If we mix the alcohol solution we have with pure water at the ratio 3:2, we will obtain a solution of 18% alcohol. If we instead mix them at a ratio of 4:1, what will be the alcohol percentage of the solution?

Answer:

-87= 1 + 8x

-88= 8x

x= -11

Basically bring over the one to the other side of the equation and solve for x by dividing.

Answer:

100 meters in 1 minute

Step-by-step explanation:

500/5=100

To find the unit rate of a question, divide.

500 / 5 = 100

100 meters per minute.

______

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Answer:

The average number of tornado's in December is 22 and the average number of tornado's in June is 226

Step-by-step explanation:

The complete question is

The average number of tornado's in June is 16 less than 11 times the average number of tornado's in December. If the difference between the average number of tornado's in June and December is 204,determine the average number of tornado's in December and June.

Let

x ----> the average number of tornado's in June

y ----> the average number of tornado's in December

we know that

[tex]x=11y-16[/tex] ---> equation A

[tex]x-y=204[/tex] ----> equation B

solve the system by substitution

substitute equation A in equation B

[tex]11y-16-y=204[/tex]

solve for y

[tex]10y=204+16[/tex]

[tex]10y=220[/tex]

[tex]y=22[/tex]

Find the value of x

[tex]x=11y-16[/tex] ----> [tex]x=11(22)-16=226[/tex]

therefore

The average number of tornado's in December is 22 and the average number of tornado's in June is 226

Answer:

Part 1)  [tex]x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})[/tex]

Part 2)  [tex]x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})[/tex]

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

Part 1)

in this problem we have

[tex]x^{2} -2x-2=0[/tex]

so

[tex]a=1\\b=-2\\c=-2[/tex]

substitute in the formula

[tex]x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-2)}} {2(1)}\\\\x=\frac{2(+/-)\sqrt{12}} {2}\\\\x=\frac{2(+/-)2\sqrt{3}} {2}\\\\x_1=\frac{2(+)2\sqrt{3}} {2}=1+\sqrt{3}\\\\x_2=\frac{2(-)2\sqrt{3}} {2}=1-\sqrt{3}[/tex]

therefore

[tex]x^{2} -2x-2=(x-(1+\sqrt{3}))(x-(1-\sqrt{3}))[/tex]

[tex]x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})[/tex]

Part 2)

in this problem we have

[tex]x^{2} -6x+4=0[/tex]

so

[tex]a=1\\b=-6\\c=4[/tex]

substitute in the formula

[tex]x=\frac{-(-6)(+/-)\sqrt{-6^{2}-4(1)(4)}} {2(1)}[/tex]

[tex]x=\frac{6(+/-)\sqrt{20}} {2}[/tex]

[tex]x=\frac{6(+/-)2\sqrt{5}} {2}[/tex]

[tex]x_1=\frac{6(+)2\sqrt{5}}{2}=3+\sqrt{5}[/tex]

[tex]x_2=\frac{6(-)2\sqrt{5}}{2}=3-\sqrt{5}[/tex]

therefore

[tex]x^{2} -6x+4=(x-(3+\sqrt{5}))(x-(3-\sqrt{5}))[/tex]

[tex]x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})[/tex]

Answer:

Step-by-step explanation:

The graph that will lie above the x-axis will be having only positive values throughout its domain,

So, We have to check which graph is having y > 0 for every x.

clearly y will be negative for many values of x , as coefficient of variable is negative.

Put x = 0, you will get y as negative .

Since, Square of anything will always be positive , and here constant term is also positive , so, It will always be positive .

Thus, it is having its graph always above x axis.

Put x = 0 , y = -7, which is negative

Answer:

Option C.

Step-by-step explanation:

The vertex form of a parabola is

[tex]y=a(x-h)^2+k[/tex]

where, a is constant, (h,k) is vertex.

If a<0, then it is a downward parabola and if a>0, then it is an upward parabola.  

A downward parabola never lies entirely above the x-axis.

First equation is

[tex]y=-(x+7)^2+7[/tex]

It is a downward parabola and vertex is (-7,7).

Second equation is

[tex]y=(x-7)^2-7[/tex]

It is an upward parabola and vertex is (7,-7).

Third equation is

[tex]y=(x-7)^2+7[/tex]

It is an upward parabola and vertex is (7,7).

Fourth equation is

[tex]y=(x-7)[/tex]

It is a linear equation with y-intercept -7.

Only equation 3 is an upward parabola whose vertex lies above the x-axis.

Hence the correct option is C.

13 * 5 = 65

So, he needs 65 stickers

65/10 = 6.5

He will need 7 sheets, but will only use 6 and a half sheets.

Kyle will need to buy 7 sheets of stickers to have enough for all 13 of his notebooks, given that each notebook requires 5 stickers and each sheet contains 10 stickers.

Kyle needs a total of 65 stickers for his 13 notebooks, since he puts 5 stickers on each notebook. There are 10 stickers per sheet, so to find out how many sheets Kyle needs, we divide the total number of stickers by the number of stickers per sheet: 65 stickers ÷ 10 stickers/sheet = 6.5 sheets. Since Kyle cannot buy half of a sticker sheet, he will need to buy 7 sheets of stickers to have enough for all his notebooks.

Answer:

For the given function, Slope is [tex]\frac{7}{9}[/tex] and y-intercept is -2.

Step-by-step explanation:

The given function in x is :

    [tex]k(x)=\frac{7}{9}x-2[/tex]              .....1

Since, we know that the general form of equation of a line is :

     [tex]y=mx+c[/tex]                             .....2

where, y is the dependent variable, x is independent variable, m is the slope and c is the y intercept of the line.

On comparing equation 1 and 2, we get :

[tex]k(x) = y[/tex];

[tex]m = \frac{7}{9}[/tex]; and

[tex]c=-2[/tex];

Thus, we can conclude that

slope of function is [tex]\frac{7}{9}[/tex] and y-intercept is -2.

Answer:

24 for 5 is higher because you have to divide 24 by 5 and if you do that it gives you $4.8, while 5 for 24 gives you a unit rate of $0.20.

Answer:

12   girls   18 boys Total 30 students

Step-by-step explanation

x=number of girls

18/3 = x/2

3x=18*2

3x=36

x=12

  Other proof

x= number of groups

3x +2x = 30

5x=30

x=6

3*(6) + 2*(6) = 30

18+12=30

When y is 4, p is 0.5, and m is 2, x is 2. If x varies directly with the product of p and m and inversely with y, which equation models the situation?

xpmy=8

xy/pm=8

xpm/y=0.5

x/pmy=0.5

The equation models the situation is [tex]\frac{x y}{p m}=8[/tex]

Given that  

x is 2, y is 4, p is 0.5, and m is 2

x varies directly with the product of p and m

x varies inversely with y

[tex]\text {Product of } p \text { and } m=p \times m=p m[/tex]

x varies directly with the product of p and m

[tex]=>x \propto p m[/tex] ---- eqn 1

As x varies inversely with y,

[tex]=>x \propto \frac{1}{y}[/tex]   ----- eqn 2

From (1) and 2, we can say that

[tex]x \propto \frac{p m}{y}[/tex]

[tex]\Rightarrow x=k \frac{p m}{y}[/tex]

where k is constant of proportionality

[tex]\Rightarrow \frac{x y}{p m}=k[/tex]   ---- eqn 3

On substituting given values of x = 2, y = 4, p = 0.5 and m= 2 in eqn (3) we get

[tex]\frac{x y}{p m}=\frac{2 \times 4}{0.5 \times 2}=k[/tex]

[tex]\begin{array}{l}{\frac{x y}{p m}=\frac{8}{1}=k} \\\\ {=>\frac{x y}{p m}=8}\end{array}[/tex]

Hence correct option is second that is [tex]\frac{x y}{p m}=8[/tex]

Answer:

B

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

You just multiply 16 by 4.

There are 16 ounces in one pound.

So, 64 ounces in 4 pounds.

The correct option is E.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

There are 16 ounces in one pound.

In 4 pounds,

= 16 x 4 ounces.

= 64 ounces.

Therefore, 64 ounces in 4 pounds.

To learn more about the multiplication;

https://brainly.com/question/19634536

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Answer:

95 nickels 19 dimes

Step-by-step explanation:

d=dimes

5d=nickels

0.05(5d) + 0.10(d) = 6.65

0.25d + 0.10d = 6.65

0.35d=6.65

Divide by 0.35

d= 19 (19 coins)

19 dimes =$1.9

6.65-1.9= $4.75

Nickels=$4.75

4.75/0.05 = 95 coins

19*5=95

  114 coins in total

19*0.10 = 1.9

95*0.05=4.74

4.75+1.9= 6.65

Answer:

There are 19 dimes and 95 nickels

Step-by-step explanation:

Represent the numbers of nickels and dimes by n and d.  Then n = 5d.

The value of the nickels is $0.05n and that of the dimes is $0.10d.  Together these two amounts come to $6.65:

$0.05n + $0.10d = $6.65.

But n = 5d.

Substituting 5d for n, we get:

$0.05(5d) + $0.10d = $6.65

Combining the two terms on the left, we get:

0.25d + 0.10d = 6.65, or

0.35d = 6.65.

Solving for d, we get d = 6.65/0.35, or d = 19.  Since n = 5d, n = 5(19) = 95.

There are 19 dimes and 95 nickels.

There are 9240 possible ways in which a president, a secretary and a treasurer can be selected from the 22 members on the board of directors.

Give that the board of directors of a corporation must select a president a secretary and a treasurer.

Need to calculate in how many possible ways this can be accomplished if there are 22 members on the board of directors

Here we are assuming that one person can hold only one position means one if get selected for president he is out of the race for remaining positions that are secretary and treasure

Lets for sake of understanding, we simplify our question.

Lets say there are 3 members A , B and C  . In how many ways two positions of Secretary and  treasurer can be filled .  

So for selecting secretary  we have three option that are A , B or C.

And once secretary is selected , number of option for selecting treasure  is two.

So it is found that number of selecting 2 positions  for  3 members is product of option available for selecting first position that is secretary  multiplied by option available for selecting second position that is treasurer   = 3 x 2 = 6

So now applying same logic for selecting members for 3 positions  from 22 menbers  we get

For selecting president members available = 22

Once president is selected, then option available for selecting a Secretary = 21

And one secretary is also selected, then option available for selecting a treasure = 20

So number of ways in which three positions can be filled by 22 member = 22 x 21 x 20 = 9240

Hence there are 9240 possible ways in which a president , a secretary and a treasurer can be selected from the 22 members on the board of directors.

Answer:

30%

Step-by-step explanation:

Here we want to setup the equation

[tex]y = a - (a\times x)[/tex]

where y is the discounted price, a is the normal price and x is the percent off. so now we wanna plug in known values and solve for percent off.

[tex]45.49 = 64.99 - (64.99x)[/tex]

through algebra,

[tex] - 19.5 = - (64.99x)[/tex]

[tex] \frac{ - 19.5}{ - 64.99} = x[/tex]

[tex]x = .3000...[/tex]

so in percentage that is 30%

Answer:

-116

Step-by-step explanation:

Answer:

-116

Step-by-step explanation:

2^-2=1/2^2=1/4

5^3=5*5*5=125

12*3=36

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

1/4(36)-125

9-125=-116

The mistake he made was that he did not consider units of measurement while comparing the lengths

He has to convert the both quantities into the same unit to compare the lengths either centimeters to meters or meters to centimeters

Step-by-step explanation:

Length of desk  =  1 meter

Henry's name tag = 8 cm

Henry says that his name tag is 7 cm longer than the desk. The mistake he made was that he did not compare the units of both quantities. He just subtracted 1 from 8 and got 7. Meter is a larger unit and centimeter is a smaller unit. In order to compare the lengths of the desk and his name tag the units have to be same.

Hence

The mistake he made was that he did not consider units of measurement while comparing the lengths

He has to convert the both quantities into the same unit to compare the lengths either centimeters to meters or meters to centimeters

Keywords: Measurement

Learn more about measurement at:

#LearnwithBrainly

Final answer:

Henry mistakenly claimed his nametag was 7 centimeters longer than his desk due to a unit conversion error. His desk is 100 centimeters long, and his nametag is 8 centimeters long, making the nametag 92 centimeters shorter than the desk. The error is corrected by accurately comparing lengths in the same unit.

Explanation:

The question asks to identify the error Henry made in stating that his nametag is 7 centimeters longer than his desk and to explain how to correct it. Henry's desk is 1 meter long, which is equivalent to 100 centimeters, and his nametag is 8 centimeters long. The error Henry made is in the comparison of the lengths in different units and misunderstanding of the concept of length comparison. To correct this error, both lengths should be in the same unit, and then we compare or subtract to find the difference or relation.

The correct comparison is as follows:

Desk length in centimeters: 100 cm

Nametag length: 8 cm

So, rather than the nametag being 7 centimeters longer, it is 92 centimeters shorter than the desk. The correction is understanding unit conversion and accurately comparing lengths.

Answer:

C. because you would multiply each of the 6 cars by the amount of people it can hold which is 6

Answer:

Step-by-step explanation:

a) To find the household income of the top 4%, we can use the standard Normal distribution table or calculator to find the Z-score associated with the 96th percentile.

The Z-score corresponding to the 96th percentile is approximately 1.75. We can then use the Z-score formula to find the income value:

Z = (x - mean) / standard deviation

1.75 = (x - 69953) / 90000

x - 69953 = 1.75 * 90000

x - 69953 = 157500

x = 227453

Therefore, the household income of the top 4% is about $227,453.

b) The answer in part a should be taken with some caution as the Normal model assumes that the incomes follow a bell-shaped distribution, which may not be the case for all income distributions.

c) The Normal model may not be a good one for incomes because incomes often have a skewed distribution with a long tail to the right, meaning there are a small number of individuals with very high incomes that can greatly affect the mean and standard deviation. In addition, incomes may have outliers or gaps that are not well captured by a Normal distribution.

Answer:

Option B) minimum value at −10

Step-by-step explanation:

we have

[tex]f(x)=x^{2} -10x+15[/tex]

This function represent a vertical parabola open upward (because the leading coefficient is positive)

The vertex represent a minimum

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]f(x)-15=x^{2} -10x[/tex]

Divide the coefficient of term x by 2

10/2=5

squared the term and add to the right side of equation

[tex]f(x)-15=(x^{2} -10x+5^2)[/tex]

Remember to balance the equation by adding the same constants to the other side

[tex]f(x)-15+5^2=(x^{2} -10x+5^2)[/tex]

[tex]f(x)+10=(x^{2} -10x+25)[/tex]

rewrite as perfect squares

[tex]f(x)+10=(x-5)^{2}[/tex]

[tex]f(x)=(x-5)^{2}-10[/tex] ----> function in vertex form

The vertex of the quadratic function is the point (5,-10)

therefore

The minimum value of the function is -10

Consecutive even integers are -8, -6 and -4

Step-by-step explanation:

Let  be the first even integer then the next two integers will be: x+2 and x+6

According to given property, we get

[tex]x - 2(x+2) = (x+4)+8\\x-2x-4 = x+4+8\\-x-4 = x+12\\-x-x = 12+4\\-2x = 16[/tex]

Dividing both sides by -2

[tex]\frac{-2x}{-2} = \frac{16}{-2}\\x = -8[/tex]

The two next integers are:

x+2 = -8+2 = -6

x+4 = -8+4 = -4

Verification:

[tex]-8-2(-6) = -4+8\\-8+12 = +4\\4 = 4[/tex]

Hence, Consecutive even integers are -8, -6 and -4

Keywords: Linear equation, Variables

Learn more about linear equation at:

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Answer:

From fourth month onwards, the growth rate of [tex]f(x)[/tex] is greater than that of [tex]g(x)[/tex].

Step-by-step explanation:

Given:

The growth rates of both bank accounts are given as:

[tex]f(x)=3^x\\g(x)=5x+25[/tex]

Now, as per question, we need to find the value of 'x' when the value of [tex]f(x)>g(x)[/tex]. Or,

[tex]3^x>5x+25[/tex]

Now, we can do this by checking the values of 'x' by hit and trial method.

Let [tex]x=1[/tex]. The inequality becomes:

[tex]3^1>5(1)+25\\3>30(False)[/tex]

Let [tex]x=2[/tex]. The inequality becomes:

[tex]3^2>5(2)+25\\9>35(False)[/tex]

Let [tex]x=3[/tex]. The inequality becomes:

[tex]3^3>5(3)+25\\27>40(False)[/tex]

Let [tex]x=4[/tex]. The inequality becomes:

[tex]3^4>5(4)+25\\81>45(True)[/tex]

Therefore, the value of 'x' for which [tex]f(x)>g(x)[/tex] is 4.

So, from the fourth month onwards, the balance in [tex]f(x)[/tex] becomes greater than [tex]g(x)[/tex].

The graphical solution is shown below to support the same.

From the graph, we can conclude that after the 'x' value equals 3.4, the graph of [tex]f(x)[/tex] lies above of [tex]g(x)[/tex]. Hence, [tex]f(x)>g(x)[/tex] for [tex]x>3.4[/tex]

Answer:

The Answer is [tex]\frac{3657}{1000} \ or \ 3.657[/tex]

Step-by-step explanation:

Given

[tex]3\times1+\frac{6\times1}{10}+\frac{5\times1}{100}+\frac{7\times1}{1000}\\[/tex]

Now Solving Above using PEDMAS rule we get;

[tex]3+\frac{6}{10}+\frac{5}{100}+\frac{7}{1000}[/tex]

Now we will make take LCM we get;

[tex]\frac{3\times1000}{1000}+\frac{6\times100}{10\times100}+\frac{5\times10}{100\times10}+\frac{7\times1}{1000}\\\\\frac{3000}{1000}+\frac{600}{1000}+\frac{50}{1000}+\frac{7}{1000}\\\\\frac{3000+600+50+7}{1000}\\\\\frac{3657}{1000} \ or \ 3.657[/tex]

Hence the answer is  [tex]\frac{3657}{1000} \ or \ 3.657[/tex]

Answer:

The answer is C. $1,250.00

Step-by-step explanation:

850+2,000×20%

First you add 850 and 2,000 and that will turn out to 2,850

2,850×20%

Then you take that 2,850 and multiply it by 20% and that would be 1,250

850+2,000×20%

2,850×20%

1,250

I hope that this helps and may I receive brainliest please

Add 6 on both sides, canceling out that -6

3x = 21

Divide both sides by 3 to isolate that variable and get your answer

x = 7.

Answer:

x=7

Step-by-step explanation:

3x-6+6=15+6

3x=21

3x/3=21/3

x=7

Answer: 8*5≥c  

sorry if wrong! Not my strong suit !

Final answer:

Scott spends at least $40 on candy if buying a minimum of 5 pounds at $8 per pound.

Explanation:

Scott buys candy at $8 per pound and will buy at least 5 pounds. Let's use c for the amount he will spend on candy. The possible amounts he will spend on candy can be expressed as:

5 pounds x $8/pound ≤ c would mean $40 ≤ c

Therefore, the inequality solved for c is $40 ≤ c.

Answer:

Infinitely many solutions.

Step-by-step explanation:

x-2y=-3

14y-7x=21

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

simplify 14y-7x=21 into 2y-x=3

x-2y=-3

2y-x=3

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

x=2y+(-3)

x=2y-3

2y-(2y-3)=3

2y-2y+3=3

0+3=3

infinitely many solutions

LCM is 3 (x + 1)(x - 5)(x + 2)

Step-by-step explanation:

Given polynomials are:

x2 - 4x – 5 and x2 – 3x – 10.

Factorizing x^2-4x-5

[tex]x^2-4x-5\\= x^2-5x+x-5\\=x(x-5)+1(x-5)\\=(x+1)(x-5)[/tex]

Factorizing  x^2 – 3x – 10

[tex]x^2 -3x -10\\=x^2-5x+2x-10\\=x(x-5)+2(x-5)\\=(x+2)(x-5)[/tex]

Looking at the fators of both polynomials we can see:

The LCM will be the combination of all factors of polynomials. The factor that occurs in both factorization will be written only once

Hence,

LCM is 3 (x + 1)(x - 5)(x + 2)

Keywords: Polynomials, LCM

Learn more about LCM at:

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Answer:

x=811/238, y=36/119. (811/238, 36/119).

Step-by-step explanation:

4x+(x-y/8)=17

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

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

4x+x-y/8=17

5x-y/8=17

40x-y=136

y=40x-136

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

2y+x-5y-2/4=2

2y-5y+x-1/2=2

-3y+x=2+1/2

-3y+x=4/2+1/2

-3y+x=5/2

-3(40x-136)+x=5/2

-120x+408+x=5/2

-119x=5/2-408

-119x=5/2-816/2

-119x=-811/2

119x=811/2

x=(811/2)/119

x=(811/2)(1/119)=811/238

y=40(811/238)-136

y=16220/119-136

y=36/119

x=811/238, y=36/119.

Answer: 40,320

Step-by-step explanation: Let's say that there is person A,B,C,D,E,F,G,H. and 8 chairs. For the first chair, 8 different people could potentially sit in it, making 8 different possibilities. No matter who sits there, the logic follows the next table. However, since one person is sitting in the first chair, there are 7 different possibilities about who would be sitting in the second chair. If you multiply the two together, there are 56 different possibilities just for the first and second chair. For the third chair, there are 6 different possibilities about whom could sit. Multiply 56*6 and you get 336 possibilities. Keep multiplying out and you get a grand total of 40,320 different arrangements!

Answer:

5040

Step-by-step explanation:

The answer is (8 - 1)!

The reason is that the first person is fixed. Any place is the same as any other place. After that there are 7! choices for the next position.

Answer: 5040