Answer:
D
Step-by-step explanation:
Using the product to sum formula
• 2cosAcosB = cos(A+B) + cos(A - B)
note that cos(- 3m) = cos 3m, hence
cos5m cos(- 3m)
= cos 5m cos3m ← A = 5m and B = 3m
= [tex]\frac{1}{2}[/tex] ( 5m + 3m) + cos(5m - 3m) ]
= [tex]\frac{1}{2}[/tex] cos 8m + [tex]\frac{1}{2}[/tex] cos 2m
The expression of cos5mcos(-3m) as a sum or difference results in 1/2cos2m + 1/2cos8m.
To express cos5mcos(-3m) as a sum or difference, we can use the trigonometric identity cos(A)cos(B) = 1/2[cos(A+B) + cos(A-B)].
Applying this identity to the given expression, we get 1/2[cos(5m - 3m) + cos(5m + 3m)] = 1/2[cos(2m) + cos(8m)].
Therefore, the given expression cos5mcos(-3m) can be simplified to 1/2cos2m + 1/2cos8m.
Kylie and her children went into a bakery and she bought $10 worth of donuts and brownies. Each donut costs $1.25 and each brownie costs $2.50. She bought twice as many donuts as brownies. Determine the number of donuts and the number of brownies that Kylie bought.
Answer:
4 donuts and 2 brownies
Step-by-step explanation:
Guess and check
2 donuts --> $2.50
1 brownie -->$2.50
Since the amount of donuts is double,
we try :
4 donuts -->$1.25(4) = $5
2 brownies --> $2.50(2) = $5
Answer:
she bought 4 donuts and 2 brownies.
Step-by-step explanation:
This is a question on simultaneous equations where two variable are given with two or more relational equations. if she bought $10 worth of donuts and brownies, and each donut costs $1.25 and each brownie costs $2.50.
Then,
1.25d + 2.50b = 10 where d and b are the numbers of donuts and brownies purchased respectively.
if She bought twice as many donuts as brownies, then
d = 2b
Therefore,
1.25(2b) + 2.50b = 10
5b = 10
b = 2
d = 2 × 2 = 4
Hence she bought 4 donuts and 2 brownies.
Does graph A have an Euler path or an Euler circuit? Explain how you know.
Does graph B have an Euler path or an Euler circuit? Explain how you know.
Does graph B have an Euler path or an Euler circuit? Explain how you know.
Answer:
Graph A: neither an Euler path nor an Euler circuitGraph B: both an Euler path and an Euler circuitGraph C: both an Euler path and an Euler circuitStep-by-step explanation:
A non-directed graph will have an Euler circuit if all vertices have even degree. It will have an Euler path if it has an Euler circuit or if it has two vertices with odd degree (where the path can start and end).
Graph A
4 of the 5 vertices have odd degree. No Euler path, no Euler circuit.
Graph B
All 6 vertices have degree 4. This graph has an Euler path and an Euler circuit.
Graph C
5 of 6 vertices have degree 4, the remaining one has degree 2. This graph has an Euler path and an Euler circuit.
Graph A: neither an Euler path nor an Euler circuit
Graph B: both an Euler path and an Euler circuit
Graph C: both an Euler path and an Euler circuit
An Euler Paths and Circuits visits every edge in a graph once, while an Euler circuit also starts and ends at the same vertex.
To determine which, if any, a graph has, count the vertices - even-degree vertices indicate an Euler circuit, while exactly two odd-degree vertices indicate only an Euler path.
A non-directed graph will have an Euler circuit if all vertices have even degree. It will have an Euler path if it has an Euler circuit or if it has two vertices with odd degree (where the path can start and end).
Graph A: neither an Euler path nor an Euler circuit
Graph B: both an Euler path and an Euler circuit
Graph C: both an Euler path and an Euler circuit
Graph A
4 of the 5 vertices have odd degree. No Euler path, no Euler circuit.
Graph B
All 6 vertices have degree 4. This graph has an Euler path and an Euler circuit.
Graph C
5 of 6 vertices have degree 4, the remaining one has degree 2. This graph has an Euler path and an Euler circuit.
Learn more about Euler Paths and Circuits here:
https://brainly.com/question/34931120
#SPJ3
x − 3 − 2(6 − 2x) = 2(2x − 5)
Multiply the first bracket by -2
Multiply the second bracket by 2
x-3-12+4x= 4x-10
- negative number times + positive number= - negative number
- negative number times -negative number = + positive number
x+ 4x-3-12= 4x-10
5x-15= 4x-10
Move 4x to the other side
5x-4x-15= 4x-4x-10
x-15= -10
Move -15 to the other side
x-15+15= -10+15
x= 5
Answer : x= 5
Answer: X = 5
Step-by-step explanation:
x - 3 - 2(6-2x) = 2(2x-5)
x - 3 - (12-4x) = (4x-10)
Simplify
5x - 15 = 4x - 10
Then move to common sides giving you the answer
X = 5
1) The ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 5 years. Using the empirical rule, approximately what percent of the trees are between 20 and 30 years old?
2)Pizza delivery times at Pizza Time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. Using the empirical rule, approximately what percent of pizzas are delivered between 24 and 30 minutes?
Answer:
1) 68%
2) 68%
Step-by-step explanation:
1) The ages of treesWe know the mean and the standard deviation.
The mean is:
[tex]\mu=25[/tex]
The standard deviation is:
[tex]\sigma=5[/tex]
The Z-score formula is:
[tex]Z = \frac{x-\mu}{\sigma}[/tex]
For x=20 the Z-score is:
[tex]Z_{20}=\frac{20-25}{5}=-1[/tex]
For x=30 the Z-score is:
[tex]Z_{30}=\frac{30-25}{5}=1[/tex]
Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.
According to the empirical rule 68% of the data is less than 1 standard deviations of the mean. This means that 68% of the trees are between 20 and 30 years old
2) Pizza deliveryFirst we calculate the Z-scores
We know the mean and the standard deviation.
The mean is:
[tex]\mu=27[/tex]
The standard deviation is:
[tex]\sigma=3[/tex]
The z-score formula is:
[tex]Z = \frac{x-\mu}{\sigma}[/tex]
For x=24 the Z-score is:
[tex]Z_{24}=\frac{24-27}{3}=-1[/tex]
For x=30 the Z-score is:
[tex]Z_{30}=\frac{30-27}{3}=1[/tex]
Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.
According to the empirical rule 68% of the data is less than 1 standard deviations of the mean. This means that 68% of pizzas are delivered between 24 and 30 minutes
If AB = 15, BC = 12, and CA = 8, list the angles of angle abc in order from smallest to largest
Answer:
B= 32.11
A= 52.82
C= 95.07
Step-by-step explanation:
To find these angles, since you have all sides, you will need to use the law of cosines.
The value of Jennifer's stock portfolio (in dollars) is given by the function f(t) = -3t +72t + 5000, where t is the time in months since she opened the account. After how many months will her portfolio be at a maximum? What is the maximum value of the portfolio?
Answer:
a) The portfolio will be at maximum after 12 months (1 year)
b) The maximum value of the portfolio is $5432
Step-by-step explanation:
The function that models Jennifer's stock portfolio (in dollars) is [tex]f(t)=-3t^2+72t+5000[/tex], where t is the time in months since she opened the account.
We complete the square to obtain this function in vertex form:
Factor -3 from the first two terms
[tex]f(t)=-3(t^2-24t)+5000[/tex].
Add the zero pairs -3(+144),-3(-144)
[tex]f(t)=-3(t^2-24t+144)+5000+-3(-144)[/tex].
Factor the perfect square trinomial and simplify.
[tex]f(t)=-3(t-12)^2+5432[/tex].
The vertex of this function is (h,k)=(12,5432)
a) The portfolio will be at maximum when t=12, the h-value of the vertex
b) The maximum value of the portfolio is the k-value of the vertex which is 5432
Jennifer's stock portfolio reaches its maximum value after 12 months, with the maximum value being $5432.
The given function is a quadratic equation in the form f(t) = -3t² + 72t + 5000. This function opens downwards because the coefficient of t2 is negative.
To find the time t when the portfolio is at its maximum, we use the vertex formula for a parabola
t = -b / (2a), where a = -3 and b = 72.
t = -72 / (2 * -3) = 72 / 6 = 12.
So, the portfolio reaches its maximum value at t = 12 months.
To find the maximum value of the portfolio, substitute t = 12 back into the function:
f(12) = -3(12)² + 72 * 12 + 5000.
f(12) = -432 + 864 + 5000 = 5432.
Therefore, Jennifer's stock portfolio will be at its maximum value after 12 months, and the maximum value of the portfolio will be $5432.
Complete Question:
The value of Jennifer's stock portfolio (in dollars) is given by the function f(t) = -3t² +72t + 5000, where t is the time in months since she opened the account. After how many months will her portfolio be at a maximum? What is the maximum value of the portfolio?
A triangle with base b and height h is shown below. If the height of the triangle is 3 units more than the base, select the function that represents the area of the triangle. A. B. C. D.
Answer:
The area of a triangle is given by the formula:
A = bh/2
If the height of the triangle is 3 units more than the base we can say that:
h = b + 3
Therefore, the area of the triangle will be:
A= b(b+3)/2
Where 'b' comes to be the base of the triangle.
Answer:
A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]
Step-by-step explanation:
Given: Height of the triangle is 3 units more than the base.
Let "b" be the base of the triangle.
So, h = b + 3
Area of a triangle A = [tex]\frac{1}{2} base * height[/tex]
Now plug in h = b +3 in the above area of formula, we get
A(b) = [tex]\frac{1}{2} b*(b + 3)[/tex]
Now we can multiply b and (b + 3), we get
A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]
Therefore, the answer is A(b) = [tex]\frac{1}{2} (b^2 + 3b)[/tex]
DBA HELP!!!! FOR PRE-CALCULUS!!!
Whats are some super useful things I should know about Parabolas, Ellipses, Hyperbolas, Parametric Equations and Polar Coordinates? My teacher wants me to explain 3 topics to her tomorrow (7-20-19). I know that I should know this but I've been studying for over an hour and I still don't understand the module. Give me an actual answer, I will report if it's not useful to me.
Answer:
Step-by-step explanation:
Here are some facts you can mention:
1. Parabola.
The equation of a parabola is one where x^2 is the term of the highest degree. ( the degree being '2' in x^2). For example y = x^2, y = 2x^2 - 5x,
y = -x^2 + 1 are all parabolas. Also we have the type x = f(y) - for example
4x = y^2.
The graph looks like a U ( which maybe on its side or upside down The graph of a parabola where the term coefficient of x^2 is positive opens upwards while if it is negative it open downwards.
It is also a 'conic section' . A parabola is formed when we intersect a right cone with a plane surface through the side wall and through the base.
When a projectile is fired from a gun at an angle, the path it follows is close to a parabola. If fired in a vacuum the path we would be exactly parabolic.
2. Ellipse.
This is another conic section formed when we intersect the cone with a plane surface at an angle to the base ( not 90 degrees) and the plane passes through both sides walls of the cone.
It is oval shaped. The path of the planets around our sun form an ellipse.
You can draw an ellipse by fixing 2 pins at a distance apart on a sheet of paper, and tie the ends of a piece of string, longer in length than the distance between the pins, to each pin. We then press a pen or pencil to the string at some point and draw around the 2 pins.
3. Parametric equations.
A third variable is introduced in a parametric equation. Both x and y are written in terms of this third variable. This variable is called a parameter , hence the name parametric equation.
Many functions can be written in the form y = f(x) or x = f(y) but there are some that cannot be written this way. An example is the circle
x^2 + y^2 = r^2. There are many other such functions. By introducing another variable we are able to identify any point on the graph and it also makes the calculus work easier.
The variable used is usually t or the Greek letter theta (for angles). An example of parametric equations are the ones for a parabola: x= at^2, y = 2at,
which are the parametric equation for the parabola y^2 = 4ax.
I hope this helps.
Answer:
Step-by-step explanation:
I have the same problem. Do you still have the answers. I know I'm two years late but just checking.
In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be
Answer:
4 and 13
Step-by-step explanation:
You want integer solutions to ...
15 ≤ n(n+1) ≤ 200
If we let the limits be represented by "a", then the equality is represented by ...
n² +n -a = 0
(n² +n +1/4) -a -1/4 = 0
(n +1/2)^2 = (a +1/4)
n = -1/2 + √(a +1/4)
For a=15, we have
n ≥ -1/2 + √15.25 ≈ 3.4 . . . . . minimum n is 4
For a=200, we have
n ≤ -1/2 + √200.25 ≈ 13.7 . . . maximum n is 13
The least and greatest integers on the cards are 4 and 13.
A certain city has one chance in two of receiving rain on June 1, one chance in five of receiving rain on July 1, and two chances in three of receiving rain on August 1. What is the probability that the city will receive rain on none of these days?
(A) 2/15
(B) 2/5
(C)14/15
Answer:
So the probability that the city won't receive rain on none of these days is [tex]\frac{2}{15}[/tex]
Step-by-step explanation:
From the question we know that the probability of rain on June 1 is [tex]\frac{1}{2}[/tex], on July 1 is [tex]\frac{1}{5}[/tex] and in August 1 is [tex]\frac{2}{3}[/tex], So the probability of no rain at any of these days is calculate as:
For June 1:
[tex]P(no-rain)=1-\frac{1}{2} =\frac{1}{2}[/tex]
For July 1:
[tex]P(no-rain)=1-\frac{1}{5} =\frac{4}{5}[/tex]
For August 1:
[tex]P(no-rain)=1-\frac{2}{3} =\frac{1}{3}[/tex]
So the probability that the city won't receive rain on none of these days is the multiplication of the probabilities of no rain for every one of these days. Then:
[tex]P=\frac{1}{2} *\frac{4}{5} *\frac{1}{3} =\frac{4}{30}[/tex]
Simplified the value of P, we obtain: [tex]P=\frac{2}{15}[/tex]
The price of a particular snack at a ballpark seems to affect the number sold in a way such that the product of the number sold and the price in dollars is roughly constant. The table shows some of the data. Price (dollars) Number sold 1.00 2100 1.50 1400 2.00 1050 2.50 840 Is the data linear? Why or why not?
Answer:
not linearan inversely proportional relationship is non-linearStep-by-step explanation:
No, the relationship is not linear. It is "roughly" an "inversely proportional" relationship, not a linear relationship. (Read the problem statement: "the product of the number sold and the price in dollars is roughly constant".)
__
The points, when graphed, are not on a straight line.
Answer:
b
Step-by-step explanation:
just took the test
HELP ME WITH THIS MATH QUESTION
Answer:
m<DEB = 62°
Step-by-step explanation:
From the figure we can see a circle with center O.
To find the measure of <DOB
From the figure we get,
m<DOC = 44° and m<COB = 80°
We know that, m<DEB = m<DOB/2
m<DOB = m<DOC +m<COB
= 44 + 80
= 124
To find the measure of <DEB
m<DOB = 124
Therefore m<DEB = m<DOB/2
= 124/2 = 62°
Answer: 236 degrees
Step-by-step explanation: Add the two angles that are given. 44+80=124. The angle DOB is 124 degrees. The angle DEB is the rest of the circle. There are 360 degrees in a circle. So subtext 360 from 124.
360 - 124 = 236
DEB = 236 degrees.
A population has a mean of 84 and a standard deviation of 12. A sample of 36 observations will be taken. The probability that the sample mean will be between 80.54 and 88.9 is
Answer:
The probability that the sample mean will be between 80.54 and 88.9 is 0.951
Step-by-step explanation:
* Lets revise some definition to solve the problem
- The mean of the distribution of sample means is called M
- The standard deviation of the distribution of sample means is
called σM
- σM = σ/√n , where σ is the standard deviation and n is the sample size
- z-score = (M - μ)/σM, where μ is the mean of the population
* Lets solve the problem
∵ The sample size n = 36
∵ The sample mean M is between 80.54 and 88.9
∵ The mean of population μ = 84
∵ The standard deviation σ = 12
- Lets find σM to find z-score
∵ σM = σ/√n
∴ σM = 12/√36 = 12/6 = 2
- Lets find z-score
∵ z-score = (M - μ)/σM
∴ z-score = (80.54 - 84)/2 = -3.46/2 = -1.73
∴ z-score = (88.9 - 84)/2 = 4.9/2 = 2.45
- Use the normal distribution table to find the probability
∵ P(-1.73 < z < 2.45) = P(2.45) - P(-1.73)
∴ P(-1.73 < z < 2.45) = 0.99286 - 0.04182 = 0.95104
∴ P(-1.73 < z < 2.45) = 0.951
* The probability that the sample mean will be between 80.54 and 88.9
is 0.951
The probability that the sample mean lies between 80.54 and 88.9 is calculated using the Central Limit Theorem and z-scores. The standard error is calculated to convert the measure into a standard normal distribution where probability can be determined.
Explanation:In order to solve this problem, we use the concept of the Central Limit Theorem in statistics. According to the theorem, as the sample size increases, the sampling distribution tends towards a normal distribution. In this case, the population mean (μ) is 84 and the standard deviation (σ) is 12. If you take a sample of 36 observations, the mean of this sample should theoretically be close to the population mean. The standard deviation of the sampling distribution of the means (also known as Standard Error) is given by σ/√N (√36 in this case).
Now, to find the probability that the sample mean lies between 80.54 and 88.9, you'd first convert these into z-scores, using the formula z = (X - μ)/standard error. Thus, you get two z-scores corresponding to 80.54 and 88.9. The probability that the sample mean lies between these two points is the area under the standard normal distribution between these two z-values, which can be found using standard statistical tables or software.
Learn more about Probability Calculation here:https://brainly.com/question/33780340
#SPJ3
(Proportions of Triangles) Find the value of x
In the figure based on proportions of triangle, the value of variable "x" is : (a) 7.5.
Proportions of a triangle based on its sides refer to the ratios between the lengths of different sides within the triangle. Common proportions include the Pythagorean theorem, where the square of the hypotenuse equals the sum of the squares of the other two sides in a right triangle.
In similar triangles, corresponding sides are in proportion, meaning they have the same ratio.
We observe that the figure is based on the property of proportions of triangle, so, the equation of proportion can be written as :
⇒ 4/6 = 5/x,
⇒ 2/3 = 5/x,
⇒ 2x = 15,
⇒ x = 15/2,
⇒ x = 7.5.
Therefore, the correct option is (a) 7.5.
Learn more about Proportions here
https://brainly.com/question/32591829
#SPJ3
Type 4/6 in the simplest form
Answer:
2/3
Step-by-step explanation:
Answer:
2/3
Step-by-step explanation:
To solve this simplest form, you'd need to divide 2 from numerator into denominator.
4/2=2
6/2=3
2/3, which is our answer.
I hope this helps!
What is the correct height ?
Answer:
30 Inches
Step-by-step explanation:
Please refer to the image we have attached to this.
The frame is ABCD and The diagonal is AC, which is 50 inches long and making an angle of 36.87° from the bottom of the frame.
We are asked the height of the frame which is h in this image. We are going to use the trigonometric ratios in order to find the same.
[tex]\sin \theta = \frac{opposite}{Hypotenuse}[/tex]
[tex]\sin 36.87[/tex]° = [tex]\frac{h}{50}[/tex]
[tex]0.60=\frac{h}{50}[/tex]
[tex]h=0.60 \times 50[/tex]
[tex]h=30[/tex]
hence height of the frame is 30 inches
What is the solution to the system of equations shown below?
2x + 5y + 3z = 10
3x - y + 4z = 8
5x - 2y + 7z = 12
a(7, 1, -3)
b(7, -1, -3)
c(7, 1, 3)
d(-7, 1, -3)
Answer:
Step-by-step explanation:
____
Good evening ,
_______________
2(7) + 5(1) + 3(-3) = 10
3(7) - (1) + 4(-3) = 8
5(7) - 2(1) + 7(-3) = 12
Then (7,1,-3) is a solution to system
____
:)
QUESTION - At a frozen yogurt store, customers are given the option of a juice-filled gelatin sphere as a yogurt topping. Each sphere contains 36π cubic millimeters of juice. Which statements are accurate?
A) The radius of the sphere is 3 millimeters.
B) The circumference of the sphere is 6π millimeters.
C) The radius of the sphere is 9 millimeters.
D) The circumference of the sphere is 18π millimeters.
E) The radius of the sphere is 12 millimeters.
F) The circumference of the sphere is 24π millimeters.
Answer:
A) The radius of the sphere is 3 millimeters.B) The circumference of the sphere is 6π millimeters.Step-by-step explanation:
Based on the answer selections, it appears we need to find the radius and circumference of the sphere. We can start with the volume formula in terms of the radius:
V = (4/3)πr³
36π = (4/3)πr³
(36π)(3/(4π)) = r³ = 27 . . . . . . mm³
r = ∛27 = 3 . . . . mm³
Then the circumference is ...
C = 2πr = 2π(3 mm) = 6π mm
The radius is 3 mm; the circumference is 6π mm.
Answer:
a and b is the answer
Step-by-step explanation:
The length of a rectangular lot is 7 yards less than twice its width. If the length was increased by 11 yards and the width decreased by 6 yards, the area would be decreased by 40 square yards. Find the original dimension of the lot.
Answer:
The width = 16 yards and the length = 25 yards.
Step-by-step explanation:
Let x yards be the original width, then the original length is 2x - 7 yards.
Therefore the original area = x(2x - 7) yd^2.
The new area = (2x - 7 + 11)(x - 6)
= (2x + 4)(x - 6) yd^2.
So we have the equation
x(2x - 7) - (2x + 4)(x - 6) = 40
2x^2 - 7x - (2x^2 - 12x + 4x - 24) = 40
2x^2 - 7x - 2x^2 + 8x + 24 - 40 = 0
x - 16 = 0
x = 16 yards = the width.
The length = 2(16) - 7 = 25 yards.
To find the original dimensions of the lot, assume the width is 'w', then solve an equation using the information given.
Explanation:To find the original dimensions of the lot, let's assume that the width is 'w' yards. The length of the lot is then '2w-7' yards, since it is 7 yards less than twice the width.
If we increase the length by 11 yards and decrease the width by 6 yards, the new dimensions would be '2w-7+11' yards for the length and 'w-6' yards for the width.
The area of the lot is given by length multiplied by width, so we can set up the equation:
(2w-7+11)(w-6) = (2w)(w) - 40
Simplifying this equation and solving for 'w', we find that the original width of the lot is 12 yards. The length is then 2(12) - 7 = 17 yards.
Learn more about Finding the original dimensions of a rectangular lot here:https://brainly.com/question/34270507
#SPJ11
The residents of a city voted on weather to raise property taxes . THe ratio of yes votes was 3 to 5. If there were 4845 no votes, what was the total number of votes ?
The total number of votes would be: 7752 total votes.
Here's how you solve it!
For every 3 yes there was 5 no's.
You would but that into a fraction so it would be 3/5
Then you take the number of no votes and multiply.
3/5 x 4845
Then you would get 2907.
4845+ 2907= 7752
4845= no votes
2907= yes votes
7752= total votes
Hope this helps! :3
John sent a telegram of 44 words and he was charged shilling 25 for the first ten words and shilling 30 for each extra word .How much did the telegram cost?
Answer:
The cost of the telegram was 1,270 shilling
Step-by-step explanation:
we know that
The total words-----> 44
The first ten words ----> 10
Extra words----> 44-10=34
so
The total cost is equal to
25(10)+30(34)=1,270 shilling
In a board game, you roll a die to win or lose points, depending on the outcome. The outcomes follow this probability distribution.
If a player can only win by accumulating 20 points, which of the following best describes the fairness of the game?
A, it's not fair because the chance to lose points far outweighs the chance to gain points
Answer with explanation:
→Total faces on the dice and marked numbers =6={1,2,3,4,5,6}
If you are rolling the dice and getting number 1 and 5 , you win 4 and 6 points respectively.
And, If you roll the dice and getting number 2,3,4 and 6 , you loose -5 points .
→→So,suppose the dice is rolled 6 times, and considering each outcome to be equally likely
then you loose more points than gaining which is equal to
= 4+(-5)+(-5)+(-5)+6+(-5)
=10-20
= -10
And, Average
[tex]=\frac{-10}{5}\\\\= -2[/tex]
So, if number of outcomes are equally likely, you can't accumulate 20 points.
Option B:→ It is not a fair game because weighted average is Negative.
two circles are externally tangent to each other. One circle has a diameter of 62 yards and the distance between the centers of the two circles is 85 yards. What is the diameter of the other crop circle
Answer:
108 yards
Step-by-step explanation:
Let circle A be the circle with the 62 yard diameter
Let circle B be the circle whose diameter we are trying to solve for.
Externally tangent circles are circles which touch each other and share a common external tangent.Circle A has a tangent of 62 yards and thus a radius ( half the diameter) of 31 yards.The distance between the centers of the 2 circles is 85 yards. If you subtract the radius ( distance from the center of the circle to its circumference) of circle A then we'll only be left with the radius of circle B.85 - 31= 54 yards which is the radius of circle BTo get the diameter: 54 x 2 = 108 yards7x+8y=10 5x+y=−7 solve by elimination
Answer:
(-2,3)
Step-by-step explanation:
7x+8y=10
5x+y=-7
To solve this by elimination, we need both equations in the same form. There are. They are both in form ax+by=c.
Now we also need for one of the columns with the variables to be opposite or same terms.
I like the way the column with the y's are looking because if I multiply that second y by 8 or -8 I will have sames or opposites.
I'm going to multiply the second equation by -8.
This will give me:
7x+8y=10
-40x-8y=56
--------------------Add the equations!
-33x+0=66
-33x =66
x =66/-33
x =-2
Now we need to find the other variable. It doesn't matter which equation you use.
I'm going to use 5x+y=-7 where x=-2 to find y.
5(-2)+y=-7
-10+y=-7
Add 10 on both sides
y=3
The solution is (-2,3)
Answer:
The solution is x = -2, y = 3. As an ordered pair it is (-2, 3).
Step-by-step explanation:
7x + 8y = 10
5x + y = −7
Multiply the second equation by -8:
-40x - 8y = 56
Add this to the first equation, we get:
-33x = 66
x = -2
Now substitute for x in the second equation:
5(-2) + y = -7
y = -7 + 10
y = 3.
Check these results in the first equation:
7(-2) + 8(3) = -14 + 24 = 10 - so correct.
Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal
Final answer:
The mathematical system of inequalities for Keitaro's walking and running routine must satisfy his target of covering at least 36 miles and not more than 90 miles in a month, given his pace.
Explanation:
Keitaro's exercise routine is defined by a system of inequalities that reflect the minimum and maximum distances he wants to cover each month by walking and running. Given his walking pace of 3 miles per hour and his running pace of 6 miles per hour, we can set up two inequalities to represent walking hours w and running hours r. The first inequality would ensure that when multiplied by their respective paces, the total distance is at least 36 miles. The second inequality ensures that the sum of distances does not exceed 90 miles:
3w + 6r ≥ 36 (for the minimum distance)
3w + 6r ≤ 90 (for the maximum distance)
Keitaro needs to allocate his walking and running hours such that these inequalities are satisfied to meet his monthly exercise goals.
PLS HELP SHOW ALL YOUR WORKING OUT
Answer:
V = 1 1/4 m³
M = 3000.0 kg
Step-by-step explanation:
Volume = Length × Width × Height
2 1/2 x 3/4 x 2/3
V = 1 1/4
M= 2.5m ⋅ 0.75m ⋅ 0.666666666666m ⋅ 2400kg/m³
Answer:
(a) 1.25 m^3
(b) 3000 kg
Step-by-step explanation:
(a) The volume of a rectangular prism is L*W*H.
So volume = [tex](2\frac{1}{2})(\frac{3}{4})(\frac{2}{3})=1.25 m^3[/tex]
(b) The mass=density*volume.
So mass = [tex]2400 \frac{kg}{m^3} \cdot 1.25 m^3=3000 kg[/tex].
If the volume of a sphere is 36 cubic units, what is the radius? 3 units 4√3 units 9 units
Answer:
radius = 2.05 units
Step-by-step explanation:
The volume of a sphere is given by the formula: [tex]V=\frac{4}{3} \pi r^3[/tex]. In this formula:
V = volume of the spherer = radius of the sphereSince we are given the volume of the sphere (36 units^3), we just need to solve for r in the equation for the volume of a sphere.
Substitute 36 for V into the formula and solve for r.
[tex]36=\frac{4}{3} \pi r^3[/tex]
Divide both sides by [tex]\frac{4}{3}[/tex]. To do this, multiply 36 by the reciprocal of [tex]\frac{4}{3}[/tex].
[tex]36\times \frac{3}{4}[/tex][tex]36\times \frac{3}{4} =\frac{108}{4} \rightarrow 27[/tex]Simplify and rewrite the equation.
[tex]27=\pi r^3[/tex]
Now divide both sides of the equation by pi ([tex]\pi[/tex]).
[tex]27\div\pi=8.59436692696[/tex]Rewrite the equation.
[tex]8.59436692696=r^3[/tex]
To isolate and solve for r, cube root both sides of the equation.
[tex]r=\sqrt[3]{8.59436692696}[/tex][tex]r=2.04835218977[/tex]The radius of this sphere is 2.04835218977 units. If your question wants this rounded to the nearest:
whole number: 2 unitstenth: 2.0 unitshundredth: 2.05 unitsthousandth: 2.048 unitsI'll just give the answer rounded to the nearest hundredth as that seems the most popular.
Answer:
Before they deleted my answer, I was correct. remember to correctly round if you have a different but similar question.
Step-by-step explanation:
What is the greatest common factor of the terms of the polynomial below?
20x4 – 10x3 + 15x2
A. 5x3
B. 10x3
C. 10x2
D. 5x2
Answer:
D. 5x2 is the GCF
The greatest common factor of the terms of the given polynomial is 5x². So, option D is correct
How do find the GCF of a polynomial?To find the GCF of a polynomial,
find all the possible factors of each term in the polynomialpick out the common factors from all the terms ( the factor must be common for all the terms)multiply all the common factors to get the greatest common factor of the polynomial.Calculation:Given that,
the polynomial is [tex]20x^4-10x^3 + 15x^2[/tex]
Finding factors for all the terms:
[tex]20x^4[/tex] = 2 × 2 × 5 × x × x × x × x
[tex]10x^3[/tex] = 2 × 5 × x × x × x
[tex]15x^2[/tex] = 3 × 5 × x × x
So, from these three terms, the common factors are 5, x, x
On multiplying them,
⇒ 5 × x × x
∴ GCF = 5x²
Therefore, the greatest common factor of the given polynomial is 5x². So, option D is correct.
Learn more about the GCF of a polynomial here:
https://brainly.com/question/3119297
#SPJ2
It took John 12 hours riding his bike to make the round trip to his uncle's. If he averaged 20 mph out and 30 mph back, how long did he travel each way? (Round answer to nearest tenth.)
Answer:
Step-by-step explanation:
Let the time taken by the john to get to his uncle be x.
Let the time taken by the john to get back from his uncle be y.
So,
x+y=12 ------ equation 1
According to the given velocities:
20x=30y
x=3/2y
Put the value x=3/2y in equation 1
3/2y+y =12
3y+2y/2=12
3y+2y=12*2
5y=24
y=24/5
y=4.8h
Now put the value of y in x=3/2y
x=3/2*4.8
x=14.4/2
x=7.2h ....
For samples of the specified size from the population described, find the mean and standard deviation of the sample mean . The population mean and the population standard deviation of the sampled population are, respectively, 55.7 and 3.8. n=256
(A) μ = 3.8; σ = 0.2
(B) μ= 14.1; σ = 1.1
(C) μ = 0.2; σ = 55.7
(D) μ = 55.7; σ = 3,8(E) μ = 55.7; σ = 0.2375.
Answer:
mean of sample is 55.7
sample standard deviation is 0.2375
Step-by-step explanation:
given data
population mean = 55.7
population standard deviation = 3.8
n = 256
to find out
the mean and standard deviation
solution
we know directly mean of sample is mean of population
i.e. mean of sample = 55.7
and standard deviation will be calculate by this formula
sample standard deviation = population standard deviation / [tex]\sqrt{n}[/tex]
sample standard deviation = 3.8 / [tex]\sqrt{256}[/tex]
sample standard deviation = 3.8/ 16
sample standard deviation = 0.2375
so last option is right
(E) μ = 55.7 , σ = 0.2375.