Answers
now, the picture looks a bit misleading, the angle on the bottom-right corner doesn't look at all like a 20° angle, so let me assume the 20° angle is the angle up above, like you see in the picture below, because that looks like a 20° one, and the number there, is not very clear which one is pointing to.
\(\cos(64^o )=\cfrac{\stackrel{adjacent}{h}}{\underset{hypotenuse}{18}}\implies 18\cos(64^o)=h \\\\[-0.35em] ~\dotfill\\\\ \cos(20^o )=\cfrac{\stackrel{adjacent}{h}}{\underset{hypotenuse}{x}}\implies x=\cfrac{h}{\cos(20^o )}\implies x=\cfrac{18\cos(64^o)}{\cos(20^o )}\implies x\approx 8.4\)
Make sure your calculator is in Degree mode.
Related Questions
Solve the inequality. Check the numbers that represent solutions.
-8x + 19 < -13
5
3
4
2
6
Answers
Answer:
x equals four
Step-by-step explanation:
collect like terms
then it will be minus 8 x equals minus 13 minus 19 which gives minus 32. Divide both sides by the coefficient of x i.e minus 8
Then x is less than 4
Because you divided with minus so the sign will change
Some help me again lol please no links please
Answers
a poll of $100$ eighth-grade students was conducted to determine the number of students who had a dog, a cat or a fish. the data showed that $50$ students had a dog, $40$ students had a cat, and $20$ students had a fish. further, $19$ students had only a dog and cat, $2$ students had only a cat and a fish, $3$ students had only a dog and a fish, and $12$ students had only a fish. how many students had none of these pets?
Answers
14 students had none of the pets mentioned in the problem.
Given Question is related to Sets and Function
By using the principle of inclusion-exclusion,
D = set of students who had a dog
C = set of students who had a cat
F = set of students who had a fish
Let's determine the sizes of the sets and their intersections:
|D| = 50
|C| = 40
|F| = 20
|D ∩ C| = 19
|C ∩ F| = 2
|D ∩ F| = 3
|D ∩ C ∩ F| = 0
|D ∪ C ∪ F| = ?
The size of the union of the sets as follows:
|D ∪ C ∪F| = |D| + |C| + |F| - |D ∩ C| - |C ∩ F| - |D ∩ F| + |D ∩ C ∩ F|
|D ∪ C ∪ F| = 50 + 40 + 20 - 19 - 2 - 3 + 0 = 86
Therefore, there were 86 students who had at least one of these pets.
To find the number of students who had none of these pets, we can subtract this number from the total number of students:
100 - 86 = 14
Therefore, 14 students had none of the pets mentioned in the problem.
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What are the solutions to the system of equations?
y=x^2 – 5x + 6
y = -4x + 6
A. (0, 6) and (1, 2)
B. (-1,0) and (6, 0)
C. (0, -1) and (6, 0)
D. (-1,0) and (0, 6)
Answers
The answer is definitely C
the different geometries that a molecule can attain by bond rotations and bends are called conformations. True/False ?
Answers
TRUE: A molecule can adopt a variety of geometries known as conformations by the rotation and bending of its bonds.
Conformational isomerism, often known as stereoisomerism, is a type of stereoisomerism in chemistry in which the isomers can be changed to one another simply by rotations about formally single bonds. Different conformations refer to any two arrangements of atoms in a molecule that differ by rotation about a single bond, whereas conformations that correspond to local minima on the potential energy surface are more specifically known as conformational isomers or conformers.
As a result, conformational isomers differ from other classes of stereoisomers (such as configurational isomers), where interconversion entails the necessary breaking and reformation of chemical bonds.
Thus, the statement, The different geometries that a molecule can attain by bond rotations and bends are called conformations is TRUE
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Use differentials to approximate the change in the volume of a spherical balloon of radius 2 meters if the balloon deflates to a radius of 1. 8 meters.
Answers
The changes in the volume of the spherical balloon is approximately o.3351-meter cube.
the volume of the sphere =\(v=\frac{4}{3}\pi r^3\)
using the definition of differential to find the change we write
\(dv=\frac{4}{3}\pi (dr)^3\)
where, \(dr\)=\(r_{2}-r_{2}\)
\(dr\)=\(2-1.8\\\)
\(dr\) \(=0.2\)
\(dv=\frac{4}{3}\pi (0.2)^3\)
\(dv=0.3351\) approx.
where dr and dv represent the differential or change with respect to radius and volume in the above calculation. so first we apply differential on both sides of the formula of the sphere then we find its approximation by the next coming equation. so, the volume of the sphere is approximately 0.3351-meter cube here approximation represents that it is not the exact solution it is basically approximated solution.
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Answer:
3.2 π
Step-by-step explanation:
The volume V of a sphere with radius r is given by the formula V = (4/3) * π * r^3.
Taking the derivative with respect to r, we get dV/dr = 4 * π * r^2.
Let dr be the change in radius, which is 1.8 - 2 = -0.2.
The differential dV is given by dV ≈ (dV/dr) * dr = 4 * π * r^2 * dr.
Substituting r = 2 and dr = -0.2, we get dV ≈ 4 * π * 2^2 * (-0.2) = -3.2 * π.
So, using differentials, we estimate that the volume of the balloon decreases by approximately 3.2 * π cubic meters as it deflates from a radius of 2 meters to a radius of 1.8 meters.
Select the correct answer from each drop-down menu.
The function f(x)= x^2
has been transformed, resulting in function g.
Answers
Answer:
to give you the real answer the first blank is DILATION and the second blank is (1/4)
Step-by-step explanation:
The function of g is dilation of function of f and the equation for g(x) = (1/4) x²
What is Dilation ?
Dilation is used to resize the object , smaller or bigger.
The resultant image will be similar to that of the original image just bigger or smaller.
When the plot of the function(x) = x² is observed , it can be seen that it is a vertical parabola , opening upwards , the vertex is at the origin.
At x = 1 , function(x) = 1
Now when the plot in the given image is observed it can be seen that
At x = 2 , g (x) = 1 , other than this everything is same.
It can be concluded from this that the function of g is dilation of function of f .
And we can also determine the degree of dilation from the above conclusion
At x = 1 , function(x) = 1
At x = 2 , g (x) = 1
Therefore the equation for g(x) = (1/4) x²
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A ticket for a school musical is $12. There is a 5% transaction fee if the ticket is purchased online. What is the total cost of a ticket that is purchased online?
Select one:
$12.65
$18.00
$12.05
$12.60
Answers
Answer:
The answer is $12.60
Step-by-step explanation:
You take 5% of 12 which =.60
The original price of the ticket is 12 so you do 12+.60= $12.60
Hope this helps!
During 21, jim butler purchased 125 shares of common stock issued by tri state manufacturing for $4700 including commission. later in the same year, jim sold the shares for $5500 after commission. calculate the following. (round all answers to two decimal places.)
Answers
The following values are calculated:
- Initial cost per share: $37.60
- Selling price per share: $44.00
- Commission paid during the purchase: $4700.00
- Commission paid during the sale: $5500.00
How to calculate the requested values?To calculate the requested values, we need to consider the initial cost of purchasing the shares, the total cost including commission, the selling price, and the selling price after commission. Let's perform the calculations:
1. Initial cost per share:
Initial cost = Total cost / Number of shares
Initial cost = $4700 / 125 shares
Initial cost = $37.60
2. Selling price per share:
Selling price = Total selling price / Number of shares
Selling price = $5500 / 125 shares
Selling price = $44.00
3. Commission paid during the purchase:
Commission paid = Initial cost per share * Number of shares
Commission paid = $37.60 * 125 shares
Commission paid = $4700.00
4. Commission paid during the sale:
Commission paid = Selling price per share * Number of shares
Commission paid = $44.00 * 125 shares
Commission paid = $5500.00
Therefore, the following values are calculated:
- Initial cost per share: $37.60
- Selling price per share: $44.00
- Commission paid during the purchase: $4700.00
- Commission paid during the sale: $5500.00
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Three experts gave opinions on how long a task will take to finish. The estimates were 29, 10, and 12 days (in no particular order). What is PERT estimate - ROUNDED
Answers
Answer:
15
Step-by-step explanation:
PERT estimate is a measuring strategy that is based on a weighted average. It is used in measuring the uncertainty and risk via three estimates to determine an estimated likelihood for a project's cost or period of completion.
The formula is (O + 4M + P) ÷ 6
Where P is the most pessimistic = 29
M is the most likely = 12
O is the most optimistic = 10
Hence we have (10 + [4*12]+ 29) ÷ 6
= (10 + 48 + 29) ÷ 6
= 87÷6 = 14.5 ≈ 15
Rounded figure is equal to 15.
Hence the final answer to the question is 15
Which fraction is equivalent to 1/3?
1/3 1/3 1/3
A. 3/6
B. 2/6
C. 1/6
D.4/6
Answers
Answer: B. 2/6
* Hopefully this helps:) Mark me the brainliest!!
all of the follwoing are incorrectly simplified explain whats wrong amd simplify the expression correctlya. (3x^4)^2 = 6x^8b. 4x^0 = 0c. 5x^2 = 1/5x^2d. 8x/4x^-1 = 2
Answers
a. The expression (3x^4)^2 is incorrectly simplified because the exponent 2 must be distributed to both the 3 and the x^4. This means that the expression should be simplified as follows: (3x^4)^2 = 3^2 * (x^4)^2 = 9x^8
b. The expression 4x^0 = 0 is incorrectly simplified because any number raised to the power of 0 equals 1.
This means that the expression should be simplified as follows:
4x^0 = 4 * 1 = 4
c. The expression 5x^2 = 1/5x^2 is incorrectly simplified because the right side of the equation is the reciprocal of 5x^2.
This means that the expression should be simplified as follows:
5x^2 ≠ 1/5x^2
d. The expression 8x/4x^-1 = 2 is incorrectly simplified because the denominator 4x^-1 can be simplified as 4/x, which means that the expression should be simplified as follows:
8x/(4x^-1) = 8x * (4/x) = 32
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Consider the following non-linear equation: i. ii. iii. iv. 6e(-x)+ 5x² - 10x = 0 Let g(x) = e(-x)+²2 Show that x is the root of the given equation if and only if x is the midpoint of function g. Prove that the sucession X(n+1) = g(xn), n = 0,1, ... Converges to the only root of the function g at the interval I := xo E I. Calculate the iterations X1 and x2 obtained by the fixed point method given in ii, assuming xo = 1. Calculate the number of iterations that allow the absolute aproximation error less than 10 (-6). I it is not necessary to calculate the iterations. = [0,1], inspite of
Answers
Since \(e^{(-x/2)}\) is always positive, for g(x) - g(x/2) to be zero, (5x² - 10x) must also be zero. Therefore, x is the midpoint of g(x)
To show that x is the root of the given equation if and only if x is the midpoint of the function g, we need to prove two statements:
1) If x is the root of the equation, then x is the midpoint of g(x):
Assume x is the root of the equation 6e⁻ˣ + 5x² - 10x = 0. We need to show that x is the midpoint of g(x) = e⁻ˣ + 2.
Let's calculate the midpoint of g(x) by evaluating g(x) at x and x/2:
g(x) = e⁻ˣ + 2
g(x/2) = \(e^{(-x/2)}\) + 2
To show that x is the midpoint, we need to prove that g(x) - g(x/2) = 0:
g(x) - g(x/2) = (\(e^{(-x/2)}\) + 2) - (\(e^{(-x/2)}\) + 2)
= e⁻ˣ - \(e^{(-x/2)}\)
If we substitute x as the root of the equation, then \(e^{(-x/2)}\) = 5x² - 10x.
So, g(x) - g(x/2) = (5x² - 10x) - \(e^{(-x/2)}\)
Since \(e^{(-x/2)}\) is always positive, for g(x) - g(x/2) to be zero, (5x² - 10x) must also be zero. Therefore, x is the midpoint of g(x).
2) If x is the midpoint of g(x), then x is the root of the equation:
Assume x is the midpoint of g(x) = \(e^{(-x/2)}\) + 2. We need to show that x satisfies the equation 6\(e^{(-x/2)}\)+ 5x² - 10x = 0.
Substitute g(x) = e^(-x) + 2 into the equation:
6e⁻ˣ+ 5x² - 10x = 0
6(g(x) - 2) + 5x² - 10x = 0
6e⁻ˣ + 5x² - 10x - 12 = 0
Since x is the midpoint of g(x), g(x) - 2 = 0, which simplifies the equation to:
6e⁻ˣ + 5x² - 10x - 12 = 0
Therefore, x is the root of the equation.
For the second part of the question, to prove that the sequence X(n+1) = g(Xn) converges to the only root of the function g within the interval I = [0, 1], we need to show two things:
1) The sequence is well-defined and stays within the interval I:
For any initial value x0 within the interval [0, 1], the subsequent values Xn = g(Xn-1) will also remain within the interval [0, 1]. This can be proven by showing that g(x) maps the interval [0, 1] to itself.
2) The sequence converges to the root of g:
We need to show that as n approaches infinity, Xn converges to the root of g within the interval I.
To calculate the iterations X1 and X2 using the fixed-point method, we start with an initial value x0 = 1:
X1 = g(X0) = g(1) = e⁻¹ + 2
X2 = g(X1)
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an arithmetic sequence with first term $1$ has a common difference of $6$. a second sequence begins with $4$ and has a common difference of $7$. in the range of $1$ to $100$, what is the largest number common to both sequences?
Answers
The largest number common to both sequences is 67.
The arithmetic sequence with first term 1 has a common difference of 6 is given by:-
1,7,13,19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, and 97
The arithmetic sequence with first term 4 has a common difference of 7 is given by:-
4,11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, and 95.
I have written the sequence until 100 only.
Hence, the numbers common to both the arithmetic sequences are :-
25 and 67
Hence, the largest number common to both sequences is 67.
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Simplify The Expression 12g + 3 - g^2 + 2 g=4
Answers
Given:
\(12g+3-g^2+2\)Where, g = 4
To simplify the expression, substitute g for 4 and evaluate.
We have:
\(\begin{gathered} 12g+3-g^2+2 \\ \\ 12(4)+3-4^2+2 \\ \\ 48+3-16+2 \\ \\ 51-16+2 \\ \\ =37 \end{gathered}\)ANSWER:
37
Is -4.8 a rational number
Answers
Answer:
Yes
Step-by-step explanation:
A number that can be made by dividing two integers (an integer is a number with no fractional part). The word comes from "ratio". Examples: • 1/2 is a rational number (1 divided by 2, or the ratio of 1 to 2)
-4.8 can be written as a fraction
Hope this helps!
-Jerc
Answer:
Yes!
Step-by-step explanation:
Rational numbers are any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions.
-4.8 is a terminating decimal, and thus, is a rational number!
Hope this helped you! If you liked my answer, please rate it and a Thanks would be nice, too!
Have a wonderful day!
Using a calculator or otherwise, calculate the exact value of 498.79×14.38. Round your answer to one (1) decimal place.
Answers
Answer:
7172.6
Step-by-step explanation:
The table below shows all of the possible outcomes for rolling two six-sided number cubes. A table with 36 possible outcomes. There are 9 desired outcomes. What is the probability of rolling an even number first and an odd number second? StartFraction 1 over 9 EndFraction StartFraction 1 over 6 EndFraction One-fourth One-half Mark this and return Save and Exit
Answers
The probability of rolling an even number first and an odd number second is; One Fourth
How to find the probability of rolling a number?As two cubes are 6 sided, the total number of possibilities as seen in the attached table are;
6 * 6 = 36 possible numbers
Now in those possibilities, the first number will be even and the second number will be odd. From the the table, such possible pairs are,
(2,1), (2,3), (2,5), (4,1), (4,3), (4,5), (6,1), (6,3), (6,5)
Therefore, we can see we have a total of 9 sets with the combination of first number even and second number odd. So, the probability of rolling with this combination will be; 9/36 = 1/4
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Can the sides of a triangle have lengths 2, 8, and 9?
yes
no
Answers
Answer:
No
Step-by-step explanation:
The sum of any two sides in a triangle have to be greater than the length of the third side.
2 + 8 > 9. 10 > 9 (true)2 + 9 > 8. 11 > 8. (true)8 + 9 > 2. 17 > 2. (false)Therefore, the answer is no.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
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the degenerative disease osteoarthritis most frequently affects weight-bearing joints such as the knee. an article presented the following summary data on stance duration (ms) for samples of both older and younger adults. age n sample mean sample sd older 28 801 117 younger 16 780 72 assume that both stance duration distributions are normal. a) calculate and interpret a 99% confidence interval (ci) for true average stance duration among elderly individuals. b) carry out a test of hypotheses to decide whether true average stance duration is larger among elderly individuals than among younger individuals. c) construct a 95% ci for the difference in means and compare results to part(b).
Answers
We are 99% confident that the true average stance duration among elderly individuals lies within the range of 744.56 ms to 857.44 ms.
To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test. The null hypothesis (H0)
Using the t-test, we compare the means and standard deviations of the two samples and calculate the test statistic
a) To calculate a 99% confidence interval for the true average stance duration among elderly individuals, we can use the sample mean, sample standard deviation, and the t-distribution.
Given:
Older adults: n = 28, sample mean = 801, sample standard deviation = 117
Using the formula for a confidence interval for the mean, we have:
Margin of error = t * (sample standard deviation / √n)
Since the sample size is relatively large (n > 30), we can use the z-score instead of the t-score for a 99% confidence interval. The critical z-value for a 99% confidence level is approximately 2.576.
Calculating the margin of error:
Margin of error = 2.576 * (117 / √28) ≈ 56.44
The confidence interval is then calculated as:
Confidence interval = (sample mean - margin of error, sample mean + margin of error)
Confidence interval = (801 - 56.44, 801 + 56.44) ≈ (744.56, 857.44)
b) To test whether the true average stance duration is larger among elderly individuals than among younger individuals, we can perform a one-tailed independent samples t-test.
The null hypothesis (H0): The true average stance duration among elderly individuals is equal to or less than the true average stance duration among younger individuals.
The alternative hypothesis (Ha): The true average stance duration among elderly individuals is larger than the true average stance duration among younger individuals.
. With the given data, perform the t-test and obtain the p-value.
c) To construct a 95% confidence interval for the difference in means between older and younger adults, we can use the formula for the confidence interval of the difference in means.
Given:
Older adults: n1 = 28, sample mean1 = 801, sample standard deviation1 = 117
Younger adults: n2 = 16, sample mean2 = 780, sample standard deviation2 = 72
Calculating the standard error of the difference in means:
Standard error = √((s1^2 / n1) + (s2^2 / n2))
Standard error = √((117^2 / 28) + (72^2 / 16)) ≈ 33.89
Using the t-distribution and a 95% confidence level, the critical t-value (with degrees of freedom = n1 + n2 - 2) is approximately 2.048.
Calculating the margin of error:
Margin of error = t * standard error
Margin of error = 2.048 * 33.89 ≈ 69.29
The confidence interval is then calculated as:
Confidence interval = (mean1 - mean2 - margin of error, mean1 - mean2 + margin of error)
Confidence interval = (801 - 780 - 69.29, 801 - 780 + 69.29) ≈ (-48.29, 38.29)
Comparison with part (b): In part (b), we performed a one-tailed test to determine if the true average stance duration among elderly individuals is larger than among younger individuals. In part (c), the 95% confidence interval for the difference in means (-48.29, 38.29) includes zero. This suggests that we do not have sufficient evidence to conclude that the true average stance duration is significantly larger among elderly individuals compared to younger individuals at the 95% confidence level.
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can someone explain how to calculate a unit rate
Answers
Answer:
It's like 60 miles per (1) hour or 20 mL per (1) second. Independent value has to equal 1.
I need help with this ASAP!
Answers
Lightning:7,6
Circle : 10,6
Heart:3,10
Cross:7,8
Triangle:1,4
Moon:10,8
Square:3,0
Diamond:5,0
Music note: 7,6
Answer:
0,10
9,7
10,6
3,10
7,8
1,4
10,8
0,3
0,5
7,6
Step-by-step explanation:
ughhhh 5x+6 x=3
im over this
Answers
Explanation:
5x3=15
15+6=21
9. Which unit of measure would be appropriate for the volume of a cube with sides of 2 meters.
Answers
Answer:
The unit of measure appropriate is cubic metre or cubic meter (m³)
Step-by-step Explanation:
we know that
The volume of a cube is equal to
V = b^3
where b is the length side of the cube
In this problem we have
b = 2m
substitute in the formula of volume
V = 2^3
V = 8 m^3
therefore
The unit of measure appropriate is cubic metre (m³)
What happens if you try to use l' Hospital's Rule to find the limit? lim_x rightarrow infinity x/Squareroot x^2 + 3 You cannot apply l' Hospital's Rule because the function is not continuous. You cannot apply l'Hospital's Rule because the denominator equals zero for some value x = a. You cannot apply l'Hospital's Rule because the numerator equals zero for some value x = a You cannot apply l'Hospital's Rule because the function is not differentiable. Repeated applications of l'Hospital's Rule result in the original limit or the limit of the reciprocal of the function Evaluate the limit using another method.
Answers
The limit lim(x→∞) x/√(x^2 + 3) is 1, and there is no need to apply L'Hospital's Rule in this case.
When trying to use L'Hospital's Rule to find the limit lim(x→∞) x/√(x^2 + 3), it is important to note that L'Hospital's Rule can only be applied if the function is continuous and differentiable. In this case, the function is continuous and differentiable, but applying L'Hospital's Rule is not necessary as the limit can be evaluated using another method.
First, let's rewrite the given function by dividing both the numerator and the denominator by x:
lim(x→∞) (x/x) / (√(x^2 + 3)/x) = lim(x→∞) 1 / √(1 + 3/x^2)
As x approaches infinity, the term 3/x^2 approaches 0, so the limit becomes:
lim(x→∞) 1 / √(1 + 0) = 1 / √(1) = 1
Therefore, the limit lim(x→∞) x/√(x^2 + 3) is 1, and there is no need to apply L'Hospital's Rule in this case.
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in the summer of 1969, which two american astronauts reached the moon? how many people watched the great event on television? quizlet
Answers
Answer:
Neil Armstrong and Buzz Aldrin
Step-by-step explanation:
Fifty years after Neil Armstrong, Buzz Aldrin and Michael Collins became etched in history, the Apollo 11 mission remains an iconic moment in broadcasting. It's estimated that between 600-650 million people tuned in around the world to Armstrong and Aldrin's broadcast from the lunar surface on July 20, 1969.
A rectangle has an area of 32 square millimeters. the length of the rectangle is 8 millimeters. what is the width of the rectangle?
Answers
If a rectangle has an area of 32 square millimeters and the length of the rectangle is 8 millimeters, then the width of the rectangle is 4 millimeters.
To find the width of a rectangle, follow these steps:
The formula to find the area of a rectangle is as follows: Area = length x width. Substituting the values of length= 8mm and area= 32mm² in the formula, we get width= Area/ length= 32/8= 4mm.Therefore, the width of the rectangle is 4mm.
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1) Janet and Miriam each bought a bicycle for $140.
A few months later they both sold it...
Janet sold hers for 30% less than the original price (what she paid for it)
Miriam sold hers for 25% less than the original price (what she paid for
it)
How much more money did Miriam get than Janet?
Answers
Answer:
$7
Step-by-step explanation:
JANET:
140 * 0.7 = 98
MIRIAM:
140 * 0.75 = 105
105-98=7
100 points if someone gets it right
A rectangluar prism has volume of 2,610 cubic inches, length 3 inches, and width 29 inches . Find its height, in inches
Answers
Step-by-step explanation:
To find the height of the rectangular prism, you will need to use the formula for the volume of a rectangular prism, which is:
Volume = Length × Width × Height
In this problem, you have:
Volume = 2,610 cubic inches
Length = 3 inches
Width = 29 inches
You'll need to solve for Height. Using the formula:
2,610 = 3 × 29 × Height
First, multiply the length and width together:
2,610 = 87 × Height
Next, divide both sides by 87 to isolate Height:
Height = 2,610 / 87
Height = 30 inches
So, the height of the rectangular prism is 30 inches.
Answer:
30 inches.
Step-by-step explanation:
Given:
Volume=2610 cubic inches,
length=3 inches
width=29inches
Volume of a rectangular prism is given by.
Volume = length * width * height
We know the volume, length and width. So, we can find the height as follows:
Substituting value
2610=3*29*height
2610=87*height
height=2610/87
height=20 inches
Therefore, the height of the rectangular prism is 30 inches.
Help me I don’t understand
Answers
Answer:
C (8,6) A (2,14)
Step-by-step explanation:
(2+m)/2 = 5
2(2+m)/2 = 5 x 2
2+m = 10
m = 10 - 2
m = 8
(-6+n)/2 = 0
2(-6+n)/2 = 2 x 0
-6 + n = 0
n = 6
(-8+x)/2 = -3
2(-8+x)/2 = -3 * 2
-8 + x = -6
x = -6 + 8
x = 2
(-2+y)/2 = 6
2(-2+y)/2 = 6 * 2
-2 + y = 12
y = 12 + 2
y = 14