Answer:
C
Step-by-step explanation:
0.5 of a mile in 20 minutes
60/20=3
0.5*3=1.5
Correct answer is C
What is f(3)?
-9
-1
1
9
Answer:
9
Step-by-step explanation:
Edge
Mr Mathes purchases 4 tickets for his family find the value of the expression when t=4
The value of the expression when t=4 is 16
How to calculate the expression?It should be noted that from the information given, it was stated that Mathes purchases 4 tickets for his family.
Therefore, the value of the expression when t=4 will be:
C = 4t
C = 4(4)
C = 4 × 4.
C = 16
Therefore, the value of the expression when t=4 is 16.
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For a normally distributed population with a mean of 150 and standard deviation of 25, approximately what percentage of the observations should we expect to lie between 100 and 200?
The percentage of observations which we expect to lie between 100 and 200 is 3.38%
Given, the mean is 150 and
standard deviation(sd) = 25
what percentage of observation lie between 100 and 200.
x + 1sd = 175
x - 1sd = 125
x + 2sd = 200
x - 2sd = 100
x + 3sd = 225
x - 3sd = 7
observation between 100 and 200 lie from x + 1sd
Therefore P(x) = (100-175)÷25
= -3
=3.38%
Hence the percentage of observations that lie between 100 and 200 is 3.38%
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What size heater will be required to heat the water in a swimming pool from
70°F to 72 °F in 1 hour if the appliance is 100% efficient and the pool holds
20,000 gallons of water?
A. 166,000 Btu/h
B. 332,000 Btu/h
C. 86,000 Btu/h
D. 224,000 Btu/h
Ps. the answer is B but i want an explanation on how to work through the problem
Answer:
B
Step-by-step explanation:
the British thermal unit (BTU or Btu) is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit.
and it is outdated. your teacher and the manufacturer should use joules as metric.
1 BTU ≈ 1055 joules
anyway, so, the solution has several parts.
we need to find how many pounds of water are in a gallon.
and then multiply by the amount of gallons (20 000) and the amount of degrees (2 from 70 to 72).
and after a little search on the internet we get
1 gallon of water = 8.34 pounds
so, we need to warm
20000×8.34 pounds of water by 2 degrees F.
that is
20000 × 8.34 × 2 = 333,600 BTU
if we use only the rounded value of pounds per gallons (8.3), this would be
20000 × 8.3 × 2 = 332,000 BTU
so in any case, B is the right answer (as being the closest to the real result), which is the situation with any size classification of devices : reality is somewhere close by, but never meets the exact specifications.
Write a compound inequality that represents the following phrase.
all real numbers that are between -4 and 5, inclusive
Write a compound inequality that represents the phrase. Choose the correct answer below.
A:[tex]-4\leq n\ \textless \ 5[/tex]
B:[tex]-4\ \textless \ n\ \textless \ 5[/tex]
C:[tex]-4\ \textless \ n\leq 5[/tex]
D:[tex]-4\leq n\leq 5[/tex]
The compound inequality that represents the set of real numbers that are between -4 and 5 inclusive is the option;
D: -4 ≤ n ≤ 5
How can the compound inequality be found?A compound inequality comprises of a sentence that makes two inequality statements that are joined by either the word 'and' or 'or'.
Given that the inequality represents the set of all real numbers that are between -4 and 5, and -4 < 5, the required set of numbers is therefore of the form;
[tex] - 4 \: \leftrightarrow \: 5[/tex]
The expression of the required set of numbers as inequalities is therefore;
-4 ≤ n and n ≤ 5The compound inequality is therefore;
D: -4 ≤ n ≤ 5
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For the stem-and-leaf plot below, what are the maximum and minimum entries?
1 | 3 4
1 | 6 6 6 7 8 9
2 | 0 1 1 2 3 4 4 5 6 6
2 | 7 7 7 8 8 9 9 9
3 | 0 1 1 2 3 4 4 5 5
3 | 6 6 6 7 8 8 9 9
4 | 1 3
Can someone help me with this question?
Answer:
A) y = 0.3x+24
B) 283.5 dollars
Step-by-step explanation:
A) To create an equation in slope-intercept form, we can start by using the numbers the problem gave us and represent them as coordinates. Generally, time is always our x-value.
(230,93)
(530,183)
Now that we have our two coordinates, we can plug them into the slope-intercept formula: y₂-y₁/x₂-x₁ to find our slope.
(183-93)/(530-230) = 0.3
Now that we have our slope, we can plug it into our equation.
y = 0.3x + b
To find our y-intercept, we can take either one of our 2 coordinates (x,y) and plug them into the equation to solve for b.
93 = 0.3(230) + b
93 = 69 + b
93 - 69 = b
b = 24
Now that we have found our y-intercept, we can plug it into b to complete the equation.
y = 0.3x +24
B) If 865 minutes are used, we can plug 865 into x in our equation to find the total cost.
0.3(865) + 24 = 283.5
Two figures are said to be SIMILAR if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.
This pair of figures is similar. Find the value of the missing side (x).
Answer:
The ratio is 8:1 and it is a rectangle so x is 56
If on the similar image the sides are the same the other image will be aswell
Hope thie helps!
If you have any other question feel free to ask!
What si the greatest multiple of 60 and 72
The greatest common multiple of 60 and 72 is 6.
The given numbers are 60 and 72.
What is the meaning of greatest common multiple?The greatest common factor (GCF) is a term used to describe the biggest number that can divide evenly into two or more numbers. Sometimes, this is also referred to as the greatest common divisor (GCD) or highest common factor (HCF). A factor is a smaller number that can divide evenly into that number.
Now, 60 = 2×2×3×5 and 72 = 2×2×2×3×3
The common factors are 2 and 3
So, the greatest common factor =2×3=6
Therefore, the greatest common multiple of 60 and 72 is 6.
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The doctor has determined that one reason for the sickness is due to Cameron’s diet and that he has a protein deficiency. A change in his diet is necessary. He must increase the amount of protein that Cameron consumes. To begin this process, Cameron has to figure out how much protein he should consume in a day. Assume that he is 25 years old and weighs 132 lbs. According to the Food and Nutrition Board, Institute of Medicine, National Academies website, adults need 0.66 g/kg/d of protein.
How many grams of protein does he need each day?
Using proportions, it is found that he needs 39.5 grams of protein each day.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
First we have to convert his weight to kg. Each lb has 0.453592 kg, hence his weight in kg is given by:
132 x 0.453592 = 59.87 kg.
Each day, he needs to consume 0.66 g for each kilogram in his body, hence the amount of protein that he needs to consume each day is given by:
0.66 x 59.87 = 39.5.
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slope of (-8,-3) and (-1,-2)
Solution :-
As we know that,
m = y_2 - y_1 / x_2 - x_1Therefore ,
>> m = -2 - (-3) / -1 - (-8)
>> m = -2 + 3 / -1 + 8
>> m = 1 / 7
We have that the data are:
(x₁ = -8, y₁ = -3) and (x₂ = -1, y₂ = -2)
The slope is equal to the change in and with respect to change in X, or what rises when moving forward.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{Change \ in \ y}{Change \ in \ x} \ \longmapsto \ \ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} } \end{gathered}$}}[/tex]
The change in X is equal to the subtraction in the X coordinate (also called advance), and the change in and is equal to the subtraction in the coordinate and (also called elevation).
Introduce the values of x and y In the equation to find the slope.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{-2-(-3)}{-1-(-8) } } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{1}{7} } \end{gathered}$}}}[/tex]
The slope of (-8, -3) and (-1, -2) is 1/7.just need help with some of them at least 5 questions please already did the first one. i put 90 points please help.
2. The solution to the given system of equation is x = 1 and y = 6
3. The solution to the given system of equations is x = 1, y = 2
4. The simplified form of the expression is y²
5. The simplified form of the expression is 2
8. the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11
9. The multiplication yields x² - 4x - 96
10. The factored form of the expression is (x + 6)(x- 6)
11. The solutions to the given quadratic equation are x = 5 and x = -6
Solving system of equationsFrom the question, we are to solve the given system of equations
The given system of equation is
y = 10 - 4x --------- (1)
2x + 3y = 20 --------- (2)
Substitute equation (1) into equation (2)
2x + 3y = 20
2x + 3(10 -4x) = 20
2x + 30 - 12x = 20
2x - 12x = 20 - 30
-10x = -10
x = -10/-10
x = 1
Substitute the value of x into equation (1)
y = 10 - 4x
y = 10 - 4(1)
y = 10 - 4
y = 6
Hence, the solution to the given system of equation is x = 1 and y = 6
3.
From the question, we are to solve the system of equations using the elimination method
The given system of equations is
5x + 2y = 9
-5x + 4y = 3
Add the two equations
5x + 2y = 9
-5x + 4y = 3
----------------------
0x + 6y = 12
6y = 12
y = 12/6
y = 2
Substitute the value of y into the first equation
5x + 2y = 9
5x + 2(2) = 9
5x + 4 = 9
5x = 9 - 4
5x = 5
x = 5/5
x = 1
Hence, the solution to the given system of equations is x = 1, y = 2
4. From the question, we are to simplify the expression
y⁻⁴(y³)²
First, multiply the exponents in (y³)²
(y³)² = y ³ ˣ ²
= y⁶
Thus,
The expression becomes y⁻⁴y⁶
Applying the multiplication law of indices
y⁻⁴y⁶ = y⁻⁴ ⁺ ⁶
= y²
Hence, the simplified form of the expression is y²
5.
From the question, we are to simplify
∛8
First, express 8 in exponent form
8 = 2³
Thus,
The expression becomes
∛2³
Applying one of the laws of indices,
∛2³ = (2³)¹/³
Multiplying the exponents, we get
2¹
= 2
8.
From the question, we are to subtract the polynomial
(3x² + 5x - 8) - (2x³ - 4x + 3)
Subtracting
(3x² + 5x - 8) - (2x³ - 4x + 3)
3x² + 5x - 8 -(2x³ - 4x + 3)
Open the parentheses by distributing negative
3x² + 5x - 8 -2x³ + 4x - 3
Collect like terms
-2x³ + 3x² + 5x + 4x - 8 - 3
Simplify
-2x³ + 3x² + 9x - 11
Hence, the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11
9.
From the question we are to multiply
(x + 8)(x - 12)
Applying the distributive property
x(x -12) +8(x -12)
x² - 12x + 8x - 96
Simplifying
x² - 4x - 96
10.
From the question, we are to factor
x² - 36
This can be written as
x² - 6²
From the rule of difference of two squares, we have that
a² - b² = (a + b)(a - b)
Thus,
x² - 6² = (x + 6)(x- 6)
11.
From the question, we are to find the solutions for
x² - x - 30 = 0
Solve by factoring
x² - x - 30 = 0
x² + 6x - 5x - 30 = 0
x(x + 6) -5(x + 6) = 0
(x - 5)(x + 6) = 0
∴ x - 5 = 0 and x + 6 = 0
x = 5 and x = -6
Hence, the solutions to the given quadratic equation are x = 5 and x = -6
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On his road trip, Leon stops to refuel and get some snacks. He has the following purchases:
12 gallons of gas at of $2.89 per gallon
2 granola bars for $1.59 each
1 apple for $0.89
2 bottles of vitamin water for $1.39 each
Leon must pay 7.5% sales tax on everything but the gas, which already has tax included in the per gallon price. If
Leon paid $44.64, then he
for his purchase.
a. did not pay enough
b. paid the correct amount
C.
paid $2.60 too much
d.
paid $3.11 too much
Please select the best answer from the choices provided
The correct option is that;
C. Leon overpaid for his purchase by $2.60 if he paid $44.64.
What is the difference between a sales tax and a use tax?The vendor, who is acting as the state's agent, collects the sales tax and remits it to the state on behalf of the final customer. The use tax, on the other hand, is self-assessed and paid by the final customer.
Given that;
Purchase fuel = 12 Gallons per $2.89 per gallons (including Tax)
2 Granola Bar for $1.59 per bar
1 apple for $0.89
2 bottles of vitamin water for $1.39
The sales Tax rate is 7.5%
Required to calculate the difference amount of Actual Paid and Actual Purchase =?
Fuel = 12 x 2.89 = $34.68 (including tax)
Granola Bar = 2 x 1.59 = $3.18
Apple = 1 x 0.89 = $0.89
Vitamin Water = 2 x 1.39 = $2.78
Total Purchase excluding fuel without tax is,
= $3.18 + $0.89 + $2.78
= $6.85.
Adding sale tax on $6.85 at the rate of 7.5% = $7.36
Hence, Total Purchase including Tax is,
$7.36 + $34.68 = $42.04
Thus, there is a clear difference that Leon paid 2.60 more than his actual purchase. He paid $ 44.64 and his actual purchase is 42.04 the difference between that is $2.60.
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The Andersons are planning to take a 960-mile trip. They will travel 840 miles by car. What percent of the distance will they not travel by car?
The percent of distance that the Andersons will not travel by car is 12.5%, If they are planning to take a 960-mile trip and they will travel 840 miles by car.
Total distance the Andersons are planning to take is 960-mile
They will travel 840 miles by car
Distance they will not travel by car = total distance - distance travelled by car
= 960 - 840 miles
=120 miles
Percentage formula = (value/ total value) x 100
percent of the distance will they not travel by car =
(total distance - distance travelled by car) x 100/total distance
=((960 - 840)/ 960) x100
=(120/ 960) x 100
12.5
If the Andersons are planning to take a 960-mile trip and they will travel 840 miles by car then the percentage of distance they will not travel by car is 12.5%
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-2x + 14y = -29
x-7y=19
elimination process
Answer:
no solution
Step-by-step explanation:
Multiplying the second equation by 2 gives 2x-14y=38.
Adding this to the first equation, we get 0=9, and thus there is no solution.
it is math for evaluating functions please help
The domain of the given function is; (0, 2)
The range of the given function is; (-2, 6)
What is the range and domain of the given function?We want to evaluate the function f(x) = 4x - 2 for x = 0, 1 and 2.
Step 1;
f(0) = 4(0) - 2
f(1) = 4(1) - 2
f(2) = 4(2) - 2
Step 2;
f(0) = 0 - 2 = -2
f(1) = 4 - 2 = 2
f(2) = 8 - 2 = 6
The domain is the set of all possible input values which is (0, 2)
The range is the set of all possible output values which is (-2, 6)
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Jayden is standing in a stadium and has the option of running up a staircase or down a staircase for exercise. The function f(x)=\frac{1}{25}\big(\left|6x\right|+5x\big)f(x)= 25 1 (∣6x∣+5x) will determine how many calories Jayden will burn if he runs up xx steps. Use a negative value for xx if he runs down the stairs. Find and interpret the given function values and determine an appropriate domain for the function.
The interpretation of the value of the function, [tex]f(x) = \frac{1}{25} \times \left( \left |6 \cdot x \right | + 5 \cdot x \right)[/tex], when x = 30 is that by running up 30 steps, Jayden burns [tex] 13 \frac{1}{3} [/tex] calories.
The domain of the function is the set of all real numbers
How can the values of the function be interpreted?The given function is presented as follows;
[tex]f(x) = \frac{1}{25} \times \left( \left |6 \cdot x \right | + 5 \cdot x \right)[/tex]
Where;
f(x) = The number of calories burnt
x = The number of steps Jayden runs
The value of x is negative while running down the stairs
Therefore;
[tex]f(30) = \frac{1}{25} \times \left( \left |6 \times 30 \right | + 5 \times 30 \right) = 13 \frac{1}{3} [/tex]
[tex]f(30) = 13 \frac{1}{3} [/tex]
The interpretation of the above function equation is that the amount of calories Jayden burns when she runs 30 steps up the stairs is [tex] 13 \frac{1}{3} [/tex]
Given that 6•x > 5•x, the function is always positive, and has a minimum value of zero, the function can take any value for x.
The domain of the function is therefore, -∞ ≤ x ≤ ∞, which is the set of all real numbers.
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Graph the image of rhombus TUVW after a reflection over the line x = 1.
104
-10 -8 -6
U
-4
T
V
W
22
8
6
4
CN
2
-2
-4
2
4
6
8
00
X
10
Answer:
its c
Step-by-step explanation:
rectangle has a length of 35 yards less than 7 times its width. If the area of the rectangle is 6468 square yards, find the length of the rectangle.
Therefore the width of the rectangle is 33 yards
length of the rectangle is 196 yards.
Let the width of the rectangle be 'x'
Given the length of the rectangle = 35 yards less than 7 times the width
= 7x - 35
Given the area of rectangle = 6468 square yards
We know that area of rectangle = length * width
= (7x - 35 ) * x
By comparing both we get,
(7x - 35) * x = 6468
7x² - 35x - 6468 = 0
By dividing the equation by '7' we get
x² - 5x - 924 = 0
Factorize the above equation we get
x² - 33x + 28x - 924 = 0
x ( x - 33) +28 (x - 33 ) = 0
( x - 33 ) ( x + 28 ) = 0
∴ x = 33 , -28
Negative values are not consider
Therefore the width of the rectangle is 33 yards
length of the rectangle = 7(33) - 35
= 231 - 35
= 196 yards
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The mapping diagram shows a relation.
A mapping diagram shows a relation, using arrows, between inputs and outputs for the following ordered pairs: (negative 6, 0), (2, 1), (negative 7, negative 4), (11, 2), (3, 2).
What is the domain of the relation?
{x| x = –4 , 0, 1, 2}.
{x| x = –7, –6, 2, 3, 11}.
{y| y = –4, 0, 1, 2}.
{y| y = –7, –6, 2, 3, 11}.
The domain of the given relation is: {x| x = –7, –6, 2, 3, 11}.
What is a domain?A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
Additionally, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
In this context, we can reasonably infer and logically deduce that the domain of the given relation include the following: {x| x = –7, –6, 2, 3, 11}.
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If 8 is 40% of N, then what does N equal?
Answer:20
Step-by-step explanation:
n x 40% =8
So n = 8 / 40%
n = 20
The electoral college is in place so that states with a greater population have more influence in a presidential election. The higher populated states have more votes. For example, Washington is roughly 3 times as populated as Idaho, so Washigton’s number of electoral college votes is 300% of Idaho’s number. If Idaho has 4 electoral college votes, how many votes does Washington have? Percent formula
Answer: 12 electoral college votes
Step-by-step explanation:
4*100%=
4*100/100=
400/100=4
4*300%=
4*300/100=
1200/100=12 votes
What is the domain of the function y = 3 l n x graphed below?
On a coordinate plane, a curve starts in quadrant 4 and then increases up into quadrant 1. It crosses the x-axis at (1, 0).
The domain of the function y = 3 ln x is (0, ∞) .
In mathematics, the logarithmic function is the inverse of power.The domain of a function is the set of inputs or x-values on which the function is defined.The graph of the function y = 3ln x is given below .
Then , coordinate point (1, 0)
The logarithmic function y = log x has the domain x > 0 (or) (0, ∞).
This is a logarithmic function. An important property of logarithms is that the domain cannot be denied. The same is true for x=0, since the logarithm of negative numbers is undefined.
The image attached shows the graph of this function, there you can notice its domain restriction.
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Factorize the equation
Answer:
[tex]\sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]
Step-by-step explanation:
Given equation:
[tex](x^2+2)^{\frac{5}{2}}+2x(x^2+2)^{\frac{3}{2}}+x^2\sqrt{x^2+2}[/tex]
[tex]\textsf{Rewrite the exponents }\frac{5}{2} \textsf{ as } \left(\frac{1}{2} \cdot 5\right)\textsf{ and }\frac{3}{2} \textsf{ as }\left(\frac{1}{2} \cdot 3\right):[/tex]
[tex]\implies (x^2+2)^{\frac{1}{2} \cdot 5}+2x(x^2+2)^{\frac{1}{2}\cdot 3}+x^2\sqrt{x^2+2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies \left((x^2+2)^{\frac{1}{2}}\right)^5+2x\left((x^2+2)^{\frac{1}{2}}\right)^3+x^2\sqrt{x^2+2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]
[tex]\implies \left(\sqrt{x^2+2}\right)^5+2x\left(\sqrt{x^2+2}\right)^3+x^2\sqrt{x^2+2}[/tex]
Factor out [tex]\sqrt{x^2+2}[/tex] from each of the three terms:
[tex]\implies \sqrt{x^2+2}\left[\left(\sqrt{x^2+2}\right)^4+2x\left(\sqrt{x^2+2}\right)^2+x^2\right][/tex]
[tex]\textsf{Factor the expression in the parentheses using} \quad a^2+2ab+b^2=(a+b)^2.[/tex]
[tex]\textsf{Let }a=\left(\sqrt{x^2+2}\right)^2 \textsf {and }b=x:[/tex]
[tex]\implies \sqrt{x^2+2}\left(\left(\sqrt{x^2+2}\right)^2+x\right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt{a^2}=a:[/tex]
[tex]\implies \sqrt{x^2+2}\left(x^2+2+x\right)^2[/tex]
[tex]\implies \sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]
50 POINTSS Solve for q.
s = 4p + 4q
find the prime factors of 6912 and cube root
The prime factors of 6912 are 2 and 3 and the cube root of 6912 is approximately 19.05 (rounded to 2 decimal places) .
Prime numbers are numbers which do not have any factors other than 1 and itself. For example 7 is a prime number, 37 is a prime number as the factors of 7 are 1 and 7 and the factors of 37 are 1 and 37.
Prime factorization of a number is given by writing all the prime factors of as number in multiplication form.
The prime factorization of 6912 gives:
6912 = 2 × 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2⁸ × 3³
Hence the prime factors of 6912 are 2 and 3.
The cube root of 6912 = 19.0488... ≈ 19.05 (rounded to 2 decimal places)
Therefore the cube root of 6912 is approximately 19.05 .
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Points P, Q, R, and S are collinear. Point Q is between P and R, R is between Q and S, and PQ =RS. If PS= 23 and PR = 17, what is the value of QR?
QR=
(Simplify your answer.)
Answer:
QR = 11
Step-by-step explanation:
P-Q-R-S
PQ = RS
PS = 23
PR = 17
so RS = PS - PR = 23 - 17 = 6
RS = PQ = 6
QR = PS - (RS + PQ) = 23 - (6 + 6) = 23 - 12 = 11
Is the relation a function yes or no circle the order pairs that cause the relation to not be a function
For the relations (tables) from left to right we have:
1) Is not a function, because the input 5 is mapped into two different values.
2) Is not a function, because the input -1 is mapped into two different values.
3) It is a function.
4) It is a function (the input x = 7 appears twice, but both times is mapped into the same output).
How to know if the relations are functions or not?A relation is an operation that maps elements from one set called the domain (set of the inputs) into elements of another set, called the range (set of the outputs).
Now, a relation is a function only if each element of the domain is mapped into only one element of the range. So, if you see the same input in a table two times (related to two different outputs) then that table does not represent a function.
Then, for the tables reading from left to right, we have:
1) Is not a function, because the input 5 is mapped into two different values.
2) Is not a function, because the input -1 is mapped into two different values.
3) It is a function.
4) It is a function (the input x = 7 appears twice, but both times is mapped into the same output).
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A mining company owns two mines. These mines produce an ore that can be graded into two classes: regular grade and low grade. The company must produce
at least 420 tons of regular-grade and 480 tons of low-grade ore per week. The first mine produces 6 tons of regular-grade and 16 tons of low-grade ore per
hour. The second mine produces 18 tons of regular-grade and 8 tons of low-grade ore per hour. The operating cost of the first mine is $20,500 per hour, and the
operating cost of the second mine is $10,200 per hour. The first mine can be operated no more than 55 hours a week, and the second mine can be operated no
more than 36 hours a week. How many hours per week should each mine be operated to minimize the cost?
The number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours
How to determine the number of hours?The given parameters can be represented using the following table of values
Mine 1 (x) Mine 2 (y) Available
Regular grade 6 18 420
Low grade 16 8 480
Operating cost 20500 10200
Time 55 36
From the table, we understand that we are to minimize cost
This means that:
Objective function: C = 20500x + 10200y
Subject to:
6x + 18y >= 420
16x + 8y >= 540
Next, we plot the constraints on a graph (see attachment)
From the graph, we have
(x, y) = (26.5, 14.5)
This means that
Mine 1 hour = 26.5 hours
Mine 2 hour = 14.5 hours
Hence, the number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours
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In cell B16, enter a function to calculate the total attendance for the years 2018 through 2022 using the totals in the range B12:F12
The Excel formulas to enter in cell B16 is = SUM(B12 : F12)
How to determine the Excel function?From the question, we can assume the following:
Range = B12 to F12The sum of entries in cells B12 through F12 represent the required sumUsing the sum function, we have:
Total = SUM(B12 : F12)
So, the formula to enter in cell B16 is:
= SUM(B12 : F12)
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