An example of situation involving quantitative variables is given by:
The gameplan of an NFL coach.
What are qualitative and quantitative variables?The variables are classified as follows:
Qualitative variables are variables that assumes labels or ranks, such as good/bad, yes/no and so on.Quantitative variables are variables that Assume numerical values.In the context of this problem, we want to use quantitative variables, that is, numbers.
Multiple examples of this are given by the gameplan of NFL coaches, as the following example:
How often to blitz? The coach has to analyze the opposing offense statistics against the blitz or against standard pressure. For example, Patrick Mahomes is known to be a blitz killer, hence a coach should visualize the statistics and conclude that he has a better chance of stopping Mahomes playing standard coverage than blitzing.
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the variable y is directly proportional to x. if y equals -0.6 when x equals 0.24, find x when y equals -31.5.
You have that y is proportional to x. Futhermore, you have y = -0.6 when x = 0.24.
Due to y is proportional to x, you have the following equation:
[tex]y=kx[/tex]where k is the constant of proportionality. In order to find the value of x when y = -31.5, you first calculate k.
k is calculated by using the information about y=-0.6 and x=0.24. You proceed as follow:
y = kx solve for k
k = y/x replace by known x and y values
k = -0.6/0.24
k = -2.5
Hence, the constant of proportionality is -2.5.
Next, you use the same formula for the relation between y and x to find the value of x when y = -31.5. You proceed as follow:
y = kx solve for x
x = y/
During a heavy rainstorm a city in Florida received 12 1/4 inches of rain in 25 1/2 hours.What is the approximate rainfall rate in inches per hour?
Data:
The city received 12 (1/4) inches of rain in 25 (1/2) hours.
Procedure:
Rewriting the numbers as decimals.
[tex]12\cdot\frac{1}{4}=12.25[/tex][tex]25\cdot\frac{1}{2}=25.5[/tex]To find the approximate rainfall rate in inches per hour, we have to do as follows:
[tex]\frac{12.25}{25.5}\approx0.48\frac{in}{h}[/tex]Rounding the result, we get...
[tex]0.48\approx0.5\approx\frac{1}{2}[/tex]Answer: D. about 1/2 inch per hour
During a tropical storm, the temperature decreased from 84° to 63º. Find the percent decrease in temperature during the storm. (a) 33% (b) 25% (c) 40% (d) 75%
To find the percentage of decrease, first, we divide.
[tex]\frac{63}{84}=0.75[/tex]This means 63° represents 75% of 84°. In other words, the temperature decreased by 25%.
Hence, the answer is B.x³=yis this a linear or nonlinear equation
ANSWER:
No, it is not a linear equation
Explanation:
Given:
x³=y
Equations are categorized base on the highest exponent of their variables.
An equation with an exponent less rthan equal to 1 is a linear equation, am equation with an exponent of 3 is a cubic equation
This equation x³=y is a non linear equation. It can also be called a cubic equation because x has an exponent of 3.
Also the satndard form of a linear equation is:
y = mx + b
In this case, x³=y is not in that form, so it is not a linear equatio.
y = x³
All the formation your name is on the picture picture provided
The range of the data is the difference between the maximum data value and the minimum.
In a box plot, the maximum and the minimum are indicated by the dots at the end of the horizontal line.
Here,
Maximum = 10
Minimum = 4.5
Thus, the range of the data is:
[tex]Range=10-4.5=5.5[/tex]Please help ASAP thank you
Answer:
Shade 6 strips out of the 9.
Step-by-step explanation:
Let us find 2/3 of 9
We can write 2/3 of 9 as 2/3 × 9
To multiply fractions through the following steps:
Now, 2/3 × 9 = (2 × 9) / 3 = 18/3 = 6
Convert the following rectangular equation to polar form.Assume a>0 3x^2+3y^2-4x+2y=0
The given equation is,
[tex]3x^2+3y^2-4x+2y=0[/tex]The polar form of the equation can be determined by using the substitution
[tex]\begin{gathered} x=r\cos \theta \\ y=r\sin \theta \end{gathered}[/tex]using the substitution,
[tex]\begin{gathered} 3(x^2+y^2)-4x+2y=0 \\ 3(r^2\cos ^2\theta+r^2\sin ^2\theta)-4r\cos \theta+2r\sin \theta=0 \\ 3r^2-4rcos\theta+2r\sin \theta=0 \\ r(3r-4\cos \theta+2\sin \theta)=0 \\ r=0\text{ and }(3r-4\cos \theta+2\sin \theta)=0 \\ (3r-4\cos \theta+2\sin \theta)=0 \end{gathered}[/tex]Thus, the above equation gives the required polar form of the circle.
is it a function? X (-2, -1, 0, 1, 2 ) Y (-7, -2, 1, -2, -7 )
To be a function, it is nesessary that the values of x correspond to a unique value of y (a value of x cannot correspond to 2 different values of y). The same value of y can correspond to two or more values of x
As in the given data each value of x has just one value of y. Then, it is a function.
A school choir needs to make t-shirts for its 75 members. A printing company charges $2 per shirt, plus a $50 fee for each color to be printed on the shirts. Write an equation that represents the relationship between the number of t- shirts ordered, the number of colors on the shirts and the total cost of the order. If you use a variable (letter) specify what it represents.
Let:
C(n,m) = Total cost
n = number of t- shirts ordered
m = fee for each color to be printed on the shirts
Therefore, the total cost of the order would be given by the following equation:
C(n,m) = $2n + $50m
Where:
n = 75
C(n,m) = $2(75) + $50m
C(n,m) = $150 + $50m
How many possible values for y are there where y = Cos-lo? O A. O Ο. O B. Infinite O C. 1 O D. 2
Answer:
B. Infinite
Explanation:
Given that:
[tex]y=\cos ^{-1}(0)[/tex]This implies that:
[tex]\cos (y)=0[/tex]From the graph of f(x)=cos(x), we observe that:
[tex]\cos (x)=0\text{ for }x=\frac{\pi}{2}+k\pi\text{ for any }k\in\Z,\text{ }\Z\text{ being the set of integers}[/tex]Therefore, there are infinitely possible values of y.
hi! im mia, and i need help with math!question: Write a statement that correctly describes the relationship between these two sequences: 6, 7, 8, 9, 10, and 18, 21, 24, 27, 30.
The Solution:
Given the pair of sequences below:
[tex]\begin{gathered} \text{ First sequence: 6,7,8,9,10} \\ \\ \text{ Second sequence: 18,21,24,27,30} \end{gathered}[/tex]We are asked to write a statement that correctly describes the relationship between the two sequences.
The two sequences are both linear sequences. Their common differences are:
[tex]\begin{gathered} \text{ First sequence: d=T}_3-T_2=\text{T}_2-T_1 \\ =8-7=7-6=1 \\ \text{ So, the co}mmon\text{ difference is 1} \end{gathered}[/tex]The general formula for the first sequence is
[tex]T_n=a+(n-1_{})d=6+(n_{}-1)1=6+n-1=5+n[/tex]Similarly,
[tex]\begin{gathered} \text{ Second sequence}\colon\text{ } \\ d=\text{T}_3-T_2=\text{T}_2-T_1 \\ d=24-21=21-18=3 \\ \text{ So, the co}mmon\text{ difference is 3} \end{gathered}[/tex]The general formula for the second sequence is
[tex]S_n=18+(n-1_{})3=18+3n_{}-3=15+3n=3(5+n)[/tex]Thus, the relationship between the two sequences is:
[tex]S_n=3T_n[/tex]Where
[tex]\begin{gathered} S_n=\text{ the second sequence} \\ T_n=\text{ the first sequence} \end{gathered}[/tex]Therefore, the correct answer is:
[tex]S_n=3T_n[/tex]Kaitlin's family is planning a trip from WashingtonD.C., to New York City New York City is 227 miles from Washington, D.C.and the family can drive an average of 55mi / h . About how long will the trip take?
Kaitlin's family's trip from Washington D.C., to New York City of 227 miles at average rate of 55 miles per hour is 4 hours 8 minutes
How to determine the how long the trip will takeinformation gotten from the question include
Washington D.C., to New York City is 227 miles
Kaitlin's family can drive an average of 55mi / h
Average speed is a function of ratio distance covered with time. this is represented mathematically as
average speed = distance covered / time
55 miles / h = 227 miles / time
time = 227 / 55
time = 4.127 hours
The trip take 4.127 hours
0.127 * 60 = 7.62 ≅ 8 minutes
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Write a pair of complex numbers whose sum is -4 and whose product is 53
The pair of complex numbers whose sum is -4 and whose product is 53 is illustrated as -b² - 4b - 53 = 0.
How to calculate the he value?Let the numbers be represented as a and b.
Therefore a + b = -4 .....i
a × b = 53 ........... ii
From equation I, a = -4 - b
Put this into equation ii
ab = 53
(-4 - b)b = 53
-b² - 4b = 53
Equate to 0
-b² - 4b - 53 = 0
The value can be found using the Almighty formula
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a mother duck lines her 8 ducklings up behind her. in how many ways can the ducklings line up?
In position one, we can have any of the 8 ducks
In position two, we can have 7 ducks, since one has to occupy position one
and so on
then, we have:
[tex]8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1=8![/tex]the factorial of 8 is 40320
A boy goes to school by first taking a bus for 1 3/4 km and then by walking 1/3 km. Find the distance of his house from the school.
The boy goes to school by bus for 1 3/4km, then he walks 1/3 km.
To determine the total distance he traveled you have to add both distances:
[tex]1\frac{3}{4}+\frac{1}{3}[/tex]To solve this sum, add the fractions first and then add the result to the whole number:
- Add both fractions:
[tex]\frac{3}{4}+\frac{1}{3}[/tex]To add both fractions you have to express them using the same denominator first. A common multiple between the denominators "4" and "3" is "12". Multiply the first fraction by 3 and the second by 4 to express them as their equivalent fractions with denominator 12. Then proceed to add them:
[tex]\frac{3\cdot3}{4\cdot3}+\frac{1\cdot4}{3\cdot4}=\frac{9}{12}+\frac{4}{12}=\frac{9+4}{12}=\frac{13}{12}[/tex]The result is 13/12, as you can see the numerator is greater than the denominator, which indicates that this is an improper fraction, i.e. its value is greater than 1. You can write this fraction as a mixed number as follows:
- Solve the division:
[tex]13\div12=1.08\bar{3}[/tex]The mixed number will have the whole number "1".
- To express the decimal value as a fraction, multiply it by 12
[tex]0.08\bar{3}\cdot12=1[/tex]The result is the numerator of the fraction, and the denominator will be 12, so:
[tex]0.08\bar{3}=\frac{1}{12}[/tex]And the resulting mixed number is:
[tex]\frac{13}{12}=1\frac{1}{12}[/tex]Finally, add the remaining whole number from the first sum to determine the distance between his house and the school:
[tex]1+1\frac{1}{12}=2\frac{1}{12}[/tex]The distance he traveled from home to school is 2 1/12 km.
10 Zara writes a sequence of five numbers. The first number is 2. The last number is 18. Her rule is to add the same amount each time. Write the missing numbers. 2,____ ,_____,______, 18
If the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that, the first number is 2 and the last number is 18,
a = 2
L=18
n=5
a₅=5
a₅=a+(5-1)d
18=2+4d
4d = 18-2
4d = 16
d= 16 / 4
d=4
The terms of the sequence are,
a₁=2
a₂=2+4=6
a₃=6+4=10
a₄=10+4=14
a₅=14+4=18
Thus, if the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
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Solve the problem15) 21 and 22 are supplementary angles. What are the measures to the nearest hundredth) of the two angles?5x - 92I
∠1 is 31.5°
∠2 is 148.5°.
Given:
∠1 = x
∠2 = 5x-9
The measure of ∠1 and ∠2 are supplementary angles.
First, the value of x can be calculated as,
[tex]\begin{gathered} \angle1+\angle2=180\degree \\ 5x-9+x=180\degree \\ 6x-9=180\degree \\ 6x=180+9 \\ 6x=189 \\ x=\frac{189}{6} \\ x=31.5 \\ x=\angle1 \end{gathered}[/tex]Substitute the value of x in ∠2.
[tex]\begin{gathered} \angle2=5x-9 \\ =5(31.5)-9 \\ =157.5-9 \\ =148.5 \end{gathered}[/tex]Hence, the measure of ∠1 is 31.5° and the measure of ∠2 is 148.5°.
Hi, can you help me answer this question please, thank you!
1. Test statistic:
To find the test statistic, we use the formula:
[tex]\begin{gathered} Z=\frac{\bar{X_d}-\mu_d}{\frac{s_d}{\sqrt[]{n}}} \\ \text{where,} \\ \bar{X}_d=sample\text{ difference} \\ \mu_d=\text{population difference} \\ s_d=\text{standard deviation of the differences } \\ n=\text{ number of people in the survey.} \\ \\ \text{ We use Z statistic because the number of people are more than 30} \end{gathered}[/tex]Solving for Z, we have:
[tex]\begin{gathered} \bar{X}-\mu_d=3.1\text{ (Average difference given in the question)} \\ \\ \therefore Z=\frac{3.1}{\frac{13.8}{\sqrt[]{40}}}=1.4207\approx1.421\text{ (To 3 decimal places} \end{gathered}[/tex]Thus, the test statistic is 1.421
2. P-value:
To find the p-value, we check the Z-distribution table.
The value for the p-value is
[tex]2\times0.077658=0.15532\approx0.1553\text{ (To 4 decimal places)}[/tex](We multiply by 2 because it is a two-tailed test.
3. Comparison:
The alpha level is 0.001.
Thus, the p-value is greater than the alpha level
Find each unit price and decide which is the better buy. Assume that we are comparing different sizes of the same brand.Frozen orange juice:$1.57 for 14 ounces$0.57 for 4 ounces----------------------------Find the unit price of a frozen orange juice which costs $1.57 for 14 ounces.$ (blank) per ounce(Type a whole number or a decimal. Round to three decimal places as needed.)Find the unit price of a frozen orange juice which costs $0.57 for 4 ounces.$ (blank) per ounce(Type a whole number or a decimal. Round to three decimal places as needed.)Which is the better buy?A. $1.57 for 14 ouncesB. $0.57 for 4 ounces
The different sizes of the given brands are
Frozen orange juice:
$1.57 for 14 ounces
$0.57 for 4 ounces
The unit price of a frozen orange juice which costs $1.57 for 14 ounces is
1.57/14 = 0.112
The unit price of a frozen orange juice which costs $0.57 for 4 ounces is
0.57/4 = 0.1425
The better buy is the size that has the lowest cost per ounce. Looking at our calculations, the lowest cost per ounce is $0.112
Therefore, the frozen orange juice which costs $1.57 for 14 ounces is the better buy.
solve the equation x 1.)132.)13/33.) 104.) none of these choices
Answer:
2. 13/3
Step-by-step explanation:
x will be equal to 13/3.
Given,
5^(2x - 1) = 5^(5x - 14)
We can see that base is the same for both the exponents on each side of the equation.
Now, on using the Logarithm on both sides with base 5, we can see that the base on both sides of the equation cancels out with the log (base 5) function.
And new equation becomes:
(2x - 1) = (5x - 14)
This derives us to another conclusion that if the base of an exponent is equal then,
the powers must be equal too.
(2x - 1) = (5x - 14)
=> 5x - 2x = -1 + 14
=> 3x = 13
which gives us,
=> x = 13/3.
Therefore x = 13/3.
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Consider the function f(x)= square root 5x-10 for the domain [2, +infinity). find f^-1(x), where f^-1 is the inverse of f. also state the domain of f^-1 in interval notation.edit: PLEASE DOUBLE CHECK ANSWERS.
let f(x) = y
To find the inverse of f(x), we would interchange x and y:
[tex]\begin{gathered} y\text{ = }\sqrt[]{5x\text{ - 10}} \\ \text{Interchanging:} \\ x\text{ = }\sqrt[]{5y\text{ - 10}} \end{gathered}[/tex]Then we would make the subject of formula:
[tex]\begin{gathered} \text{square both sides:} \\ x^2\text{ = (}\sqrt[]{5y-10)^2} \\ x^2\text{ = 5y - 10} \end{gathered}[/tex][tex]\begin{gathered} \text{Add 5 to both sides:} \\ x^2+10\text{ = 5y} \\ y\text{ = }\frac{x^2+10}{5} \\ \text{The result above is }f^{\mleft\{-1\mright\}}\mleft(x\mright) \end{gathered}[/tex][tex]\begin{gathered} f^{\mleft\{-1\mright\}}\mleft(x\mright)\text{ = }\frac{x^2+10}{5} \\ The\text{ domain of the inverse is all real numbers} \\ \text{That is from negative infinity to positive infinity} \end{gathered}[/tex]In interval notation:
[tex]\begin{gathered} \text{Domain = (-}\infty,\text{ }\infty) \\ f^{\{-1\}}(x)\text{ = }\frac{x^2+10}{5}\text{for domain (-}\infty,\text{ }\infty) \end{gathered}[/tex]2 ABC Company has a large piece of equipmentthat cost $85,600 when it was first purchased 6years ago. The current value of the equipment is$30,400. What is the average depreciation of theequipment per year?F. $ 5,800G. $ 9,200H. $15,200J. $27,600K. $42,800
The intial cost of the equipment is C, which is given as 85,600.
The present value is PV, which is given as 30,400.
This simply means the total depreciation over the last 6 years can be derived as;
Depreciation = C - PV
Depreciation = 85600 - 30400
Depreciation = 55200
However, the method of depreciation is not given/specified, and hence the question requires that you calculate the average depreciation per year. That is, the total depreciation would be evenly spread over the 6 year period (which assumes that the depreciation per year is the same figure)
Average depreciation = Total depreciation/6
Average Depreciation = 55200/6
Average Depreciation = 9200
The correct option is option G: $ 9,200
Brayden was given a box of assorted chocolates for his birthday. Each night, Brayden
treats himself to some chocolates. The number of chocolates remaining in the box t
days after Brayden's birthday can be modeled by the equation C = -3t+ 12. What
is the slope of the equation and what is its interpretation in the context of the
problem?
Answer:
Step-by-step explanation:
The slope of the function is -3 which reveals the number of chocolates Brayden eats each night.
What is a feature of function g if g(x) = log (x-4) -8
The domain and range of the logarithmic function are
[tex]\begin{gathered} \text{domain}(\log x)=(0,\infty) \\ \text{range}(\log x)=(-\infty,\infty) \end{gathered}[/tex]Therefore, if
[tex]g(x)=\log (x-4)-8[/tex]We require that
[tex]\begin{gathered} x-4>0 \\ \Rightarrow x>4 \end{gathered}[/tex]Notice that the -8 term does not affect the range of function g(x); thus,
[tex]\begin{gathered} \text{domain}(g(x))=(4,\infty) \\ \text{range}(g(x))=(-\infty,\infty) \end{gathered}[/tex]Set g(x)=-8; then,
[tex]\begin{gathered} \Rightarrow\log (x-4)-8=-8 \\ \Rightarrow\log (x-4)=0 \\ \Rightarrow x=5 \end{gathered}[/tex]Therefore, y=-8 is not an asymptote of g(x), and, as shown above, the domain and range of g(x) are x>4, y->all real numbers.
Calculate the limit when x->4 as shown below,
[tex]\lim _{x\to4}g(x)=(\lim _{x\to4}\log (x-4))-8=(-\infty)-8=-\infty[/tex]Therefore, there is a vertical asymptote at x=4
Answer:
Hope this helps ;)
Step-by-step explanation:
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?
c = price of a slice of Cheese pizza
m= price of a slice of mushroom pizza
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza fora total cost of $12.50
3c + 4 m = 12.50
Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50.
3c + 2m = 8.50
We have the system of equations:
3c + 4 m = 12.50 (a)
3c + 2m = 8.50 (b)
Subtract (b) to (a) to eliminate c
3c + 4m = 12.50
-
3c + 2m = 8.50
_____________
2m = 4
Solve for m:
m = 4/2
m=2
The cost of one slice of mushroom pizza is $2
Find the set An B.
U = {1, 2, 3, 4, 5, 6, 7, 8)
A = {1, 2, 3, 4)
B = {1, 2, 6}
Step-by-step explanation:
I assume A n B means the intersection of the sets A and B.
that means all the elements that are in A and in B.
that is the set {1, 2}
Consider the equation below. 4(x - 4) + 6x = 14 Part A: Enter the value for x that makes the equation true. X = Part B: Explain the algebraic steps you took to get the solution. thea Part C: Explain how you know your solution in Part A is correct.
Part A) To find out the value for x that makes it an identity, (true), we need to solve it.
4(x-4) +6x=14 Distiribute
4x -16 +6x = 14 Combine like terms
2x -16 = 14 Add 16 to both sides
2x = 30 Divide both sides by 2
x =15
Part B) Above explained.
Part C) We can know it by plugging it into the original equation:
4(15 -4) +6(15) = 14
4(11) +90 = 14
44
Benny is flying a kite directly over his friend Frank, who is 125 meters away.When he holds the kite string down to the ground, the string makes a 39° anglewith the level ground. How high is Benny's kite?Draw a sketch depicting the situation above.b.)Use trigonometry to determine the height of Benny's kite.
Solution
Let us draw a diagram to illustrate the information
Using SOHCAHTOA
[tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ \\ tan39=\frac{h}{125} \\ cross\text{ multiply} \\ h=125\times tan39 \\ \\ h=101.2230041 \\ \\ h=101.22m\text{ \lparen to two decimal places\rparen} \end{gathered}[/tex]Solve the inequality and graph the solution on the line provided.
< > M >
Inequality Notation:
Number Line:
or
-12 -10 -8 -6
-4 -2
0 2 4
Click and drag to plot line.
2x64 -48
6
8
10 12
Answer:
x ≥ 8Step-by-step explanation:
GivenInequality 2x - 64 ≥ - 48Solution2x - 64 ≥ - 482x ≥ 64 - 482x ≥ 16x ≥ 8To graph the solution, plot the point x = 8, make it closed dot, shade the line to the right from this point.
state income tax? Jim Koslo earns $156,200 annually as a plant manager. He is married and supports 3 children. The state tax rate in his state is 3.55% of taxable income. What amount is withheld yearly for state income tax?
Answer:
44,000
Let me know if its wrong
