1/6 of a birthday cake is left over from a party. The next day, it is shared among 7 people. How big A piece of the original cake did each person get?

Answer:

In an indirect proof, instead of showing that the conclusion to be proved is true, you show that all of the alternatives are false.

The indirect proof serves as a powerful tool in mathematical reasoning, allowing mathematicians to establish the truth of statements by strategically exploiting logical inconsistencies within assumed false premises.

An indirect proof is a method in math where you assume the opposite of what you want to prove, then show that this assumption leads to a contradiction or inconsistency.

This means that the opposite assumption must be false, making the original statement true.

It's a way to prove something by showing that its opposite can't be true.

Hence, Indirect proof assumes opposite, leads to contradiction, proving original statement true. Used when direct proof is challenging or problem suits contradiction.

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Answer:

The cost for selling 100 lunches is 150 dollars.

Step-by-step explanation:

First, consider the equation: y = mx + b
y in this case is the profit in dollars (what' on the y axis) x in this case is the number of lunches sold (x- axis), m is the slope.

How do we calculate the slope of a graph? we take two points from the graph, let's say, (65,45) and (20,-90)

the formula for finding the slope is:

[tex]\frac{rise}{run} = \frac{y2 - y1}{x2-x1} \\\\[/tex]

where (x1, y1) is coordinates of first point in the line

where (x2, y2) is coordinates of second point in the line

[tex]\frac{45-(-90)}{65-20} = 3[/tex]

m = 3

y = 3x + b

now we need to find b. We just insert one point of your choice from the grpah, let's choose (50,0) now plug them in out newfound equation (y = 3x + b)

0 = 3(50) + b

find b using algebra:

0 = 150 + b

b = -150

Yay! we found b, now we have the equation y = 3x - 150

(by the way I just noticed you can find b from the graph, the point that touches the y-axis is b)

now we are told to find the cost for selling 100, we need to plug in 100 instead of x in our equation.

y = 3(100) - 150 = 150

therefore the cost is 150 dollars.

hope this helps, tell me if you misunderstood something.

Their new velocity after the collision is 2.97m/s

According to the law of momentum, the sum of momentum of bodies before the collision is equal to their sum after the collision.

The formula for calculating the momentum of a body is expressed as:
Momentum = mass * velocity

According to the law

m1u1 + m2u2 = (m1 + m2)v

v is the new velocity after the collision

Substitute the given values

1000(3) + 10(0) = (1000+10)v

3000 = 1010v

v = 3000/1010

v = 2.97m/s

Hence their new velocity after the collision is 2.97m/s

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Answer:

x = 88 -5y/2

Step-by-step explanation:

(2x - 4) + 5y + x = 180
x = 180 - (2x - 4) -5y -x

x = 180 - x - 4 -5y

x = 176 - x -5y

2x = 176 - 5y
x = 88 -5y/2
Hope this helps :)

The amount Don must pay on his card without  going over the credit limit is $125.

Don's credit limit is $500. If Don does not want to go over the limit, he must not exceed the $500 limit. In order to determine the amount he should pay, add the sum of the charges and subtract it from the credit limit.

Amount to be paid = (425 + 200) - 500 = $125

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Volume Formula: length x width x height

---Let's first write down what we're given.

Volume = 80

Length = 4

Width = 4

Height = ?

---Now, plug what we know into the formula for volume and solve for the missing variable.

80 = 4 x 4 x h

80 = 16 x h

h = 5

g = 5 centimeters

Hope this helps!

Answer:

Step-by-step explanation:

He is incorrect.

We are not only subtracting 1 from 5 but 1/4 also,  so the result has to be less than 4.

5 - 1 1/4

= 5 - 1 -1/4

= 3 3/4.

Answer:

1/2 of a chance.

Step-by-step explanation:

There are 2 numbers out of 4, which is 2/4 or 1/2

Answer:

16

Step-by-step explanation:

You're doing a subtraction problem between (x+5) and (2x+3)

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

**You need to solve for x first then plug it in to find the answer.***

(I had to break the parentheses because that is the only way to solve)

-x +8

x= -8

-8 + 5 - (-16+3)

-3 + 16 + 3

13 + 3 = 16

Answer:

-x+2

Step-by-step explanation:

(x+5)-(2x+3)
distribute
x+5-2x-3
combine like terms
x-2x+5-3
-x+2

Using it's concept, it is found that there is a 0.125 = 12.5% experimental probability that a randomly selected preschooler would choose to read books today.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For an experimental probability, these numbers of outcomes are taken from previous trials.

In this problem, in the previous trial, one out of eight students read a book, hence:

p = 1/8 = 0.125 = 12.5%.

There is a 0.125 = 12.5% experimental probability that a randomly selected preschooler would choose to read books today.

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Answer: D

Step-by-step explanation:

Answer:

the answer to question a is 24

the answer to question b is 8

Answer:

4/24,,,5/24,,7/24

hope it helps u

[tex]===========================================[/tex]

Let's create an expression that always results in 6 more than a multiple of 5.

First, let the unknown number be x.

Then, we should multiply it times 5 and add 6 (6 more means we add 6)

So the expression is

5x+6

Will this work? We can easily check by plugging in some numbers:

5(2)+6

10+6

10 is a multiple of 5

16 ✓

Try another number:

5(3)+6

15+6

21 ✓

Try a negative number:

5(-3)+6

-15+6

-9 ✓

Try zero:

5(0)+6

0+6

6 ✓

[tex]============================[/tex]

[tex]^\square\boxed{An~Emotional~Helper}^\square^\bigstar[/tex]

An algebraic expression results in 6 more than a multiple of 5 if the variable is an integer is 5x+6.

The given statement is "6 more than a multiple of 5 if the variable is an integer".

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Let the unknown number be x.

A multiple of 5 is 5x

6 more than a multiple of 5 if the variable is an integer

= 5x+6

Hence, an algebraic expression results in 6 more than a multiple of 5 if the variable is an integer is 5x+6.

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Hey there!

Answer:

336.84%

3200 out of 950 is 336.84%

Solution:

3200 out of 950 is what %?

3200 out of 950 is P%

Equation: Y/X = P%

Solving our equation for P

P% = Y/X

P% = 3200/950

p = 3.3684

Convert decimal to percent:

P% = 3.3684 * 100 = 336.84%

well, if we take 3200 to be the 100%, what is 950 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 3200 & 100\\ 950& x \end{array} \implies \cfrac{3200}{950}=\cfrac{100}{x}\implies \cfrac{64}{19}=\cfrac{100}{x} \\\\\\ 64x=1900\implies x=\cfrac{1900}{64}\implies x = 29.6875[/tex]

Answer:

89.97

Step-by-step explanation:

5.99+79.99 = 85.98 + 3.99  = 89.97

Answer:

D

Step-by-step explanation:

Answer:

C is the answer

Step-by-step explanation:

people who usually volunteers really don't get represented

solution:

[tex]\frac{299}{6}=49\frac{5}{6}[/tex]

decimal result:

[tex]49.833[/tex]

1. Simplify the expression

[tex]26/3*23/4[/tex]

Multiply the fractions:

[tex]\frac{\left(26\cdot23\right)}{\left(3\cdot4\right)}[/tex]

Cancel terms:

[tex]\frac{\left(13\cdot23\right)}{\left(3\cdot2\right)}[/tex]

Simplify the arithmetic:

[tex]\frac{299}{\left(3\cdot2\right)}[/tex]

Simplify the arithmetic:

[tex]\frac{299}{6}[/tex]

Simplify the fraction:

[tex]\frac{299}{6} =49\frac{5}{6}[/tex]

[tex]==========================================[/tex]

First, let's convert the mixed numbers into improper fractions:-

[tex]\bf{8\displaystyle\frac{2}{3}[/tex]

[tex]\displaystyle\frac{26}{3}[/tex]

Now, do the same for the second fraction:-

[tex]\displaystyle\frac{23}{4}[/tex]

Now, the formula for the area is

[tex]\bold{A=bh}[/tex]

We know both b and h, so we can just plug in the values and solve:

[tex]\bold{A=\displaystyle\frac{26}{3} *\frac{23}{4} }}[/tex]

Actually, we can reduce some fractions here (we can divide 26 and 4 by 2)

[tex]\bold{\displaystyle\frac{13}{3} *\frac{23}{2}}[/tex]

Multiplying 13 times 23 is easier than multiplying 26 times 13.

Now, this can only be done if the numbers do have some common factors. Both fractions are now in simplest form; 13, 23, 3 & 2 don't have common factors.

Multiply:

[tex]\bold{\displaystyle\frac{13*23}{3*2}}}[/tex]

The answer is

[tex]\bold{\displaystyle\frac{299}{6}}[/tex]

Convert to a Mixed Number:-

[tex]\bold{49\displaystyle\frac{5}{6}}[/tex]

[tex]==================================[/tex]

Nickname:- [tex]\mathbb{DiAmOnD}[/tex]

[tex]\boxed{An~emotional~helper}[/tex]

first amount:

second amount:

total amount:

Hey there!

Guide:

• Penny = 0.01¢ (1 cent)
• Nickel = 0.05¢ (5 cents)
• Dime = 0.10¢ (10 cents)
• Quarter = 0.25¢ (25 cents)
• Half dollar = 0.50¢ (50 cents)

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
EQUATION #1.

$10.00 + $5.00

= $15.00

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

0.25¢ + 0.25¢ + 0.25¢ + 0.05¢ + 0.05¢

= 0.75¢ + 0.10¢

= 0.85¢

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
$15.00 + 0.85¢

= $15.85
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

Total/Answer: $15.85

______________________________
EQUATION #2.

$5.00 + 0.00

= $5.00

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

0.25¢ + 0.25¢ + 0.01¢ + 0.01¢ + 0.01¢ + 0.01¢

= 0.50¢ + 0.04¢

= 0.54¢

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

$5.00 + 0.54¢

= $5.54

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

Total/Answer: $5.54

______________________________
NOW ADD THEM TOGETHER!

$15.85 + $5.54

= $21.39

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

I don't know sorry, I wish I could help you

Let's combine like terms:-

[tex]\bigstar{\sf{-4k+15k-30=-78}[/tex]

Add the k's:-

[tex]\bigstar{\sf{11k-30=-78}[/tex]

Add 30 to both sides:-

[tex]\bigstar{\sf{11k=-78+30}[/tex]

[tex]\bigstar{\sf{11k=-48}[/tex]

Divide both sides by 11:-

[tex]\bigstar{\boxed{\sf{k=4.36}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

The reason for one graph appears skewed, and one graph appears symmetric is the interval on the x-axis of the histogram is inconsistent.

A histogram is the way of representation of data which is used to show the frequency distribution using the rectangle similar to a bar graph.

In the problem, the data given as,

Thus, the reason of one graph appears skewed, and one graph appears symmetric is the interval on the x-axis of the histogram is inconsistent.

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Answer:

the rest aren't wholly visible;like the signs under the letters

Step-by-step explanation:

intervals of +4

intervals of -5

Answer:29.2

Step-by-step explanation:The equation used to add a markup percent to a product is the cost plus the markup percentage multiplied by the cost.

Answer:

$29.20

Step-by-step explanation:

The original price of an item is 100%, so a 60% mark up means that the price will now be 160% of the original price.

160% = 160/100 = 1.6

⇒ 160% of $18.25 = 1.6 × 18.25 = $29.20

Answer:

C. Narrower and the margin of error would decrease

The required, option b (wider and the margin of error would increase) is the correct answer.

In statistics, the margin of error (MOE) is the degree of uncertainty associated with a statistical estimate, usually an estimate of a population parameter based on a sample of data. It is the range of values above and below a sample statistic that is likely to contain the true population parameter with a certain level of confidence.

Compared to a 90% confidence interval, a 95% confidence interval will be wider and the margin of error would increase.

This is because a higher confidence level requires a larger range of possible values to be included in the interval, which in turn leads to a wider interval. With a higher confidence level, the z-score used to calculate the margin of error increases, resulting in a larger margin of error.

Therefore, option b (wider and the margin of error would increase) is the correct answer.

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Answer:

19.6 gallons

Step-by-step explanation:

divide 225 by 10 and you get 22.5 this means you are getting 22.5 miles per gallon so all you have to do is divide 441 by 22.5 and you get 19.6 so you are going to need 19.6 gallons to drive 441 miles

Step-by-step explanation:

[tex]radius = \frac{12}{2} \\ = 6 \\ area \: of \: circle =\pi \: {r }^{2} \\ = \pi \times {6}^{2} \\ \pi \times 36 \\ = 113.14[/tex]

anss....wer....

Answer:

can be solved in two ways here you go

one is by either by finding r and using the formula

Area = πr²

Or by directly using the formula

Area = 1/4 πd²

Answer:

6x3=18 pieces

6/18 = 1/3

=

18 pieces

72 inches