Jack has some marbles. He has ten more red marbles than blue marbles. He has fewer yellow marbles than blue marbles.

How many of each color marble could Jack have?

(This is the whole question)​

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

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

Answer:

5 2/3

Step-by-step explanation:

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:

103,1

Step-by-step explanation:

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

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

Read more about probability at:

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The area of a triangle is 1/2*base*height

If h=8, b=15, then we have 1/2*8*15 which is 1/2*120 which is 60

So the right choice is B

Hope this helped!

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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Answer:

The answer is C, 5.4 units

Step-by-step explanation:

Answer:

hola

Step-by-step explanation:

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.

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:

(1, -3)

Step-by-step explanation:

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.

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:

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.

Answer: 7.2 * 10 to the negative four

Step-by-step explanation:

Answer:

3/5 x d = 345

Step-by-step explanation:

got the question right on the quiz

Answer:

[tex]Rate\ of\ commission=22\%[/tex]

Step-by-step explanation:

Let her rate of commission[tex]=x\%[/tex]

Salary[tex]=\$ 1000[/tex]

Weekly Amount[tex]=\$ 6500[/tex]

So earning from commission=Weekly Amount-Salary

Earning from the commission[tex]=6500-1000[/tex]

Earning from the commission[tex]=\$ 5500[/tex]

Total Sales[tex]=\$ 25000[/tex]

Commission is[tex]=x\%\ of\ 25000[/tex]

[tex]x\%\ of\ 25000=5500\\\\\frac{x}{100}\times 25000=5500\\\\x\times 250=5500\\\\x=\frac{5500}{250}\\\\x=22\%[/tex]

[tex]Rate\ of\ commission=22\%[/tex]

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]

To solve for 'y' in the equation 'y + 1.05 = 7.26', subtract 1.05 from both sides of the equation, the answer is 'y = 6.21'.

In mathematics, solving for 'y' involves rearranging the equation to isolate the 'y' variable. In this case, the equation is 'y + 1.05 = 7.26'.
To solve for y, begin by performing the inverse operation of addition on both sides of the equation. This means subtracting 1.05 from both sides.
After doing so, the equation would look like this:

So the solution for y in this equation is 6.21.

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Answer:

A. 178.35°F

B. ≅ 5.64 minutes or 5 minutes 38 seconds approximately

C. 76°F.

Step-by-step explanation:

1. Let's review the information given to us to answer the questions correctly:

Temperature of the pizza in the oven = 400°F

Temperature of the kitchen = 76°F constantly

Temperature of the pizza after 3 minutes = 267°F

2. A. What is the temperature  T(t)  of the pizza after 5 minutes?

We will use the ratio of how much degrees the temperature of the pizza decreases per minute, this way:

Ratio = (Temperature of the pizza in the oven - Temperature of the pizza after 3 minutes)/ Minutes

Ratio = (400 - 267)/3 = 133/3 = 44.33 (Rounding to two decimal´places)

It means that the temperature of the pizza diminishes 44.33°F per minute.

Therefore, the temperature  T(t)  of the pizza after 5 minutes, will be:

T(5) = 400 - (44.33 * 5) = 400 - 221.65 = 178.35°F

B. Determine the time when the temperature of the pizza is 150°F.

min.

Time when the pizza is 150°F = (400 - 150)/44.33 = 250/44.33 = 5.64 minutes or 5 minutes 38 seconds approximately

C. After a very long period of time, what is the approximate temperature of the pizza? It will be the temperature of the kitchen, 76°F.

Answer:

3/5

Step-by-step explanation:

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

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

m=3/5

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 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: $720.37

Step-by-step explanation:

interest = 2000(1.0155)^20 - 2000

= 720.37

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

Answer:5

Step-by-step explanation:

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:

The family bought approximately 2 bags of chips.

Step-by-step explanation:

Given:

Total spent by family = $5.50

We need to find bags of chips did the family buy.

Solution:

Let number of bags of chips bought be 'x'.

Also Given:

The number of candy bars was twice as much as the number of bags of chips.

number of candy bars = [tex]2x[/tex]

Now we can say that;

Total spent by family is equal to sum of the number of bags of chips bought and number of candy bars.

framing in equation form we get;

[tex]x+2x=5.5\\\\3x=5.5[/tex]

Dividing both side by 3 we get;

[tex]\frac{3x}{3}=\frac{5.5}{3}\\\\x=1.83\approx2[/tex]

Hence the family bought approximately 2 bags of chips.