The gas tank holds 60 quarts.
What is quarts?
The quart is an English volume unit equivalent to one-quarter gallon. There are now three types of quarts in use: the liquid quart and dry quart of the US customary system, as well as the imperial quart of the British imperial system. All of them are essentially equivalent to one liter. It is split into two pints or four cups (in the United States). The exact size of the quart has historically fluctuated with the varying values of gallons over time and in relation to different commodities.
1 US gallon = 4 US quarts
so, 15 US gallons = 15 x 4 = 60 quarts
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The total cost of water heater including a
7% sales tax is $524.30. What is the cost
of the water heater without the tax?
How much would $500 invested at 9% interest compounded monthly be worth after 4 years ? A(t)=P(1+r/n)^nt
The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be $715.7.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
We know that the compound interest is given as
[tex]\rm A = P \left ( 1 + \dfrac{r}{n} \right ) ^{nt}[/tex]
Where A is the amount, P is the initial amount, r is the rate of interest, and t is the number of years.
For interest compounded monthly, the value of n is 12.
The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be
[tex]\rm A = 500 \left ( 1 + \dfrac{0.09}{12} \right ) ^{12 \times 4}[/tex]
Simplify the equation, then we have
A = 500 (1.0075)⁴⁸
A = 500 x 1.4314
A = $715.70
The amount when 500 invested at 9% interest compounded monthly be worth after 4 years will be $715.7.
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-6+2y=10 and 6x-2y=-10
Answer:
Step-by-step explanation:
-6+2y=10
2y=10+6
2y=16
2y/2=16/2
y=8
so the final answer of first question is y=8
The next one is
6x-2y=-10
as we got from the first question y=8 so
6x-2(8)=-10
6x-16=-10
6x=-10+16
6x/6=6/6
so the final answer is 1
For the following exercise, find the domain and range of the function below using interval notation.
Domain:
Range:
The domain and range of the function is -3 ≤ x < 7 and -7 ≤ x < 6 respectively.
What is domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
For domain :-
Since, the domain is the set of all allowed x inputs of a function.
The smallest x can get is x = -3 as shown by the left-most point.
The largest x can get is x = 7, though we can't actually reach this value due to the open hole at the right-most point.
The interval of all possible x values is -3 ≤ x < 7 which converts to the interval notation [-3, 7)
We use a square bracket to include the endpoint and a parenthesis to exclude the endpoint.
We can say "x is any number between -3 and 2, including -3 but excluding 2".
For range :-
Since, the range is the set of all allowed y inputs of a function.
The smallest x can get is x = -7 as shown by the left-most point.
The largest x can get is x = 6, though we can't actually reach this value due to the open hole at the right-most point.
The interval of all possible x values is -7 ≤ x < 6 which converts to the interval notation [-7, 6)
We use a square bracket to include the endpoint and a parenthesis to exclude the endpoint.
Hence, the domain and range of the function is -3 ≤ x < 7 and -7 ≤ x < 6 respectively.
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For the equation given below, evaluate y' at the point (2, 1).
2x³y - 3x² = 4
y' at (2, 1) = ??
The value of y' according to the given equation in the task content is; 1.
What is the value of y'?According to the task content, it follows that the equation given is; 2x³y - 3x² = 4y'.
On this note, the value of y' can be determined by substituting the given values of x and y as follows;
2(2)³×1 - 3(2)² = 4y'
16 - 12 = 4y'
y' = 4/4
y' = 1.
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Which of the following conditions will create a biased estimator of a population parameter? The sampling distribution of the estimator is skewed to the left. The sampling distribution of the estimator is skewed to the left. The sampling distribution of the estimator is skewed to the right. The sampling distribution of the estimator is skewed to the right. The sampling distribution of the estimator is not the same shape as the distribution of the population parameter. The sampling distribution of the estimator is not the same shape as the distribution of the population parameter. The expected value of the estimator is not equal to the population parameter. The expected value of the estimator is not equal to the population parameter. The variability of the sampling distribution of the estimator is not equal to the variability of the population parameter.
The condition that will create a biased estimator of a population parameter is D. The expected value of the estimator is not equal to the population parameter.
What is a population parameter?It should be noted that a parameter is a descriptive measure applied to a whole population. There are numerous population parameters exist. For instance, the population size (N) is one parameter.
For T(x) to be an unbiased estimator of population parameter, it is necessary that the expected value of the estimator is equal to population parameter.
Therefore, the condition that will create a biased estimator of a population parameter is that the expected value of the estimator is not equal to the population parameter.
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The length of a rectangle is three more than triple the width. If the perimeter is 166 inches, find the
dimensions.
The dimensions of the rectangle are; length 63 inches and width is 20 inches.
What is defined a the perimeter of rectangle?The perimeter (P) of such a rectangle would be the total distance of all its sides. A rectangle has two equal lengths as well as two equal widths because its opposite sides are equal.Let 'L' be the length of the rectangle.
Let 'W' be the breadth of the rectangle.
As, the length of a rectangle is three more than triple the width.
Thus,
L = 3 + 3W
The formula for the perimeter is;
Perimeter = 2 (L+W)
The value of perimeter is 166 inches.
Thus,
166 = 2(3 + 3W +W)
166 = 2(3 + 4W)
166 = 6 + 8W
166 - 6 = 8W
W = 20
W = width = 20 inches
L = 3 + 3W
L = 3 + 3(20)
L = 3 + 60
L = 63 inches.
Thus, the dimensions of the rectangle are; length 63 inches and width is 20 inches.
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He wants to include a school and a hospital, which are 10 kilometers apart.
What should the distance between the school and the hospital be on the map?
The distance between the school and the hospital on the map is 8 cm
How to calculate the distance?Here, we want to find the distance between the school and the hospital on the map
The scale is that 4cm to 5km
So ;
if 4 cm = 5km
Then x cm = 10km
x * 5 = 4 * 10
5x = 40
x = 40/5
x = 8 cm
Therefore the distance between the school and the hospital on the map is 8 cm
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Find the measurement of the angle indicated for the trapezoid.
*
Answer: 105 degrees
Step-by-step explanation:
two sides of a trapezoid add up to 180 degrees
180 - 75 = 105
Family has 2 whole pizzas. They eat 1 3/8 of pizza, how much is left?
Answer:
5/8 of pizza left
Step-by-step explanation:
Hiya!
[tex]\rightarrow{\bf{What \: is \: x =\frac{a^2 \: + \: a^2}{ab \: + \: 1 } ?[/tex]
Explain into your own words.
I don't want no nonsense answer in my question!
Thanks ~
The value of x in the equation x = [a^2 + a^2]/[ab + 1] is [2a^2]/[ab + 1]
What are equations?Equations are mathematical expressions that are represented by the equal to or equality sign i.e =
Examples of equations are:
a + b = c
y = mx + c
Ax + By = C
y = ax^2 + bx + c
y = x
How to determine the value of x?The equation is given as
x = [a^2 + a^2]/[ab + 1]
To start with, we evaluate the like terms i.e. we add a^2 and a^2
This is represented as
a^2 + a^2 = 2a^2
Substitute 2a^2 for a^2 + a^2 in the given equation
So, we have
x = [2a^2]/[ab + 1]
The above equation cannot be further simplified
Hence, the value of x in the equation x = [a^2 + a^2]/[ab + 1] is [2a^2]/[ab + 1]
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The length of a rectangular parking area is four times the width. The perimeter is 150 yd . Find the length and width of the parking area.
The width of the rectangle = 15 yd
The length of the rectangle = 60 yd.
What is the Perimeter of a Rectangle?Perimeter of a rectangle = 2(length + width).
Given the following:
Width of the rectangle = w
Length of the rectangle = 4w
Perimeter of the rectangle = 150 yd.
Therefore:
2(4w + w) = 150
2(5w) = 150
10w = 150
10w/10 = 150/10
w = 15
Width of the rectangle = w = 15 yd
Length of the rectangle = 4w = 4(15) = 60 yd.
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\int_0^1 (e^(x)-2)^(2)dx
The value of integral ₀∫¹ ( eˣ - 2 )² dx is 8 + ( e² - 1) / 2 - 4e.
When infinitesimal data are combined, notions such as displacement, area, and volume can be created. An integral assigns numbers to functions in a way that describes these concepts. Integration is the action of locating integrals.
Consider the integral expression,
₀∫¹ ( eˣ - 2 )² dx
Using ( a + b )² = a² + b² + 2ab
[tex]\int_0^{1}( e^{x} - 2 )^{2} dx = \int_0^{1}(e^{2x}+4-2e^{x})dx[/tex]
[tex]\int_0^{1}( e^{x} - 2 )^{2} dx = \int^0_{1}e^{2x} dx +\int_0^{1}4 dx - \int_0^{1}4e^{x} dx[/tex]
Now, integration of eˣ is eˣ + c where c is constant.
Therefore,
[tex]\int_{0}^{1} ( e^{x} - 2 )^{2} dx = [ \frac{e^{2x}}{2} ]_0^{1} + [ 4x ]_0^{1} - [ 4e^{x}]_0^{1}[/tex]
₀∫¹ ( eˣ - 2 )² dx = ( e² / 2 - e⁰/2 ) + ( 4 - 0 ) - ( 4e¹ - 4e⁰ )
₀∫¹ ( eˣ - 2 )² dx = e² / 2 - 1/2 + 4 - 4e + 4
₀∫¹ ( eˣ - 2 )² dx = e² / 2 - 4e + 8 - 1/2
₀∫¹ ( eˣ - 2 )² dx = = 8 + ( e² - 1) / 2 - 4e
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James invests his money in an account paying 3.7% interest compounded quarterly. What is the effective annual yield on this account?
Answer:
3.7517%
Step-by-step explanation:
take 3.7 and divide it by 4 to get 0.925
then apply 0.925% to x 4 times to find out the compounded rate
In the point-slope form of a line, y - y, = m(x- xp), the slope is represented by?
the x- coordinate of a point is represented by?
and the coordinate
of the point is represented by?
the slope is represented by m
the x coordinate of the ordered pair is x1
the y coordinate of the preferred pair is y1
y-y1=m(x-x1)
Hazel and Luna are in different sections of MTH 134. They both took Test 1 and their instructors indicated that in each section, the scores fell into a normal distribution. Hazel made a score of 93 points and Luna made a score of 68 points. In Hazel's section, the Test 1 scores had a mean of 80 and a standard deviation of 8. In Luna's section, the mean was 40 with a standard deviation of 15. Use the Empirical Rule to determine which student did "better" and why.
Using z-scores, it is found that due to the higher z-score, Luna did better on the exam.
What are z-scores?The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.From the two bullet points, it is found that the student who did "better" is the one whose grade has the higher z-score.
For Hazel, the parameters are given as follows:
[tex]X = 93, \mu = 80, \sigma = 8[/tex]
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (93 - 80)/8
Z = 1.625.
For Luna, the parameters are given as follows:
[tex]\mu = 68, X = 40, \sigma = 15[/tex]
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (68 - 40)/15
Z = 1.87.
Due to the higher z-score, Luna did better on the exam.
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Cookies are sold singly or in packaging of 6 or 18 how many way can you buy 36 cookies
Based on the packaging of the cookies, the number of ways you can buy 36 cookies is 12 ways.
How many ways can you buy the cookies?The ways you can buy the cookies include:
30 singles and 1 six pack 24 singles and 2 six packs 18 singles and 3 six packs 12 singles and 4 six packs 6 singles and 5 six packs 2 eighteen packs 6 six packs 3 six packs and 1 eighteen pack2 six packs, 6 singles, 1 eighteen pack 1 eighteen pack and 18 singles 1 six pack, 12 singles, and 1 eighteen pack 36 singlesIn conclusion, there are 12 ways to buy the cookies.
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Let f(x)= 3x^2+3.
Evaluate
lim h ==> 0 (f(2+h)-f(2))/h
[tex]f(x)=3x^2+3\hspace{5em}\displaystyle \lim_{h\to 0}~\cfrac{f(2+h)~~ - ~~f(2)}{h} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{f(2+h)~~ - ~~f(2)}{h}\implies \cfrac{[3(2+h)^2+3]~~ - ~~[3(2)^2+3]}{h} \\\\\\ \cfrac{[3(4+4h+h^2)+3]~~ - ~~[3(4)+3]}{h}\implies \cfrac{[(12+12h+3h^2)+3]~~ - ~~[15]}{h} \\\\\\ \cfrac{[12h+3h^2+15]~ - ~~[15]}{h}\implies \cfrac{12h+3h^2}{h}\implies \cfrac{h(12+3h)}{h}\implies 12+3h \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \lim_{h\to 0}~\cfrac{f(2+h)~~ - ~~f(2)}{h}\implies \lim_{h\to 0}~12 + 3h\implies 12+3(0)\implies \text{\LARGE 12}[/tex]
A population has SS= 50 and s^2 = 5. How many scores, (N).are in the population?
There are 11 scores, (N) in the population.
How many scores, (N) are in the population?The given parameters are:
Variance, s^2 = 5
Sum of squares, SS = 50
The variance of the population is calculated using
s^2 = SS/[N - 1]
So, we have
5 = 50/[N - 1}
Cross multiply
So, we have
5(N - 1) = 50
This gives
N - 1 = 10
Add 1 to both sides
N = 11
Hence, there are 11 scores, (N) in the population.
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evaluate this please
Answer:
the answer would be x=8
Step-by-step explanation:
6×4=24
24/3=8
If Fernando paid $450 for a netbook that was 75% of the original price, what was the original price?
Answer:
$600
Step-by-step explanation:
450 = 3/4 (because 75%=3/4)
450/3=150. 150 = 1/4, or 25%. Now it's just as simple as multiplying 150 4 times to get 100%, or the original cost, 150 times 4 equals 600. Therefore the notebooks original price is $600
Find the sum or difference of the following fractional parts
Pasagot po need now po Thankyouuu
1. 1/2
2. 3/10
3. 2 and 3/5
4. 1 and 7/12
5. 1 and 1/3
Given that xy = 36 and x - y = 5, Find the value of x² + y².
Answer:
97
Step-by-step explanation:
To find x² + y², use the identity (x - y)² = x² + y² - 2xy.
(x - y)² = x² + y² - 2xy
Substitute xy = 36 and x - y = 5 in the above formula,
5² = x² + y² - 2*36
25 = x² + y² - 72
Add 72 to both sides,
25 + 72 = x² + y²
x² + y² = 97
Given f(x)=x²- 5x + 6, what is the value of f(-3.5)?
Step-by-step explanation:
no calculator at hand ?
f(-3.5) means that we have to replace every x in the function expression by -3.5 and then calculate.
f(-3.5) = (-3.5)² - 5(-3.5) + 6 = 12.25 + 17.5 + 6 = 35.75
5 What two points are a distance of 7 units from the
point 4 on the number line?
A.
3 and 11
B.
-3 and 11
C. -3 and -11
D. 3 and -11
A fox sees a rabbit 35 feet away and starts chasing it. As soon as the fox starts
moving, the rabbit sees it and starts running away at a speed of 40 feet per second.
What should the fox's speed be to catch up to the rabbit in no more than 10 seconds?
What is the yield on a corporate bond with a $1000
face value purchased at a discount price of $900, if
it pays 7% fixed interest for the duration of the
bond?
yield = [?] %
Give your answer as a percent rounded to the nearest
hundredth.
The yield on the corporate bond of a face value of $1000 is 7.77%.
What is the percentage discount?
The percentage discount is the discount given on a product as compared to the given discount on 100 rupees.
Given, the face value of the bond is $1000.
Discounted price of the bond is $900.
Therefore, the fixed interest on the bond for that period will be
= $1000 × 7/100 = $70.
Now, the yield on that corporate bond = 70 × 100/900 % = 7.77% .
Hence, the yield on the corporate bond of a face value of $1000 is 7.77%.
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Solve the following equation. x/9 + 8 = 8Then place the correct number in the box provided.
Answer:
x = 0
Step-by-step explanation:
Let's solve the problem,
→ (x/9) + 8 = 8
→ x/9 = 8 - 8
→ x = 0 × 9
→ [ x = 0 ]
Thus, the value of x is 0.
(2x+4)(x-4) multiply
Answer: 2x²-4x-16
Step-by-step explanation:
[tex](2x+4)(x-4)=\\2x(x)+2x(-4)+4(x)+4(-4)=\\2x^2-8x+4x-16=\\2x^2-4x-16[/tex]
Clare is cycling ata speed of 12. Miles per hour if she starts at a position chosen as zero what will
Clare will have traveled 9 miles in 45 minutes.
What is speed?The definition of speed is the rate at which an object's position changes in any direction. Speed is defined as the ratio of distance traveled to time spent traveling.So, Clare is riding her bike at a speed of 12 miles per hour.
Her starting point is zero.Distance traveled in 45 minutes or 45/60 hours at the same speed will be = Speed Time
= 12 × 45/60= 45/5= 9 milesTherefore, Clare will have traveled 9 miles in 45 minutes.
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