Sara buys a sweater at a department store. The sweater costs $15. The store is having a 20% off sale on everything in the store.


With this sale, what is the final cost of the sweater? Do not consider the sales tax.

The sweater will cost $
dollars.

Number of oranges is (2a + 2)

Half the number of oranges is 1/2(2a + 2)

Half the number of apples is 1/2a

The difference between half the number of oranges and half the number of apples equals 4 looks like this:

1/2(2a + 2) - 1/2a = 4

Now solve.

1/2(2a + 2) - 1/2a = 4 (multiply 1/2 by what's inside the parenthesis)

1a + 1 - 1/2a = 4

1a + 1 -1 - 1/2a = 4 - 1

1a - 1/2a = 3

1/2a = 3

1/2a ÷ 1/2 = 3 ÷ 1/2

a = 6

He has 6 apples.

Substitute 6 into the equation for the number of oranges.

2a + 2

2(6) + 2 = 14

He has 14 oranges.

Check your work.

The difference between half the number of oranges (7) and half the number of apples (3) does indeed equal 4.

Therefore, the equation has one solution.

Answer:

Step-by-step explanation:

Answer:

8/5=x

Step-by-step explanation:

1/2x+12=8x

Subtract 1/2x from both sides

12=15/2x

Multiply 2/15 on both sides

8/5=x

Answer: (0, 1) Usually, we put the solutions in parenthesis.

Step-by-step explanation: x(x+1) = x(2) which = x²+ x = 2x = x² + x - 2x = 0

x² - x = 0. Now we divide by x which = x(x - 1) = 0 and the new solution set is x = 0 and x -1 = 0 which equals x = 1

Let x be the amount of pure water that you use.

The solution you have contains 0.45 • 180 mL = 81 mL of alcohol.

However much water you use, it won't add any alcohol to the solution, so only its total volume changes. Its new volume would be (180 + x) mL. You want the new solution to have a concentration of 15% so that

(81 mL) / ((180 + x) mL) = 0.15

Solve for x :

81 / (180 + x) = 0.15

81 / 0.15 = 180 + x

540 = 180 + x

x = 360

Then the new solution will have a total volume of 180 mL + 360 mL = 540 mL.

So you need to use 360 mL of pure water to get 540 mL of 15% solution.

Answer:

v=-5

Step-by-step explanation:

39=4 -7v

39-4= (4-4) -7v

35=-7v

35/-7= -7v/-7

-5=v

Step-by-step explanation:

sum of three no =94

first no =X

second no x-8

third no =4(x-8)

X+(x-8)+4x-32=94

6x-40=94

6x=94-40

6x=54

X=54/6

X=9

Answer: The first number is 9, the second number is 17, and the third number is 68.

Step-by-step explanation:

Using the given information we will represent the first number by f , the second number by s, and the third number by t.

The first number is 8 less than the second  and we will represent that by the equation,   f= s-8

The third number is 4 times the second and it will be represented by the expression,  t= 4s  

We know the sum of the numbers has to equal  94 so we will add them.

The first number is s-8, the second is s, and the third is 4s.

(s - 8) + (s) + 4(s) = 94   Solve for s to find the second number.

6s - 8 = 94

    +8     +8

6s = 102    

s = 17  

The second number is 17 and we will input 17 in for s to solve for the first and third numbers.

f= 17 - 8

f= 9  

The first number is 11.

t= 4(17)

t = 68    

The third number is 68.

Check: Now add them to see if they equal to 94.

9+ 17 + 68 = 94

   94 = 94      

Answer: -13k+11

Step-by-step explanation:

Combine like terms

-15k+2k=-13k

-1+12=11

Answer:

a) 20

b) ab

Step-by-step explanation:

[tex]a.\\\\\frac{9}{5}=\frac{36}{x}\\\\x\cdot 9=36\cdot 5\\\\x=\frac{36\cdot5}{9}\\\\x=4\cdot 5\\\\x=20[/tex]

[tex]b.\\\\\frac{a}{6b}=\frac{y}{6b^2}\\\\\frac{6b^2\cdot a}{6b}=y\\\\y=b\cdot a\\\\y=ab[/tex]

Answer:

The days will it take the store to make $50,000 in a whole number are:

Step-by-step explanation:

Remember that x represents the number of days, so, you must replace different values in the formula until you obtain a value of $50,000, in this form:

So, I'll show you that the value that you need is 30 in a whole number.

I know that the value exceeds the amount of $50,000, but if you use just a day before:

How you can see, if you use 29 days, the value doesn't reach $50,000, by this reason, you must use 30 days to reach it.

Answer:

6) 130

7) x = 35

8) y = 100

9) 50

10) 130

11) DEF = 29

12) FEG = 61

13) DEF = 91

14) FEG = 89

Step-by-step explanation:

angle AEB is 50°

supplementary is when 2 angles add together to make 180°

50 + x = 180

x = 180 - 50

x = 130

angles AEB and DEC are vertical angles

vertical angles are equal.

50 = x + 15

50 - 15 = x

35 = x

AEB and AED are supplementary angles

supplementary angles add together to make 180

50 + (y + 30) = 180

y + 30 = 180 - 50

y + 30 = 130

y = 130 - 30

y = 100

DEC is vertical to AEB

vertical angles are equal.

AEB = 50

DEC = 50

AED = y + 30

as established earlier, y = 100

substitute Y for 100

AED = 100 + 30

AED = 130

DEF and FEG are complimentary.

complimentary means they add together to make 90

(3x - 4 ) + (5x + 6 ) = 90

3x - 4 + 5x + 6 = 90

8x + 2 = 90

8x = 90 - 2

8x = 88

x = 88/8

x = 11

substitute x into the equations

DEF = 3x - 4

DEF = 33 - 4

DEF = 29

FEG = 5x + 6

FEG = 55 + 6

FEG = 61

DEF and FEG are supplementary.

supplementary means they add together to make 180

(9x + 1) + (8x + 9) = 180

9x + 8x + 1 + 9 = 180

17x + 10 = 180

17x = 170

x = 10

substitute x into the equations

DEF =  9x + 1

DEF = 90 + 1

DEF = 91

FEG = 8x + 9

FEG = 80 + 9

FEG = 89

Answer:

A=8

b=15

c=40

Step-by-step explanation:

5/8 as well as 10/16 = .625

a=8 blocks for 5 min given in question

b:24*0.625=15

c:25*40=.625 or 8 * 5=40 , since 5×5=25 taking 1st column times 5

Answer:

2n+14

Step-by-step explanation:

Answer:

the answer is A. -16

Step-by-step explanation:

3(-16)+3= -45

-45/5=

-9

5(-16)-1=-81

-81/9=

-9

-9=-9

Answer:

5.64/12= .47 but that box cost 10cents more than box B so you then you subtract .10 and get .37 per ounce for box B

Answer:

3.012 × 10^ − 6

Step-by-step explanation:

hope this helps

Answer:

There are NO solutions

Step-by-step explanation:

On the left hand side, we have an absolute value;

which means that the left hand side will always be greater than or equal to 0

On the right hand side, we have a negative value;

Since the LHS can NEVER be negative, it will never be less than a negative number

Hence, No value of y can make this equation true

Answer:

uhmmmmm... i no understand...

Step-by-step explanation:

Answer:

25 baggies; each bag has 2 blueberry scones, and three cranberry scones.

Step-by-step explanation:

The question format is a bit bugged, but I assume the question is asking "You have 50 blueberry scones and 75 cranberry scones. You want to make as many identical bags as possible. What is he greatest number of bags you can fill?"

The first thing to realize when solving this question is that whatever the answer is equal to, it must be able to be equally divided from both 50 and 75, otherwise it will have a remainder, and at least one bag will have too many or not enough scones.

This means that the answer must be a factor of both 50 and 75.

The factors of 50 includes {1, 2, 5, 10, 25, 50}

The factors of 75 includes {1, 3, 5, 15, 25, 75}

In the two sets, only 1, 5, and 25 are common factors. Of the three factors, 25 is the greatest number, and thus the greatest number of bags that can you can fill.

Answer:

0.8

Step-by-step explanation:

6/10=0.6

0.6/3=0.2

0.2*4=0.8

I hope it's correct

Answer: Choice A

U = (x+3)

V = 7

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

Explanation:

If we let U = (x+3), then the original expression turns into U^2 + 14U + 49

This factors to (U+7)^2 when using the perfect square factor rule which in general is (a+b)^2 = a^2+2ab+b^2

Comparing the last term 49 with b^2, we see that b^2 = 49 leads to b = 7

So that must mean V = 7 in order to have

(U+V)^2 = U^2+2UV+V^2 = U^2 + 14U + 49

be a true statement

Answer:

98,000 bacteria.

Step-by-step explanation:

We are given the formula:

[tex]P=le^{kt}[/tex]

Where l is the initial population, k is the rate of growth, and t is the time ( in hours).

We know that it has an initial population of 500. So, l is 500.

We also know that the population grows to 7000 after 2 hours.

And we want to find the population after 4 hours.

First, since we know that the population grows to 7000 after 2 hours, let's substitute 2 for t and 7000 for P. Let's also substitute 500 for l. This yields:

[tex]7000=500e^{2k}[/tex]

Divide both sides by 500:

[tex]e^{2k}=14[/tex]

We can solve for the rate k here, but this is not necessary. In fact, when can find our solution with just this.

Let's go back to our original equation. We want to find the population after 4 hours. So, substitute 4 for t:

[tex]P=500e^{4k}[/tex]

We want to find the total population, P. Notice that we can rewrite our exponent as:

[tex]P=500(e^{2k})^2[/tex]

This is the exact same thing we acquired earlier. So, we know that the expression within the parentheses is 14. Substitute:

[tex]P=500(14)^2[/tex]

Square and multiply:

[tex]P=500(196)=98000[/tex]

So, after 4 hours, there will be 98,000 bacteria.

And we're done!

Answer:

C: up two over 1

Answer:

(a)7.185

(b)0.000371

(c) 0.019

(d)Sample variance and Sample standard deviation

Step-by-step explanation:

We are given the following sample data.

7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.17, 7.18.

(a) Calculate the sample mean. Round your answer to 3 decimal places.

The formula for sample mean =

Sum of terms/Number of terms

= 7.15 + 7.20+ 7.18+7.19+7.21+7.20+7.17+ 7.18/8

= 57.48/8

= 7.185

(b) Calculate the sample variance. Round your answer to 6 decimal places.

The formula for sample Variance =

(x - mean)²/n - 1

n = 8

Sample variance = (7.15 - 7.185)² + (7.20-

7.185)²+ (7.18 -7.185)² + (7.19 -7.185)² + (7.21 - 7.185)² + (7.20 - 7.185)² + (7.17 - 7.185)² + (7.18 - 7.185)² /8 - 1

= 0.001225 + 0.000225+ 0.000025+ 0.000025 + 0.000625 + 0.000225 + 0.000225 + 0.000025/7

= 0.0026/7

= 0.000371428571

Approximately to 6 decimal places = 0.000371

(c) Calculate the sample standard deviation. Round your answer to 3 decimal places.

The formula for Sample Standard Deviation = √Sample variance

= √0.000371428571

= 0.01927248223

To 3 decimal places = 0.019

(d) Which of the following are potential major sources of variability in the experiment

Sample variance

Sample standard deviation

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The  probability is  [tex]P(X \ge 1 ) = 0.003996[/tex]

Given that the probability is less than 0.05 , it means that it is  low enough so that further testing of the individual samples is rarely​ necessary

Step-by-step explanation:

From the question we are told that

     The probability of finding bacteria in a public swimming area  is  p =  0.002

 Generally the probability of not finding bacteria in a public swimming area  is mathematically represented as

      [tex]q = 1- p[/tex]

=>    [tex]q = 1- 0.002[/tex]

=>   [tex]q =0.998[/tex]

Generally the the probability that a combined sample from public swimming areas will reveal the presence of bacteria is equivalent to the probability that at least one of the sample will reveal the  presence of bacteria and this is mathematically represented as

       [tex]P(X \ge 1 ) = 1 - P(X')[/tex]

Here  [tex]P(X')[/tex] means that none of the 2  sample have bacteria which is mathematically represented as

       [tex]P(X') = q^2[/tex]

Here 2 signifies that we are considering two samples  

So  

        [tex]P(X') = 0.998^2[/tex]

        [tex]P(X') = 0.996004[/tex]

So

       [tex]P(X \ge 1 ) = 1 - 0.996004[/tex]

=>     [tex]P(X \ge 1 ) = 0.003996[/tex]

Answer:

Price of one pretzel = $1.5

Step-by-step explanation:

Let the price of a hot dog = [tex]x[/tex]

Let the price of a drink = [tex]y[/tex]

Let the price of a pretzel = [tex]z[/tex]

As per the given question statement:

[tex]3x+2y+z=\$16.50..... (1)\\4x+4y+2z=\$26........ (2)\\2x+y+3z=\$13.75..... (3)[/tex]

To find:

The price of one pretzel, i.e. [tex]z=?[/tex]

Multiplying (3) with 2 and subtracting (1) from it:

[tex]x+5z=11[/tex] ..... (4)

Multiplying (3) with 4 and subtracting (2) from it:

[tex]4x+10z=29[/tex] ..... (5)

Multiplying (4) with 4 and subtracting (5) from it:

[tex]10z=15\\\Rightarrow z =\bold{1.5}[/tex]

The price of one pretzel is $1.50.

Let the price of a hot dog = x

Let the price of a drink = y

Let the price of a pretzel = z

So,

The equations are

3x + 2y + z = $16.50 .....(1)

4x + 4y + 2z = $26..........(2)

2x + y + 3z = $13.75........(3)

Now

Here we Multiplying (3) with 2 and subtracting (1) from it:

So, it gives x + 5z = 11 ......(4)

Now

Multiplying (3) with 4 and subtracting (2) from it:

So, 4x + 10z = 29...(5)

Now

Multiplying (4) with 4 and subtracting (5) from it:

So, 10z = 15

x = 1.5

Therefore, The price of one pretzel is $1.50.

Learn more about price here: https://brainly.com/question/20763817

Answer:

This is the identity property.  It means that any number added by zero would be the same number.  In the second expression the zeroes were taken away.

Step-by-step explanation:

like and 5 start luv u

Answer

Step-by-step explanation:

10g = 40

g = 4

Answer:

Stop yellin

Step-by-step explanation:

Answer: y=x+5

Step-by-step explanation:

So the dots are going at a slope of 1 up and 1 right each time, so your slope would be 1, or simply x if you times it. To line it up with the slope, you have to move up 5 on your y-axis, known as your b. Then from there, you go up 1 over 1 which will line up with all the dots.

Answer:

56

Step-by-step explanation:

Answer:

56

Step-by-step explanation: