What is the area of the figure?

What is the area of the figure?

Answers

Answer:

I thik it is B

Step-by-step explanation:


Measia rode her bike 174 miles in six days, riding the same distance each day. Jamal rode his bike 135 miles in five
days, riding the same distance each day. Which of the following statements is true?

Answers

Answer:

6

Step-by-step explanation:

, , , , ,, , , , , , , , ,sssss

write the equation of a line that is parallel to y=12-5x and passes through the point (1,-7)

Answers

Answer:

y= -5x-2

Step-by-step explanation:

Parallel equations have the same slope, so we know our slope will be -5. To get our y-intercept, we need to plug in our slope. 1 times -5 is -5, so we need to figure out how to get from -5 to -7. We're going to subtract 2, so the y-intercept is -2.

The equation of the line parallel to y=12-5x and passes through the point (1,-7) will be y= -5x-2.

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation of a line that is parallel to y=12-5x and passes through the point (1,-7).

The slope of the parallel lines is always the same. The slope of the line will be -5.

The y-intercept of the line will be calculated as,

y = mx + c

-7 = -5(1) + c

c = -7 + 5

c = -2

The equation of the line will be written as,

y = mx + c

y = -5x - 2

Therefore, the equation of the line parallel to y=12-5x and passes through the point (1,-7) will be y= -5x-2.

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Write the equation of the line passing through the point (3, 5) that is
PEREPENDICULAR to y = -3/4x + 5 in slope-intercept form.

Answers

Answer:

Step-by-step explanation:

perp. 4/3

y - 5 = 4/3(x - 3)

y - 5 = 4/3x - 4

y = 4/3x + 1

using the smallest number of pebbles possible and without using blue pebbles, what is the value in pebbles of 2 blue pebbles?

Answers

According to the combination, The value of the Two blue pebbles is a 3 red pebbles and 1 yellow pebbles.

According to the statement

We have to find that the value of the combination.

So, For this purpose, we know that the

A combination could be a mathematical technique that determines the quantity of possible arrangements in an exceedingly collection of things where the order of the choice doesn't matter.

From the given information:

A red pebble is capable 3 yellow pebbles. A blue pebble is adequate a red pebble and a couple of yellow pebbles. Therefore, the blue pebbles will be:

= 3 yellow pebble + 2 yellow pebbles

= 5 yellow pebbles or 15 red pebbles

And

Two blue pebbles will be:

= 10 yellow pebbles

= 3 red pebbles and 1 yellow pebbles.

So, According to the combination, The value of the Two blue pebbles is a 3 red pebbles and 1 yellow pebbles.

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Disclaimer: This question was incomplete. Please find the content below.

Question:

A red pebble is equal to 3 yellow pebbles A blue pebble is equal to a red pebble and 2 yellow pebbles. A green pebble is equal to 3 red pebbles

Using the smallest number of pebbles possible and without using blue pebbles, what is the value in pebbles of 2 blue pebbles?

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1. Given the function f(x) = 7(3 - x) + 5, which of the following is a true
statement? *
O A. f(9) = -42
O B. f(-3) = 5
O C. f(-4) = 54

Answers

C is the answer! (3-(-4)=7 then 7x7 equals 49 then + 5= 54

PLEASE HELP!! ILL GIVE YOU BRAINLIEST


Using your equation from step 2d, estimate the GPA of a student who studies for 15 hours a week. Justify your answer.


hours on left side (x) , gpa on right side (y)

PLEASE HELP!! ILL GIVE YOU BRAINLIESTUsing your equation from step 2d, estimate the GPA of a student

Answers

The GPA of a student who studies for 15 hours a week is 2.935.

What is a GPA?

Grade point average, or GPA, is a conventional method of evaluating academic performance in the United States on a scale of 0 to 4.

How to calculate GPA?

To calculate your GPA, divide the total number of grade points earned by the total number of letter-graded units undertaken.

Here,

We have an equation y = 0.164x + 0.475

put x= 15

we get,

y = 0.164* 15 + 0.475

y = 2.935

Hence, The GPA of a student who studies for 15 hours a week is 2.935

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in a study, the sample is chosen by dividing population by voting district, and sampling everyone in five districts selected what is the sampling method? simple random systematic stratified cluster convenience chegg

Answers

The sampling method used in the given study is stratified sampling. In this method, the population is divided into homogeneous groups called strata, and a random sample is selected from each stratum to form the final sample. stratified sampling is a useful method for selecting a representative sample from a heterogeneous population when subgroups are well defined.

The given study chooses the sample by dividing the population by voting district and sampling everyone in five districts selected. Therefore, it is an example of stratified sampling where the strata are defined by voting districts. The method is preferred when the population is heterogeneous and it is important to ensure that the sample represents all subgroups of the population.

By dividing the population into strata, the variability within each stratum is reduced, making the sample more representative of the entire population.

In the given study, stratified sampling was used because the researchers wanted to ensure that the sample represents the entire population by selecting individuals from different voting districts. By dividing the population into strata based on voting districts, the researchers were able to reduce the variability within each stratum, making the sample more representative of the entire population.

In addition, the method also ensures that each stratum is represented in the sample, providing a more accurate estimate of the population parameters. Overall, stratified sampling is a useful method for selecting a representative sample from a heterogeneous population when subgroups are well defined.

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Let x be a random variable distributed as normal(5,4). Find the probabilities of the following events: (i) p(x::; 6). (ii) p(x > 4 ). (iii) p( ix- 5 1 > 1

Answers

From the given information provided, the probability of P(X ≤ 6), P(X˃ 4) and P(|X- 5| ˃ 1) is 0.6915, 0.6915 and 0.3829 respectively.

(i) To find P(X ≤ 6), we need to standardize the value of 6 using the formula:

Z = (X - μ) / σ

where μ = 5 and σ = 2 (since the standard deviation is the square root of the variance, which is 4).

So, we have:

Z = (6 - 5) / 2

Z = 0.5

We can then look up the probability of Z ≤ 0.5 in a standard normal distribution table, or use a calculator to find:

P(X ≤ 6) = P(Z ≤ 0.5) = 0.6915

(ii) To find P(X > 4), we again need to standardize the value of 4:

Z = (4 - 5) / 2

Z = -0.5

Then, we can use the fact that the total area under a normal distribution curve is 1 to find the probability of X being greater than 4:

P(X > 4) = 1 - P(X ≤ 4) = 1 - P(Z ≤ -0.5)

Using a standard normal distribution table:

P(X > 4) = 0.6915

(iii) To find P(|X - 5| > 1), we first need to transform this inequality into a standard normal distribution by standardizing both sides:

|X - 5| > 1

implies:

X - 5 > 1 or

X - 5 < -1

which gives:

X > 6 or X < 4

We can then standardize each inequality separately. For X > 6, we have:

Z = (6 - 5) / 2

Z = 0.5

and for X < 4, we have:

Z = (4 - 5) / 2 = -0.5

Then, using the fact that the total area under a normal distribution curve is 1, we can find the probability of both events occurring:

P(|X - 5| > 1) = P(X > 6 or X < 4) = P(Z > 0.5 or Z < -0.5)

Since the standard normal distribution is symmetric around 0:

P(Z > 0.5 or Z < -0.5) = 2 × P(Z < -0.5)

Using a standard normal distribution table:

P(|X - 5| > 1) = 0.3829

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Add.

(6x³ + 3x² − 2) + (x³ - 5x² − 3)

Express the answer in standard form. (Please and thank you)

Answers

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

7x^3 - 2x^2 - 5

----------------------------------------

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Hope this helps! :)

Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Which equation is equivalent to 5= 105​ divided by y?

Answers

Answer:

1=21

Step-by-step explanation:

for every one you go up you move over 21


A bus is moving at a uniform speed of 48 km per hour. How far will it
go
in 25
minutes?​

Answers

I hope it helps you ❤️❤️❤️

A bus is moving at a uniform speed of 48 km per hour. How far will itgoin 25minutes?

What is the surface area of the shaded front face of the composte solid?

A. 16 square centimeters
B. 18 square centimeters
C. 26 square centimeters
D. 32 square centimeters

What is the surface area of the shaded front face of the composte solid?A. 16 square centimetersB. 18

Answers

18 it’s b 18 square centimeters

Answer:

answer is c 26 square centi metres

Step-by-step explanation:

(8*4)-(2*3) cm²

(32-6) cm²

27cm²

what is the probability that the mean lifetime of 25 randomly selected tires of this type will exceed than 42,000 miles?

Answers

The probability that the mean lifetime of 25 randomly selected tires of this type will exceed than 42,000 miles is 25.14.

To break this problem, we need to use the standard normal distribution, assuming that the distribution of tire continuances is roughly normal. We can regularize the value of 42,000 using the formula

z = ( x- μ)/ σ

where x is the value of interest( 42,000 long hauls), μ is the mean tire continuance( 40,000 long hauls), and σ is the standard deviation( 3,000 miles). Plugging in the values, we get

z = ( 42,000- 40,000)/ 3,000 = 0.67

Using a standard normal distribution table or calculator, we can find the probability that an aimlessly named tire will last further than 42,000 long miles by looking up the area to the right of z = 0.67 under the standard average wind. This probability is roughly 25.14.

thus, the probability that a tire named arbitrarily from this brand will last more than 42,000 miles is roughly 25.14.

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The correct question is given below-

A particular brand of tires lasts an average of 40,000 miles with a standard deviation of 3,000 miles. What is the probability a tire selected at random lasts more than 42,000 miles?

someone help, need the answer asap

someone help, need the answer asap

Answers

Answer:

A : 2x\(\sqrt{15}\)    b: 23.2

Step-by-step explanation:

The steps to convert 18 over 8 to a decimal are shown below: Division is shown with divisor 8 and quotient 2.35 and dividend 18. The numbers below 18 in sequence are subtract 16 labeled as Step 1, 20, subtract 16 labeled as Step 2, 40 labeled as Step 3, subtract 40, and 0 labeled as Step 4. In what step is the first error?

Answers

Answer:

Step 2

18 over 8 to a decimal is 2.25

Step-by-step explanation:

Step 1, 20, subtract 16 labeled as

Step 2, 40 labeled as

Step 3, subtract 40, and 0 labeled as Step 4.

Divisor = 8

Divided = 18

Quotient = 2.25

2.25

8 √18

- 16

2 0

- 16

4 0

- 40

0

The first error is at step 2

18 over 8 to a decimal is 2.25

See the attached image for better understanding

The steps to convert 18 over 8 to a decimal are shown below: Division is shown with divisor 8 and quotient

Answer:

step 2

Step-by-step explanation:

Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship.

Answers

Based on the information provided, it is not possible to determine the likely correlation between the two variables. The presence or absence of a linear relationship between the variables is also unclear.

To determine the correlation and relationship between two variables, it is necessary to collect data and perform statistical analysis. It is important to note that correlation does not necessarily imply causation and that other factors may also influence the relationship between variables.
To determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship, follow these steps:
1. Analyze the data: Look for trends in the data points to see if they are moving in a specific direction.
2. Positive correlation: If both variables increase together, it indicates a positive correlation.
3. Negative correlation: If one variable increases while the other decreases, it indicates a negative correlation.
4. No linear relationship: If there is no consistent pattern in the way the variables change, they are not likely to display a linear relationship.
By examining the data for the given variables and applying these steps, you can determine the type of correlation or if a linear relationship exists between them.

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The price of books are $180 but he uses a 30% discount but there is a 4% tax what is the total price?

Answers

well, so the book is 180 and is discounted by 30%, how much will that be?

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 180}}{\left( \cfrac{30}{100} \right)180}\implies 54\qquad \qquad \underset{\textit{discounted price}}{\stackrel{180-54}{126}}\)

so from that discounted price, a tax of 4%

\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4\% of 126}}{\left( \cfrac{4}{100} \right)126}\implies 5.04\qquad \qquad \underset{\textit{final price}}{\stackrel{126+5.04}{131.04}}\)

Write the equation of the line that has an undefined slope and passes through the point (4, -4). The equation is

Answers

The equation is x=4  that has an undefined slope and passes through the point (4, -4).

A point's coordinates have been provided to us (4,7). The task is to determine the equation of the line that passes through the specified location and has an ambiguous slope.

We are aware that a vertical line's slope is ill-defined. As a result, the slope of the vertical line across point (4,7) will be ill-defined.

When the x-coordinates of every point on the line are the same, the slope of the line cannot be determined.

Therefore, X=4 is  the best option because the line will have the identical x-coordinates for all of the y-coordinates

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What is the value of x in the triangle?

What is the value of x in the triangle?

Answers

Answer:

hey

sin 30 = x/8

1/2=x/8

x=8/2=4

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