Answer:
The answer is B. 5/8 quarts
Step-by-step explanation:
1 ounce is equal to .03125 quarts so to find the amount of quarts, you multiply 20 times .03125 to get .625 or 5/8.
Final answer:
There are 5/8 quarts of soda in a 20 ounce bottle, which is found by dividing 20 by the conversion factor of 32 ounces per quart.
Explanation:
The student has asked how many quarts of soda are in a 20 ounce bottle. To convert ounces to quarts, we use the conversion factor that there are 32 ounces in a quart. To find the number of quarts in 20 ounces, we divide 20 by 32.
20 oz ÷ 32 oz/qt = 0.625 qt
This can also be written as 5/8 quarts, which is option B. Therefore, there are 5/8 quarts of soda in a 20 ounce bottle.
find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-4,-8), B(0,0) ; 3 to 1
To find the coordinates of point P along the directed line segment AB so that AP to PB is in the ratio 3 to 1, we use the section formula. Substituting the values into the formula, we find that the coordinates of point P are (-1, -2).
Explanation:To find the coordinates of point P along the directed line segment AB so that AP to PB is in the ratio 3 to 1, we can use the concept of section formula.
The section formula states that if we have two points A(x1, y1) and B(x2, y2), and we want to find a point P along the line segment AB such that AP to PB is in the ratio m to n, then the coordinates of P can be found using the following formulas:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
In this case, A(-4, -8) and B(0, 0).
Let's substitute the values into the formula:
x = (3 * 0 + 1 * -4) / (3 + 1) = -4/4 = -1
y = (3 * 0 + 1 * -8) / (3 + 1) = -8/4 = -2
Therefore, the coordinates of point P are (-1, -2).
Final answer:
To find point P on line segment AB where AP:PB = 3:1, we use section formula to get P's coordinates as (-1,-2). This method applies interpolation of the endpoints' coordinates, A(-4,-8) and B(0,0), by their respective weights in the given ratio.
Explanation:
To find the coordinates of point P on the directed line segment AB such that the ratio of AP to PB is 3 to 1, we can use the section formula which combines the x and y coordinates of A and B weighted by the given ratio, since P divides AB internally in the ratio 3:1.
The coordinates of A are (-4, -8) and the coordinates of B are (0, 0). Using the section formula, we can find the coordinates of P as follows:
Let x and y be the coordinates of P.
The x-coordinate of P is given by ((3 * 0) + (1 * (-4))) / (3 + 1) = -1.
The y-coordinate of P is given by ((3 * 0) + (1 * (-8))) / (3 + 1) = -2.
Therefore, the coordinates of P are (-1, -2).
This process involves interpolation of the given points in the specific ratio to find the required coordinates.
A gallon of chevron gas is currently $3.75 per gallon. If your car's tank holds 12.25 gallons, about how much will it cost to fill the tank
Multiply the number of gallons by the price per gallon:
12.25 gallons x 3.75 per gallon = $45.94 total.
What is the measure of ∠CAB?
34°
68°
146°
56°
Question 2
If ∠AOR is 76°, what is the measure of ∠AOS?
14°
110°
24°
104°
27/22 as a decimal rounded to the nearest tenth
The fraction 27/22, when converted into a decimal and rounded to the nearest tenth, is approximately 1.2.
To convert a fraction to a decimal, divide the numerator by the denominator. In this case, divide 27 by 22.
Explanation:The question asks to convert the fraction 27/22 into a decimal, rounded to the nearest tenth. First off, we calculate the division of 27 by 22, which gives us approximately 1.227. However, we need to round this figure to the nearest tenth, which results in the value of 1.2. Be sure to understand that when we say 'rounded to the nearest tenth', we refer to the first digit after the decimal point.
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Hey circular trampoline has an area of 132.2 ft.² what is the radius of the trampoline rounded to the nearest tenth
The radius of trampoline is 6.5 feet
Step-by-step explanation:
Area of circular trampoline = 132.2 ft²
Let,
r be the radius of trampoline.
We know that area of circle = [tex]\pi r^2[/tex]
Therefore,
[tex]\pi r^2 = 132.2\\[/tex]
Putting value of [tex]\pi = 3.14[/tex]
[tex]3.14r^2=132.2[/tex]
Dividing both sides by 3.14
[tex]\frac{3.14r^2}{3.14}=\frac{132.2}{3.14}\\r^2=42.10[/tex]
Taking square root on both sides
[tex]\sqrt{r^2}= \sqrt{42.10} \\r=6.48 \ ft[/tex]
Rounding to nearest tenth,
Radius of trampoline = 6.5 feet
The radius of trampoline is 6.5 feet
Keywords: Area, circle, radius
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solve the system using elimination -x+5y=13 x-y=15
Answer:
the value of x= 22 and y = 7
Let g(x) be the reflection of f(x) = x² + 3 in the y-axis. What is a function rule for g(x)?
It's [tex]g(x)=f(-x)=f(x)[/tex].
Reflection over y-axis is the same as original function.
Hope this helps.
Look at the photo worth 30 points hurry pleases
[tex]\frac{6^{12}}{6^{10}}[/tex] is equal to 36.
Step-by-step explanation:
Given expression is;
[tex]\frac{6^{12}}{6^{10}}[/tex]
When the base is same, the exponent of denominator is subtracted from the exponent of numerator, therefore,
[tex]6^{12-10} = 6^2\\= 36[/tex]
Hence,
[tex]\frac{6^{12}}{6^{10}}[/tex] is equal to 36.
Keywords: exponent, fractions
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Bevo has $5000 to invest. Bank A offers a savings account that has an APR of 1.15% and compounds monthly. Which equation will determine how much money Bevo will have in his account after 9 years?
The equation [tex]A=5000(1.000958333)^{108}[/tex] will determine how much money Bevo will have in his account after 9 years
Step-by-step explanation:
The formula for compound interest, including principal sum is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where:
A is the future value of the investment/loan, including interestP is the principal investment amount (the initial deposit or loan amount)r is the annual interest rate (decimal)n is the number of times that interest is compounded per unit tt is the time the money is invested or borrowed forBevo has $5000 to invest. Bank A offers a savings account that has an APR of 1.15% and compounds monthly
We need to find Which equation will determine how much money Bevo will have in his account after 9 years
Because there is no choices we will write the equation
∵ Bevo has $5000 to invest
∴ P = 5000
∵ Bank A offers a savings account that has an APR of 1.15%
and compounds monthly
∴ r = 1.15% = 1.15 ÷ 100 = 0.0115
∴ n = 12 ⇒ compounds monthly
∵ t = 9
- Substitute all of theses values in the formula below
∵ [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
∴ [tex]A=5000(1+\frac{0.0115}{12})^{(12)(9)}[/tex]
∴ [tex]A=5000(1.000958333)^{108}[/tex]
The equation [tex]A=5000(1.000958333)^{108}[/tex] will determine how much money Bevo will have in his account after 9 years
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The equation to find out how much Bevo will have in his account after 9 years by investing $5000 in a saving account at Bank A which offers an APR of 1.15% compounding monthly is given by the future value formula of compound interest: FV = P(1 + r/n)^(nt). By plugging the values into this formula, Bevo can determine his future balance.
Explanation:The subject of this question is about understanding compound interest. Specifically, it is about interpreting how Bevo's financial investment would grow over a certain period at a specific rate of interest in a savings account. The equation to calculate the future value (FV) of Bevo's investment, compounded monthly, is given by the compound interest formula:
FV = P(1 + r/n)^(nt)
Where:
P is the principal amount (the initial amount of money Bevo has to invest, in this case $5000).r is the annual interest rate in decimal form (the APR divided by 100, for Bank A this would be 1.15/100 = 0.0115).n is the number of times that interest is compounded per unit t, in this case, this value is 12 (as it is compounded monthly).t is the time the money is invested for in years (specified in the question as 9 years).This gives a better understanding of how savings accounts and compounded interest work.
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What is 7x+5=-9? Show your work.
Verify the solution?
Please help, it will be much appreciated!
We have
[tex]7x+5=-9[/tex].
1. Subtract 5 from both sides to get
[tex]7x=-9-5\Longrightarrow 7x=-14[/tex].
2. Divide both sides by 7 to get
[tex]x=\dfrac{-14}{7}=\boxed{-2}[/tex]
Hope this helps.
In which of the tables below x and y are inversely proportional? Find the constant of variation. If there is one. (a) x:y, 3:8, 4:6, 5:4.8, 5.5:4
(b) x:y, 0.1:300, 0.5:60 75:0.4, 100:0.3
Answer:
The table B represent an inverse variation
The constant of variation k is 30
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
Verify table A
For x=3, y=8 ----> [tex]k=y*x[/tex] ----> [tex]k=8*3=24[/tex]
For x=4, y=6 ----> [tex]k=y*x[/tex] ----> [tex]k=6*4=24[/tex]
For x=5, y=4.8 ----> [tex]k=y*x[/tex] ----> [tex]k=4.8*5=24[/tex]
For x=5.5, y=4 ----> [tex]k=y*x[/tex] ----> [tex]k=5.5*4=22[/tex]
The values of k are different
therefore
The table A not represent an inverse variation
Verify table B
For x=0.1, y=300 ----> [tex]k=y*x[/tex] ----> [tex]k=300*0.1=30[/tex]
For x=0.5, y=60 ----> [tex]k=y*x[/tex] ----> [tex]k=60*0.5=30[/tex]
For x=75, y=0.4 ----> [tex]k=y*x[/tex] ----> [tex]k=75*0.4=30[/tex]
For x=100, y=0.3 ----> [tex]k=y*x[/tex] ----> [tex]k=100*0.30=30[/tex]
All the values of k are the same
therefore
The table B represent an inverse variation
The equation is equal to
[tex]y*x=30[/tex]
Answer: Only (A)
If you go RSM this the Answer.
Solve by converting to the easiest form of the rational numbers to use in the problem. Show your work.
Arwen uses a dropper that produces drops that have a volume of 1/8 millimeter test tube. How many drops does it take to fill the test tube?
Answer:
8 drops will take to fill the test tube.
Step-by-step explanation:
A volume of [tex]\frac{1}{8}[/tex] millimeter test tube is produced by the dropper that Arwen uses.
Now, we are asked to calculate the number of drops it will take to fill the test tube.
Then, [tex]\frac{1}{8}[/tex] of the millimeter test tube is equivalent to 1 drop.
So, 1 of the millimeter test tube will be equivalent to [tex]\frac{1}{\frac{1}{8} } = 8[/tex] drops.
Therefore, 8 drops will take to fill the test tube. (Answer)
Mrs. Jones ordered 5 cheese pizzas and 1 pepperoni pizza. She ordered a total of 6 pizzas. What fraction of pizzas are cheese?
Answer:
5/6
Step-by-step explanation:
5 is the amount of cheese pizzas Mrs. Jones ordered out of the 6 pizzas in total. 5 is a prime number, so the fraction cannot be simplified.
what is the mode of this data?
1.7 8.9 3 5.9 3.2 4.1 6.6 0.7
Answer:
The value of Mode is 2.43
Step-by-step explanation:
To find the mode of the given data first we have to arrange it in a increasing order then find out mean and median of the given data 0.7,1.7,3,3.2,4.1,5.9,6.6,8.9 is in increasing order For finding the median we need to take the average of 4th and 5th terms because we have the no of terms in the sequence is even not odd so we need to take the average the 4th term=3.2 and the 5th term =4.1so average =(3.2+4.1)/2=3.65so the median is equal to 3.65For mean we have to take the average of the data so mean= sum of all data /no of data mean =(0.7+1.7+3+3.2+4.1+5.9+6.6+8.9)/8=4.26so by using the formula we can get modeMode=3×Median-2×MeanMode=3×3.65-2×4.26=2.43∴The value of Mode is given as 2.43Blaine buys 2 books and the total cost is $24.18. What is the constant of proportionality that relates the cost in dollars, y, to the number of books, x?
Answer:
$ 12.09
Step-by-step explanation:
formula Y = KX
Where; y = $ 24.18
x = 2 books
k = constant of proportionality
Step 1. Do the equation based on the formula
Y = kx
$24.18 = k2
Step 2. Divide by 2
$24.18/2 = k2/2
k = $12.09 (answer)
equation in slope-intercept form for the two points (5,0) and (12,7)
Answer:
y=x-5
Step-by-step explanation:
Take the 2 points
(5,0)
(12,7)
7-0[tex]\frac{7-0}{12-5}[/tex]
You should get 7/7=1
The slope is 1
Next find the y int or B
y=(1)x+b Take one point and plug it in : (5,0)
0=5+b
b=-5
The final answer is y=x-5
1) 5(3g-2)+8=58.
2) 7x-(4x-15)=13
Find the variable value.
Answer:
Step-by-step explanation:
5(3g-2)+8=58
5(3g-2)=58-8
5(3g-2)=50
3g-2=50/5
3g-2=10
3g=10+2
3g=12
g=12/3
g=4
-----------------
7x-(4x-15)=13
7x-4x-(-15)=13
3x+15=13
3x=13-15
3x=-2
x=-2/3
What is cos θ when sin θ = 2/5? Rationalize the denominator if necessary.
Answer:
[tex]cos(\theta)=\frac{\sqrt{21}}{5}[/tex]
Step-by-step explanation:
we have that
The angle [tex]\theta[/tex] belong the the First Quadrant (see the figure)
so
[tex]cos(\theta)\ and\ sin(\theta)[/tex] are positive values
we know that
[tex]sin^2(\theta)+cos^2(\theta)=1[/tex] ----> trigonometric identity
we have
[tex]sin(\theta)=\frac{2}{5}[/tex]
substitute in the identity
[tex](\frac{2}{5})^2+cos^2(\theta)=1[/tex]
[tex]cos^2(\theta)=1-\frac{4}{25}[/tex]
[tex]cos^2(\theta)=\frac{21}{25}[/tex]
square root both sides
[tex]cos(\theta)=\frac{\sqrt{21}}{5}[/tex]
Thirteen more than three times a number is equal to the difference between -29 and three times the number.
Answer:
-7
Step-by-step explanation:
Thirteen more than three times a number can be written as (3x+13).
The difference between -29 and three times the number can be written as (-29-3x).
Then set them equal and solve.
3x+13=(-29)(-3x)
3x=(-42)(-3x)
6x=(-42)
x=-7
The algebraic equation of the statement is 3x + 13 = -29 - 3x and the solution is x = -7.
What is the value of the unknown number?Given the parameter:
Thirteen more than three times a number is equal to the difference between -29 and three times the number.
Let 'x' represent the unknown number:
Now, let's translate the given sentence into an algebraic equation.
Thirteen more than three times a number ⇒ 3x + 13
equal to the difference between -29 and three times the number ⇒ = -29 - 3x
Now, we combine:
3x + 13 = -29 - 3x
We solve for x:
3x + 3x = -29 - 13
6x = -42
x = -42/6
x = -7
Therefore, the value of x is -7.
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What is 3z+3/4-2z equal
The simplified expression of 3z + (3/4) - 2z is z + (3/4).
Explanation:The expression 3z + (3/4) - 2z can be simplified by combining like terms. Like terms have the same variable and exponent. In this case, the like terms are the 3z and the -2z. When you combine them, you get z. So the simplified expression is z + (3/4).
Mrs Sims cut a melon into fifths. She gave 1 piece to each of her four children.She used equal amounts of leftover melon to make the fruit cup. What fraction of the original melon does she used to make each fruit cup?
The fraction of the original melon that was used to make each fruit cup is 1/5, as there was one piece left after giving each of the four children their share.
Explanation:Mrs. Sims cut a melon into fifths and gave 1 piece to each of her four children. Therefore, there would be one piece of the melon left after giving each child a piece.
To determine the fraction of the original melon used to make each fruit cup from the leftover piece, we simply need to account for the remaining melon. As there is only one piece left out of the original five pieces, the fraction of the original melon used for each fruit cup is 1/5.
Find the 15th term of the geometric sequence 3, -6, 12, ...
Answer:
49152
Step-by-step explanation:
To find the 15th term of the geometric sequence 3, -6, 12, ..., we identify the common ratio as -2 and use the formula for the nth term of a geometric sequence. By calculating 3 * (-2)^14, we find that the 15th term is 49152.
Explanation:To find the 15th term of the geometric sequence 3, -6, 12, ... we first need to determine the common ratio. By dividing the second term by the first term, we find that the common ratio is -2.
Formula for the nth term of a geometric sequence:
an = a1 × r(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.
Finding the 15th term:
Plugging in the values, we get: a15 = 3 × (-2)(15-1) = 3 × (-2)14. Since (-2)14 is positive (because any even power of a negative number is positive), the 15th term will be positive. Calculating the value, a15 = 3 × 16384 = 49152.
Therefore, the 15th term of the geometric sequence is 49152.
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For the basic function f(x) = x, what conclusions can you make about fix) and
f(x) - 5? Select all that apply.
a. They intercepts are the same.
b. The function () - 5 has a greater rate
of change
c. They are parallel lines:
d. The graph of the function(x) is translated
down 5 units to produce fix) - 5.
Answer:
c, d
Step-by-step explanation:
If f(x) = x, then f(x) - 5 = x - 5.
The two functions in slope-intercept form (y = mx+ b) are:
[1] y = x and [2] y = x - 5
In equation [1], the slope is 1 and the y-intercept is 0.
In equation [2], the slope is 1 and the y-intercept is -5.
a. The y-intercepts are not the same. 0 ≠ -5
b. The rates of change, or the slopes, are the same, neither are greater than the other. 1 = 1
c. They are parallel lines. Lines are parallel when they have the same slope. 1 = 1.
d. The (-5) indicates that the new function is translated down (-) by 5 units (5) from the parent function f(x) = x.
c and d are correct.
I will give brainliest
give it to me and not her
Write an equation in standard form of the line that has x-intercept 6 and y-intercept -2
Answer:
6x-2
Step-by-step explanation:
Which pair of angles are same side exterior angles?
2 and 8
1 and 8
2 and 4
3 and 7
Answer:
Exterior angles are the ones on the outside and same side means they sit on the same side of the bisector so your answer is 1 and 8
Step-by-step explanation:
∠1 and ∠8 are same side exterior angles
If a transversal line intersect 2 parallel lines, then same sides exterior angles
are supplementary.
This means same side exterior angles sum up to 180 degrees. Therefore,
∠1 and ∠8 are same side exterior angles.
This means ∠1 and ∠8 are supplementary angles . They sum up to 180 degrees.
∠1 + ∠8 = 180°
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Is the sum of 5/16 + 7/15
greater than 1, less than 1, or equal to 1?
Answer:
It is less than 1
Step-by-step explanation:
5/16 is equal to 0.3125 and 7/15 is equal to 0.466. When added together is equals 0.779.
The figure shows two parallel lines KL and NO cut by the transversals KO and LN:
Which statement best explains the relationship between AKLM and AONM?
AKLM - AONM because mx3 = m_4 and m_1= m25
AKLM - AONM because m23 = m26 and mZ1=m24
AKLM E AONM because mZ3 =m24 and m_1=m25
AKLM = AONM because m23 =mZ6 and mZ1=m24
Answer:
the first answer posted is wrong
Step-by-step explanation:i put it in my exam and it was wrong and i think the right answermight be
AKLM = AONM because m23 =mZ6 and mZ1=m24
What would you expect the size of the audience to be if the ticket price was £26.50
Answer: the size would be big
Step-by-step explanation: because image a lot of people going there the had to make the cost go up because so many people was going that is why its size would be big
Manny can complete a sales route in 7 hours. Jane can do the same job in 3hours. How long will it take them to the job together
Answer:
Step-by-step explanation:
1/7x+1/3x=1
3/21x+7/21x=1
10/21x=1
x=21/10 hour or 2 hours and 1 minute
Final answer:
Manny and Jane will take approximately 2.1 hours to complete the job together.
Explanation:
To find out how long it will take Manny and Jane to complete the job together, we need to determine their combined rate of work. Manny can complete the job in 7 hours, so his work rate is 1/7 of the job per hour. Jane can complete the job in 3 hours, so her work rate is 1/3 of the job per hour. To find their combined rate, we add their individual rates: 1/7 + 1/3 = 3/21 + 7/21 = 10/21.
Since their combined work rate is 10/21 of the job per hour, it will take them 21/10 hours to complete the job together. Simplifying this fraction, we get 2.1 hours. Therefore, it will take Manny and Jane approximately 2.1 hours to complete the job together.