What is the radius of a cylinder with a volume of 950 inches to the third power in a height of 10 inches
Answer:
Step-by-step explanation:
Given the volume of a cylinder, V = πr^2h, where r is the radius, h is the height, and π is Pi, we can find the radius by rearranging the equation and solving for r.
V = πr^2h, so r^2 = V / (πh)
Taking the square root of both sides, we have:
r = √(V / (πh))
Substituting the given values:
r = √(950 / (π * 10))
Since Pi is approximately equal to 3.14, we can calculate the approximate value of r:
r = √(950 / (3.14 * 10))
r ≈ 7.46
Therefore, the radius of the cylinder with a volume of 950 cubic inches and a height of 10 inches is approximately 7.46 inches.
Estelle is having her birthday party at Gold Frames Art
costs $265
Museum this year. A party package
and covers the entrance fee for guests, a private party room, and an activity
guide. Estelle
upgraded her package to include a favor for each of her 8 guests, bringing the
total to $305.
Answer:
Step-by-step explanation:
im guessing youre finding the price of the favour.
(305-265)/8=answer
"/" means divide.
Yuki Says that 43 is a 2 digit odd number that is composite is she correct explain
No. The statement given by Yuki that 43 is a 2 digit odd number that is composite is not correct.
A composite number is a positive integer greater than 1 that has more than two positive divisors. In other words, a composite number is a number that can be divided by more than just 1 and itself. For example, 4 is a composite number because it can be divided by 1, 2, and 4.
On the other hand, a prime number is a positive integer greater than 1 that has exactly two positive divisors, 1 and itself. For example, 5 is a prime number because it can be divided only by 1 and 5.
Now, let's consider the number 43. 43 is a two-digit odd number, which means it has two digits and is not divisible by 2. However, 43 is a prime number, which means it has exactly two positive divisors, 1 and 43. Therefore, 43 is not a composite number.
To further verify this, we can check the divisors of 43. The divisors of 43 are 1 and 43, because 43 is not divisible by any other positive integer. Therefore, we can conclude that 43 is a prime number and not a composite number.
To learn more about composite click on,
https://brainly.com/question/709622
#SPJ4
what is the rate of change
if a restaurateur wants to know how many dollars the restaurant makes per day, which process metric is needed?
To determine how many dollars a restaurant makes per day, the restaurateur would need to measure the "revenue" metric.
Revenue is the total amount of money a business earns from its sales or services provided over a specific period of time, in this case, daily. It includes all income generated by the restaurant from selling food and drinks to customers.
Measuring revenue is essential for any business as it helps the owner understand the financial health of their enterprise. By tracking revenue over time, the restaurateur can identify patterns and trends and make informed decisions to increase profits and improve the business's overall performance.
To learn more about revenue, visit here
https://brainly.com/question/28497313
#SPJ4
A school T-shirt costs $7.84. The cost of 4 school T-shirts and a school sweater is $1.40 less that the cost of 2 school sweaters. Create an equation that can be used to find the cost of the sweater?
Answer:
4a + b - $1.40 = 2b
Step-by-step explanation:
Different style of problem here, so here's my guess
Let...
A = Tshirts
B = Sweaters
4a + b - $1.40 = 2b
4a + b indicates 4 shirts plus 1 sweater
The -$1.40 at the end indicates $1.40 less than
=2b indicates 2 sweaters
The Serenity and the Mystic are sail boats. The Serenity and the Mystic start at the same point and travel away from each other in opposite directions. The Serenity travels at 14 mph and the Mystic travels at 21 mph. How far apart will they be in 3 hours?
They will be 74 km apart after 2 hours.
What is the relative speed of two moving objects?
For two objects, the relative speed between them equals the change in distance between them divided by the change in time. If two bodies are going in opposite directions, their relative speed is equal to the sum of their individual speeds. If they are moving in the same direction, their relative speed is equal to the difference in their individual speeds.
Given here, the Serenity travels at 17 mph and the Mystic travels at 20 mph in the opposite direction .
therefore, the relative speed is sum of their speeds = 17 + 20 = 37 mph
After 2 hours the distance between them would be = 37 × 2 = 74 mph
Hence, they will be 74 km apart after 2 hours.
Learn more about relative speed here:
brainly.com/question/14362959
#SPJ1
In the diagram, BA BE and CE CD.
What is mZDAE?
m2DAE =
Submit
B
68⁰
52%
E
mZDAE is a line segment that connects the midpoints of line segments BA and CE. In the diagram, its coordinates are (66⁰, 52%).
AB and BC form a right angle at point B. If A = (-3-1) and B = (4,4) what is the equation of Bc
Answer: The equation of a line in the form y = mx + b can be found using the slope-intercept form, where m is the slope of the line and b is the y-intercept. To find the equation of BC, we need to find the slope of the line and one point on the line.
The slope of the line can be found using the two points A and B. The slope of the line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively. Plugging in the values, we get:
m = (4 - (-1)) / (4 - (-3)) = 5 / 7
So the slope of the line BC is 5/7.
One point on the line BC is B = (4, 4), so we can use this point and the slope to find the y-intercept:
b = y - mx
where y and x are the y and x coordinates of point B, respectively. Plugging in the values, we get:
b = 4 - (5/7) * 4 = 4 - 20/7 = -16/7
So the equation of line BC in the slope-intercept form is:
y = (5/7)x - 16/7
Step-by-step explanation:
The length of a rectangle is shown below:
On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis, two points A and B are shown. The point A is on ordered pair 1, 2, and the point B is on ordered pair negative 2, 2. A straight line joins the points A and B.
If the area of the rectangle to be drawn is 12 square units, where should points C and D be located, if they lie vertically below the line that connects B and A, to make this rectangle? (5 points)
C(−2, −1), D(1, −1)
C(−2, −4), D(1, −4)
C(−2, −2), D(1, −2)
C(−2, −5), D(1, −5
I NEEP HELP WITH THIS ONE LISTED BELOW:A solid is composed of squares and equilateral triangles. Its net is shown below:
A triangular prism and its net are shown. The net is three squares with side length 4 units. Attached above and below the middle square are equal sized triangles.
The area of each triangle is 7 square units. The surface area of the triangular prism is
square units. (Input whole number only.) (5 points)
PLEASE
The surface area of the triangular prism is 62 square units.
What is surface area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.
The side length of each of the three squares is 4 units.
The area of each would be:
4² = 16 sq. units.
For the three squares we have:
16(3) = 48 sq. units.
The area of each triangle is 7 sq. units.
This means together the area of the two triangles is 2(7) = 14 sq. units.
The surface area of the prism is:
14 + 48 = 62 sq. units.
Hence, the surface area of the triangular prism is 62 square units.
Learn more about surface area here:
https://brainly.com/question/27847638
#SPJ1
The volume V (in cubic feet) of the pyramid is given by F(x)=-4
The function (x) = (3x) gives the volume (in cubic feet) of the pyramid when x is measured in yards. Write a rule for W.Find and interpret W(5)
The volume is 3315 cubic feet.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given polynomial function is V(x)=x³-4x.
Here, W(x)=V(3x)
Replace x by 3x in the function V(x)=x³-4x, we get
V(3x)=(3x)³-4(3x)
V(3x)=27x³-12x
W(x)=27x³-12x
Replace x by 5 in the function W(x)=27x³-12x, we get
Now, W(5)=27(5)³-12(5)
= 27×125-60
= 3375-60
= 3315 cubic feet
Hence, the volume is 3315 cubic feet.
To learn more about the function visit:
https://brainly.com/question/28303908.
#SPJ9
"Your question is incomplete, probably the complete question/missing part is:"
A polynomial function V(x)=x³-4x that represents the volume of the right triangle pyramid when measured in cubic feet.
The function (x) =(3x) gives the volume (in cubic feet) of the pyramid when x is measured in yards.
Find a function W(x) that gives us the volume when measured in yards also to find W(5).
2. 20 m 24 m 24 26 m
Note that the body starts "with an initial velocity and moves with uniform acceleration."(Option C)
What is Acceleration?In mechanics, acceleration is defined as the rate of change of an object's velocity with respect to time. Vector quantities are accelerations. The orientation of an object's acceleration is determined by the orientation of its net force.
The distance covered by the particle in nth second
Sₙ = u + a/2(2n-1)
S₈ = 20m
S₈ = u + a/2(2x(8-1)
20 = u + 7.5a ...................()
S₉ = 22 = u + a/2(2*9-1)
22 = u + 8.5a ..................(2)
By solving equations 1 and 2 we have :
u=5m/s , a=2m/s²
Thus,
S₁₀ = u+ a/2(2*10-1)
S₁₀ = 5 + 1/2 * 2 (2 * 10-1)
S₁₀ = 5 + 19
S₁₀ = 24m
Thus, it is correct to state that the body starts with the initial velocity and moves with uniform acceleration, and the correct option is C.
Learn more about Acceleration:
https://brainly.com/question/12550364
#SPJ1
Full Question:
A body covers 20 m, 22 m, 24 m, in 8th, 9th, and 10th seconds respectively. The body starts:
from rest and moves with uniform velocity.
from rest and moves with uniform acceleration.
with an initial velocity and moves with uniform acceleration.
with an initial velocity and moves with uniform velocity.
y-x²-14x=54
43=y-6x
non linear simultaneous equations
Solution of the system of equations y - x²- 14x = 54 and 43 = y - 6x are
x = -4 ± √5 and y = ± 6√5 + 19
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given equations
y - x²- 14x = 54
y = x² + 14x + 54 -------------(1)
43 = y - 6x
y = 6x + 43 ------------(2)
By equation (1) and (2)
6x + 43 = x² + 14x + 54
x² + 14x + 54 - 6x -43 = 0
x² + 8x + 11 = 0
a = 1, b = 8, c = 11
x = (-b ± √(b² - 4ac))/2a
x = (-8 ± √(64 - 4.11))/2
x = -4 ± √16-11
x = -4 ± √5
Putting value of x in equation (2)
y = 6(-4 ± √5) + 43
y = -24 ± 6√5 + 43
y = ± 6√5 + 19
Hence, x = -4 ± √5 and y = ± 6√5 + 19 are the solutions of equations
y - x²- 14x = 54 and 43 = y - 6x.
Learn more about equations here:
https://brainly.com/question/1529522
#SPJ9
round 0.1347 to the nearest tenth
The rounding off the value 0.1347 to the nearest tenth is 0.1
What is rounding off?
When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.
The act of rounding off is merely an estimation. Rounding off is the process of estimating an actual number to a close number.
Given, 0.1347 round to the nearest tenth
While rounding to the nearest tenth, the value after the digit has been noticed.
In the number 0.1347, rounding to the nearest tenth, digit 3 should play a role to round the digit 1 which is in the tenth position. 3 is not equal to 5 and less than 5.
So, 0.1347 becomes 0.1
Hence, the required answer is 0.1
To learn more about rounding off
https://brainly.com/question/15977627
#SPJ1
18.85% of the pupils in Form 2 study craft, 72% study music and 60% study both subjects. What percentage study neither craft nor music?
Answer:
Step-by-step explanation:
Sorry cant help 18.85%
Select all of the ways the system of equations can be solved.
9x - 2y = 4
3x+8y=12
A) Multiply the first equation by 4, then add the equations.
B) Multiply the second equation by 3, then add the equations.
C) Multiply the first equation by 3, then add the equations.
D) Multiply the second equation by 3, then subtract the equations.
E) Multiply the first equation by 4, then subtract the equations.
The ways the system of equations 9x - 2y = 43x+8y=12can be solved are:
A) Multiply the first equation by 4, then add the equations.
D) Multiply the second equation by 3, then subtract the equations.
How can the system of equations?From the given equations,9x - 2y = 43x+8y=12we need to use wyas of solving simultaneous equation to solve it.
Then if we Multiply the first equation by 4, thge we can then perform addition to the second equation like
9x - 2y = 4
36x - 8y = 4
3x+8y=12
then if we add to equation 2 we have
39x =12
then we can solve x = 12/39
The same can be done with equation D .
Therefore, option A and D are correct.
Learn more about system of equations at:
https://brainly.com/question/13729904
#SPJ1
Answer:
Step-by-step explanation:
To solve the system of equations:
9x - 2y = 4 ...(1)
3x + 8y = 12 ...(2)
We can use elimination method by adding or subtracting the equations in a way that one variable is eliminated.
Here are the possible ways to solve the system:
A) Multiply the first equation by 4, then add the equations.
Multiplying the first equation by 4 gives:
36x - 8y = 16
Adding the resulting equation to the second equation gives:
36x - 8y + 3x + 8y = 16 + 12
Simplifying the equation:
39x = 28
x = 28/39
Substituting x in equation (1) gives:
9(28/39) - 2y = 4
Solving for y gives:
y = -155/78
Therefore, the solution is (x,y) = (28/39, -155/78).
B) Multiply the second equation by 3, then add the equations.
Multiplying the second equation by 3 gives:
9x + 24y = 36
Adding the resulting equation to the first equation gives:
9x - 2y + 9x + 24y = 4 + 36
Simplifying the equation:
18x + 22y = 40
Dividing the equation by 2 gives:
9x + 11y = 20
Substituting 9x from equation (2) gives:
3x + 8y = 12
Solving for x gives:
x = (12 - 8y)/3
Substituting x in equation (3) gives:
9[(12-8y)/3] + 11y = 20
Solving for y gives:
y = 16/39
Substituting y in equation (2) gives:
3x + 8(16/39) = 12
Solving for x gives:
x = 28/39
Therefore, the solution is (x,y) = (28/39, 16/39).
C) Multiply the first equation by 3, then add the equations.
Multiplying the first equation by 3 gives:
27x - 6y = 12
Adding the resulting equation to the second equation gives:
27x - 6y + 3x + 8y = 12 + 12
Simplifying the equation:
30x = 24
x = 4/5
Substituting x in equation (1) gives:
9(4/5) - 2y = 4
Solving for y gives:
y = -23/10
Therefore, the solution is (x,y) = (4/5, -23/10).
D) Multiply the second equation by 3, then subtract the equations.
Multiplying the second equation by 3 gives:
9x + 24y = 36
Subtracting the second equation from the first equation gives:
6x - 26y = -8
Solving for x gives:
x = (26y - 8)/6
Substituting x in equation (2) gives:
3[(26y-8)/6] + 8y = 12
Solving for y gives:
y = 16/39
Substituting y in equation (1) gives:
9x - 2(16/39) = 4
Solving for x gives:
x = 28/39
Therefore, the solution is (x,y) = (28/39, 16/39).
a researcher divided subjects into three groups according to whether or not they have brown, blue or green eyes, and then selected members from each group for her sample. what sampling method was the researcher using? group of answer choices random systematic cluster stratified
If the researcher divided subjects into three groups according to whether or not they have brown, blue or green eyes, then the researcher was using a stratified sampling method.
Here a researcher divided subjects into three groups according to whether or not they have brown, blue, or green eyes.
The selected members from each group for their sample
The stratified sampling method is defined as the sampling method that divides the total population into the smaller group
Here the total population is divided into three groups according to whether they have brown, blue or green eyes.
Therefore, researcher was using stratified sampling method
Learn more about stratified sampling here
brainly.com/question/20544692
#SPJ4
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $8,000, annual interest: 7%, interest periods: 4, number of years: 10
Please help
Which equation has infinitely many solutions?
1/3(6x - 12) = 2(x-2)
1/2(4x+8)=2x+8
3(2x-7)= 6(x-4)-3
5 (2+1)= 3x + 2(x+1)+4
Answer: 1/3(6x-12)=2(x-2)
Step-by-step explanation:
the proper way to construct a stem-and-ieaf display for the data set {62,67,68,73, 73, 79,91,94,95,97} is to
The proper way to construct a stem-and-leaf plot to display the data set {62,67,68,73, 73, 79,91,94,95,97} is to include a stem labeled ‘8’ and enter no leaf on the stem. So, the correct choice is option (b).
A stem and leaf graph is like a special table where each data value is separated into a "stem" (the first number) and a "leaf" (usually the last number). Leaves are sorted in ascending order from left to right. We have a data set with values {62,67,68,73, 73, 79,91,94,95,97}. Now, to construct the stem- leaf plot for our data.
Stem | Leaf
6 | 2 7
7 | 3 3 9
9 | 1 4 5 7
For stem and leaf diagram if some values are not present for some stem, then no leaf should be added to that stem. If we skip that stem than it would distort the shape of distribution of the data.
stem | leaf
6 | 2 7
7 | 3 3 9
8 |
9 | 1 4 5 7
Hence, include a stem labeled 8 and enter no leaves on the stem.
To learn more about stem-and-eaf plot, visit :
https://brainly.com/question/12276901
#SPJ4
Complete question:
The proper way to construct a stem-and-leaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to
a)exclude a stem labeled ‘8
b)include a stem labeled ‘8’ and enter no leaves on the stem.
c) include a stem labeled ‘(8)’ and enter no leaves on the stem.
d) include a stem labeled ‘8’ and enter one leaf value of ‘0’ on the stem.
Franny's suitcase weighs 35.7 pounds. Which statement is not true?
A. The 35 represents whole pounds. The 7 represents part of a
pound.
B. The 7 represents more weight than the 5.
OC. The suitcase weighs more than 35 pounds, but less than 36
pounds.
OD. All of these statements are true.
Angle QRS is an equilateral triangle. If QR is seven less than twice x, RS is 61 less than five times x, and QS is 11 more than x, find the value of x and the measure of each side
The value of x is 18 and the measure of each side is:
QR = RS = QS = 29
What is called equilateral?An equilateral triangle is a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure. Therefore, it is also called an equiangular triangle, where each angle measure 60 degrees.
Now, According to the question:
Angle QRS is an equilateral triangle.
QRS is an equilateral triangle, thus all the three sides of the given triangle will be equal.
we have
QR = 2x - 7___(1)
RS = 5x - 61 ___(2)
QS = 11 + x_____(3)
Now, As all the sides of the triangle are equal, therefore
QR = RS = QS
⇒QR = RS
⇒2x - 7 = 5x - 61
⇒ -7 + 61 = 5x - 2x
⇒ 54 = 3x
⇒ x = 18
Put the value of x in above equations:
Thus, the measure of
QR = 2(18) - 7=29,
RS = 5(18) - 61 = 29 and
QS = 11 + 18 = 29.
Learn more about Equilateral Triangle at:
https://brainly.com/question/3461022
#SPJ4
Casey Na's average workweek during the first quarter of the year (13 weeks) was 43 hours. As part of his company's perfect attendance program, he earned a bonus of $975. Determine the extra overtime pay due Na for the first quarter
Casey Na is due an extra overtime pay of $1,170 for the first quarter as part of his company's perfect attendance program.
What is overtime pay?
Overtime pay is the additional compensation paid to an employee for any hours worked in excess of the standard working hours or beyond the standard workweek. The rate of overtime pay is usually higher than the regular rate of pay for an employee's normal working hours.
To determine the extra overtime pay due to Casey Na for the first quarter, we need to know his regular pay rate and the number of hours he worked each week.
Let's assume that Casey Na's regular pay rate is $20 per hour and that he worked 40 hours each week during the first quarter. This means that he worked 3 hours of overtime each week, for a total of 39 hours at his regular rate and 3 hours at his overtime rate.
To calculate his overtime pay for the first quarter, we can use the following formula:
Overtime pay = overtime hours x overtime rate
Since Casey Na worked 3 hours of overtime each week for 13 weeks, his total overtime hours for the first quarter were:
Total overtime hours = 3 hours/week x 13 weeks = 39 hours
His overtime rate is 1.5 times his regular rate, or $20 x 1.5 = $30 per hour.
Therefore, his overtime pay for the first quarter was:
Overtime pay = 39 hours x $30/hour = $1,170
Since he also earned a bonus of $975 for perfect attendance, his total extra pay for the first quarter was:
Extra pay = Overtime pay + Bonus = $1,170 + $975 = $2,145
Therefore, Casey Na is due an extra overtime pay of $1,170 for the first quarter as part of his company's perfect attendance program.
To learn more about overtime pay, visit:
https://brainly.com/question/29276587
#SPJ1
HELPP!! please!!! asap
Answer:
6 units
Step-by-step explanation:
Since the two angles are equal, this means that the triangle is isosceles. So x+4 = 3x-8. After solving, 2x = 12, x = 6. So AC is 6 units.
Answer: 6 units
Step-by-step explanation:
Since this is an isosceles triangle lines AB and BC are congruent so
x + 4 = 3x - 8 ---- add 8 and subtract x on both sides
12 = 2x ---- divide by 2 to isolate the x
x = 6
The graph of the linear function f(x) = -5x + 6 shows the number of cases of the flu, y, in thousands, x months after a vaccine was administered. What are the rate of change and the initial
value?
A 6,000 cases of the flu per month; initial value: -5,000 cases
B-5 cases of the flu per month; initial value: 6 cases
C 1 case of the flu per month, initial value: 0 cases
D -5,000 cases of the flu per month; initial value: 6,000 cases
Answer:
D
Step-by-step explanation:
The 6 represents the initial value of 6000. The cases are going down 5,000 a month.
When a scientist conducted a genetics experiments with peas, one sample of offspring consisted of 933 peas, with 729 of them having red flowers. If we assume, as the scientist did, that under these circumstances, there is a 3/4 probability that a pea will have a red flower, we would expect that 699.75 (or about 700) of the peas would have red flowers, so the result of 729 peas with red flowers is more than expected.
. If the scientist's assumed probability is correct, find the probability of getting 729 or more peas with red flowers.
b. Is 729 peas with red flowers significantly high?
c. What do these results suggest about the scientist's assumption that 3/4 of peas will have red flowers
The solution to the statistics have been given below
How to solve for the probabilityThe probability = 3 / 4 = 0.75
n = 933
x≥ 729
np = 0.75 * 933
= 699.75
√933 * 0.75 * 0.25
= √174.9375
= 13.23
using the continuity correction we have
729 - 0.5
= 728.5 - 699.75 / 13.23
= 2.17
The p value is 0.015003.
there is a 1.5% chance of getting 729 peas with red flowers
b. given that Z is greater than 2, this can be said to be high
c. These results suggest that the scientist maybe wrong in his assumption
Read more on statistics here:https://brainly.com/question/25082768
#SPJ1
Jody is picking a movie to watch this evening.
Of the movies in her cabinet, 9 are romantic
comedies. She will pick one movie at random.
If the probability of the selected movie being
a romantic comedy is 25%, how many movies
are on the shelf?
The number of movies on the shelf is given as follows:
36 movies.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
For this problem, the parameters are given as follows:
Probability of 25% = 1/4.Number of desired outcomes is of 9.Hence the total number of outcomes, representing the number of movies on the shelf, is obtained as follows:
1/4 = 9/x
x = 9 x 4
x = 36 movies.
More can be learned about probability at https://brainly.com/question/24756209
#SPJ1
the only items in each of containers a, b, and c are 28 disks. in each container, each of the disks is numbered with a different integer from the integers 1 through 28 inclusive. one disk is to be selected at random from each of the 3 containers. what is the probability that at least one of the disks selected has a number greater than 24?
The probability that at least one of the disks selected has a number greater than 24 is 127/343.
To find the probability that at least one of the disks selected has a number greater than 24, we can find the probability that all three disks have numbers less than or equal to 24 and subtract this from 1.
The probability that a disk selected from a container has a number less than or equal to 24
24/28= 6/7
Since,
there are 24 disks with numbers less than or equal to 24 out of a total of 28 disks in each container.
We can assume that the selection of a disk from one container is independent of the selection of a disk from another container, so the probability that all three disks selected have numbers less than or equal to 24 is (6/7)³
since we are making three independent selections.
Therefore,
The probability that at least one of the selected disks has a number greater than 24 is 1 - (6/7)³ ,
which simplifies to 343/343 - 216/343 = 127/343
Learn more about probability here brainly.com/question/30034780
#SPJ4
pls help asap it’s annoying me
Answer:
b. 53.1°
c. 126.9⁰
Step-by-step explanation:
These are SSA triangles; use Law of Sines to find the unknown angle:
b) sin30/15 = sinA/24
sinA(15) = sin30(24)
sinA = sin30(24)/15 = 0.80
m∠A = sin⁻1(0.80) = 53.1°
c) m∠A = 180 - 53.1 = 126.9⁰
Answer:
∠ BAC = 53.13° , ∠ BAC = 126.87°
Step-by-step explanation:
using the Sine rule in Δ ABC
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]
where a is the side opposite ∠ A and c is the side opposite ∠ C
here a = BC = 24 and c = AB = 15 , then
[tex]\frac{24}{sinA}[/tex] = [tex]\frac{15}{sin30}[/tex] ( cross- multiply )
15 sinA = 24 sin30° ( divide both sides by 15 )
sin A = [tex]\frac{24sin30}{15}[/tex] , then
A = [tex]sin^{-1}[/tex] ( [tex]\frac{24sin30}{15}[/tex] ) = 53.13°
(b)
acute angle BAC = 53.13°
(c)
the sine of an angle is positive in both the first and second quadrant , so
obtuse angle BAC = 180° - 53.13° = 126.87°
Help please!
I don’t understand how to do any of this.
The answers to the geometry questions are given as follows:
2)
a)
A = 8
b = 10
x = 118°
y = 62°
b)
a = 8
b = 15
y = 50
x = 100°
3)
(a)
∠2 = 25°
3 = 65°
∠4 = 65°
∠5 = 90°
(b)
since SL = 10,
i) LT 10
ii) TM = 10
iii) SM = 10
4)
a) Since m∠118
∠2 = 18°
∠3 = 72°
∠4 = 72°
If FA = 27, then LO = 13.5
5)
a) All the angles in the diagram are equal to ∠45°
b) Line BC = 6√2
c) Line BE = 6
The above are solved using the principles behind the properties of Parallelograms; Rhombus, Rectangle, and Square.
What is the Justification for the above responses?Since the above answers are justified by the qualities or properties of :
Parallelograms; Rhombus, and Rectangle, let's look at them one by one.
2
a)
A = 8 - opposite sides of a parallelogram are equal in length
b = 10 -opposite sides of a parallelogram are equal in length
y = 62° - opposite angles of a parallelogram are of equal measure.
x = 118° - Sum of angles of a parallelogram - 360°. x = (360 - (62*2))/2
= 118°
3)
(a) Here we have a Rhombus.
∠2 = 25° - Opposite angles of a rhombus are equal; Diagonals bisect the angles of a rhombus. Thus ∠1≅∠2
∠3 = 65° - Since diagonals bisect each other at right angles, ∠3 = 180 - (25+90) = 65°
∠4 = 65° - Diagonals bisect the angles of a rhombus. Thus, ∠3≅∠3
∠5 = 90° - [properties of a Rhombus]
(b)
since SL = 10,
i) LT 10 - All sides of a Rhombus are equal
ii) TM = 10 - All sides of a Rhombus are equal
iii) SM = 10 - All sides of a Rhombus are equal
4) Here we have a Rectangle.
a) Since m∠18
∠2 = 18° because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠2≅∠1 (AAS)
∠3 = 72° - Each interior angle is equal to 90 degrees. Thus, m∠ = 90-18 = ∠72°
∠4 = 72° - because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠4≅∠3(AAS)
If FA = 27, then LO = 13.5 - The diagonals bisect each other.Thus,
LO = FA/2
LO = 27/2
LO = 13.5
5) Here we have a square.
a) All the angles in the diagram are equal to ∠45°. This is because, the diagonals bisect all interior angles. Since each interior angle is 90°, thus, each of the resulting angle bisected 45°
b) Line BC = 6√2 - This is be
c) Line BE = 6
The length of one-half of the diagonal of a square can be found using the Pythagorean theorem, which relates the lengths of the sides of a right triangle.
Let s be the side length of the square. Then, the length of the diagonal of the square (d) can be found using the equation d = s√2.
In this case, s = 6√2. So, the length of the diagonal (d) is:
d = s√2 = (6√2)√2 = 6(√2)(√2) = 6(2) = 12
Therefore, one-half of the diagonal of the square is:
(1/2)d = (1/2)(12) = 6
So, the length of one-half of the diagonal of the square ABCD is 6.
Learn more about square:
https://brainly.com/question/28776767
#SPJ1
