Cory drinks water from a bottle during a bike ride. The average amount of water, in
ounces, in his water bottle can be represented by the equation y = -8x+32, where y is the amount of water remaining after x hours. Based on the equation, what amount of water, in ounces, will remain in the bottle after Cory rides for 2 1/2 hours?
Answers
Reason
They give you the formula
Y= -8x +32
Y is water remaining, the number we are looking for
X = 2.5 hours, insert in place of X
Y= (-8) (2.5) + 32
Y= -20 + 32
Y = 12
The amount of water will remain in the bottle after Cory rides for 2 1/2 hours will be;
⇒ y = 12 ounces
What is Equation of line?
The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The average amount of water, in ounces, in his water bottle can be represented by the equation,
⇒ y = - 8x + 32
Where, y is the amount of water remaining after x hours.
Now,
Since, The average amount of water, in ounces, in his water bottle can be represented by the equation,
⇒ y = - 8x + 32
Hence, The amount of water will remain in the bottle after Cory rides for 2 1/2 hours is,
Substitute x = 2 1/2 in above equation,
⇒ y = - 8 × 2 1/2 + 32
⇒ y = - 8 × 5/2 + 32
⇒ y = - 20 + 32
⇒ y = 12 ounces
Thus, The amount of water will remain in the bottle after Cory rides for 2 1/2 hours is,
⇒ y = 12 ounces
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Related Questions
list 4 factors of 24. list 4 multiples of 24.
Answers
Answer:
Factors of 24: 1, 2, 3, 4, 6 etc.
Multiples of 24: 48, 72, 96, 120
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
Factors of 24:24 can be written as:
= 1 × 24
= 2 × 12
= 3 × 8
= 4 × 6
So, 1, 2, 3, 4, 6, 8, 12 and 24 are the factors of 24.
Multiples of 24 are:1 × 24 = 24
2 × 24 = 48
3 × 24 = 72
4 × 24 = 96
and so on...
So, the first 4 multiples of 24 are 24, 48, 72 and 96.
[tex]\rule[225]{225}{2}[/tex]
Find the area of the rectangle.
A rectangle is shown. The left side is labeled with the expression 8 x. The top side is labeled with the expression 7 x plus 1. (1 point)
15x + 1
56x2 + 8x
56x + 8
15x2 + 9x
Answers
Answer:
B
Step-by-step explanation:
= (7x+1) • (8x)
= 56x^2 + 8x
Find the value of x.
Answers
Answer:
Step-by-step explanation:
plug in x try numbers
x = 14.2
When completing the square on the equation c^2 + 11c = 12, the resulting solution is
Answers
Answer:
Attached file is the solutions
Step-by-step explanation:
A business student is interested in estimating the 95% confidence interval for the proportion of students who bring laptops to campus.
He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within five percentage points
of the population proportion. What is the minimum sample size required by this student, given that no prior estimate of the population
proportion is available?
(You may find it useful to reference the z table. Round intermediate calculations to at least 4 decimal places
and "2" value to 3 decimal places. Round up your answer to the nearest whole number.)
Answers
Using the z-distribution, the minimum sample size required by this student is of 385.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
We want a margin of error of M = 0.05, with no prior estimate, hence [tex]\pi = 0.5[/tex], then we have to solve for n to find the minimum sample size.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96(0.5)[/tex]
[tex]\sqrt{n} = 1.96 \times 10[/tex]
[tex](\sqrt{n})^2 = (1.96 \times 10)^2[/tex]
n = 384.16
Rounding up, the minimum sample size is of 385.
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Find X and QT. The shape is a Rhombus
Answers
Answer:
See below ~
Step-by-step explanation:
Sides of a rhombus are equal.
⇒ QT = TS
⇒ x² - 4x - 10 = 6x + 14
⇒ x² - 10x - 24 = 0
⇒ x² + 2x - 12x - 24 = 0
⇒ x (x + 2) - 12 (x + 2) = 0
⇒ (x + 2)(x - 12) = 0
⇒ x = -2 or x = 12
Substitute both values and see which gives a positive value for QT :
When x = -2 :
QT = (-2)² - 4(-2) - 10QT = 4 + 8 - 10QT = 2When x = 12 :
QT = (12)² - 4(12) - 10QT = 144 - 48 - 10QT = 86The 2 possible answers are :
x = -2, QT = 2x = 12, QT = 86Which results only in a horizontal compression of Y=1/x
by a factor of 6?
Answers
Step-by-step explanation:
[tex] y = \frac{1}{x} [/tex]
In order to compress by a factor of 6, we multiply the variable x by 6. It would compress the hyperbola
[tex]y = \frac{1}{6x} [/tex]
True or False? A corollary is a statement that can be easily proved by using theorem.
Answers
An electrician charges a $40 fee to make a house call plus an hourly rate for labor. If the total bill that takes 2 hours comes to $99 what is the electrician hourly labor rate?
Answers
Reason
You can use the formula y=mx+b for this
We know y is the total bill of $99
We know b is the $40 fee (y intercept or starting point)
We know x is 2 hours
We are looking for m or rate
Substitute numbers for letters in formula
99= m(2) +40
Subtract 40 from both sides to isolate m
59=2m
Divide both sides by 2 to solve for m
M=$29.50
We can prove our answer by inserting our answer for “m” in the formula
99=29.50x2+40
99=99
Answer is correct
simplify (4+i)(3-2i)
Answers
Answer: 14 - 5i
Step-by-step explanation:
Answer:
-10i+15 or 15-10i
Step-by-step explanation:
Use the cross multiply method
(4+1)(3-2i)
4x3=12
4x-2i=-8i
1x3=3
1x(-2i)=-2i
now we sum our similarities.
-10i+15
forty percent of participants in a math contest were boys. fifty percent of the boys revived medals. the number of boys who received the medals was equal to the number of girls who received the medals. what percent of the participants were girls who received medal?
Answers
20% of the participants are girls and got a medal, and 33% of the girls got a medal.
What percent of the participants were girls who received medal?
First, we know that 40% of the participants were boys, so the other 60% were girls.
We know that 50% of the boys got a medal, so the percentage (in decimal form) of participants that are boys and got a medal is:
P = (0.4)*(0.5) = 0.2
So, 20% of the participants are boys and got a medal.
We know that the number of girls that got a medal is the same as the number of boys, then we also have that 20% of the participants are women who got a medal.
Then if the percentage of girls that got a medal is x (in decimal form), we must have that:
Q = (0.6)*(x) = 0.2
x = 0.2/0.6 = 0.33
x = 0.33
This means that 33% of the girls got a medal.
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Tickets for a soccer game cost $5 for students and $8 for adults. the number of students was 7 less than 11 times the numbers of adults. the amount of the money from tickets was 3682 how many of each tickets were sold?tichets
Answers
The number of students will be 642 and the number of the adults will be 59.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
Tickets for a soccer game cost $5 for students and $8 for adults.
The number of students was 7 less than 11 times the numbers of adults.
The amount of the money from tickets was 3682.
Let x be the number of students and y be the number of the adults.
Then the equation will be
x = 11y – 7 …1
5x + 8y = 3682 …2
From equation 1 and 2, we have
5(11y – 7) + 8y = 3682
55y + 8y – 35 = 3682
63y = 3717
y = 59
Then the value of x will be
x = 11 × 59 – 7
x = 642
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find the distance around one-fifth of a circle with diameter of 14 inches
Answers
To solve this problem, you will need to know the formula to find the circumference of a circle given the diameter of a circle. After calculating the circumference, you will then divide this result by 5 to obtain the final answer needed for this problem.
Find the CircumferenceThe circumference of a circle is found using the formula C = 2πr.
[tex]C = 2\pi r[/tex]
We are given the diameter. The radius can be found using r = D/2.
[tex]\displaystyle r=\frac{D}{2}[/tex]
[tex]\displaystyle r=\frac{14}{2}[/tex]
[tex]r=7[/tex]
Plug in the radius to the formula for a circle's circumference: C = 2πr.
[tex]C = 2 \pi (7)[/tex]
Rearrange the equation to distribute the 7 into the 2π.
[tex]C = 7(2\pi)[/tex]
Distribute the 7.
[tex]C=14\pi[/tex]
Find One-Fifth of the DistanceTo find one-fifth of the distance (formally termed the circumference) around the circle, divide the circumference by 5.
[tex]\displaystyle \frac{14\pi}{5}[/tex]
If you are looking for a simplified answer in terms of π, this will suffice. If you need an exact answer that does not reference π, continue reading.
For a solution not in terms of π, first, multiply 14 by π.
[tex]14\times\pi = 43.98229715[/tex]
Divide this value by 5.
[tex]\displaystyle \frac{43.98229715}{5} = 8.7964594[/tex]
To make this easier to present, round to the hundredths place.
[tex]8.7964594 \approx 8.80[/tex]
The final answer, dependent on the value you are asked to provide, is:
[tex]{\boxed{\displaystyle \frac{14\pi}{5} \ \text{inches}}[/tex]
[tex]\boxed{\text{approximately} \ 8.8 \ \text{inches}}[/tex]
Suppose there is a big drop in interest rates in Mexico and a small drop in U.S. interest rates. Everything else equal, what is likely to happen to value of the MXN?
Answers
If we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.
The foreign exchange market works according to the principles of firms, households, and investors:
These three constituent factors of the foreign exchange market determine the demand and supply patterns in the market. Demand for a foreign currency might increase in the foreign exchange market is linked to the expectation of an increase in the value of a foreign currency. Supply of a foreign currency in the foreign exchange market is linked to an inverse principle, where the expectation of a decrease in the value of foreign currency pushes supply upwards. If we are to suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A., then the value of the MXN will decrease, with everything being equal. A higher interest rate leads to the appreciation of a foreign currency relative to other currencies in the foreign exchange market. A lower interest rate leads to the depreciation of a foreign currency relative to other currencies in the foreign exchange market.Therefore, if we suppose that there is a big drop in the interest rates in Mexico and a small drop in the interest rates in the U.S.A, with everything else equal, the value of MXN will decrease.
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What is the domain of the function represented by the list of ordered pairs?
(0, 2), (-3, 6), (4, 8), (2, 5), (-2, 4)
Answers
Answer:
D: (-3,4).
Step-by-step explanation:
There is really no need to solve it. Plot those points onto a graph and draw lines. I have done it on desmos. Looking at the x-axis to find the domain. From the left to right x-axis we can see that the domain should be D: (-3,4).
Based on the vertical bar chart below, in which of the following months were just over 10% of professional European soccer players
born?
March
B) January
April
May
Professional European soccer player birth months
Relative frequency (%)
20%
15%
10%
5%
Jan Feb Mar Apr May Jun
ایل
Month
....
Aug Sep Oct Nov Dec
Answers
By critically observing the vertical bar chart, only the month of May had a birth of just over 10%.
What is a bar chart?A bar chart refers to a type of chart that is used for the graphical representation of a data set, especially by using rectangular bars or vertical columns.
Based on the vertical bar chart (see attachment), the relative frequency (&) with the birth of over 10% are:
Jan Feb Mar Apr MayHowever, only the month of May had a birth of just over 10%.
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What is the surface area of the cylinder below?
Answers
Answer:
Surface Area = 378.25
Step-by-step explanation:
Comment
It's not clear whether the figure has 0 1 or 2 lids. Since it is a cylinder, I will assume 2 lids like a can of soup.
Area lids
diameter = 11.4
radius = d/2
radius = 11.4/2
radius = 5.7
Area = pi * r^2
Area = (3.14 * 5.7^2) * 2 There are 2 lids.
Area = 102.01 yd^2
Area body
This is found by finding the circumference of the lid and multiplying by the height
Circumference
C = 2*pi*r
2*r = the diameter
2*r = 11.4
C = 3.14*11.4
C = 35.80
Area body
Area body = C* h
h = 7.8
Area body = 35.80 * 7.8
Area body = 279.24
Total Area = 102.01 + 279.24 = 378.25
3a =2b + -6 (solve for a)
Answers
Answer:
shown below
Step-by-step explanation:
3a = 2b - 6
a = (2b - 6) / 3 or 2b / 3 - 2
Answer:
a = (2b-6)/3
Step-by-step explanation:
3a = 2b + -6
lets make a the subject of the formula
divide both sides of the equation by 3
3a/3 = a = (2b-6)/3
a = (2b-6)/3
Factor out the GCF from the polynomial.
r(2²-24) + (2²-24)
Answers
Answer: -20
Step-by-step explanation: i hope its right
Find DG.
DE
2x+17
EF
8
FG
2
x + 20
Answers
The value of DG is 4x + 45
Determine the length of a line segmentFrom the question, we are to determine the value of DG
From the given information,
DE = 2x + 17
EF = 8
FG = 2x + 20
Then,
DG = DE + EF + FG
DG = 2x + 17 + 8 + 2x + 20
DG = 4x + 45
Hence, the value of DG is 4x + 45
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On Monday, the water was shut off 3 times for ¼ hours, 2/3 hours, and 1-3/4 hours, respectively. What was the total number of hours the water was off?
Answers
Answer:
2-2/3 hours
Step-by-step explanation:
1/4 + 2/3 + 1-3/4 = 1/4 + 2/3 + 7/4. Use common is 12, so we get 3+8+21/12 = 32/12. Simplify equal 8/3 or 2-2/3 hours!
Calculate the gross earning for an apple picker based on the following differential pay scale: 1- 1000:$0.03 each 1001-1600:$0.06 each over 1600:$0.07 each. Calculate the Gross earning
Answers
If he picks 1965, then the Gross earning will be $85.55.
The missing part of the question is given below.
If he picks 1965, then Calculate the Gross earning.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Calculate the gross earning for an apple picker based on the following differential pay scale:
1 – 1000: $0.03 each
1001 – 1600: $0.06 each
over 1600: $0.07 each
Total apples picked by Lindbergh = 1965
So, for 1000 apples, he will get =1000 × 0.03 = $30
Now, remaining apples = 1965 – 1000 = 965
Now for next 600 apples (from 1001-1600), he will get = 600 × 0.05 =$30
Now, remaining apples = 965 – 600 = 365
So, for remaining 365 (above 1600) apples, he will get = 365 × 0.07 = $25.55
So, total gross earning = $30 + $30 + $25.55
⇒ $85.55 is total gross earning
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Find the perimeter of the following polygon. Be sure to include the correct unit in your answer. 19 cm 15 cm 14 cm 9 cm
Answers
A student has a test scores of 87, 89, 94 points. What must he score on the fourth exam to have an average of at least 92 points?
Answers
Answer: He must have atleast 98 points on the next exam in order to get an average of 92 points.
Step-by-step explanation: To calculate average, you need to add all the numbers given, and divide the sum by how many numbers there are. 87 + 89 + 94 + 98 (equals 368), and divide 368 by 4. You will get the average of 92 as its result.
In your own words, explain the discriminant test. Use the discriminant test to decide whether the equation represents a parabola, ellipse or a hyperbola and explain why you know this is true. x^2 − 4xy + 3x + 25y − 6 = 0
Answers
A discriminant test is one that tells whether a formula has one, two or no solutions.
The equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
What is a discriminant test?A discriminant test is a test that tells whether there are one, two or no solutions for a formula.
The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac.
The discriminant of a quadratic equation is given as ax2 + bx + c = 0
A discriminant is said to be a parabola either x or y is squared and not both unlike that of an eclipse and a hyperbola.
With the given equation, x^2 − 4xy + 3x + 25y − 6 = 0, only x is squared and not both x and y.
Thus, the equation represents a parabola because the discriminant of a parabola has either x or y squared and not the both.
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Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations.
3x-4y-5z=-27
5x+2y-2z=11
5x-4y+4z=-7
a. (1,5,51)
b. ( 10, 5, 51)
c. (10, 51, 23)
d. ( 1, 5, 2)
Answers
The value of x, y and z will be 1, 5 and 2 respectively
An augmented matrix in linear algebra is a matrix created by joining the columns of two supplied matrices, often so that the same basic row operations may be applied to each of the given matrices individually.
Lets write the augmented matrix by writing the coefficients of all the variables:
3 -4 -5 -27 Row 1
5 2 -2 11 Row 2
5 -4 4 -7 Row 3
We need to get
1 0 0
0 1 0
0 0 1
then the values of x, y, and z will be in the last column.
The row operation (R1=R1/3) is used to get the identity matrix.
1 -4/3 -5/3 -9 Row 1
5 2 -2 11 Row 2
5 -4 4 -7 Row 3
Add row 2 to row 1 and multiply by 5 (R2=R2(5)R1).
1 -4/3 -5/3 -9 Row 1
0 26/3 19/3 56 Row 2
5 -4 4 -7 Row 3
Add row 3 to row 1 and multiply by 5 (R3=R3(5)R1).
1 -4/3 -5/3 -9 Row 1
0 26/3 19/3 56 Row 2
0 8/3 37/3 38 Row 3
Multiply row 2 by 326 (R2=(3/26)R2)
1 -4/3 -5/3 -9 Row 1
0 1 19/26 84/13 Row 2
0 8/3 37/3 38 Row 3
Add row 2 multiplied by 4/3 to row 1 (R1=R1+(4/3)R2)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 8/3 37/3 38 Row 3
Add row 3 to row 2 and multiply the result by 8/3 (R3=R3(8/3)R2).
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 0 135/13 270/13 Row 3
Multiply row 3 by 13/135 (R3=(13/135)R3)
1 0 -9/13 -5/13 Row 1
0 1 19/26 84/13 Row 2
0 0 1 2 Row 3
Add row 3 multiplied by 9/13 to row 1 (R1=R1+(9/13)R3)
1 0 0 1 Row 1
0 1 19/26 84/13 Row 2
0 0 1 2 Row 3
Row 2 is reduced by row 3 multiplied by 19/26 (R2=R2(19/26)R3).
1 0 0 1 Row 1
0 1 0 5 Row 2
0 0 1 2 Row 3
Hence the value of x, y and z will be 1, 5 and 2 respectively
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Toyota manufactures most of the vehicles it sells in the United Kingdom in Japan. The base platform for the Toyota Tundra truck line is ¥1,650,000. The spot rate of the Japanese yen against the British pound has recently moved from ¥197/£ to ¥190/£. How does this change the price of the Tundra to Toyota's British subsidiary in British pounds? Explain.
Answers
When the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.
Prices = 1,650,000
Exchange rates = ¥197/£
Change in exchange rate = ¥190/£
So, here Original price of the Toyota tundra is
= 1,650,000 ÷ 197
= 8375.63
New import price is = 1,650,000 ÷ 190
= 8,684.21
Percentage change in the price of the imported trucks should be
= ( New price - Old price) / old price *100 = (8,684.21 - 8375.63) ÷ 8375.63 = 3.68%
Hence , when the spot rate of the Japanese yen against the British pound moves from ¥197/£ to ¥190/£. This change the price of the Tundra to Toyota's British subsidiary in British pounds by 3.68%.
(This is the percentage change in the Japanese yen as the price of the truck remains unchanged).
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Which linear function represents the line given by the point-slope equationy-2=4x-3)?
O fx)=6x-1
Of(x)=8x-6
Of(x)=4x-14
Of(x)=4x-10
Answers
f(x)= 4x - 10
what is the measure of 4?
Answers
Answer:
∠ 4 = 80°
Step-by-step explanation:
∠ 5 and 100° are vertical angles and are congruent , so
∠ 5 = 100°
∠ 4 and ∠ 5 are same- side interior angles and sum to 180° , that is
∠ 4 + ∠ 5 = 180°
∠ 4 + 100° = 180° ( subtract 100° from both sides )
∠ 4 = 80°
Problem
Suppose that J is between H and K. If HJ=2x+4, JK=3x+3, and KH=22, find the lengths of HJ and JK. Remember to always draw an image first and to pay attention to what the question is asking for!
Solution
Find the Segment Addition Postulate
Use the Segment Addition Postulate and then substitute what we know. Do not use any spaces in your answers.
HJ+JK= Answer
( Answer
)+( Answer
)= Answer
Find x
Once we combine our like terms we get:
Answer
x+ Answer
= Answer
x= Answer
Find HJ and JK
Our questions asked us for the lengths of HJ and JK so we must plug in the value of x to solve for those values. We were given HJ=2x+4 and JK=3x+3.
HJ=2x+4
HJ=2( Answer
)+4
HJ= Answer
And
JK=3x+3
JK=3( Answer
)+3
JK= Answer
3x-4
Check Work
View checked work
Answers
Answer:
The lengths of HJ and JK are 50 and 72 respectively.
Given:
J is between H and K.
HJ=2x+4
JK=3x+3
HK=22
Step-by-step explanation:
The total length is given as:
HJ+JK=HK
⇒ (2x+4)+(3x+3)=22
⇒ 5x+7=22
⇒ 5x=22-7
⇒ 5x=15
⇒ x=3
Thus, the length of HJ is (2x+4)=(2*3+4)=10
And the length of JK is (3x+3)=(3*3+3)=12
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The lengths of HJ and JK are 50 and 72 respectively.
Given: J is between H and K. the length of HJ=2x+4, JK=3x+3, and HK=22.
The line HJ and JK are collinear then the total length is given as: HJ+JK=HK
substitute values
⇒ (2x+4)+(3x+3)=22
⇒ 5x+7=22
⇒ 5x=22-7
⇒ 5x=15
⇒ x=3
Thus, the length of HJ is (2x+4)=(2*3+4)=10
And the length of JK is (3x+3)=(3*3+3)=12
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