To find the angular speed in rpm, we need to use the formula for tangential speed, which is the speed at which an object moves along a circular path. The formula for tangential speed is:
v = r * omega
where v is the tangential speed, r is the radius of the circle, and omega is the angular speed.
In this case, we are given that v = 25 mph and r = 15 feet. We can solve for omega by dividing both sides of the equation by r:
omega = v / r
Substituting the given values, we get:
omega = 25 mph / 15 feet
To convert the units of speed from mph to feet per second, we need to use the conversion factor that 1 mph is equal to 5280/3600 feet per second. We can use this conversion factor to rewrite the expression for omega in terms of feet per second:
omega = (25 mph * (5280/3600)) / 15 feet
This simplifies to:
omega = 0.7222 feet/second
Next, we need to convert the angular speed from feet per second to rpm. To do this, we need to use the formula for converting from linear speed to angular speed, which is:
omega = (v * 60) / (2 * pi * r)
where v is the linear speed, r is the radius of the circle, and omega is the angular speed in rpm.
In this case, we are given that v = 0.7222 feet/second and r = 15 feet. We can solve for omega by plugging these values into the formula and simplifying:
omega = (0.7222 feet/second * 60) / (2 * pi * 15 feet)
= 0.7222 feet/second * 60 / (2 * pi * 15 feet)
= 0.7222 * 60 / (2 * pi * 15)
= 4.3332 / (2 * pi * 15)
= 0.2821 / (pi * 15)
Therefore, the angular speed in rpm is 0.2821 / (pi * 15), or approximately 0.0046 rp
a price is discounted by 20 percentage and the discounted price is 200 euro. how many euros was the discount?
Answer:
Step-by-step explanation:
40
The perimeter of a triangle is 3x² + 6x - 9. If one side length is x² + 2x - 1 and the
other is x² + x - 5, what is the length of the 3rd side?
Answer:
x^2+3x-3
Step-by-step explanation:
(x^2+2x-1)+(x^2+x-5)
2x^2+3x-6
(3x^2+6x-9)-(2x^2+3x-6)
x^2+3x-3
hopes this helps
Answer:
[tex]x^2 + 3x - 3[/tex]
Step-by-step explanation:
The perimeter of a triangle, can be calculated as, the sum of the sides.
So let's first assume the third side is a polynomial, and more specifically, a quadratic in the form: [tex]ax^2+bx+c[/tex]. This assumption is denoted from the fact that the perimeter only has terms up to the degree of 2, also known as x squared. The answer is also a quadratic, so it isn't an unreasonable assumption that if we add two quadratics (the ones given), and add one more quadratic, we should still have quadratic.
So, the sum of the three sides can be expressed as: [tex](x^2 + 2x - 1) + (x^2 + x - 5) + (ax^2 + bx + c)[/tex]
We can combine like terms to get:
[tex](x^2+x^2+ax^2)+(2x+x+bx)+(-1-5+c)[/tex]
Now from here, we can combine like terms (add coefficients):
[tex](2+a)x^2 + (3+b)x + (-6+c)[/tex]
From here, we simply set this equal to the given perimeter of: [tex]3x^2 + 6x-9[/tex], which gives us the equation:
[tex](2+a)x^2 + (3+b)x+(-6+c) = 3x^2 + 6x - 9[/tex]
Now from here, the coefficients need to correspond for both quadratics to be equal to each other, so that means that the following must be true:
[tex](2+a)=3\implies a = 1\\(3 + b) = 6\implies b = 3\\(-6 +c) = -9 \implies c = -3[/tex]
We now plug this into the quadratic standard form to get:
[tex]x^2 + 3x - 3[/tex]
Which is our third side!
A tool set is on sale for $424.15. The original price of the tool spt was $499.00. What percent of the original price
is the sale price?
Answer:
94 percent.
Step-by-step explanation:
Since the tool set used to be worth 499, but is now worth 424.15, we divide the two prices.
Calculation.
424.15/499 = 0.944654788.
We are figuring out the percent, so we need to round.
0.94465478 is about 0.94
0.94 IS EQUALVENT to 94%, so that is our answer.
. Acme Burgers sells a large pop which is 14 oz and comes in a 8" high container. The small pop comes
in a 6" high container which is the same shape as the small pop container. How much does the small
container hold?
Answer:
10.5 oz
Step-by-step explanation:
The large pop and container are similar to the small pop and container.
Thus, we can use proportions to find how much the small container can hold, letting x represent the volume of the small container:
[tex]\frac{14}{8}=\frac{x}{6}\\ 8x=84\\ x=21/2=10.5[/tex]
3. The graph of function g(x) is shown below.
Answer:
Step-by-step explanation:
g(x) = 2*[tex]\sqrt{x}[/tex] + 4
Domain is the input so what limits are there to the input?
for the square root, you are told that you can't not put in negative numbers until you learn about imaginary number in the for m a+bi, but for now, just say the input is 0 to ∞, for now The domain is 0 to ∞
Range is the output
so that is from 4 to ∞
Answer:
a. translation 2 right and up 4
b. g(x) = √(x -2) +4
c. domain: x ≥ 2; range: y ≥ 4
Step-by-step explanation:
You have the graph of a square root function with its vertex at (2, 4). You want to know what transformation that represents, the equation of the graph, and the domain and range of the function.
a. TransformationThe vertex of the square root function f(x) = √x is located at (0, 0). In the given graph, it has moved to (2, 4). The vertical and horizontal scale factors remain unchanged. This transformation is ...
translation right 2 units and up 4 units
b. EquationTranslation of function f(x) by h units right and k units up gives you ...
g(x) = f(x -h) +k
Here, we have (h, k) = (2, 4), and f(x) = √x, so the transformed function is ...
g(x) = √(x -2) +4
c. Domain and RangeThe domain is the horizontal extent of the graph. For a square root function it is the x-value of the vertex, and all points to the right of that.
domain of g(x): x ≥ 2
The range is the vertical extent of the graph. For a square root function it is the y-value of the vertex, and all points above that.
range of g(x): y ≥ 4
The path of the airplane the astronauts are flying
in can be modeled using the function h(x) =
10000cos(0.0001x) + 20000 in which h indicates
the height in feet. What is the approximate period
of the wave?
Answer:
The approximate period of the wave representing the airplane's path is 0.9 hours.
Step-by-step explanation:
The period of a wave is the time it takes for one complete cycle of the wave to occur. In the case of the airplane's path, this would be the time it takes for the airplane to complete one full oscillation, or "up and down" motion.
To find the period of the wave, we need to determine the value of x that corresponds to one complete cycle of the wave. In this case, the wave is defined by the function h(x) = 10000cos(0.0001x) + 20000.
To find the period, we can use the formula T = 2π/ω, where T is the period, π is the mathematical constant pi, and ω is the angular frequency of the wave. The angular frequency is related to the frequency of the wave, which is the number of cycles per second.
In this case, the angular frequency is given by the coefficient of the x term in the function, which is 0.0001. Plugging this value into the formula above, we get T = 2π/0.0001 = 200000π seconds.
Since one cycle of the wave corresponds to one complete oscillation of the airplane, the period of the wave is approximately 200000π seconds. This is a very large number, so it is usually more useful to express the period in minutes or hours. To convert to minutes, we can divide the period by 60, which gives us a value of about 3334 minutes. To convert to hours, we can divide the period by 3600, which gives us a value of about 0.9 hours.
In summary, the approximate period of the wave representing the airplane's path is 0.9 hours.
Ask me any questions you may have!
The amount of time it takes for a wave to complete one full cycle is known as the wave's period. This would be the amount of time needed for the plane to perform one full oscillation, or “up and down” motion, in the case of the flight path.
What path airplane the astronaut's period of the wave?Finding the value of x that represents the wave's full cycle is necessary to calculate the wave's period. The equation h(x) = 10000cos(0.0001x) + 20000 in this instance defines the wave.
The formula T = 2/, where T is the period, is the mathematical constant pi, and is the wave's angular frequency, can be used to determine the period. The wave's frequency, or the number of cycles per second, and the angular frequency are connected.
We may convert the period to hours by dividing it by 3600, which gives us a number of approximately 0.9 hours.
Therefore, The wave that represents the course of the airplane has an approximate period of 0.9 hours.
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Let f(x) = –7x + 9. Suppose you add 2 to the input of f to create a new function g, then multiply the output of function g by –3 to create function h. What are the slope and y-intercept of the graph of function h?
We will see that the linear function h(x) is:
h(x) = -21x - 15
The slope is -21, and the y-intercept is -15.
What are the slope and y-intercept of function h?
Remember that a general linear function is:
y = a*x + b
Where a is the slope and b is the y-intercept.
Here we start with the linear function:
f(x) = -7x + 9
First, we need to add 2 to the input of f (the input is x) to get function g(x), so we have:
g(x) =f(x + 2)
Replacing the actual function we will get:
g(x) = -7*(x + 2) + 9
Now we multiply the output of function g by 3 to get h(x), then:
h(x) = 3*g(x)
We will get:
h(x) = 3*[-7*(x + 2) + 9]
h(x) = -21*(x + 2) + 27
h(x) = -21x - 42 + 27
h(x) = -21x - 15
So we can see that the slope of function h(x) is -21, while the y-intercept is -15.
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A roller coaster ride holds a total of 48 passengers. The ratio of males to females on the ride is 5 : 7. Let x represent the number of males on the ride. Let y represent the number of females on the ride. Which two linear equations form a system that you can use to find the number of males and the number of females on the ride?
Answer:
5x + 7y = 48 (total number of passengers on the ride)
x + y = 48 (total number of males and females on the ride)
Step-by-step explanation:
To find the number of males and the number of females on the roller coaster ride, you can use the following two linear equations to form a system:
5x + 7y = 48 (total number of passengers on the ride)
x + y = 48 (total number of males and females on the ride)
The first equation states that the total number of passengers on the ride is equal to the sum of the number of males (5x) and the number of females (7y). The second equation states that the total number of males and females on the ride is equal to the sum of the number of males (x) and the number of females (y).
To solve this system, you can use algebraic techniques to eliminate one of the variables and solve for the other. For example, you could multiply the first equation by 5 and the second equation by 7, then subtract the two equations to eliminate the y variable:
5 * 5x + 7 * 7y = 5 * 48
7 * x + 7 * y = 7 * 48
25x + 49y = 240
49x + 49y = 336
24x = 336 - 240
24x = 96
x = 4
Substituting this value for x in the first equation, we can solve for y:
5 * 4 + 7 * y = 48
20 + 7 * y = 48
7 * y = 28
y = 4
Therefore, there are 4 males and 4 females on the roller coaster ride.
Suppose that events F and S are conditional independent events given D and ~D respectively with p(F|D)=p(S|D)=0.9, p(~F|~D)=p(~S|~D)=0.9, and p(D)=0.2. Find p(D|F∩S).
P(D|FS)=.9529
If F and S are conditionally independent given D and ~D, then
P(FSD)= P(D)P(F|D)P(S|D)
P(FS~D) = P(~D)P(F|~D)P(S|~D)
P(F|~D) = 1 - P(~F|~D)
P(S|~D) = 1 - P(~S|~D)
P(~D) = 1 - P(D)
P(D|FS) = P(FSD)/(P(FSD) + P(FS~D))
P(F|D) = P(S|D) = .9
P(~F|~D) = P(~S|~D) = .9
P(D = .2)
Then, P(FSD) = P(D)P(F|D)P(S|D) = .2*.9*.9 = .162
P(FS~D) = P(~D)P(F|~D)P(S|~D) = (1 - .2)(1 - .9)(1 - .9)= .008
P(D|FS) = P(FSD)/(P(FSD) + P(FS~D)) = .162/(.162+.008) = 162/170=81/85 = .9529
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What reason would you use to prove ΔFGH ≅ ΔJHK ?
Select one:
ASA
HL
SAS
cannot prove congruency
SAA
The reason that is used to prove ΔFGH ≅ ΔJHK is SAS property
If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other.
According to the question,
Given : (1) ∠FGH and ∠JHK are right angles
(2) H is midpoint of GK
(3) GH ≅ JK
In ΔFGH and ΔJHK
∠FGH = ∠JHK ( right angles )GH ≅ JK (given) GH = KH ( H is midpoint of GK )Therefore , ΔFGH ≅ ΔJHK using SAS property
Hence , The reason use to prove ΔFGH ≅ ΔJHK is SAS
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A tree is 108 inches tall. A second tree is 120 inches tall. What is the combined height of the trees?
Answer:228
Step-by-step explanation:
All you have to do is add 108 to 120.
0+8=8, 2+0=2, 1+1=2
120
108
+_____
228
The positive integers greater than 3 are arranged in rows and columns as illustrated.
In which column is the number 5018?
A) 2
B) 4
C) 6
D) 5
E) 3
The rows and columns of the positive integers greater than three are as shown. And the number 5018 is found in the third column.
When performing a permutation test, you repeatedly rearrange one of the variables without affecting the other variable (s). From the given table, we can start with column 4. Here, each row has about 6 numbers. That is singular row has numbers from columns 1 to 6 and an even row from columns 7 to 2.
Then subtract 5018 by 3. We get 5018-3=5015.
Divide this by 6,
5015/6 = 836.
So 5018 is located in an even row from 7 to 2.
Therefore, 5018 is located in the 836th row and 3rd column.
So the required answer is E) 3.
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a response variable y has correlation coefficient 0.3 with each of the predictors x1 and x2. however, these predictors are heavily correlated r x1x2
If the response variable y has a correlation coefficient of 0.3 with each of the predictors x1 and x2, it means that there is a weak linear relationship between y and both x1 and x2.
This means that as x1 and x2 increase or decrease, y is likely to change by a small amount. If x1 and x2 are heavily correlated, it means that there is a strong linear relationship between the two variables. This means that as x1 increases or decreases, x2 is likely to change by a large amount in the same direction. When two predictors are highly correlated, it can be difficult to determine the individual contribution of each predictor to the response variable y.
In this situation, it may be useful to use techniques such as multi-collinearity analysis or principal component analysis to understand the relationship between the predictors and the response variable better.
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Secondary Mortgage Purchasing Company (SMPC) wants to buy your mortgage from the local savings and loan. The original balance of your mortgage was $153,000 and was obtained five years ago with monthly payments at 10 percent interest. The loan was to be fully amortized over 30 years.
Required:
a. What should SMPC pay if it wants an 11 percent return?
b. What is the balance of the original loan after five additional years (10 years from origination)?
SMPC should pay 136,992.36$ if it wants an 11 percent return. and the balance of the original loan after additional years 142,229.05$.
What is the monthly rate of the loan?A monthly rate is a fee for services calculated over a thirty-day period.
Given, Your mortgage will be purchased by the Secondary Mortgage Purchasing Company (SMPC) from the nearby savings and loan. Your mortgage had an initial amount of $153,000 and was obtained five years ago with regular payments at a 10% interest rate. The loan was to be completely repaid over a 30-year period.
Payment Formula = PMT (monthly rate, month, -mortgage)
Present value formula = PV( monthly rate, month left, - payment, - repayment)
Loan value formula = PV (monthly rate, month left, -payment)
a. formula = PMT( 10%/12, 30*12, -153000)
Payment = $1342.68
Formula = PV(11%/ 12, (30-5)* 12, -1342.68)
Smpc pays = $136,992.36
b. Loan balance = 139134.70$
Formlua = PV(11%12,5*12, - 1342.68, -139134.7)
Smpc pays = 142,229.05$
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Which of the following is the correct boolean expression to test for:
int x is being a value between, including, 500 and 650, or int y not equal to 1000?
O ((x >= 500 && x <= 650)|| (y != 1000))
O ((x > 500 AND x < 650) OR !(y. equal(1000)))
O ((x > 500 && x < 650) || (y != 1000))
O ((x < 500 && x > 650) || !(y == 1000))
The correct boolean expression to test for int x being a value between, including, 500 and 650, or int y not equal to 1000 is:
((x >= 500 && x <= 650)|| (y != 1000))
This expression uses the "&&" operator to test for x being greater than or equal to 500 and less than or equal to 650, and the "||" operator to test for y not being equal to 1000. The expression is using the correct comparison operators and logical operators to test for the desired conditions.
A boolean expression is a statement that evaluates to either true or false. It is commonly used in programming to control the flow of a program, as the result of a boolean expression can be used to determine whether a certain block of code should be executed or not.
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the sugar sweet company delivers sugar to its customers. let be the total cost to transport the sugar (in dollars). let be the amount of sugar transported (in tons). the company can transport up to tons of sugar. suppose that gives as a function of . identify the correct description of the values in both the domain and range of the function. then, for each, choose the most appropriate set of values.
The domain and the range of a function are the possible input and output values of the function.
The function is given as:
C = 130S + 3500
The domain
This is the possible S values of the function.
S cannot be less than 0, because it represents a physical quantity (i.e. tons of sugar)
The value of S can be any value greater than 0
Hence, the domain of the function is [0, ∞)
The range
This is the possible C values of the function.
The function is given as:
C = 130S + 3500
When S = 0
C = 130(0) + 3500
C = 3500
The above means that:
C cannot be less than 3500
The value of C can be any value greater than 3500
Hence, the range of the function is [3500, ∞)
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For 7.45 - 3.029 why do you rewrite 7.45 as 7.450
For 7.45 - 3.029 the reason why they rewrite 7.45 as 7.450 is so as to have both values in three decimal place so the calculation can be easier.
What is decimal place?It should be noted that the first digit after the decimal represents the tenths place then the next digit after the decimal could be reffered to as hundredths place however the remaining digits continue to fill in the place values until there are no digits left.
It should be noted that Decimal place value can be described as the place values of all the digits in a given decimal number.
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You are refilling your inventory of welcome packets for new customers. For each packet, it takes 5 minutes to print, 2 minutes to organize, and 5 minutes to proofread. The ink in the printer will need to be changed every 5 packets, which takes 3 minutes. You have 3 hours to dedicate to this task. Assume thathe ink in the printer was already changed before beginning and that you have to complete each packet before completing any steps for the next one. How many welcome packets will you be able to fully complete in the time allotted?
The number of welcome packets that you will be able to fully complete in the time allotted would be = 14
What is the time for refilling the packets?The time allotted for the refilling of the whole welcome packets = 3 hours
To convert to mins = 3 × 60 = 180 mins.
To run each packet will take the following time:
5 minutes to print,
2 minutes to organize, and
5 minutes to proofread which is a total of 12mins
But for every 5 packets = 5×12+3 = 63 mins.
Therefore X packets = 180 mins.
Make X packets the subject of formula;
X packets = 5 × 180/63
= 900/63
= 14.2
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What is the value of the expression:
6 - 5x when x = -2?
Answer: 16
Step-by-step: 6 - (5(-2)=-10 then the - turns into + and your answer is 6 + 10
How do you classify -15
-15 is an integer , rational and a real number
What are rational,real numbers and integers?Real numbers are mainly classified into rational and irrational numbers. Rational numbers include all integers and fractions. All negative integers and whole numbers make up the set of integers. Whole numbers comprise of all natural numbers and zero.
A negative number is not a natural number.
This means that -15 is a real number because real number comprises of rational and irrational number and rational numbers include negative numbers and they are called negative integers.
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An entry-level civil engineer earns an average bi-weekly net pay of $2,175.25. The engineer has created a monthly budget using the following percentages for expenses:
Percent
Housing 35%
Food/Household 10%
Savings 10%
Transportation 15%
Debt 5%
Entertainment 6%
Medical/Personal Care 5%
Giving 5%
Clothing 4%
Miscellaneous 5%
Which balance sheet correctly represents the engineer's income, expenses, and balance?
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $2,175.25
Expenses
Percent Amount
Housing 35% $761.34
Food/Household 10% $217.53
Savings 10% $217.53
Transportation 15% $326.29
Debt 5% $108.76
Entertainment 6% $130.52
Medical/Personal Care 5% $108.76
Giving 5% $108.76
Clothing 4% $87.01
Miscellaneous 5% $108.76
$2,175.25
Balance
Income $2,175.25
Expenses $2,175.25
Balance $0
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $3,262.88
Expenses
Percent Amount
Housing 35% $1,142.01
Food/Household 10% $326.29
Savings 10% $326.29
Transportation 15% $489.43
Debt 5% $163.14
Entertainment 6% $195.77
Medical/Personal Care 5% $163.14
Giving 5% $163.14
Clothing 4% $130.52
Miscellaneous 5% $163.14
$3,262.88
Balance
Income $3,262.88
Expenses $3,262.88
Balance $0
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,713.04
Expenses
Percent Amount
Housing 35% $1,649.56
Food/Household 10% $471.30
Savings 10% $471.30
Transportation 15% $706.96
Debt 5% $235.65
Entertainment 6% $282.78
Medical/Personal Care 5% $235.65
Giving 5% $235.65
Clothing 4% $188.52
Miscellaneous 5% $235.65
$4,713.04
Balance
Income $4,713.04
Expenses $4,713.04
Balance $0
Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,350.50
Expenses
Percent Amount
Housing 35% $1,522.68
Food/Household 10% $435.05
Savings 10% $435.05
Transportation 15% $652.58
Debt 5% $217.53
Entertainment 6% $261.03
Medical/Personal Care 5% $217.53
Giving 5% $217.53
Clothing 4% $174.02
Miscellaneous 5% $217.53
$4,350.50
Balance
Income $4,350.50
Expenses $4,350.50
Balance $-
PLEASE HELP
The balance sheet that correctly represents the engineer's income, expenses and balance is balance number 4.
How tp determine percentages of income?We should know that balance sheet is a summary of assets and liabilities and income and expenses of a legal person.
We are told that the the balance sheet shows a bi-weekly net pay
This implies that a month has two bi-weeks. therefore every income and expenses is multiplied by 2 to get the following figures.
Income Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,350.50
Expenses Percent Amount
Housing 35% $1,522.68
Food/Household 10% $435.05
Savings 10% $435.05
Transportation 15% $652.58
Debt 5% $217.53
Entertainment 6% $261.03
Medical/Personal Care 5% $217.53
Giving 5% $217.53
Clothing 4% $174.02
Miscellaneous 5% $217.53
$4,350.50
Balance
Income $4,350.50
Expenses $4,350.50
Balance $0
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11 A fisherman wants to know how many fish there are in a lake. One day, he catches 50, marks them and puts them back. The next day he catches 80 fish. 20 of these fish have marks on them. Estimate the total number of fish in the lake.
The total number of fish in the lake would be = 60 fishes
What is total of a data set?The total of a data set is the addition of the various components that makes up a data set which gives a particular value.
On the first day the number of fish that was marked by the fisher man = 50 fishes.
On the second day the total amount of fishes that was caught = 80 fishes
The number of fishes that where among the 80 fishes that are marked= 20
Therefore the total amount of fishes in the lake = 80 - 20
= 60 fishes.
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the table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. which statements about the function described by the table are true? check all that apply. the independent variable is the number of people. the initial value (initial fee) for the picnic is $40. the rate of change is $8.67 per person. as the number of people increases, the total cost of the picnic increases. if 4 people attended the picnic, the total cost would be $46.
Required function y = 2x + 40 to represents linear relationship between number of people and total cost shows following statements are true:
a. Independent variable represents the number of people.
b. Initial value for the picnic is $40.
d. Cost of the picnic increases as per the number of people.
As given in the question,
Let 'x' represents the number of people
And 'y' represents the total cost
Linear relationship between number of people and total cost is:
y = mx + b
Consider two points (x₁ , y₁) = (6, 52) and ( x₂ , y₂ ) = ( 9 , 58)
Slope 'm' = ( y₂ - y₁)/ (x₂ - x₁)
= (58 - 52)/ (9 -6)
= 6 / 3
= 2
y = 2x + b
Now for, (x. y) = ( 12,64)
64 = 2(12) +b
⇒b = 64 - 24
⇒b = 40
Hence, required function is :
y = 2x + 40
a. Independent variable is the number of people.
Here it is x which represents the number of people.
True.
b. Initial value for the picnic is $40
y- intercept when x =0 ⇒ y = $40
True.
c. Rate of change is $8.67 per person.
No, rate of change is $2 per person.
d. Number of people increases as total cost of picnic increases
True .
e. If x = 4
⇒y = 2(4) + 40
= 48 ≠46
False.
Therefore, function y = 2x + 40 represents that following statements are true:
a. Independent variable represents the number of people.
b. Initial value for the picnic is $40.
d. Cost of the picnic increases as per the number of people.
The above question is incomplete, the complete question :
The table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. Which statements about the function described by the table are true? Check all that apply. a. The independent variable is the number of people.
b. The initial value (initial fee) for the picnic is $40.
c. The rate of change is $8.67 per person.
d. As the number of people increases, the total cost of the picnic increases.
e. If 4 people attended the picnic, the total cost would be $46.
Number of people Total cost ($)
6 52
9 58
12 64
15 70
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does anyone know this
The correct equivalent expression to the square root containing a variable is 2a³/5 and the correct option is E.
How to determine the equivalent expressionWe shall simplify the expression of the square root containing a variable by carrying out basic mathematics operations to derive its equivalent as follows:
squre root of (36a⁸/255a²) = square root of (36a⁶ × a²/255 × a²)
a² is common and can be cancel out
square root of (36a⁸/255a²) = square root of (36a⁶/255)
square root of (36a⁸/255a²) = square of 36 multiplied by the square root of a⁶ all divided by the square root of 255 {take square root of each}
square root of (36a⁸/255a²) = 6a³/15
square root of (36a⁸/255a²) = 2a³ × 3/5 × 3
we divide through by the common factor 3
square root of (36a⁸/255a²) = 2a³/5
Therefore, the equivalent expression to square root of (36a⁸/255a²) is derived as 2a³/5 which is option E.
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Find The length of the third side. If necessary, round to the nearest tenth. need answer ASAP
The length of the third side is 16.5 for the given right-angle triangle. By using Pythagoras' theorem, the required length is calculated.
What is the Pythagoras theorem?The theorem is given by (hyp)² = (opp)² + (adj)².This theorem applies to a right-angle triangle only.Calculation:The given triangle is a right-angle triangle.
It has two lengths. They are
length of the hypotenuse = 21
length of the adjacent or base = 13
Then, the third side i.e., the opposite side length is calculated by
(hyp)² = (opp)² + (adj)²
⇒ (21)² = (opp)² + (13)²
⇒ 441 = (opp)² + 169
⇒ (opp)² = 441 - 169 = 272
⇒ opposite side length = √272 = 16.49 ≅ 16.5
Therefore, the length of the third side is 16.5.
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Which equation is the inverse of 2(x - 2)² = 8(7+ y)?
O-2(x-2)2 = -8(7+ y)
Oy-x²-x-6
O y=-2± √√28+4x
Oy-2± √√28+4x
Answer:
[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]
Step-by-step explanation:
The inverse of [tex]2(x-2)^2=8(7+y)[/tex] is
[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]
i need help asap!!!!!
Answer:
The slope is same for both points.
Step-by-step explanation:
1st set of points: (1, 4) and (7, 2)
m = 2-4/7-1
m = -2/6
m = -1/3
2nd set of points: (7, 2) and (10, 1)
m = 1-2/10-7
m = -1/3
The slope is same for both points.
Please explain your answer to this question! Thank you!
Answer:
B. Incorrectly applied the distributive property
Step-by-step explanation:
You want to find Maria's error in her solution of -2(3x -5) = 40.
StepsThe solution can proceed as follows:
-2(3x -5) = 40 . . . . . . . . given
-6x +10 = 40 . . . . . . . . . use the distributive property
-6x = 30 . . . . . . . . . . subtract 10
x = -5 . . . . . . . . . . divide by -6
Comparing this solution to Maria's, we find that Maria incorrectly applied the distributive property. (She multiplied (-2)(-5) and got -10 instead of +10.)
Determine the whole number of standard deviations that includes all data values. The mean price of the nonfiction books on a best-sellers list is $24.18; the standard deviation is $ 3.98.
$19.95, $24.00, $21.00, $28.95, $19.00, $27.95, $19.00, $25.95, $26.00, $29.95
All of the values fall within __ standard deviation (s) of the mean.
All of the values fall within 1.45 standard deviation of the mean.
How to illustrate the standard deviation?From the information given, the mean price of the nonfiction books on a best-sellers list is $24.18 and the standard deviation is $3.98.
It should be noted that from the problem, the variable that is the farthest from the mean is $29.25.
Therefore, the z score will be illustrated as:
Z = (29.95 - Mean) / Standard deviation
Z = (29.95 - 24.18)) / 3.98
= 1.45
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What is the slope in the given line?
Answer:
[tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
The slope/gradient of a line is defined by this formula:
[tex]\frac{y_{1}-y_{0} }{x_{1}-x_{0} }[/tex]
Where you pick two coordinates, find the change in the [tex]y[/tex] values, and divide it by the change in the [tex]x[/tex] values.
Two coordinates that this line passes through are (3, -2) and (-3, 2).
You can take the second [tex]y[/tex]-value (2) from the first [tex]y[/tex]-value (-2) or vice versa, so long as you do it in the same order the [tex]x[/tex] values.
For this example, I will take the first [tex]y[/tex]-value (-2) from the second [tex]y[/tex]-value (2), and take the first [tex]x[/tex]-value (3) from the second [tex]x[/tex]-value (-3).
The gradient/slope is defined by [tex]m[/tex] in the following:
[tex]m=\frac{2--2}{-3-3}=\frac{4}{-6}=-\frac{4}{6}=-\frac{2}{3}[/tex]