Final answer:
In this Biology question, a veterinarian is investigating the possible causes of enteroliths in horses and suspects that feeding alfalfa may be responsible. She conducted a study to estimate the proportion of horses with enteroliths who are fed two or more flakes of alfalfa per day.
Explanation:
The subject of this question is Biology. The veterinarian is investigating the possible causes of enteroliths in horses and suspects that feeding alfalfa may be to blame. She wants to estimate the proportion of horses with enteroliths who are fed at least two flakes of alfalfa per day.
She conducted a study where she sampled 62 horses with enteroliths and found that 42 of them are fed two or more flakes of alfalfa. She estimates the standard error to be 0.0594.
Need help as soon as possible!
Answer:
[tex]\boxed{ \text{8 p.m.}}[/tex]
Step-by-step explanation:
First, we must plot the graph of your system of equations (see below).
The two lines cross at (12, 360).
Thus, machine A had been going for 12 h. It started at 8 a.m., so it ended at 8 p.m.
Both machines had made 360 ft of wire by [tex]\boxed{ \text{8 p.m.}}[/tex]
Check:
360 = 30 × 12 360 = 40(12 – 3)
360 = 360 360 = 40 × 9
360 = 360
OK.
(a) For what positive integers $n$ does $\left(x^2+\frac{1}{x}\right)^n$ have a nonzero constant term?
(b) For the values of $n$ that you found in part (a), what is that constant term? (You can leave your answer in the form of a combination.)
a. By the binomial theorem,
[tex]\displaystyle\left(x^2+\frac1x\right)^n=\sum_{k=0}^n\binom nk(x^2)^{n-k}\left(\frac1x\right)^k=\sum_{k=0}^n\binom nkx^{2n-3k}[/tex]
which produces a constant term when [tex]2n-3k=0[/tex], or [tex]2n=3k[/tex]. [tex]2n[/tex] is even for any choice of [tex]n[/tex], so [tex]n[/tex] must be any positive integer for which [tex]2n[/tex] is an even multiple of 3 i.e. a multiple of 6. Then [tex]n[/tex] can be any of the integers in the sequence {6, 12, 18, ...}.
b. Let [tex]n=6m[/tex] for some positive integer [tex]m[/tex]. Then
[tex]\displaystyle\left(x^2+\frac1x\right)^{6m}=\sum_{k=0}^{6m}\binom {6m}k(x^2)^{6m-k}\left(\frac1x\right)^k=\sum_{k=0}^{6m}\binom{6m}kx^{12m-3k}[/tex]
and the constant term occurs when [tex]12m-3k=0[/tex], or [tex]4m-k=0[/tex], or [tex]k=4m[/tex]. At this value of [tex]k[/tex], we get the term
[tex]\dbinom{6m}{4m}x^{12m-3(4m)}=\dfrac{(6m)!}{(4m)!(6m-4m)!}=\dfrac{(6m)!}{(4m)!(2m)!}[/tex]
An employee at a gym wants to select a random sample of gym members for a survey about their exercise habits.
Select Yes or No to tell whether each method results in a random sample of the population.
Answer:
No, no, yes, no
Step-by-step explanation:
The first one is not random. He is sampling only the earliest gym goers.
The second one is not random. He is sampling only from one zip code.
The third one is random. He is using a random number generator.
The fourth one is not random. He is sampling only volunteers.
The third is completely random. He's generating numbers with a random number generator. So yes, for the third statement and No, for the first, second, and fourth statements.
What is a random sample?Random sampling is the method of selecting the subset from the set to make a statical inference.
An employee at a gym wants to select a random sample of gym members for a survey about their exercise habits.
The first is not a fluke. He's simply tasting the first gym attendees.
The second is not a coincidence. He's just taking samples from one zip code.
The third is completely random. He's generating numbers with a random number generator.
The fourth is not a fluke. Only volunteers are being sampled.
More about the random sample link is given below.
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PLZ HELP BRAINLIEST and 60 POINTS
Answer:
c d a b d
Step-by-step explanation:
Answer:
C, D, A, B, and D
Step-by-step explanation:
A jar contains four black buttons and five brown buttons. If five buttons are picked at random, what is the probability that at least three of them are black?
The probability that at least three out of five randomly picked buttons are black is approximately 0.6614.
To find the probability that at least three out of five randomly picked buttons are black, we can consider the different combinations of buttons that satisfy this condition.
There are two cases where at least three buttons are black:
1. Exactly 3 buttons are black.
2. All 5 buttons are black.
Let's calculate the probabilities for each case:
1. Exactly 3 buttons are black:
This can happen in [tex]\( \binom{4}{3} \)[/tex] ways (choosing 3 black buttons) multiplied by [tex]\( \binom{5}{2} \)[/tex] ways (choosing 2 brown buttons).
Probability of this case:
[tex]\[ P(\text{3 black}) = \frac{\binom{4}{3} \times \binom{5}{2}}{\binom{9}{5}} \][/tex]
2. All 5 buttons are black:
This can happen in [tex]\( \binom{4}{5} = 0 \)[/tex] ways (because there are only 4 black buttons).
The probability that at least three buttons are black is the sum of the probabilities of these two cases.
[tex]\[ P(\text{at least 3 black}) = P(\text{3 black}) + P(\text{5 black}) \]\[ P(\text{at least 3 black}) = \frac{\binom{4}{3} \times \binom{5}{2}}{\binom{9}{5}} + 0 \][/tex]
[tex]\[ P(\text{at least 3 black}) = \frac{\frac{4!}{3!(4-3)!} \times \frac{5!}{2!(5-2)!}}{\frac{9!}{5!(9-5)!}} \]\[ P(\text{at least 3 black}) = \frac{\frac{4 \times 5}{3!} \times \frac{5 \times 4}{2!}}{\frac{9 \times 8 \times 7 \times 6 \times 5}{5!}} \][/tex]
[tex]\[ P(\text{at least 3 black}) = \frac{\frac{4 \times 5}{6} \times \frac{5 \times 4}{2}}{\frac{9 \times 8 \times 7 \times 6 \times 5}{5 \times 4 \times 3 \times 2 \times 1}} \]\[ P(\text{at least 3 black}) = \frac{\frac{20}{6} \times \frac{20}{2}}{\frac{3024}{120}} \][/tex]
[tex]\[ P(\text{at least 3 black}) = \frac{\frac{100}{6}}{\frac{3024}{120}} \]\[ P(\text{at least 3 black}) = \frac{100 \times 120}{6 \times 3024} \]\[ P(\text{at least 3 black}) = \frac{1000}{1512} \][/tex]
[tex]\[ P(\text{at least 3 black}) ≈ 0.6614 \][/tex]
Anthony spend $34.56 at the shopping mall. Brad was also shopping at the mall with Anthony. The value of the digit 6 in the amount of money he spent is 100 times more than the value of the digit 6 in the amount Anthony spent. Did Brad spend $56.71 or $57.61? Show all work. Explain how you know which number is correct
Answer:
$56.71
Step-by-step explanation:
with Anthony's spendings of $34.56, the 6 is in the hundredth place. If the value of the six is 100 times more in Brad's spending, the six would be in the ones place. You would move the six over two place values (because of 100) and end up with 6 dollars. If it was 10 times more, than you would only move one place value over and it would be 57.61.
Answer:
$56.71
Step-by-step explanation:
The value of the 6 in which Anthony spent is the hundredth value, or 0.06
Brad spent 100x more than the value of the digit 6 in which Anthony spent. Multiply 0.06 with 100: 100 x 0.06 = 6
6 is in the ones place value, & $56.71 is the only answer choice with 6 in the ones place value, so it is your answer.
~
If Social Security takes 6.2 percent, and Medicare takes 1.45 percent of your paycheck, how much would you have left on a $300 monthly salary?
$277.05
$227.05
$277.55
$227.55
The answer would be the first option.
6.2 percent of 300 is 18.6,
and 1.45 percent of 300 is 4.35
It makes a total of 22.95
300 - 22.95 = 277.05
Please help me with this....
Answer:
[tex]3\sqrt{13}[/tex]
Step-by-step explanation:
Using the Theorem of the side of a triangle:
[tex]x^2 = 4 * (4 + 9) = 42\\x = \sqrt{42}[/tex]
And using the Height Theorem:
y = [tex]\sqrt{4 \cdot 9} = \sqrt{36} = 6[/tex]
And by the Pythagorean Therorem:
z = [tex]\sqrt{6^2 + 9^2} = \sqrt{117} = 3\sqrt{13}[/tex]
Volume of cylinder help??? PLEASE HURRY EXAMPLES DOWN BELOW WILL VOTE BRAINLIEST VERY URGENT
Answer:
Here I leave an example that you will understand more easily so that you understand the process better but it is easy.
First you must substitute the values for the letters, and then you multiply it so basic remember to change the Pi by 3.14
Could someone please help thank you
Answer:
Step-by-step explanation:
Law of Sines.
a/sin(A) = b/sin(B)
In this case, a = y and A = 26.5. b = 15 and B = 90.
y/sin(26.5) = 15/sin(90).
y/sin(26.5) = 15/1
y = sin(26.5) * 15, which is about 6.69 feet.
The answer to your question is
6.69
Please help..........
Answer:
x = 2[tex]\sqrt{34}[/tex]
Step-by-step explanation:
Since the triangle is right use Pythagoras' theorem to solve for x
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, thus
x² = 6² + 10² = 36 + 100 = 136
Take the square root of both sides
x = [tex]\sqrt{136}[/tex] = [tex]\sqrt{4(34)}[/tex] = 2[tex]\sqrt{34}[/tex]
Answer:
2√34
Step-by-step explanation:
6² + 10² = x²
x² = 6² + 10²
x² = 36 + 100
x² = 136
x = √136
x = 2√34
1. Which reason completes the proof below?
Given: BC is tangent to Circle A at D
Prove: AB = AC
Answer:
(C)
Step-by-step explanation:
Given: BC is tangent to the circle A at D.
To prove: AB is congruent to AC
Proof:
Statements Reason
1. BC is tangent to the circle A at D. Given
2. DB≅DC Given
3.AD⊥BC If a line is tangent to a circle then it is perpendicular to the radius at the point of tangency.
4. ∠ADB and ∠ADC are right angles Definition of perpendicular lines
5. ∠ADB≅∠ADC Right angles are congruent
6. AD≅AD Reflexive property of congruence
7. ΔADB≅ΔADC SAS rule
8. AB≅AC CPCTC
Hence, option (C) is correct.
Tangent to a circle is straight line just touching the circle at one point. The reason to complete the proof is: If a line is tangent to a circle, then it is perpendicular to the point of tangency
What is tangent to a circle?A line segment which touches a circle specified to only one point is called a tangent to that circle.
There is a theorem in mathematics that:
If there is a circle O with tangent line L intersecting the circle at point A, then the radius OA is perpendicular to the line L.
For the given case, the missing statement for the proof is:
If a line is tangent to a circle, then it is perpendicular to the point of tangency(the point on circle where the tangent intersects it).
Hence, the reason to complete the proof is: If a line is tangent to a circle, then it is perpendicular to the point of tangency
Learn more about tangent here:
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Identify the relative maximum value of g(x) for the function shown below.
[tex]g(x)=\frac{2}{x^2+3}[/tex]
Answer:
The maximum value of g(x) = 2/3 at x = 0
Step-by-step explanation:
* Lets find the maximum value of a function using derivative of it
- The function g(x) = 2/(x² + 3)
- 1st step use the negative power to cancel the denominator
∴ g(x) = 2(x² + 3)^-1
- 2nd use derivative of g(x) to find the value of x when g'(x) = 0
* How to make the derivative of a function
# If f(x) = a(h(x))^n, then f'(x) = an[h(x)^(n-1)](h'(x))
∵ [tex]g(x)=2(x^{2}+3)^{-1}[/tex]
∴ [tex]g'(x) = 2(-1)(x^{2}+3)^{-2}(2x)=-4x(x^{2}+3)^{-2}[/tex]
# Put g'(x) = 0
∴ [tex]-4x(x^{2}+3)^{-2}=0====\frac{-4x}{(x^{2}+3)^{2}}=0[/tex]
∴ [tex]-4x=(0)(x^{2}+3)^{2}====-4x = 0[/tex]
∴ x = 0
* The maximum value of g(x) at x = 0
- Substitute the value of x in g(x)
∴ g(0) = 2/(0 + 3) = 2/3
* The maximum value of g(x) = 2/3 at x = 0
60 POINTS PLEASE HURRY!!
Rashid solved a fraction division problem using the rule “multiply by the reciprocal.” His work is shown below.
3/4 divided by 9
3/4 x 1/9 = 3/36 or1/2
Which is the most accurate description of Rashid’s work?
A. Rashid solved the problem correctly.
B. Rashid multiplied the dividend by the divisor instead of finding the reciprocal.
C. Rashid multiplied the denominators instead of finding a common denominator.
D. Rashid multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.
Answer:
As long as you mistyped Rashid's work and meant that the answer was 3/36 or 1/12, the answer would be
A. Rashid solved the problem correctly
Step-by-step explanation:
When you are dividing, it is the same thing as multiplying by the reciprocal of that value. This means that
[tex]\frac{\frac{3}{4} }{9} =\frac{3}{4} *\frac{1}{9} =\frac{1}{12}[/tex]
bro this is middle school work, its B
question 63 true or false
Answer:
False
Step-by-step explanation:
we know that
In this problem the vertical distance is equal to 12 ft (the horizontal distance must be equal to the vertical distance, by angle of 45 degrees)
so
The length of the ladder is equal to
Applying Pythagoras Theorem
[tex]L=\sqrt{12^{2}+12^{2}} \\ \\L=\sqrt{288}\ ft\\ \\L=16.97\ ft[/tex]
Match the numbers in standard notation with the corresponding numbers in scientific notation.
Tiles
864,000,000,000
8,640,000,000
86,400,000,000,000
864,000,000,000,000
Boxes
8.64E9
8.64E14
8.64E11
8.64E13
Answer:
a) 864,000,000,000 8.64E11
b) 8,640,000,000 8.64E9
c) 86,400,000,000,000 8.64E13
d) 864,000,000,000,000 8.64E14
Step-by-step explanation:
A scientific notation is a way to represent very large values into the decimal form.
Steps to write in scientific notation:
Move the decimal to left before first digit of the given number.
Find the number of times decimal is moved to left.
Put that number in the exponent of e.
So, matching:
a) 864,000,000,000 8.64E11
b) 8,640,000,000 8.64E9
c) 86,400,000,000,000 8.64E13
d) 864,000,000,000,000 8.64E14
Greg drove 522 miles in 9 hours. At the same rate, how long would it take him to drive 754 miles?
Answer:
It would take 13 hours
Step-by-step explanation:
522/9 = 58
754/58= 13
A triangle has sides of lengths 28, 195, and 197. Is it a right triangle?
Final answer:
A triangle with sides of lengths 28, 195, and 197 satisfies the Pythagorean theorem (a² + b² = c²), which confirms it is a right triangle.
Explanation:
To determine if a triangle with sides of lengths 28, 195, and 197 is a right triangle, we can apply the Pythagorean theorem. According to this theorem, for a triangle to be a right triangle, the square of the length of the hypotenuse (the longest side) must be equal to the sum of the squares of the lengths of the other two sides.
Let us calculate:
a² + b² = c²28² + 195² = 197²784 + 38025 = 3880938809 = 38809As we can see, 784 plus 38025 indeed equals 38809. Hence, the triangle with sides 28, 195, and 197 satisfies the condition of the Pythagorean theorem and therefore is a right triangle.
I don't understand this, someone please help me
Answer:
the distance between the points is about 9.2 units
Step-by-step explanation:
It is well you should not understand it. No question is asked.
__
The answer choices suggest you are to find the distance between the two points. There is only one choice in a reasonable range: 9.2 units.
Each point is more than 2 units from any axis, so 2 units is clearly not the answer. The size of the graph is much less than 81 units, so clearly that is not the answer.
The difference of coordinates in the x-direction is 6; in the y-direction the difference is 7 units. The distance between the points will be more than the longest of these (7) and less than about 1.5 times that (10.5). Only one choice is in this range: 9.2 units.
__
The Pythagorean theorem is used to calculate the distance between points. The distance is considered to be the hypotenuse of a right triangle with legs of lengths equal to the differences of coordinates. Here, that means the distance (d) is ...
d² = 6² + 7² = 36 +49 = 85
d = √85 ≈ 9.2 . . . . grid squares, or "units"
Please help me out with this
Answer:
(x - 5)² + (y + 3)² = 16
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (5, - 3) and r = 4, so
(x - 5)² + (y - (- 3))² = 4², that is
(x - 5)² + (y + 3)² = 16
What is the component form of the vector shown in the graph?
Answer:
C) (-3, 4)
Step-by-step explanation:
Subtract the tail from the head:
(-2, 3) -(1, -1) = (-3, 4)
The component form is (-3, 4).
The component form of the vector from (1, -1) to (-2, 3) is (-3, 4), as it reflects the changes in the x and y directions.
The correct answer is option C.
To find the component form of the vector from (1, -1) to (-2, 3), we need to calculate the change in the x-direction and the change in the y-direction. The component form of a vector is typically written as (Δx, Δy), where Δx represents the change in the x-direction, and Δy represents the change in the y-direction.
In this case, the initial point is (1, -1), and the terminal point is (-2, 3). To find Δx and Δy, we subtract the x-coordinates and the y-coordinates, respectively:
Δx = x_terminal - x_initial = (-2) - 1 = -3
Δy = y_terminal - y_initial = 3 - (-1) = 4
So, the component form of the vector is (-3, 4).
Among the answer choices:
A. (1, 0) is not the correct component form.
B. (-5, 2) is not the correct component form.
C. (-3, 4) is the correct component form.
D. (-1, 2) is not the correct component form.
The correct answer is C, (-3, 4), which represents the change in the x-direction and the change in the y-direction as you move from (1, -1) to (-2, 3) on the graph.
Therefore, from the given options the correct one is C.
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Can you help with answer this and if there’s work to be shown please let me know. Thank you!
f(x) = /x - 2/
f(-1) = /-1 - 2/ = /-3/ = 3
f(0) = /0 - 2/ = /-2/ = 2
f(1) = /1 - 2/ = /-1/ = 1
f(2) = /2 - 2/ = /0/ = 0
Floor tile costs $11 $11 per square yard. How much will it cost to tile a bathroom that is 90 90 square feet?
Answer: $1980
Step-by-step explanation:
Well, based off of the question being asked, I assume that you will need to pay $11 for 90 square footage of tiling, and then the same for the other square footage of tiling. Therefore your answer will be $1980. If you are looking for the equation, it is (11x90)=990 (990)2 = 1980
you do not need to multiply 11 by 90 again because you already know the answer.
Answer:
$110
Step-by-step explanation:
We are given that
Cost of 1 square yard of floor tile =$11
We have to find the cost of 90 square feet of tile.
To find the cost of 90 square feet we will convert it into square yard.
We know that
9 square foot=1 square yard
1 square foot=[tex]\frac{1}{9}[/tex]
90 square feet=[tex]\frac{1}{9}\times 90=10[/tex] square yard
By unitary method
Cost 1 square yard=$11
Cost of 10 square yard=[tex]11\times 10=[/tex]$110
Hence, the cost of 90 square feet to tile a bathroom=$110
39,975 + 6.5% tax rate every month
1014.065 hope this helps
What are the degree and leading coefficient of the polynomial? 9y ² + 8 – 18y ⁹ + 7y
Degree:
Leading Coefficient:
answer: y²-y+9
coefficient is 2
degree is 1
Based on a poll of 200 citizens, a community action group claims that 40% of the population is in favor of a curfew for children under 18 on weekday nights. A local parent group claims that the poll is not valid and that only 22% of the citizens favor a curfew. To determine whether this sample supports the population proportion of 0.40, a simulation of 100 trials is run, each with a sample size of 50 and a point estimate of 0.22. The minimum sample proportion from the simulation is 0.15, and the maximum sample proportion from the simulation is 0.27. The margin of error of the population proportion is found using an estimate of the standard deviation. What is the interval estimate of the true population proportion?
(0.18, 0.26)
(0.14, 0.30)
(0.06, 0.38)
(0.16, 0.28)
Final answer:
The interval estimate of the true population proportion is (0.16, 0.28) that is option D is correct.
Explanation:
The interval estimate of the true population proportion is (0.16, 0.28).
A simulation of 100 trials with a sample size of 50 was conducted to determine whether the sample supports the population proportion of 0.40. The minimum sample proportion from the simulation is 0.15 and the maximum sample proportion is 0.27. Based on this simulation, the interval estimate for the true population proportion can be calculated.
Interval estimate formula: (point estimate - margin of error, point estimate + margin of error)
Point estimate = 0.22
Margin of error = (maximum sample proportion - minimum sample proportion) / 2 = (0.27 - 0.15) / 2 = 0.06
Interval estimate = (0.22 - 0.06, 0.22 + 0.06) = (0.16, 0.28)
The correct interval estimate of the true population proportion is (0.14, 0.30).
To determine the interval estimate of the true population proportion, we use the following formula for a 95% confidence interval:
[tex]\[ \text{Confidence Interval} = \text{Point Estimate} \pm (Z_{\alpha/2} \times \text{Standard Error}) \][/tex]
where[tex]\( Z_{\alpha/2} \)[/tex] is the Z-score corresponding to the desired confidence level (for a 95% confidence interval, [tex]\( Z_{\alpha/2} \)[/tex] is approximately 1.96), and the Standard Error (SE) is calculated using the formula:
[tex]\[ \text{SE} = \sqrt{\frac{\text{Point Estimate} \times (1 - \text{Point Estimate})}{\text{Sample Size}}} \][/tex]
Given the point estimate from the simulation as 0.22 and the sample size as 50, we calculate the standard error as follows:
[tex]\[ \text{SE} = \sqrt{\frac{0.22 \times (1 - 0.22)}{50}} \] \[ \text{SE} = \sqrt{\frac{0.22 \times 0.78}{50}} \] \[ \text{SE} = \sqrt{\frac{0.1716}{50}} \] \[ \text{SE} = \sqrt{0.003432} \] \[ \text{SE} \approx 0.0586 \][/tex]
Now, we calculate the margin of error (ME):
[tex]\[ \text{ME} = Z_{\alpha/2} \times \text{SE} \] \[ \text{ME} = 1.96 \times 0.0586 \] \[ \text{ME} \approx 0.1146 \][/tex]
The margin of error is approximately 0.1146. Therefore, the 95% confidence interval for the population proportion is:
[tex]\[ \text{Point Estimate} \pm \text{ME} \] \[ 0.22 \pm 0.1146 \][/tex]
Lower bound:
[tex]\[ 0.22 - 0.1146 \approx 0.1054 \][/tex]
Upper bound:
[tex]\[ 0.22 + 0.1146 \approx 0.3346 \][/tex]
However, the simulation results provide a range for the sample proportion from 0.15 to 0.27. Therefore, the interval estimate should be adjusted to reflect this range while still incorporating the margin of error.
Lower bound (adjusted for simulation range):
[tex]\[ 0.15 - 0.1146 \approx 0.0354 \][/tex]
Upper bound (adjusted for simulation range):
[tex]\[ 0.27 + 0.1146 \approx 0.3846 \][/tex]
Since the lower bound of the confidence interval cannot be less than the minimum sample proportion from the simulation (0.15), and the upper bound cannot exceed the maximum sample proportion from the simulation (0.27), we adjust the interval to:
Lower bound:
0.15
Upper bound:
0.27
Now, we apply the margin of error to these bounds:
Lower bound with ME:
[tex]\[ 0.15 - 0.1146 \approx 0.0354 \][/tex]
Since the lower bound cannot be less than 0, we round up to the nearest reasonable value, which is 0.14.
Upper bound with ME:
[tex]\[ 0.27 + 0.1146 \approx 0.3846 \][/tex]
Since the upper bound cannot exceed 1, we round down to the nearest reasonable value, which is 0.30.
Therefore, the interval estimate of the true population proportion, taking into account the simulation results and the margin of error, is (0.14, 0.30).
2 blue shirts
1 white shirt
1 red shirt
2 black slacks
1 white pair of pants
1 pair of jeans
1 pair of sandals
2 pairs of running shoes
Alex is on vacation and has the clothes listed above with her. She is trying to pick out an outfit. What is the probability she chooses a red shirt and running shoes?
A) 0.02
B) 0.17
C) 0.84
D) 0.92
Answer:
its b
Step-by-step explanation:
Answer:
B) 0.17
Step-by-step explanation:
Which statements are true?
If all angles of a quadrilateral are right angles, then the quadrilateral must be a square.
Two shapes are similar if and only if their corresponding angles are equal.
All quadrilaterals have four sides, and the sum of all angles in a quadrilateral is 180°.
If the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus.
There are three vertices in a triangle, or there are four sides in a pentagon.
Any two triangles are either similar or congruent.
Answer:
The statement which is true is, If the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus.
Step-by-step explanation:
In a rhombus, the diagonals bisect at perpendicular angles to form 4 triangles.Because the diagonals bisect at right angles, then it is possible to prove that the four small formed triangles are similar using the SAS theorem: two triangles are equal if two sides are equal and the angles between the two sides are equal.In your case, the sides are that on the base and that forming a height of the triangles with both having angle 90° between the sides.So you see if these the two are congruent, the hypotenuse of these triangles are congruent, making this quadrilateral a rhombus.
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You have 36 apples to share with your friends. If each friend gets exactly 2 apples, which equation could you use to solve for the number of friends, n?
Final answer:
To find the number of friends when 36 apples are shared with each friend getting 2 apples, divide the total apples by the number of apples each friend gets. The equation to solve for the number of friends, n, is n = 36 / 2 = 18.
Explanation:
To solve for the number of friends, n, sharing 36 apples when each friend gets 2 apples:
Identify the total number of apples = 36 and the number of apples each friend gets = 2.
Divide the total apples by the apples each friend gets: 36 ÷ 2 = 18, which represents the number of friends (n). So, the equation would be n = 36 / 2 = 18.
your friend has locked themselves out of the house, and they need your help to get back in. they have a 10 foot long ladder, and there is an open window height feet above the ground. How far from the wall of should you hold the ladder while they climb back in?
A. w = 2 feet
B. w = 12.8 feet
C. w = 9.6 feet
D. w = 6 feet
Answer:
6 feet
D
Step-by-step explanation:
Givens
l = 10
h = 8
w = ?
Formula
l^2 = h^2 + w^2
Solution
10^2 = 8^2 + w^2
100 = 64 + w^2
100 - 64 = 64 - 64 + w^2
w^2 = 36
sqrt(w^2) = sqrt(36)
w = 6 feet.