3. Robert let 100 students listen to his Ipod. After listening to his Ipod 75 students said they
liked his music while 25 students said they did not like his music. Johnny says that for every
3 students who liked Robert's music, there was 1 person who did not like his music. Is this
true?

Answer:

6 1/8 and 11 7/8

Step-by-step explanation:

Just use algebra. x+y is equal to 18. 3x=4y+5. Then you substitute the value x for y by dividing by three. From there it is just computation

Answer:

The numbers are 11 and 7

Step-by-step explanation:

Let the numbers be P and V

Let P be the greater number and V be the smaller number.

From the question, the sum of the numbers equals 18 i.e

P + V = 18

Also from the question,

We were told that three times the greater number exceeds four times the smaller number by 5 i.e

3P = 4V + 5

P = (4V + 5) / 3

Substituting the value of P into equation (1), we obtain:

P + V = 18.

(4V + 5) / 3 + V = 18

Multiply through by 3 to express in linear form, we have:

4V + 5 + 3V = 54

Collect like terms

4V + 3V = 54 - 5

7V = 49

Divide both side by the coefficient of V i.e 7

V = 49/7

V = 7

P + V = 18

P = 18 - V

P = 18 - 7

P = 11

The numbers are 11 and 7

Answer:

The answer is C, 5.4 units

Step-by-step explanation:

Answer:

[tex]\frac{1}{4}[/tex] of circumference of the circle

Step-by-step explanation:

We are given that

Arc NOP=Central angle=[tex]\theta=90^{\circ}[/tex]

Radius of circle=5 units

We have to find the statement which describes best the length of arc NOP.

Arc length=[tex]\frac{central\;angle}{360}\times 2\pi r[/tex]

Using the formula

Arc length=[tex]\frac{90}{360}\times circumference\;of\;circle[/tex]

Where Circumference of circle=[tex]2\pi r[/tex]

Arc length NOP=[tex]\frac{1}{4}[/tex]circumference of circle

Hence, the arc length NOP=[tex]\frac{1}{4}[/tex] of circumference of the circle

Answer:

1/4 the circumference of circle L

Step-by-step explanation:

See the explanation

Theorem:

A perpendicular dropped from the center of the circle to a chord bisects it. It means that both the halves of the chords are equal in length.

In my own words, I'd explain this by drawing a circle and the diameter of the circle drawn in red. Also, we have a chord of the circle drawn in blue. The theorem says that the diameter bisects the chord in a right angle, so we will have two halves that measure the same so that's why we drew two  hash marks on each half of the chord.

A problem about this is indicated in figure 2. Suppose you have a perpendicular dropped from the center of the circle to a chord and you know that the left half measures 2 cm, so we want to know the x-value of the right half. Since the diameter bisects the chord, then it is true that [tex]x=2cm[/tex] as well.

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ALL OF THESE WILL BE SOLVE FOR X AND Y!!!

Problem 1 Solve For x: x=−6y−7

Show work: Add -6y to both sides.

x+6y+−6y=−7+−6y

x=−6y−7

Problem 1 Solve For y: y = -1/6x + -7/6

Show work: Add -x to both sides.

x+6y+−x=−7+−x

6y=−x−7

Step 2: Divide both sides by 6.

6y/6 = -x -7/6

Problem 2 Solve For x: x=−6y−7

Show work:  Add -12y to both sides.

2x+12y+−12y=−14+−12y

2x=−12y−14

Step 2: Divide both sides by 2.

2x/2 = -12y - 14/2

Problem 2 Sovle For y: y=-1/6x + -7/6

Show work: Add -2x to both sides.

2x+12y+−2x=−14+−2x

12y=−2x−14

Step 2: Divide both sides by 12.

12y/12 = -2x-14/12

6 cats/kittens were adopted.

Step-by-step explanation:

Given,

Number of cats/kittens at the event = 44

Number of cats/kittens adopted = x

Number of cats/kittens returned = Twice returned as adopted = 2x

New total = 50

We will subtract the adopted and add the returned cats/kittens.

Total cats/kittens at event - adopted + returned = New total

[tex]44-x+2x=50\\44+x=50\\x=50-44\\x=6[/tex]

6 cats/kittens were adopted.

Keywords: expression, variables

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Answer: $720.37

Step-by-step explanation:

interest = 2000(1.0155)^20 - 2000

= 720.37

Hope this helps!!! Good luck!!! :)      

Answer:

30

Step-by-step explanation:

It states that it rained twice as much in 5 days all you do is multiply the 2 times 3 which is 6 so then u multiply 6 times 5 which is 30.

The river rose a total of 93 inches over five days.

The question asks how much a river rises in five days given a certain pattern of increase. To find the solution, we use a geometric sequence because the river rises by a constant multiple each day. On the first day, the river rises three inches. Since on each subsequent day the river rises by twice the amount it did the previous day, the sequence of increases over five days is: 3 inches, 6 inches, 12 inches, 24 inches, and 48 inches.

The total rise of the river is the sum of these increases:

3 + 6 + 12 + 24 + 48 = 93 inches.

Therefore, the river rose a total of 93 inches over the span of five days.

Answer:

3/12

Step-by-step explanation:

To solve this problem, we can use square roots. Due to x being squared, we can square root both the top and the bottom. The square root of 9 is 3 with 144 being 12. In the end, x equals 3/12

[tex]\text{Hey there!}[/tex]

[tex]\mathsf{What\ is\ the\ value\ of\ x: x^2=\dfrac{9}{144}\ ?}[/tex]

[tex]\mathsf{First,\ you\ have\ to\ simplify\ both\ sides\ of\ your\ equation!}[/tex]

[tex]\mathsf{\dfrac{9}{144}= \dfrac{9\div9}{144\div9} = \boxed{\dfrac{1}{16}}}[/tex]

[tex]\mathsf{New\ equation\ (for\ now): x^2=\dfrac{1}{16}}[/tex]

[tex]\mathsf{Take\ your\ square\ root!}[/tex]

[tex]\mathsf{x=\pm\sqrt{\dfrac{1}{16}}}[/tex]

[tex]\boxed{\boxed{\mathsf{Thus,\ your\ answer\ is: x =0.25\ or\ x = -0.25}}}[/tex][tex]\boxed{\boxed{\checkmark}}[/tex]

[tex]\boxed{\boxed{\boxed{\mathsf{You\ could\ also\ say\ x= \dfrac{3}{12}\ or\ x=-\dfrac{3}{12}}}}}[/tex][tex]\boxed{\boxed{\boxed{\checkmark}}}[/tex]

[tex]\mathsf{Side\ note: that's\ when\ the\ plus\ or\ minus\ sign\ (\pm)\ came\ in\ handy!}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

Step-by-step explanation:

Assuming the problem you want to solve is finding the number of each coin, you can let variables represent those numbers. I like to use mnemonic variables, such as q for the number of quarters, and d for the number of dimes.

The two equations you can write are based on the given information:

  q + d = 60 . . . . . . you have 60 coins

  .25q +.10d = 9.45 . . . . . their value is 9.45

_____

You have 23 quarters and 37 dimes.

_____

I like to solve these by substitution, using an expression to replace the variable representing the lowest-value coin.

  d = 60 -q . . . . . . . expression for the number of dimes

  .25q +.10(60 -q) = 9.45

  .15q +6.00 = 9.45 . . . . . eliminate parentheses, collect terms

  .15q = 3.45 . . . . . . . . . . .subtract 6.00

   q = 23 . . . . . . . . . . . . . . . divide by 0.15

   d = 60 -q = 37

2x^2 + 5x + 3

What are the factors of the polynomial?

(2x+3)(x+1)

(2x-3)(x-1)

(3x+2)(x+1)

(3x-2)(x-1)

Option A

The factors are:

[tex]2x^2+5x+3 = (2x+3)(x+1)[/tex]

Given that, the quadratic equation is:

[tex]2x^2 + 5x + 3[/tex]

We have to find the factors of polynomial

[tex]2x^2+5x+3[/tex]

Split 5x as 2x and 3x

[tex]2x^2+5x+3 = 2x^2 +2x + 3x + 3[/tex]

[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]

[tex]2x^2+5x+3=\left(2x^2+2x\right)+\left(3x+3\right)[/tex]

[tex]\mathrm{Factor\:out\:}2x\mathrm{\:from\:}2x^2+2x\mathrm{:\quad }2x\left(x+1\right)[/tex]

Thus we get,

[tex]2x^2+5x+3 = 2x(x+1) + (3x+3)[/tex]

[tex]\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x+3\mathrm{:\quad }3\left(x+1\right)[/tex]

Thus we get,

[tex]2x^2+5x+3 = 2x(x+1) + 3(x+1)[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}x+1[/tex]

Thus we get,

[tex]2x^2+5x+3 = (2x+3)(x+1)[/tex]

Thus the factors are found for given polynomial

Final answer:

The correct factors of the polynomial +5x+3 are (2x+3)(x+1), as they multiply to give the original polynomial. None of the other provided options yield the correct polynomial upon multiplication.

Explanation:

The question asks to identify the factors of the polynomial +5x+3. Factors are expressions that, when evaluated, produce the value of the polynomial. Let's examine the provided options to find which pair of binomials gives us the correct polynomial upon multiplication:

(2x+3)(x+1) = 2x² + 2x + 3x + 3 = 2x² + 5x + 3, which matches the original polynomial.

(2x-3)(x-1) = 2x² - 2x - 3x + 3 = 2x² - 5x + 3, which does not match the original polynomial.

(3x+2)(x+1) = 3x² + 3x + 2x + 2 = 3x² + 5x + 2, which does not match the original polynomial.

(3x-2)(x-1) = 3x² - 3x - 2x + 2 = 3x² - 5x + 2, which does not match the original polynomial.

Therefore, the correct factors of the polynomial +5x+3 are (2x+3)(x+1).

Answer:

slope-intercept form: y = 3x - 14

slope: 3

y-intercept: -14

Step-by-step explanation:

To find the equation in slope-intercept form, isolate the "y" variable by moving everything to the other side. Slope-intercept form looks like y = mx + b.

"x" and "y" mean points that are on the line.

"m" is the slope.

"b" is the y-intercept.

Rearrange the equation to isolate "y"

3x - y = 14

3x - 3x - y = 14 - 3x          Subtract 3x from both sides

-y = 14 - 3x          Multiply both sides by -1.

y = -14 + 3x          Put "3x" in front of "-14" because it has the 'x'

y = 3x - 14          Looks like y = mx + b

State the "m" and "b".

m = 3     (Slope of the line)

b = -14    (y-intercept of the line)

Therefore the equation of the line in slope-intercept form is y = 3x - 14. The slope is 3 and the y-intercept is -14.

[tex]\boxed{sinA=\frac{a}{c}} \\ \\ \boxed{cosA=\frac{b}{c}}[/tex]

The trigonometric functions are very important in math and physics. Sound, light and electricity all involve oscillations and are modeled by sine and cosine functions. So, we can provide a trig ratio for the sine and cosine function by taking a right triangle as shown in the figure below. So the relationships are as follows:

[tex]sinA=\frac{Opposite \ side}{Hypotenuse} \\ \\ cosA=\frac{Adjacent \ side}{Hypotenuse} \\ \\ \\ For \ the \ figure: \\ \\ a:Opposite \ side \\ \\ b:Adjacent \ side \\ \\ c:Hypotenuse[/tex]

So we can write:

[tex]\boxed{sinA=\frac{a}{c}} \\ \\ \\ \boxed{cosA=\frac{b}{c}}[/tex]

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Answer:

99% Confidence interval: (63.65,69.65

Step-by-step explanation:

We are given the following data:

63, 68, 60, 59, 68, 65, 67, 64, 69, 69, 61, 67, 61, 60,  66, 67, 68, 66, 70, 79, 76, 75, 65

Formula:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{1533}{23} = 66.65[/tex]

Sum of squares of differences = 575.217

[tex]S.D = \sqrt{\dfrac{575.217}{22}} = 5.11[/tex]

99% Confidence interval:

[tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex]  

Putting the values, we get,  

[tex]t_{critical}\text{ at degree of freedom 22 and}~\alpha_{0.01} = \pm 2.818[/tex]  

[tex]66.65 \pm 2.818(\dfrac{5.11}{\sqrt{23}} ) = 66.65 \pm 3.002 = (63.65,69.65)[/tex]

Answer:5

Step-by-step explanation:

answer is 5 2/3.............

Answer:

5 2/3

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-1)/(5-0)

m=3/5

Answer:

Step-by-step explanation:

Let x represent the number of tickets sold, and y represent the total amount of money raised. Since each ticket is $2.50, the total amount of money raised is equal to $2.50 times the number of tickets. The equation would be y = 2.50x.

Answer:

y=2.5x

The total amount of money raised(y) = how many tickets are sold(x) x the price per ticket(2.5)

Hypothetically, if 24 tickets were sold, we could substitute 24 into x...

y=2.5(24)

y=60

Let x represent the number of tickets sold, and y represent the total amount of money raised. Since each ticket is $2.50, the total amount of money raised is equal to $2.50 times the number of tickets. The equation would be y = 2.50x.

The x variable represents the number of tickets sold.

The y variable represents the total amount of money raised from ticket sales.

The equation for the scenario is y = 2.50x.

Answer:

The house is increasing in value by 2% each year.

Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:

[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]

Step-by-step explanation:

For this case if we have this expression

[tex] 210000(1.02)^x[/tex]

We have the same functional forma like the exponential model given by:

[tex] y = a b^x[/tex]

Where a = 210000 represent the constant or initial value and b = 1.02 represent the base.

So let's analyze the possible options:

The house has a starting value of 1.02.

False the starting value for this case is 210000 since if x=0 then we see that the value is 210000

The house is decreasing in value by 2% each year.

False the increase is 1.02 each year so then in % we have

[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]

We  have an increase of 2% each year

The house is increasing in value by 2% each year.

Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:

[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]

The value of the house is changing by 0.02% each year.

False the increase is 2% per year

Answer:

103,1

Step-by-step explanation:

Use this formula: 100*(1+3.1%)

Answer:2/3

Step-by-step explanation:

So you add 8 plus 2 And keep the denominator the same and then simplify with 5

Answer:

hola

Step-by-step explanation:

Answer:

5/3

Step-by-step explanation:

30/18

you can easily simplify a large improper fraction by finding a common number.

in this case the number is 6.

6x5=30 & 6x3=18

therefore, if you divide each number by 6 you get 5/3

decimal: 1.66667 or 1.67 or 1.7

improper fraction: 5/3

proper fraction 1 2/3

Final answer:

30 divided by 18 as an improper fraction is ⅓, or 5/3, obtained by converting the division result into a mixed number and then back into an improper fraction.

Explanation:

To convert 30 divided by 18 into an improper fraction, you first divide 30 by 18 to get the decimal form, which is approximately 1.666. To express this as an improper fraction, we recognize that 1.666 is 1 and 2/3 in mixed number form.

Since 2/3 is already a fraction, we can convert the mixed number back into an improper fraction by multiplying the whole number 1 by the denominator 3 and then adding the numerator 2. This gives us 3 + 2 = 5, so the improper fraction is 5/3.

Step-by-step explanation:

The given expression is

[tex]x^3.x^2[/tex]

To write the given expression is equivalent = ?

The given expression is

[tex]x^3.x^2[/tex]

We know that,

The exponential identity,

[tex]a^{m}.a^{n}=a^{m+n}[/tex]

= [tex]x^{3+2}[/tex]

= [tex]x^{5}[/tex]

∴ The given expression is equivalent = [tex]x^{5}[/tex]

Thus, the given expression is equivalent to [tex]x^{5}[/tex].

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Answer:

The answer to (x3*x2)5 is x25

Step-by-step explanation:

Answer:

v = 2

Step-by-step explanation:

Answer: 10.5

Step-by-step explanation:

Hello the answer is 10.5 you just have to multiply 3 1/2 times 3 and there's your answer

Have a great day hope this helps!:):):

Answer:

10 1/2

Step-by-step explanation:

convert 3 1/2 into an improper fraction

3 1/2 = 7/2

if the flour is tripled that means

3 1/2 x 3

= 7/2 x 3

= (7x3) / 2

= 21/2  (convert to mixed fraction, by long division)

= 10 1/2

Answer:

3/20

Step-by-step explanation:

Prob. (For green (Bag A)) = 3/12

Prob. (For Black (Bag B)) = 9/15

3/12 x 9/15 = 3/20

The probability of selecting one green marble from bag A and one black marble from bag B is 0.15

There are 3 green marbles in bag A out of a total of 12 marbles (i.e. 3 green and 9 red).

So, the probability of selecting a green marble from bag A is:

[tex]Pr = \frac 3{12}[/tex]

There are 9 black marbles in bag B out of a total of 15 marbles (i.e. 9 black and 6 orange).

So, the probability of selecting a black marble from bag B is:

[tex]Pr = \frac 9{15}[/tex]

The required probability is then calculated as:

[tex]P = \frac 3{12} * \frac 9{15}[/tex]

Multiply

[tex]P = 0.15[/tex]

Hence, the probability of selecting one green marble from bag A and one black marble from bag B is 0.15

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Answer:

(1, -3)

Step-by-step explanation: