Answer:
Height = 8 yards, base = 15 yards.
Step-by-step explanation:
Let the height be x yards then the base = x+7 yards.
Area = 1/2 * base * height, so:
1/2 * (x+7) * x = 60
1/2x(x + 7) = 60 Multiply through by 2:
x(x + 7) = 120
x^2 + 7x - 120 = 0
(x - 8)(x +15) = 0
x = 8, -15
x = 8. ( we ignore the negative root).
So the base is 8+7 = 15 yards long.
A 1-inch rise for a 16-inch run makes it easier for the wheelchair rider to ascend a ramp. How long must a ramp be to easily accommodate a 24-inch rise to the door?
Answer: The ramp must be 32 feet long. In inches, 384.
Step-by-step explanation:
For each 16 inches of run, there is one inch of rise. To get 24 inches of rise, multiply 16 by 24 to get 384 inches. To convert to a more useful measurement, convert to feet. 12 inches per foot. 384/12 = 32
Measurement is the process of assigning numbers to physical quantities and phenomena.
If a 1-inch rise for a 16-inch run makes it easier for the wheelchair rider, this can be expressed as:
1inch rise = 16-inch run
In order to determine how long must a ramp be to easily accommodate a 24-inch rise to the door, we can write:
24in rise = x
Divide both expressions:
[tex]\dfrac{1}{24}=\dfrac{16}{x}\\[/tex]
Cross multiply:
[tex]x=16 \times 24\\x=384inches[/tex]
Hence the ramp must be 384inches long in order to easily accommodate a 24-inch rise to the door.
Learn more here: https://brainly.com/question/14503610
I NEED HELP PLEASE, THANKS! :)
Answer:
Assume that Sk is valid for n=k and prove that Sn is valid for n= k+ 1
Step-by-step explanation:
This is Principle of Mathematical Induction ---PMI
Step 1: Verify that Sn is valid for n =1
Step 2:Assume that Sk is valid for n=k and prove that Sn is valid for n= k+ 1
please help. Find the value of x
Answer:
x =24
Step-by-step explanation:
Call the angle in the lower right corner y
The outside angles add to 180 degrees for the large triangle
41+ 94+ y = 180
135 + y = 180
y = 180-136
y =45
The small triangle in the lower right also has angles that add to 180
y+ 111+x = 180
45+111+x = 180
156 + x = 180
x = 180-156
x =24
Answer:
x = 24
Step-by-step explanation:
Angles on a straight line add up to 180 degrees.
a + 111 = 180
180 - 111 = a
a = 69
Angles in a quadrilateral add up to 360 degrees.
69 + 41 + 94 + c = 360
204 + c = 360
c = 360 - 204
c = 156
Angles on a straight line add up to 180 degrees.
x + 156 = 180
x = 180 - 156
x = 24
Find the missing side and round the answer to the nearest tenth. Thanks.
Answer:
22.2
Step-by-step explanation:
The missing side is x
cos19° = 21/x switch x and cos19° x = 21/cos 19°x = 22.21≈ 22.2
Lindsey made an error while solving this equation. 143.5 = 2 - (7(x+3). What line has the error?
(Refer to image)
A: Step 1
B: Step 2
C: Step 3
D: Step 4
Answer:
Step 1
Step-by-step explanation:
She didn't distribute the negative while she distributed 7. It should be -7x - 21, not 7x - 21.
he dot plot shows the number of words students spelled correctly on a pre-test. A number line going from 2 to 11. 0 dots are above 2. 0 dots are above 3. 1 dot is above 4. 2 dots are above 5. 4 dots are above 6. 4 dots are above 7. 3 dots are above 8. 2 dots are above 9. 2 dots are above 10. 0 dots are above 11. Which statement best describes the shape of the graph? The graph is skewed right. The graph is nearly symmetrical. The graph is skewed left. The graph is perfectly symmetrical.
Explanation:
Given information:
A number line going from 2 to 11. 0 dots are above 2. 0 dots are above 3. 1 dot is above 4. 2 dots are above 5. 4 dots are above 6. 4 dots are above 7. 3 dots are above 8. 2 dots are above 9. 2 dots are above 10. 0 dots are above 11.From that we can see the data set is {4,5,5,6,6,6,6,7,7,7,7,8,8,8,9,9,10,10} which produces the dot plot you see in the image attachment below.
It's a bit tricky to see, but the graph is nearly symmetrical. If we were to remove the blue points in the dot plot I provided, then we'll get a perfectly symmetrical distribution. Symmetrical means one half is a mirror copy of the the other half. The center line of a symmetrical distribution is both the mean and median.
Answer:
The Answer On Edge Is A.), Have Fun Dreamers!
Step-by-step explanation:
Which statement explains if a dilation was applied? A dilation was applied to the fabric because the width of the fabric was preserved. A dilation was applied to the fabric because the angle measures were preserved. A dilation was not applied to the fabric because the angle measures are the same. A dilation was not applied to the fabric because the length was changed, not the width.
Answer:
A dilation was not applied to the fabric because the length was changed, not the width.
Step-by-step explanation: B was not the answer it was D.
Answer:
D.
Step-by-step explanation:
Edge 2022.
Immediately after filling my gas tank, I drove 237.1 miles to my favorite campground. I filled my tank again at the campground, and computed that I got 28.7 miles per gallon on the trip. How many gallons of gas did I use on the trip to the campground
Answer:
57,838.4 - 57,491.9 = 346.5 miles
346.5/17.5 = 19.8 miles per gallon.
Hope this helps :-)
Step-by-step explanation:
The solution to -45= n/5 is
Answer:
n=5*-45
n=225
:)
Step-by-step explanation:
Answer:
n = -225
Step-by-step explanation:
-45 = n/5
cross multiply
n = -45 x 5
n= -225
Which statements about the circle are correct? Check all that apply Arc PQ is congruent to arc SR. The measure of arc QR is 150 The circumference of circle C is cm. Arc PS measures about 13.1 cm. QS measures about 15.7 cm.
Answer:
1st 2nd 4th 5th
What is the exact volume of a cone whose base radius is 9ft and whose height is 14 ft. Show your work
━━━━━━━☆☆━━━━━━━
▹ Answer
V ≈ 1187.52
▹ Step-by-Step Explanation
V = πr²[tex]\frac{h}{3}[/tex]
V = π9²[tex]\frac{14}{3}[/tex]
V ≈ 1187.52
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer: The exact volume of a cone with a base radius of 9 feet and height of 14 feet is 1187.52.
Step-by-step explanation:
Using the formula V=1/3hπ, we can substitute each variable that we have. Once simplified we will get 1185.52 exactly. Good Luck!
Olivia is thinking of a number.She says, "My number is odd. It is a factor of 30 and a multiple of 3"
Answer:
15
Step-by-step explanation:
Factors of 30:
1 , 2, 3, 5, 6, 10, 15, 30
Multiples of 3:
3, 6, 9, 12, 15, etc.
The first number (and only number) shared by both sets is 15, therefore 15 is your answer.
~
Answer:
Your answer would be 15
Step-by-step explanation:
It would be 15 because you can multiply it by 30, it goes into 3 evenly and 15 is an odd number
If a carton contains 6 eggs, how many eggs are there in 13 cartons? would it be 6x13?? which is equal to 78 I'm not sure.
Answer:
78 eggs
Step-by-step explanation:
13 × 6 = 78 eggs
Hope this helps! :)
Answer:
Yes it would be 6x13=78
Step-by-step explanation:
cross multiplication and divide:
1 cartoon = 6 eggs
13 cartoons = x
Two similar biscuit tins hold the same type of biscuits. The net mass of biscuits in the smaller tin is 1 kg. Find the net mass of biscuits in the larger tin. Net mass of biscuits in larger tin = __?_ kg
Answer:
1.5 kg
Step-by-step explanation:
Assuming it scales linearly: the higher tin holds 9/6 as many biscuits, so:
9/6 · 1 kg = 1.5 kg
g Determine whether the statement is true or false. If fx(a, b) and fy(a, b) both exist, then f is differentiable at (a, b). True False Correct: Your answer is correct.
Answer:
False
Step-by-step explanation:
A function is said to be differentiable over a given region if the function is continuous and has only one value for each input.
Therefore in order to conclude that f is differentiable at (a, b), the partial derivatives must be continuous at (a, b).
It is true that the function has to be defined over a given region because without it, you cannot determine if a partial derivative is continuous or otherwise.
But the fact that the partial derivatives exist at a point is not a sufficient condition for continuity.
The amount of time t(in minutes) that it takes to put out a fire varies inversely with G, the volume of water used (in hundreds of gallons). When G is 2, t is 20. Find how long it takes to put out a fire when 500 gallons of water (G = 5) are used.
Answer:
50 minutes.
Step-by-step explanation:
You can use a ratio to solve:
[tex]t[/tex] : [tex]G[/tex]
20 : 2
10 : 1
[tex]x[/tex] : 5
[tex]x[/tex] must be 50 minutes since 100 gallons of water takes 10 minutes.
the instantaneous growth rate r of a colony of bacteria t hours after the start of an experiment is given by the function r=0.01t^3-0.07t^2+0.07t+0.15 for 0≤t≤7. find the times for which the instantaneous growth rate is zero.
Answer:
t = 5,-1,3
Step-by-step explanation:
r=0.01t^3-0.07t^2+0.07t+0.15
For simplification let's multiply the equation by 100
100r = t³ - 7t² + 7t + 15
When r= 0
t³ - 7t² + 7t + 15= 0
Let's look for the value of t.
Let's try a possible division
(t³ - 7t² + 7t + 15)/(t-5) = t² -2t -3
So we've gotten one as t-5
Let's factorize t² -2t -3
= t² +t -3t -3
= t(t+1) -3(t+1)
= (t+1)(t-3)
So we have
(t-5)(t+1)(t-3)
What it means is that the possible values are when
t = 5,-1,3
These are also called the roots of the equation
Answer:I don’t know
Step-by-step explanation: fruit flys are weird
Find the equation of the line with slope m=1/2 that contains the point (4,6)
Answer:
y = 1/2x + 4
Step-by-step explanation:
Use the formula for the equation of a line.
y = mx + b
Where m is the slope, and b is the y-intercept.
The slope is given.
y = 1/2x + b
The points (x, y) are given.
(4, 6)
Put y as 6 and x as 4, solve for b.
6 = 1/2(4) + b
6 = 2 + b
6 - 2 = b
4 = b
The y-intercept is 4 or (0, 4).
The equation of the line is y = 1/2x + 4.
A random sample of adult drivers was obtained where 52% were men and 46% were women. Note that everyone is not classified as a man or a women. A survey showed that 65% of the drivers rely on GPS systems. 30% of the drivers are men and use GPS while 34% of the drivers are women and use GPS. Suppose a person included in this survey is randomly selected.
a) Suppose the person selected is a man. What is the probability that he relies on a GPS system? Your answer should have at least 3 decimal places.b) Suppose the person selected relies on a GPS system. What is the probability that the person is a woman? Your answer should have at least 3 decimal places.c) What is the probability that the person is a man and does not rely on a GPS system? Your answer should have at least 3 decimal places.d) What is the probability that an individual is a man or uses a GPS system? Your answer should have at least 3 decimal places.e) What is the probability that an individual does not use a GPS system? Your answer should have at least 3 decimal places.
Answer:
a) P(G | M) = 0.577
b) P(W | G) = 0.523
c) P(M and G') = 0.220
d) P(M or G) = 0.870
e) P(G') = 0.350
Step-by-step explanation:
A random sample of adult drivers was obtained where 52% were men and 46% were women.
P(M) = 0.52
P(W) = 0.46
A survey showed that 65% of the drivers rely on GPS systems.
P(G) = 0.65
30% of the drivers are men and use GPS while 34% of the drivers are women and use GPS.
P(M and G) = 0.30
P(W and G) = 0.34
a) Suppose the person selected is a man. What is the probability that he relies on a GPS system? Your answer should have at least 3 decimal places
P(G | M) = ?
Recall that conditional probability is given by
∵ P(B | A) = P(A and B)/P(A)
For the given case,
P(G | M) = P(M and G)/P(M)
P(G | M) = 0.30/0.52
P(G | M) = 0.577
b) Suppose the person selected relies on a GPS system. What is the probability that the person is a woman? Your answer should have at least 3 decimal places.
P(W | G) = ?
Recall that conditional probability is given by
∵ P(B | A) = P(A and B)/P(A)
For the given case,
P(W | G) = P(W and G)/P(G)
P(W | G) = 0.34/0.65
P(W | G) = 0.523
c) What is the probability that the person is a man and does not rely on a GPS system? Your answer should have at least 3 decimal places.
P(M and G') = ?
Where G' means does not rely on a GPS system
P(M and G') = P(M) - P(M and G)
P(M and G') = 0.52 - 0.30
P(M and G') = 0.220
d) What is the probability that an individual is a man or uses a GPS system? Your answer should have at least 3 decimal places.
P(M or G) = ?
Using the addition rule of probability,
∵ P(A or B) = P(A) + P(B) - P(A and B)
For the given case,
P(M or G) = P(M) + P(G) - P(M and G)
P(M or G) = 0.52 + 0.65 - 0.30
P(M or G) = 0.870
e) What is the probability that an individual does not use a GPS system? Your answer should have at least 3 decimal places.
P(G') = ?
P(G') = 1 - P(G)
P(G') = 1 - 0.65
P(G') = 0.350
The triangle ABC formed by AB = 13cm, BC=5cm and
AC = 12cm is
Answer:
Right-angle triangle
Step-by-step explanation:
A box is filled with 3 yellow cards , 4 green cards. A card is chosen at random from the box. What is the probability that the card is not green?
Answer:
3/7
Step-by-step explanation:
total cards 3+4 = 7
Not green = 7-4 = 3 cards
P ( not green )= not green cards / total = 3/7
Answer:
3/7.
Step-by-step explanation:
There are seven cards in total, four of them being green.
The knowledge of the color of the other cards aren't really nessesary, so you can just subtract four from seven, which is three.
Hope this helped!
What are the zeroes of f(x) = y2 - 2x - 3?
Answer:
x=y^2/2 - 3/2
Step-by-step explanation:
Answer:
Step-by-step explanation:
Product = -3
Sum = -2
Factors = -3 , 1
y² - 2y - 3 = y² + y - 3y - 3
= y( y + 1) - 3(y + 1)
= (y +1) (y - 3)
The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname If more than one surname begins with a letter besides A and O, how may surnames begin with that letter?
Step-by-step explanation:
40children - 23 (with A, O) = 17left
26 letter in alphabet- ( A, O) = 24 letter left
24 letters left - 14 (not used for 1st letters) = 10
10 letters left to use/ 17 children left
10÷17 = 0.5882352941 x 10 =5.8 or as close to 6 I can get
There are six surnames that start with each letter other than A and O when more than one surname does.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
Given, The surnames of 40 children in a class are arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A.
Since, 14, of the letters of the alphabet do not appear as the first letter of a surname
14 of the letters of the alphabet do not appear as the first letter of the surname
∴ the no. of letters that appeared = 26-14 = 12 alphabets
15 surnames begin with 10 letters beside O and A
∴ 6 surnames begin with a letter
Therefore, If more than one surname begins with a letter besides A and O, 6 surnames begin with that letter.
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A quantity, T , Varies inversely with a quantity, r. If t=6 then r=5 what is the constant of variation
Answer:
t varies inversely to 30/r
Step-by-step explanation:
t varies inversely to r
(lol I can't seem to find the variation sign in the keyboard)
when you introduce the constant K the sign changes to =
t=k/r
if t=6, r=5
substitute the values
6=k/5
k= 6×5
k=30
we have found the constant so we add it to our initial equation
t inversely varies to 30/r
PLZ I need Help the Question is: 5+13·18+85÷17−11
Answer:
233
Step-by-step explanation:
Solve the system of linear equations.
Answer:
work is shown and pictured
Given: a concave polygon Conjecture: It can be regular or irregular
Answer:
[tex]false[/tex]Step-by-step explanation:
A concave polygon can never be regular (all sides and angles must be congruent). Hope this helps..
Write the equation of each line in slope intercept form (If possible please show work)
Hope it make sense now :)
The target population is all students in your university. You wish to estimate the average current Visa balance for each student. How large would the university student population have to be in order to be regarded as effectively infinite in each of the following samples?
(a) A sample of 24 students.
(b) A sample of 52 students.
(c) A sample of 96 students.
Answer:
For each of the sample sizes given, for the population to be regarded as effectively infinite, student population has to be more than
a) 240 students.
b) 1,040 students.
c) 1,920 students.
Step-by-step explanation:
A population may be treated as infinite when the population size, N, is at least 20 times the sample size, n.
Mathematically,
(N/n) > 20
N > 20n
(a) A sample of 24 students.
If sample size = n = 24
For the population size to be effectively infinite,
N > 20n
N > 20×24
N > 480 students
(b) A sample of 52 students.
If sample size = n = 52
For the population size to be effectively infinite,
N > 20n
N > 20×52
N > 1,040 students
(c) A sample of 96 students.
If sample size = n = 96
For the population size to be effectively infinite,
N > 20n
N > 20×96
N > 1,920 students
Hope this Helps!!!
PLEASE HELP!!(PIC INCLUDED)
Which of the following steps were applied to ABCD to obtain A'B'C'D?
A. shifted 3 units right and 2 units down
B. shifted 4 units right and 2 units down
C. shifted 2 units right and 3 units down
D. shifted 3 units right and 1 unit down
Answer:
A. Shifted 3 unit right and 2 unit down
Step-by-step explanation:
Let's determine the reason for the answer.
We will use a reference point, only one point to determine the reason.
Because the both shape are identical.
Let's use point A
The position of A is 2 on the y axis and 1 on the x axis
While the position of A' is 0 on the y axis and 4 on the X asis
Let's know how many units where moved from the position.
A' -A
For X axis
4-1= 3
For y axis
0-2= 2(we need only the magnitude)
So its 2 units Down and 3 unit right