Answer:
20/28 which is about 71%
Step-by-step explanation:
so first you add up how many balls there are. 8+20=28. So 28 is the denominator for the fraction. there are 20 black balls, so that is the numerator. so 20/28 is the fraction. then you divide 20 by 28 to get the rounded percent.
Find the sum of the $x$-coordinates of all possible positive integer solutions to $\frac1x+\frac1y=\frac17$. enter your answer
To find the sum of the x-coordinates of all possible positive integer solutions to the equation 1/x + 1/y = 1/7, we can rearrange the equation and use Simon's Favorite Factoring Trick to solve for x.
Explanation:To find the sum of the x-coordinates of all possible positive integer solutions to the equation 1/x + 1/y = 1/7, we can rearrange the equation to 7x + 7y = xy. Simplifying further, we have xy - 7x - 7y = 0. Applying Simon's Favorite Factoring Trick, we add 49 to both sides of the equation: xy - 7x - 7y + 49 = 49. Factoring the left side gives us (x - 7)(y - 7) = 49. Since we are looking for positive integer solutions, we can set x - 7 and y - 7 to be divisors of 49 and solve for x.
The divisors of 49 are 1, 7, and 49. Setting x - 7 = 1, we get x = 8. Setting x - 7 = 7, we get x = 14. And setting x - 7 = 49, we get x = 56. So the sum of the x-coordinates is 8 + 14 + 56 = 78.
PLEASE HELP ASAP 50 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
51
Step-by-step explanation:
Given
P(x) = 2x³ + 4x² - 10x - 9, then
P(a) = 2a³ + 4a² - 10a - 9 ← substitute x = a into P(x)
To evaluate P(3) substitute a = 3 into P(a)
P(3) = 2(3)³ + 4(3)² - 10(3) - 9 = 54 + 36 - 30 - 9 = 51
Since P(3) ≠ 0 then (x + 3) is not a factor of P(x)
Answer:
51
Step-by-step explanation:
2(3)³ + 4(3)² - 10(3) - 9
= 51
A line through which two points would be parallel to a line with a slope of 3/4?
F. (0,5) and (-4,2)
G. (0,2) and (-4,1)
H. (0,0) and (0,-2)
J. (0,-2) and (-4,-2)
Answer:
F. (0, 5) and (-4, 2)
Step-by-step explanation:
We need to calculate the slope of each of the given sets of points until we find the set associated with a slope of 3/4:
F. (0,5) and (-4,2) As we go from (-4, 2) to (0,5), x increases by 4 and y increases by 3, so the slope is m = rise / run = 3/4. This is the line with slope 3/4.
Please help me out please
radius=diameter/2
therefore r=3÷2 ie 1.5m
area=pi (r^2)m^2
=1.5^2 pi m^2
2.25 pi m^2 is required area
Probability of pulling a green marble out of a bag of coloured marble is 2:5 if you were to pull coloured marbles out of the bag for 600 times how many times would you select a green marble
Answer: 171 green marbles
Step-by-step explanation: There are 7 total marbles so 100/7 equals 14.28
Then there is a 2 out of 7 total tries so 14.28 * 2 equals 28.57% chance to get a green marble.
600 * 0.2857 = 171.41 marbles but you cant get half a marble so 171 green marbles.
The prism is completely filled with 1750 cubes that have edge length of 1/5 ft. What is the volume of the prism? Enter your answer in the box.
Answer:
14 ft³
Step-by-step explanation:
First, find the volume of a single cube: V = s³, where s = side length
V = s³; s = 1/5
V = (1/5)³
V = 0.008 ft³
**Note: (1/5)³ is equal to 1/125 as a fraction. I put it down in decimal form because it's easier for me to work with decimals.**
Now, to find the volume of the prism (which is completely filled with cubes), multiply the volume of one cube by the total number of cubes: 1750.
(1750)(0.008)
14 ft³
The volume of the prism is 14 ft³.
Hope this helps!
Line segment XY is a directed line segment beginning at point X(9, 2) and ending at point Y(-6, 2). Find the point Z on the line segment that partitions the line segment into the segments XZ and ZY at a ratio of 5:3.
Answer:
[tex](-\frac{3}{8},2)[/tex]
Step-by-step explanation:
Point Z divides XY into a 5:3 ratio, so Z is 5/3 of the way from X to Y. That ratio is k, found by writing the numerator of the ratio (5) over the sum of the numerator and the denominator (5 + 3 = 8). Our k value is 5/8. Now we will find the rise and run values which is the slope of this line segment:
[tex]m=\frac{2-2}{-6-9} =\frac{0}{-15}[/tex]
Coordinates are found in this formula:
[tex]Z(x,y)=(x_{1}+k(run),y_{1} +k(rise))[/tex]
Filling that in:
[tex]Z(x,y)=(9+\frac{5}{8}(-15),2+\frac{5}{8}(0))[/tex]
which simplifies to
[tex]Z(x,y)=(9-\frac{75}{8},2+0)[/tex]
which gives us the final coordinates of Z to be [tex]Z(x,y)=(-\frac{3}{8},2)[/tex]
How many distinct permutations of the letters of the word ALFALFA are there?
ANSWER
There are 210 different permutations
EXPLANATION
The word 'ALFALFA' has 7 letters.
The letter 'A' repeats three times.
The letter 'F' repeats two times.
The letter 'L' also repeats two times.
The number of different permutation is
[tex] \frac{7!}{3!2!2!} = 210[/tex]
There are 210 different permutations.
Answer: There are 210 distinct permutations of the letter of that word.
Step-by-step explanation:
Since we have given that
ALFALFA
Here, 3 A,
2 F,
2 L
Number of letters in that word = 7
So, Number of distinct permutations of the letters of the word "ALFALFA":
[tex]\dfrac{7!}{3!\times 2!\times 2!}\\\\=210[/tex]
Hence, there are 210 distinct permutations of the letter of that word.
Jammal makes a cut through a block of florist's foam, as shown. What are the dimensions of the exposed cross section?
A. 6 in x 10 in
B. 3 in x 5 in
C. 3 in x 6 in
D. 5 in x 6 in
Answer:
C. 3 in x 6 in
Step-by-step explanation:
Jammal cuts the block in a straight line parallel to one side... so the section revealed when he finishes his cut will be identical as the parallel side to which the cut is done.
We know the the left side of the prism on the image is 3 inches wide and 6 inches high... so that will also be the dimensions of the exposed cross section.
The answer is then 3 inches y 6 inches. The thickness of the block (5 inches) has no impact on the exposed area of the cross-section.
x^2−1.78x, if x=2.78
Answer:
2.78
Step-by-step explanation:
We are given the expression [tex]x^2-1.78x[/tex]
As we know that x=2.78, we can plug that value into the expression and simplify it
[tex](2.78)^2-1.78(2.78)\\\\7.7284-4.9484\\\\2.78[/tex]
Yuri and his brother arrive at the park at 12:30.They spent 2 3/4 hours there.What time d they leave.
They left the park at 3:05
What is the area of a triangle with vertices at (–2, –1), (4, –1), (6, 5)?
6 square units
9 square units
18 square units
36 square units
The calculated area of the triangle is 18 square units
How to calculate the area of the triangle in square units?
From the question, we have the following parameters that can be used in our computation:
(–2, –1), (4, –1), (6, 5)
The area of the triangle in square units is calculated as
Area = 1/2 * |x₁y₂ - x₂y₁ + x₂y₃ - x₃y₂ + x₃y₁ - x₁y₃|
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * |-2 * -1 - 4 * -1 + 4 * 5 - 6 * -1 + 6 * -1 - 5 * -2|
Evaluate the sum and the difference of products
Area = 1/2 * 36
So, we have
Area = 18
Hence, the area is 18 square units
A school is taking a group of students to the aquarium. Including chaperones, 132 people will be going on the field trip. The ratio of chaperones to students is 1:5.
Answer:
660
Step-by-step explanation:
Because the ration is 1:5, then 132 chaperones times 5 is 660 students. Please like me and rate!!
Please please help me out
Answer:
1/2
Step-by-step explanation:
see the picture.
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1, then
cosx = [tex]\sqrt{1-sin^2x}[/tex]
note that ([tex]\frac{\sqrt{3} }{2}[/tex] )² = [tex]\frac{3}{4}[/tex]
cosΘ = [tex]\sqrt{1-\frac{3}{4} }[/tex] = [tex]\sqrt{\frac{1}{4} }[/tex] = [tex]\frac{1}{2}[/tex]
Identify the equation of the circle M with center M(−3,−2) and radius 5. HELP ASAP!
This is actually quite comical as I just had a DBA concerning equations of circles so, I'm pretty sure I'm qualified to help you.
Equation of a Circle: (x-h)²+(y-k)²=r² where (h, k) is the center and r is the radius.
So, all we need to do is plug in your info:
(x+3)²+(y+2)²=5²
And, there goes your answer.
The Equation of Circle with center (-3, -2) and radius 5 is (x+3)²+(y+2)²=25.
What is Circle?
A circle is a round 2-dimensional shape. It is a closed shape with a distance from center to circumference termed as radius 'r' and distance from one point on the circumference to another point passing through center termed as diameter 'd'.
Here,
Equation of a Circle:
(x-h)²+(y-k)²=r²
where (h, k) is the center and r is the radius.
So, all we need to put the value of h, k and r in equation of circle:
(x+3)²+(y+2)²=5²
(x+3)²+(y+2)²=25
Thus, the Equation of Circle with center (-3, -2) and radius 5 is (x+3)²+(y+2)²=25.
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Ethan's car can travel 30 miles per gallon on gasoline. Gasoline costs $4 per gallon, including tax. Ethan drove his car 180 miles on the trip. What was the total cost, in dollars, of the gasoline that the car used for Ethan's trip?
Ethan's car used 6 gallons of gasoline for his 180 miles trip, which at a cost of $4 per gallon, results in a total gasoline cost of $24.
Explanation:To calculate the total cost of gasoline for Ethan's trip, you need to understand how many gallons were used and then multiply that figure by the cost per gallon. As Ethan's car can travel 30 miles per gallon, and Ethan drove 180 miles in total, Ethan's car used 6 gallons of gasoline (180 miles ÷ 30 miles/gallon). Given that gasoline costs $4 per gallon including tax, Ethan therefore spent a total of $24 on gasoline for his trip (6 gallons x $4/gallon).
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The cost per gallon is $24.
Explanation:To calculate the total cost of the gasoline, we need to divide the distance driven by the car by the car's gas mileage to find the number of gallons used.
Then, we can multiply the number of gallons used by the cost per gallon to find the total cost. In this case,
Ethan drove 180 miles and his car can travel 30 miles per gallon, so he used 180/30 = 6 gallons of gasoline.
The cost per gallon is $4, so the total cost is 6 * $4 = $24.
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Describe the roots of the equation shown below.
[tex]3x^2+4x+2=0[/tex]
A. There are two complex roots.
B. There is one real, double root.
C. There are two real, rational roots.
D. There are two real, irrational roots.
Answer A becaus descriminant =16-4*3*2=-8
ANSWER
A. There are two complex roots.
EXPLANATION
The given quadratic equation is
[tex]3x^2+4x+2=0[/tex]
when we compare this to
[tex]a {x}^{2} + bx + c = 0[/tex]
we have a=3,b=4 and c=2.
We use the discriminant to determine the nature of roots.
[tex]D= {b}^{2} -4ac [/tex]
[tex]D= {4}^{2} -4(3)(2) [/tex]
[tex]D= 16-24[/tex]
[tex]D= - 8[/tex]
Since the discriminant is less than zero, the equation will have 2 complex roots.
A used car is priced at $2,695. If you borrow the money for the car, your payments will be $122 a month for 30 months. How much will you save by paying cash? A. $333 B. $1,075 C. $965 D. $233
Answer: $965
Step-by-step explanation:
The used car is priced at $2,695.
If you borrow the money for the car, your payments will be $122 a month for 30 months. This means that the total amount of money that you would have paid at the end of 30 months at a rate of $122 per month is the amount paid per month multiplied by the total number of months. It becomes
Total payment = 122×30 = $3660
This means that you ended up paying higher than you would have paid if you paid cash.
Amount that you would have saved = amount paid over 30 months - cost of the car
Amount that you would have saved
= 3660 - 2695 = $965
By paying cash for the used car priced at $2,695, you will save $965. Option C is correct.
The total amount paid when financing the car can be found by multiplying the monthly payment by the number of months:
Total amount paid when financing = Monthly payment × Number of months
= $122 × 30
= $3,660
To find the savings, we subtract the total amount paid when financing from the total cost of the car when paying cash:
Savings = Total cost of the car when paying cash - Total amount paid when financing
= $2,695 - $3,660
= -$965
Since the result is negative, it means you would actually be paying more when financing the car compared to paying cash.
Absolute value of savings = |- $965|
= $965
Therefore, the correct answer is $965.
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Jeremy is recording the weights, in ounces, of different rock samples in a lab. The weights of seven rocks are listed below.
11, 13, 14, 6, 10, 9, 10
The eighth rock that he weighed was 5 ounces. How would the interquartile range of the data be affected if Jeremy includes the weight of the eighth rock?
A.
The interquartile range does not change.
B.
The interquartile range cannot be determined.
C.
The interquartile range increases.
D.
The interquartile range decreases.
CCCCCCCCCCCCCCCCCCCCCC
Answer:
The correct answer is option "C"
"The interquartile range increases"
The value of the (RIC) will increase from 4 to 5.75, that is, 44%
Step-by-step explanation:
The range is defined as the difference between the maximum and minimum value of a series of data. Xmax - Xmin
The interleaving range (RIC) is a measure of dispersion that measures the central range of 50% of the data.
Therefore, if a low value is included, such as five, the variance of the data would be greater and, consequently, the value of the (RIC) will increase from 4 to 5.75, that is, 44%
The price of the box of 15 stickers is $6. The price of the box of 25 stickers is $8. All prices are without tax, and the price of the boxes is the same. A Write an equation which tells the price Y for the number of X stickers.
Answer:
[tex]y=0.2x+3[/tex]
Step-by-step explanation:
Let
x ----> the number of stickers
y ----> the price of the boxes
we have the points
[tex]A(15,6),B(25,8)[/tex]
Find the slope
[tex]m=(8-6)/(25-15)[/tex]
[tex]m=2/10=0.20[/tex]
Find the equation of the line into point slope form
The equation is equal to
[tex]y-y1=m(x-x1)[/tex]
substitute the value of m and the point A
[tex]y-6=0.2(x-15)[/tex]
[tex]y=0.2x-3+6[/tex]
[tex]y=0.2x+3[/tex] ----> linear equation that represent the situation
Use graphs and tables to find the limit and identify any vertical asymptotes of the function.
limit of 1 divided by the quantity x minus 8 as x approaches 8 from the left
Answer:
The line x = 8 is our vertical asymptote
The limit of [tex]\frac{1}{x-8}[/tex] as x approaches 8 from the left is negative infinity; -∞
Step-by-step explanation:
We have been given the following function;
[tex]\frac{1}{x-8}[/tex]
Considering that the function is rational, it will defined everywhere on the real line except where the expression in the denominator will be 0;
That is the function will not be defined where;
x - 8 = 0
solving for x yields;
x = 8
The function will be approaching the vertical line x = 8 asymptotically, meaning that the function will never touch or cross this line. We can therefore say that,
The line x = 8 is our vertical asymptote for the given function
The limit of [tex]\frac{1}{x-8}[/tex] as x approaches 8 from the left;
[tex]\lim_{x \to8^{-} }\frac{1}{x-8}[/tex]
For x approaching 8 from the left, [tex]x<8[/tex] which implies that [tex]x-8<0[/tex]
The denominator will be a negative quantity approaching 0 from the left, that is -∞.
Thus;
[tex]\lim_{x \to8^{-} }\frac{1}{x-8}[/tex] = -∞
Find the graph attached.
Answer:
it goe towards negative infinity
Step-by-step explanation:
1/6-8=-1/2
1/7-8=-1
1-7.999-8=-10000
therefore you can assume that it is going to a negative infinity direction
Anyone willing to help me?
Answer:
I think it's the last one, BD/AE
Step-by-step explanation:
Which graphs have a positive average rate of change?
Answer:
Step-by-step explanation:
In general, graphs that go from lower left to upper right have a positive slope (think of it as going up the stairs...positive), and graphs that go from upper left to lower right have a negative slope (think of it as going down the stairs...negative). I don't see graphs here but use this general idea and you'll be fine. Of course, this applies to graphs of lines of the form y = mx + b.
Which of these is a correct expansion of (4x – 2)(2x 2 + 3)?
Answer:
4x*2x^2+4x*3+(-2)*2x^2+(-2)*3
Step-by-step explanation:
The expansion of the given (4x – 2)(2x 2 + 3) is
4x*2x^2+4x*3+(-2)*2x^2+(-2)*3.
We have given that the (4x – 2)(2x 2 + 3)
We have to determine the expansion of the(4x – 2)(2x 2 + 3)
What is the expansion?the act of expanding or the state of being expanded · something expanded; an expanded surface or part · the degree, extent, or amount by which something expands.
Therefore the expansion is given by
[tex](4x -2)(2x^ 2 + 3)=4x*2x^2+4x*3+(-2)*2x^2+(-2)*3[/tex]
Therefore we get the expansion of the given (4x – 2)(2x 2 + 3) is
4x*2x^2+4x*3+(-2)*2x^2+(-2)*3.
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Jackie has set up a lemonade stand this summer. The line plot represents how many liters she has sold during her first 13 days in business. How much lemonade has Jackie sold in all? A) 5 8 L B) 70 8 L C) 13 8 L D) 33 8 L
Answer the answer is c
Step-by-step explanation:
I also got C for this answer
Will give brainliest answer. Simplify and select the answer with the appropriate restrictions for the variable.
Answer:
4:The denominator can't be equal to 0, therefore - 5
5: 4)The denominator can't equal to 0 -4
Answer:
Question 4:
(x² - 25) / (x - 5)
= (x² - 5²) / (x - 5)
= [(x - 5) · (x + 5)] / (x - 5)
= x + 5
The denominator can't be equal to 0, therefore:
x - 5 ≠ 0 ⇔ x ≠ 5
Question 5:
(3x² - 6x) / (x² - 2x - 8)
= [3x (x - 2)] / (x² + 4x - 2x - 8)
= [3x (x - 2)] / [x (x + 4) - 2 (x + 4)]
= [3x (x - 2)] / [(x - 2) (x + 4)]
= 3x / (x + 4)
The denominator can't equal to 0, therefore:
x + 4 ≠ 0 ⇔ x ≠ -4
A baker needs 4 3⁄4 cups of flour. if she uses a 1 1⁄2 cup measuring scoop, how many scoops of flour must the baker use to have at least 4 3⁄4 cups?
Final answer:
A baker would need to use 7 scoops of flour with a 1 1⁄2 cup measuring scoop to have at least 4 3⁄4 cups of flour.
Explanation:
The question at hand requires us to determine how many scoops of flour a baker would need to use to obtain at least 4 3⁄4 cups of flour with a scoop that holds 1 1⁄2 cups. To solve this, we will divide the total amount of flour needed by the capacity of the scoop:
Convert the mixed numbers to improper fractions: 4 3⁄4 cups = 19⁄4 cups and 1 1⁄2 cups = 3⁄2 cups.Now, divide 19⁄4 cups by 3⁄2 cups to find the number of scoops.19⁄4 ÷ 3⁄2 = 38⁄8 ÷ 3⁄2 = 38⁄8 x 2⁄3 = 38⁄12 x 2⁄1 = 76⁄12 = 19⁄3. This result is an improper fraction which corresponds to 6 1⁄3 scoops.Since a baker can't use a fraction of a scoop, they will need to use at least 7 full scoops to ensure they have enough flour.Therefore, the baker must use 7 scoops to have at least 4 3⁄4 cups of flour.
Ira has 128 stamps in his stamp album he has the same number of stamps in each of 8 pages how many stamp are on each page
Answer:
16
Step-by-step explanation:
128 stamps and 8 pages have the same amount to add up to 128
So 128 ÷ 8 I'll make it easier
8÷8=1
40÷8=5
80÷8=10
(128÷8)
10+5+1 = 16
There are 16 stamps per page.
Answer:
16 stamps.
Step-by-step explanation:
128 stamps divided by 8 stamps per page is 16 stamps.
find the product of 3√-3 and 3 √-5
a.9 √15
b.3 √-15
c.3 √15
d.3 √-8
(3√-3)(3√-5) multiply 3 and 3, and multiply √-3 and √-5 together, the √ stays
9√15 Your answer is A
Answer:
The correct answer is option A. 9 √15
Step-by-step explanation:
It is given that, 3√-3 and 3 √-5
To find the product
we have, 3√-3 and 3 √-5
(3√-3) * (3 √-5) = 3√-3 * 3 √-5
= (3 * 3) (√-3 * √-5)
= 9 * √(-3 * -5)
= 9* √15
= 9√15
Therefore the correct answer is option A. 9√15
Gina wants to go to the water park with her friends. They have a total of www dollars to buy 555 tickets. Each ticket costs 151515 dollars. Select the equation that matches this situation. Choose 1 answer: Choose 1 answer: (Choice A) A 5 = 15 \times w5=15×w5, equals, 15, times, w (Choice B) B w = 15 +5w=15+5w, equals, 15, plus, 5 (Choice C, Checked) C w = 5 \times 15w=5×15w, equals, 5, times, 15
Answer:
Option C. w=5×15
Step-by-step explanation:
Let
w ----> the amount of dollars to buy 5 tickets
we know that
The variable w is equal to multiply the numbers of tickets by the cost of each ticket
so
The equation that represent this situation is
w=5(15)
Answer:
Thus, the required equation is W=15×5
Step-by-step explanation:
Consider the provided information.
Gina wants to go to the water park with her friends. They have a total of w dollars.
W represents the total money they have.
They buy 5 tickets and each ticket cost 15 dollars.
Thus the total cost for 5 tickets is:
15×5
She had W dollars. That means the above expression is equal to W.
W=15×5
Thus, the required equation is W=15×5.