Answer:
C, E
Step-by-step explanation:
You want the equations that represent 2 boys for every 5 girls in a class.
RatioThe number of boys is represented by x, and the number of girls is represented by y, so you have ...
x : y = 2 : 5
As fractions, this is ...
x/y = 2/5
Other representationsMultiplying by 5y gives ...
5x = 2y . . . . . . matches equation C
Dividing by 5, we have ...
x = 2/5y . . . . . . matches equation E
3
The ratio of desktop computers to laptop computers sold by
a mail-order company last week was 8 to 3. What could be
the numbers of computers sold by the company last week?
A
B
C
D
448 desktops, 168 laptops
448 desktops, 165 laptops
440 desktops, 168 laptops
400 desktops, 165 laptops
using the ratio given, the number of computers could be sold by the company last week is: A. 448 desktops, 168 laptops.
How to Calculate Ratios?To find the actual numbers of desktop and laptop computers sold, we need to choose a common factor for the ratio 8:3.
Let's assume that the total number of computers sold is 33x (where x is a positive integer). Then, the ratio 8:3 corresponds to 8x desktops and 3x laptops. We can check which of the given options satisfies this condition:
A. 8x = 448, 3x = 168 --> This satisfies the condition, as 8:3 = 448:168
B. 8x = 448, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 448:165
C. 8x = 440, 3x = 168 --> This does not satisfy the condition, as 8:3 is not equal to 440:168
D. 8x = 400, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 400:165
Therefore, the answer is option A: 448 desktops and 168 laptops could be the numbers of computers sold by the company last week.
Learn more about ratios on:
https://brainly.com/question/29053563
#SPJ1
show that v is an eigenvector of A and find the corresponding eigenvalue, λ.A= [\begin{ccc}-1&1\\6&0\end{array}\right], v = [\begin{ccc}1\\3\end{array}\right]λ=_____
The matrix A does not eigenvector v corresponding to the given eigen value.
λ.A = [ -11 60 ]
v = [ 1 3λ ]
v is an eigenvector of A calculate corresponding eigenvalue,
A × v = λ × v
where A is the given matrix.
v is the given vector.
λ is the corresponding eigenvalue.
× denotes matrix multiplication.
Let's first calculate A × v we have,
A × v
= [-11 60] × [ 1 3λ]
= [-11-33λ 60+ 180λ]
Check A× v is equal to λ × v ,
λ × v =
λ × [ 1 3λ]
= [λ 3λ^2]
Set these two vectors equal to each other and get the following system of equations ,
-11-33λ = λ __(1)
60+ 180λ = 3λ^2 ___(2)
From equation (1) we get,
⇒34λ = -11
⇒ λ = -11/34
Substituting this value of λ into the second equation, we have,
60+ 180λ = 3λ^2
⇒ 60 + 180(-11/34) = 3(-11/34)^2
⇒ (2040 -1980)/ 34 = 3(-11/34)^2
⇒ 60/34 = 3( 11/34)^2
⇒ 60 × 34 = 3 × 11 × 11
⇒20× 34 = 11 × 11
Which is not true.
so the value of λ does not satisfies both equations.
Therefore, v is not an eigenvector of A with corresponding eigenvalue λ.
Learn more about eigen vector here
brainly.com/question/11865376
#SPJ4
The above question is incomplete, the complete question is:
Check whether v is an eigen vector of A if yes find the corresponding eigen value.
λ.A = [ -11 60 ]
v = [ 1 3λ ]
I NEED HELP ON THIS ASAP!!
a) Graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380
b) The maximum profit of $5200 achieved.
Define the term selling profit?Selling profit is the profit that a business makes on the sale of its products or services. It is the difference between the selling price and the cost of product.
a) Let x be the number of boards of mahogany sold and y be the number of boards of black walnut sold. Then, the constraints of the problem can be represented by the following system of inequalities:
x ≥ 0 (non-negative constraint)
y ≥ 0 (non-negative constraint)
x ≤ 260 (maximum number of mahogany boards available)
y ≤ 320 (maximum number of black walnut boards available)
x + y ≤ 380 (maximum number of boards that can be sold)
To graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380 on a coordinate plane and shade the feasible region that satisfies all of the constraints. The feasible region is the area that is bounded by these lines and includes the origin (0, 0).
b) The profit function P(x, y) can be defined as follows:
P(x, y) = 20x + 6y
To maximize the profit, we need to find the values of x and y that satisfy all of the constraints and maximize the profit function P(x, y).
One way to do this is to use the corner-point method. We can evaluate the profit function at each of the corners of the feasible region and find the corner that gives the maximum profit.
The corners of the feasible region are (0, 0), (0, 320), (260, 0), and (120, 260).
P(0, 0) = 0
P(0, 320) = 6(320) = 1920
P(260, 0) = 20(260) = 5200
P(120, 260) = 20(120) + 6(260) = 4720
Therefore, the maximum profit of $5200 can be achieved by selling 260 boards of mahogany and 0 boards of black walnut.
To know more about inequalities, visit:
https://brainly.com/question/30238989
#SPJ1
One family spent $45 on movie tickets for 2 adults and 3 childr
Another family spent $40 for 2 adults and 2 children. What are
prices of the adult movie tickets and the child movie tickets?
Answer:The prices of the adult movie tickets and the child movie tickets are $15 and $5 respectively.
Given that, the Jones family spent $45 on movie tickets for 2 adults and 3 children.
Step-by-step explanation:What is a linear system of equations?
A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let cost of adult tickets be x and the cost of children tickets be c.
The Jones family spent $45 on movie tickets for 2 adults and 3 children.
2a+3c=45 ------(I)
The Smith family spent $40 for 2 adults and 2 children.
2a+2c=40
a+c=20 ------(II)
From equation (II), we have a=20-c
Substitute a=20-c in equation (I), we get
2(20-c)+3c=45
⇒ 40-2c+3c=45
⇒ c=$5
Put c=5 in equation (II), we get
a+5=20
⇒ a=$15
What is the probability of
drawing a face card, then
drawing a heart with
replacement
Answer:
n(s) =52. n(f) = 12 n(h) = 13
p (f)= 13/52. p(f)= 12/52
i do not understand how to answer this question
a. Hence proved that the sum of fractions [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
b. The value will be 7 for the expression
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
What is square root?Square rοοt οf a number is a value, which οn multiplicatiοn by itself, gives the οriginal number. The square rοοt is an inverse methοd οf squaring a number. Hence, squares and square rοοts are related cοncepts.
Suppοse x is the square rοοt οf y, then it is represented as x=√y, οr we can express the same equatiοn as x² = y. Here, ‘√’ is the radical symbοl used tο represent the rοοt οf numbers. The pοsitive number, when multiplied by itself, represents the square οf the number. The square rοοt οf the square οf a pοsitive number gives the οriginal number.
Here,
a. [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
Using (a + b)(a - b) = a² - b²
⇒ [tex]${\frac{1 \cdot \sqrt{1}-\sqrt{2}}{\sqrt{1}+\sqrt{2}\cdot \sqrt{1 }-\sqrt{2}}+{\frac{1 \cdot \sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}\cdot \sqrt{1}-\sqrt{2}}}+{\frac{1 \cdot \sqrt{3}-\sqrt{4}}{\sqrt{3}+\sqrt{4}\cdot \sqrt{3}-\sqrt{4}}}$[/tex]
⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{1-2}+{\frac{ \sqrt{2}-\sqrt{3}}{2-3}+{\frac{\sqrt{3}-\sqrt{4}}{3-4}}$[/tex]
⇒ [tex]${\frac{ \sqrt{1}-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-\sqrt{4}}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+{\frac{\sqrt{3}-2}{-1}}$[/tex]
⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}}-{\sqrt{3}+2}$[/tex]
⇒ [tex]$ -1+2}$[/tex]
⇒ 1
a. Hence proved that the sum of fractions [tex]${\frac{1}{\sqrt{1+\sqrt{2}}}}+{\frac{1}{\sqrt{2+\sqrt{3}}}}+{\frac{1}{\sqrt{3}+\sqrt{4}}}=1$[/tex]
B. This will be done with the same process,
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
⇒ [tex]$ -1+\sqrt{2}}- \sqrt{2}+\sqrt{3}} \cdot \cdot \cdot -{\sqrt{63}+8}$[/tex]
There, will be same roots of every number until - 8
So,
⇒ [tex]$ -1+8}$[/tex]
= 7
b. The value will be 7 for the expression
⇒ [tex]${\frac{ 1-\sqrt{2}}{-1}+{\frac{ \sqrt{2}-\sqrt{3}}{-1}+ \cdot \cdot \cdot+{\frac{\sqrt{63}-8}{-1}}$[/tex]
To know more about Square rοοt visit:
https://brainly.com/question/4533036
#SPJ1
Una pintura incluyendo su marco tiene 25 cm de largo y 10 cm de ancho cuánto es el area del marco, si este tiene 4cm de ancho?
216 cm2 is the size of the rectangle border.
the translation of the question is
A painting including its frame is 25 cm long and 10 cm wide, what is the area of the frame if it is 4 cm wide?
What is a rectangle's area?
When the dimensions of a rectangle with length and width are multiplied, the area of the rectangle is determined as follows:
A = lw.
The total area is therefore given by:
A = 25 x 10 = 250 cm².
The white region's size is shown by:
A = (25 - 2 x 4) x (10 - 2 x 4) is equal to 17x 2 and 34 cm2.
Hence, the border's area is as follows:
216 cm2 = 250 cm2 - 34 cm2.
To know more about rectangle's area, click the below link
brainly.com/question/25292087
#SPJ4
suppose we are interested in estimating the difference in survival rate between the control and treatment groups using a confidence interval. explain why we cannot construct such an interval using the normal approximation. what might go wrong if we constructed the confidence interval despite this problem?
We cannot construct an interval using the normal approximation of survival rate between control and treatment groups because the samples must be random, independent, and their sample sizes must be sufficiently large.
What is the normal approximation?The normal approximation is valid when the sample sizes are large enough to ensure that the sampling distribution of the mean of the variable is approximately normal.
The central limit theorem applies to the distribution of the sample mean when the sample size is large enough, according to the normal approximation.
As a result, the mean difference between the two groups must have a normal distribution. The normal distribution may not be an accurate representation of the underlying distribution of the difference between the two population means in the absence of this requirement, causing the confidence interval to be inaccurate. It will lead to incorrect inferences about the difference in the survival rates of the two groups.
The confidence interval constructed despite this problem will lead to incorrect inferences about the difference in the survival rates of the two groups. This would make it difficult to draw any conclusions based on the findings of this experiment.
Learn more about Confidence interval here:
https://brainly.com/question/24131141
#SPJ11
If P(A)=0. 3, P(B)=0. 2, and P(A∩B)=0. 1, find the probability
a. P(
)
b. P(A∪B)
c. P(
∩B)
d. P(A∩
)
e. P(
∪B)
P(∅) = 0, P(A∪B) = 0.4 , P(A∩B) = 0.1 ,Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').and P(A∪B) = 0.4. are the required solutions ofgiven probability check .
a. The probability of an empty set is always zero. Therefore, P(∅) = 0.
b. The probability of the union of two events, A and B, is given by the formula P(A∪B) = P(A) + P(B) - P(A∩B). Substituting the values given in the question, we get:
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.3 + 0.2 - 0.1
= 0.4
Therefore, P(A∪B) = 0.4.
c. The probability of the intersection of A and B is given by the formula P(A∩B). Substituting the values given in the question, we get:
P(A∩B) = 0.1
Therefore, P(A∩B) = 0.1.
d. The probability of the intersection of A and the complement of B is given by the formula P(A∩B'). The complement of B is the set of all outcomes that are not in B. Since the sample space is not defined in the question, we cannot calculate P(B'). Therefore, we cannot calculate P(A∩B').
e. The probability of the union of A and B is given by the formula P(A∪B). Substituting the values given in the question, we get:
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.3 + 0.2 - 0.1
= 0.4
Therefore, P(A∪B) = 0.4.
In probability theory, the union of two events A and B is the set of outcomes that belong to either A or B or both. The intersection of two events A and B is the set of outcomes that belong to both A and B. The complement of an event A is the set of outcomes that do not belong to A. These concepts are fundamental in probability theory and are used extensively in solving various problems.
To know more about probabilityclick here:
brainly.com/question/11234923
#SPJ4
n+d=21
0.05n + 0.10d= 1.70
Answer:
To solve the system of equations:
n + d = 21 ---(1)
0.05n + 0.10d = 1.70 ---(2)
We can use the substitution method by solving for one variable in terms of the other from equation (1) and substituting it into equation (2).
Solving equation (1) for n:
n = 21 - d
Substituting this expression for n into equation (2):
0.05(21 - d) + 0.10d = 1.70
Distributing the 0.05:
1.05 - 0.05d + 0.10d = 1.70
Combining like terms:
0.05d = 0.65
Dividing both sides by 0.05:
d = 13
Substituting this value of d into equation (1):
n + 13 = 21
Solving for n:
n = 8
Therefore, the solution to the system of equations is n = 8 and d = 13.
Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
The discount percentage is different, the amount that Lisa pays will also be different.
What exactly is the discounted method?The act of estimating the present value of a future payment or series of cash flows that will be received in the future is referred to as discounting. A discount rate (also known as a discount yield) is the rate at which future cash flows are discounted back to their present value.
We need to know what percentage of the regular ticket price Lisa saves with her railcard. We cannot calculate the exact amount Lisa pays for the ticket without this information.
Assuming Lisa receives a 1/3 discount with her railcard, we can calculate the cost of her ticket as follows:
Discounted price = Regular price minus discount amount
Normal price x Discount percentage = Discount amount
Discount rate = 1/3 = 33.33% (rounded to two decimal places)
Discount amount = £24.90 multiplied by 33.33% = £8.30 (rounded to two decimal places)
Price after discount = £24.90 - £8.30 = £16.60 (rounded to two decimal places)
As a result, if Lisa receives a 1/3 discount with her railcard, she will pay£16.60 for the ticket. However, if the discount percentage is different, Lisa's payment will be different as well.
To know more smiliar question visit:
brainly.com/question/11848320
#SPJ1
Lisa uses her railcard to buy a ticket.
She gets off the normal price of the ticket.
The normal price of the ticket is £24.90
Work out how much Lisa pays for the ticket.
Simplify 650 – 0.394 + 18. 77
If you answer on 10 minutes i will mark you as the brainliest
Answer:
668.376
Step-by-step explanation:
Please hit brainliest if this was helpful!
To simplify 650 – 0.394 + 18.77, we can first add 650 and 18.77 since they're both whole numbers:
650 + 18.77 = 668.77
Then, we can subtract 0.394 from 668.77:668.77 - 0.394 = 668.376
Therefore, 650 – 0.394 + 18.77 simplifies to 668.376.
James have 18 litres of water. He poured unequally into 3 tank
I. Poured three quarter of water from tank one into tank 2
II. Poured half of the water that is now in tank 2 into tank 3
III. Poured one third of water that is now in tank 3 into tank 1
Answer:
Tank 1: 6 litres
Tank 2: 6.75 litres
Tank 3: 4.5 litres
Step-by-step explanation:
Initially, James had 18 litres of water, and he poured three-quarters of it from tank 1 into tank 2. This means that the volume of water left in tank 1 is:
18 - (3/4) * 18 = 4.5 litres
The volume of water in tank 2 is:
(3/4) * 18 = 13.5 litres
Next, he poured half of the water in tank 2 (which is now 13.5 litres) into tank 3. The volume of water left in tank 2 is:
(1/2) * 13.5 = 6.75 litres
The volume of water in tank 3 is:
13.5 * (1/2) = 6.75 litres
Finally, he poured one-third of the water in tank 3 (which is now 6.75 litres) into tank 1. The volume of water in tank 1 after this is:
4.5 + (1/3) * 6.75 = 6 litres
The volume of water in tank 3 after this is:
6.75 * (2/3) = 4.5 litres
So the final volume of water in each tank is:
Tank 1: 6 litres
Tank 2: 6.75 litres
Tank 3: 4.5 litres
the length of a rectangle is 3 in longer than its width. if the perimeter of the rectangle is 50 in, find its length and widths
First, re-read the problem until you understand it and can put it into your own words. I re-wrote it like this: "Find the area of a rectangle by first finding the length (L) and the width (W)." [note that I added "find L and W," but that is how I'm going to solve the problem; I could also have said that we will need the formulas, P=2L+2W and A=LW, but you knew that already, right?).
Translate the problem:
"The length of a rectangle is 3 ft longer than its width" means
L = 3 + W (eq1)
"the perimeter of the rectangle is 30 ft" means
P = 50 (eq2)
So, now the math is easy, just find L and W so we can compute the area:
P = 50 = 2L + 2W (eq3; from eq2 and the formula for P)
50 = 2(3+W) + 2W (use eq1 to substitute for L)
50 = 6 + 2W + 2W (distribute)
50 = 6 + 4W (collect terms)
44 = 4W (subtract 6 from both sides)
11 ft = W (divide both sides by 4)
Use the easiest equation (either eq1 or else eq3) to find L:
L = 3 + W (eq1)
L = 3 + 11
L = 14 ft
What is the area (A)?
A = L*W
A = (14 ft) x (11 ft)
A = 154 sq ft
What is the volume of the prism below?
Answer:30
Step-by-step explanation: the formula is base x height over 2, so (6x10)/2 is 30.
In △PQR
how many degrees is m∠Q?
Answer:
105 degrees
Step-by-step explanation:
sum of angles in triangle is 180 degrees
11x-5+6x+5+x = 180
simplify this to get 18x=180
180/18 = 10 = x
plug in 10 for x
11(10) - 5
110-5
105
How do you do this I need help please
Answer:
30,000 grams
Step-by-step explanation:
multiply the 30KG by 1,000 (that is the conversion) and you get 30,000g
Answer:
hi I'm really sorry I can't help
Help please & thanks
The function f(t)=−5t^2+20t models the approximate height of an object t seconds after it is launched. Which of the following equations correctly shows the quadratic formula being used to determine the number of seconds it will take for the objects to be at a height of 18 feet after launch?
The equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.
What is trigοnοmetric equatiοns ?Trigοnοmetric equatiοns are equatiοns that invοlve trigοnοmetric functiοns such as sine, cοsine, tangent, etc. These equatiοns usually invοlve finding values οf the unknοwn angle(s) that satisfy the given equatiοn. They can be sοlved using algebraic techniques οr by using the prοperties οf trigοnοmetric functiοns.
Accοrding tο the given infοrmatiοn:
The given functiοn is [tex]f(t) = -5t^2 + 20t[/tex], which mοdels the height οf an οbject in feet as a functiοn οf time in secοnds.
Tο find the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch, we need tο sοlve the equatiοn [tex]-5t^2 + 20t = 18[/tex].
Tο sοlve this quadratic equatiοn using the quadratic fοrmula, we first identify the values οf a, b, and c frοm the general fοrm οf a quadratic equatiοn, [tex]ax^2 + bx + c = 0[/tex].
In this case, a = -5, b = 20, and c = -18. Substituting these values intο the quadratic fοrmula, we get:
[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]
Plugging in the values οf a, b, and c, we get:
[tex]t = (-20 \± \sqrt{+(20^2 - 4(-5)(-18)})) / 2(-5)[/tex]
Simplifying this expressiοn, we get:
[tex]t = (-20 \± \sqrt{(400 - 360))} / (-10)[/tex]
[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]
[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]
[tex]t = 2 \± 0.632[/tex]
Therefοre, the twο pοssible values οf t are:
t = 2 + 0.632 = 2.632 secοnds
t = 2 - 0.632 = 1.368 secοnds
Therefοre, the equatiοn that cοrrectly shοws the quadratic fοrmula being used tο determine the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch is:
[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]
[tex]t = (-20 \± \sqrt{(20^2 - 4(-5)(-18))}) / 2(-5)[/tex]
[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]
[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]
t = 2 ± 0.632
Therefοre, the equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.
To know more about trigonometric equations visit :
brainly.com/question/30710281
#SPJ1
Write in the standard form of a conic if possible, and identify the conic section represented by r = 6/(cos x + 3sin x)
The standard form of a conic section represented by r = 6/(cos x + 3sin x) is r^2 = 6(x + 3y) and the represented equation is a line.
The equation r = 6/(cos x + 3sin x) is in polar form, where r represents the distance from the origin to a point (x, y) in the plane, and x is the angle that the line connecting the origin to (x, y) makes with the positive x-axis. To determine the standard form of the conic represented by this equation, we need to convert it to Cartesian coordinates.
Using the trigonometric identity cos x = x/r and sin x = y/r, we can rewrite the equation as:
r = 6/(x/r + 3y/r)
Multiplying both sides by r, we get:
r^2 = 6(x + 3y)
This is the standard form of a conic section in Cartesian coordinates, namely an equation of a line. Therefore, the conic represented by the equation r = 6/(cos x + 3sin x) is a line in the Cartesian coordinate system.
In summary, to determine the standard form of a conic represented by an equation given in polar form, we can use trigonometric identities to rewrite it in Cartesian coordinates.
To learn more about conic section click on,
https://brainly.com/question/21250903
#SPJ4
A movie theater is attracting customers with searchlights. One circular searchlight has a
radius of 2 feet. What is the searchlight's circumference?
Use 3.14 for л. If necessary, round your answer to the nearest hundredth.
The nearest hundredth, we get:
C ≈ 12.56 feet.
What is the value of 2r of a circle?Circle circumference (or perimeter) = 2R
where R denotes the circle's radius. 3.14 is the approximate (up to two decimal points) value of the mathematical constant. Again, Pi () is a special mathematical constant that represents the circumference to diameter ratio of any circle.
The circumference of a circle is calculated as follows:
C = 2πr
where C is the circumference, (pi) is a constant close to 3.14, and r is the radius of the circle.
When the given values are substituted, the following results are obtained:
C = 2(3.14)(2) \s= 12.56
We get the following when we round to the nearest hundredth:
C ≈ 12.56 feet.
To know more about Circle circumference visit:
https://brainly.com/question/26605972
#SPJ1
Problem: Power Output. In each case, find your average power in watts. Assume that riding a bike burns 100 Calories per mile. If you ride at a speed of 20 miles per hour, what is your average power output, in watts?
The average power output of a bike rider at a speed of 20 miles per hour is 556 W
Given, Riding a bike burns 100 Calories per mile. Speed of riding a bike is 20 miles per hour. Power is a measure of the rate at which work is done over time.
Therefore, the formula for average power is given by,
P = W/t
Where, P is power, W is work and t is time.
Now, We know that riding a bike burns 100 Calories per mile, but we have to find out the work done.
So, work done = 100 Calories × distance traveled= 100 × 1.609 × 1000 = 160900 J
Time taken = distance/speed= 1.609/20 = 0.08045 hours
Putting values in the formula of power, we get,
P = W/t= 160900/0.08045= 1999999.9 J/hour
Converting hour to seconds,1 hour = 3600 seconds1 J/s = 1 watt1 J/hour = 1 / 3600 watt
Therefore, power = 1999999.9 / 3600= 555.5556 watts (approx)
Therefore, the average power output of a bike rider at a speed of 20 miles per hour is 556 W (approx). Answer: 556
Learn more about average power output:https://brainly.com/question/14558400
#SPJ11
what is the z-score for the 25th percentile of the standard normal distribution?A. -0.625
B. 0.50 C. 0.60 D. -0.50 E. 0.00
The z-score for the 25th percentile of a standard normal distribution is approximately -0.625. Here option A is the correct answer.
To find the z-score for the 25th percentile of a standard normal distribution, we need to use a standard normal distribution table or calculator. The 25th percentile corresponds to a cumulative area under the standard normal curve of 0.25.
Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative area of 0.25 is about -0.68. This means that approximately 25% of the area under the standard normal curve lies to the left of -0.625.
So, among the given options, the correct answer is Option A, -0.625, Option D, -0.50, which is also incorrect. Option E, 0.00, is definitely incorrect because the 25th percentile is to the left of the mean.
To learn more about standard normal distribution
https://brainly.com/question/29509087
#SPJ4
You have $3,200 to invest in stocks. You purchase shares for $11.95/sh. You decide to sell the stock at $11.87/sh?
How much did you net with this transaction?
A $21.36
B $30.71
C $11.87
D $0.08
Therefore, the net result of the transaction is a loss of $21.36. The answer is A) $21.36.
What is selling price?Selling price refers to the price at which a product or service is sold to customers or clients. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost of producing or acquiring the product or service, and the difference between the selling price and the cost is the profit earned by the seller. In some cases, the selling price may also include additional charges such as taxes, shipping fees, or handling fees.
by the question.
To calculate the net result of the transaction, we need to determine how many shares were purchased with the $3,200 investment.
$3,200 divided by $11.95/sh = approximately 267.36 shares (rounded to the nearest hundredth)
Therefore, the total cost of purchasing 267 shares at $11.95/sh is:
267 shares x $11.95/sh = $3,195.65
The total revenue from selling 267 shares at $11.87/sh is:
267 shares x $11.87/sh = $3,174.29
To determine the net result of the transaction, we subtract the total revenue from the total cost:
$3,174.29 - $3,195.65 = -$21.36
To learn more about cost:
https://brainly.com/question/30045916
#SPJ1
Find the total amount and total interest after six months if the interest is compounded every quarter. Principal =₹10 000 Rate of interest =20% per annum.
Answer:I=(PxRxT)/100
I=(10000x20x1)/100x2
I=200000/200
I=1000
Step-by-step explanation:
The interest rate of an auto
loan is 4%. Express this
number as a decimal.
Answer: 0.04
Step-by-step explanation:
In order to get 4% as a decimal, you must divide 4 by 100.
4/100 = 0.04
Thus, the answer to your question is 0.04
a school pays 1,852 for 150 shirts . this includes the 25$ flat-rate shipping costs. c. what are the initial value and rate of change of the function? what does each on represent
Therefore, the initial value of the function is $1,852 and the rate of change is $12.18 per shirt. The initial value represents the cost of the shirts before any were purchased,
What is function?In mathematics, a function is a rule that assigns to each element in a set called the domain, a unique element in another set called the range. In other words, a function is a mathematical object that takes an input and produces a specific output, according to a specific set of rules or operations.
by the question.
et the initial value be represented by a and the rate of change by r.
The given information can be represented by the following equation:
a + 150r = 1,852
Since the flat-rate shipping cost is $25, the cost of the 150 shirts alone would be:
a + 150r - 25 = 1,827
The initial value, a, represents the cost of the shirts before any shirts were purchased. In this case, it would be the cost of the shirts if no shirts were purchased plus the flat-rate shipping cost of $25.
So, a = 1,827 + 25 = 1,852.
The rate of change, r, represents the increase in cost for each additional shirt purchased. In this case, it would be the cost of one shirt.
So, r = (1,852 - 25)/150 = 12.18.
To learn more about cost:
https://brainly.com/question/30045916
#SPJ1
Find the range of possible measures of X if the set of expressions represents measures of the sides of a triangle x, 4, 6
If the set of expressions represents measures of the sides of a triangle x, 4, 6 , the range of possible measures of x is 2 < x < 10.
To determine the range of possible measures of X if the set of expressions represents measures of the sides of a triangle x, 4, 6, we need to use the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Mathematically, this can be expressed as:
x + 4 > 6
x + 6 > 4
4 + 6 > x
Simplifying these inequalities, we get:
x > 2
x > -2
x < 10
The first two inequalities indicate that x must be greater than 2, since the sum of any two sides of a triangle must be greater than the third side. The third inequality indicates that x must be less than 10, since the longest side of a triangle cannot be greater than the sum of the other two sides.
This means that x can take any value between 2 and 10, but not including 2 or 10, in order for the set of expressions to represent the measures of the sides of a triangle.
To learn more about range click on,
https://brainly.com/question/26170058
#SPJ4
an inner city revitalization zone is a rectangle that is twice as long as it is wide. the width of the region is growing at a rate of 32 m per year at a time when the region is 220 m wide. how fast is the area changing at that point in time?
The area is changing at a rate of 28,160 m²/year at that point in time.
The area of the rectangular region is given by:
A = lw
Where l is the length of the rectangular region and w is the width of the rectangular region.
The width of the rectangular region is given to be 220 m. Therefore, we have the width w = 220 m. The length l of the rectangular region can be found knowing that it is twice as long as it is wide. Therefore, the length of the rectangular region is given by:
l = 2w
l = 2 x 220
l = 440
Therefore, the length l of the rectangular region is 440 m.
At the given point in time, the width of the rectangular region is growing at a rate of 32 m per year. Therefore, we have the rate of change of the width dw/dt to be 32 m per year. We need to find how fast the area of the rectangular region is changing at that point in time. Therefore, we need to find the rate of change of the area of the rectangular region dA/dt.
A = lw
dA/dt = w dl/dt + l dw/dt
dA/dt = 220 d/dt(2w) + 440 dw/dt
dA/dt = 220 x 2 dw/dt + 440 dw/dt
dA/dt = 880 dw/dt
Substitute the value of dw/dt to get:
dA/dt = 880 x 32
dA/dt = 28,160 m²/year
Therefore, the area of the rectangular region has a rate of change of 28,160 m² per year at that point in time.
Learn more about rate of change here: https://brainly.com/question/29504549
#SPJ11
please help guys, I need this done
Answer:
18+m=24, 6
Step-by-step explanation:
You will get the first part by understanding that 24 is the whole and 18 is the part. Part + the other part, m, is the whole. You will then solve this by isolating the variable m, and subtracting 18 on both sides of the equation. Since 24-18=6, that is the final answer.
Calculate the amount of interest on $4,000. 00 for 4 years, compounding daily at 4. 5 % APR. From the Monthly Interest Table use $1. 197204 in interest for each $1. 00 invested
The amount of interest earned on $4,000.00 for 4 years, compounding daily at 4.5% APR, is $1,064.08.
To calculate the amount of interest on $4,000.00 for 4 years, compounding daily at 4.5% APR, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we have P = $4,000.00, r = 0.045, n = 365 (since interest is compounded daily), and t = 4. Plugging these values into the formula, we get:
A = $4,000.00(1 + 0.045/365)^(365*4)
A = $4,000.00(1.0001234)^1460
A = $4,889.68
The final amount is $4,889.68, which means that the interest earned is:
Interest = $4,889.68 - $4,000.00 = $889.68
We are given that the monthly interest table shows that $1.197204 in interest is earned for each $1.00 invested. Therefore, to find the interest earned on $4,000.00, we can multiply the interest earned by the factor:
$1.197204 / $1.00 = 1.197204
Interest earned = $889.68 x 1.197204 = $1,064.08
To learn more about interest click on,
https://brainly.com/question/28895435
#SPJ4
