Answer:
542.74 m
Step-by-step explanation:
Tan(48.3) = 250/a Multiply by a
a*tan(48.3) = 250 Divide by tan(48.3)
a = 250/Tan(48.3)
a =222.74
By a similar method b = 250/tan(38)
b = 319.99'
The total length =542.73 meters
The hypotenuse of a right triangle is two more than the length of one of its legs. Find the side lengths of the right triangle given the perimeter= 60 and it's area= 120
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Answer:
10 and 24
Step-by-step explanation:
We know that some of the Pythagorean triples that appear in math problems are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17).
These have (perimeter, area) values of (12, 6), (30, 30), (56, 84), (40, 60).
For some scale factor n, we want (p·n, a·n²) = (60, 120). Of the triangles listed, we see that the (5, 12, 13) triangle scaled by n=2 will satisfy the problem requirements. (30·2, 30·2²) = (60, 120)
The side lengths are 10 and 24.
__
Check
For the side lengths we found, the perimeter is 10+24+26 = 60; the area is 1/2(10)(24) = 120. The hypotenuse is 2×13 = 26 = 24+2.
__
In the attached, one side is x, the other is y. The hypotenuse is (x+2). The square root equation comes from ...
x² +y² = (x+2)² ⇒ y² = (x² +4x +4) -x² ⇒ y² = 4x +4 = 4(x +1)
_____
Additional comment
The graph shows the solution of the various constraints. At least, the combination of constraints will give a quadratic equation in x. They can be combined in a way that gives a cubic equation in x. Either way, we prefer the graphical or "guess and check" approach (above) as being easier to do.
Using the third equation in the attachment to write an expression for y, we have ...
y = 58 -2x
Substituting that into the second equation gives ...
(x(58 -2x)/2 = 120
29x -x² = 120
x² -29x +120 = 0
(x -5)(x -24) = 0 . . . . x = 5 or 24.
The root x=5 is a legitimate solution to the pair of equations we chose to solve. The line y=58-2x intersects the hyperbola xy/2 = 120 in two places. However, (x, y) = (5, 48) does not satisfy the hypotenuse requirement that x+2 > y.
I want to know how to solve this equation
Answer:
one property of log is that if the log expressions have the same base (in this case, 2), then you can multiply the added logs.
The answer would then be D
which decimal is equivalent to 6×100+7×10+4×1/10+8×1/1,000
The answer is 670.408, because 6x100=600, 7x10=70, 4x1/10 as a decimal is 0.4, 8x1/1,000 as a decimal is 0.008. Then, you add all of those [tex]600+70+0.4+0.008=670.408[/tex].
I really need help with this one
Write the ratio 4 L : 5.6 L as a fraction in the simplest form with whole numbers in the numerator and denominator
Answer:
Step-by-step explanation:
It's 5/7
You get that by having a calculator that does that. If you don't then the way to do it is multiply the numerator and denominator by 1.25
4 * 1.25 = 5
5.6 * 1.25 = 7
Find x (round to the nearest tenth)
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Answer:
x = 8
Step-by-step explanation:
By AA similarity, ΔABD ~ ΔCDE. So, corresponding sides are proportional.
AB/BD = CD/DE
x/12 = 4/6
x = 12(4/6)
x = 8
Test scores are normally distributed with a mean of 68 and a standard deviation of 12. Find the z – score for a grade of 74. Round your answer to two numbers after the decimal.
Answer:
gang nem
Step-by-step explanation:
Find f(2) given f(x) = -3x^2 + 2x+11
Answer:
Answer:f(2)=-3(2)^2+2*2+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11 =3
hence, f(2)=3
How many roots does the equation (8/(x^2 - 16) )+ 1 = 1/(x -4) have?
Plz show ALL STEPS
Answer:
Step-by-step explanation:
Use the diagram to answer the question below.
Name a point not on line AC
Answer:
It can be the point E or the point D
Your help is very much appreciated I will mark brainliest:)
Answer:
B. Yes. By SSS~
Step-by-step explanation:
From the diagram given, we have the corresponding sides of both triangles as follows:
RQ/KL = 24/20 = 6/5
QP/LM = 18/15 = 6/5
RP/KM = 12/10 = 6/5
From the above, we can see that the ratio of the corresponding side lengths of both triangles are equal. This means that all three sides of one triangle are proportional to all corresponding sides of the other triangle.
The SSS similarity theorem states that if all sides of one triangle are proportional to all corresponding sides of another, then both triangles are similar to each other.
Therefore, ∆KLM ~ ∆RQP by SSS similarity.
ANSWER PLS!! :DD
Which of the following is not a property of a regular pyramid?
A. lateral faces that are parallel
B. lateral faces that are congruent isosceles triangles
C. lateral edges that are congruent
D. volume of the pyramid is equal to one-third the product of the area of its base and its altitude
Answer:
a
Step-by-step explanation:
Lateral faces that are parallel is not a property of a regular pyramid. The correct option is A.
What is a regular pyramid?Any pyramid whose base is a regular polygon and whose lateral edges are all of the same lengths is said to be regular.
The properties of a regular pyramid are:-
Lateral faces that are congruent isosceles triangles. Lateral edges that are congruent and the volume of the pyramid is equal to one-third the product of the area of its base and its altitude.
Hence, option A is correct.
To know more about the regular pyramid follow
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What effect will replacing x with (x−4) have on the graph of the equation y=(x−3)2 y = ( x − 3 ) 2 ?
Answer:
y"= 2 wich is positive
Step-by-step explanation:
Step-by-step explanation:
Our equation is: y=(x-3)²
x should be replaced by x-4
y=(x-3)²
y=[(x-4)-3]²
y=(x-4-3)²
y=(x-7)²
The graph is still a parabola but with a different vertex
The vertex here is :
y= (x-7)²
y= x²-14x-49
y'= 2x-14
solve y'=0
2x-14=0
2x=14
x=7
You can easily find it without derivating by dividing -14 by -2
since: x²-14x-49
a=1 b= -14 c=-49
-b/2a = 14/2 = 7
the image of 7 is:
y=(7-7)² = 0
so the coordinates of the new vertex are (7,0) and it's a maximum
since y">0
y'= 2x-14
y"= 2 wich is positive
write each of the following fraction as equivalent fractions with a denominator of 10 a. 1/2 b. 1/4 c. 3/30 d. 12/30
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Answer:
a. 5/10
b. 2.5/10
c. 1/10
d. 4/10
Step-by-step explanation:
To find the numerator, multiply each fraction by 10.
a. (1/2)(10) = 5, so 1/2 = 5/10
b. (1/4)(10) = 2.5, so 1/4 = (2.5)/10 or (5/2)/10
c. (3/30)(10) = 1, so 3/30 = 1/10
d. (12/30)(10) = 4, so 12/30 = 4/10
Which fraction is greater than the fraction represented by the model?
HURRY PLS IM BEING TIMED!!!!
Answer:
7/16
Step-by-step explanation:
7/16>3/8
It would be 7/16 because 3/8 is what is being shown. If you make them both have a common denominator then it would be 6/16.
1. You are given the 3rd and 5th term of an arithmetic sequence. Describe in words how to determine the general term.
2. You are given the 3rd and 5th term of an geometric sequence. Describe how to determine the 10th term without finding the general term.
Step-by-step explanation:
1. In an arithmetic sequence, the general term can be written as
xₙ = y + d(a-1), where xₐ represents the ath term, y is the first value, and d is the common difference.
Given the third term and the fifth term, and knowing that the difference between each term is d, we can say that the 4th term is x₃+d and the fifth term is the fourth term plus d, or (x₃+d)+d =
x₃+2d. =x₅ Given x₃ and x₅, we can subtract x₃ from both sides to get
x₅-x₃ = 2d
divide by 2 to isolate d
(x₅-x₃)/2 = d
This lets us solve for d. Given d, we can say that
x₃ = y+d(2)
subtract 2*d from both sides to isolate the y
x₃ -2*d = y
Therefore, because we know x₃ and d at this point, we can solve for y, letting us plug y and d into our original equation of
xₙ = y + d(a-1)
2.
Given the third and fifth term, with a common ratio of r, we can say that the fourth term is x₃ * r. Then, the fifth term is
x₃* r * r
= x₃*r² = x₅
divide both sides by x₃ to isolate the r²
x₅/x₃ = r²
square root both sides
√(x₅/x₃) = ±r
One thing that is important to note is that we don't know whether r is positive or negative. For example, if x₃ = 4 and x₅ = 16, regardless of whether r is equal to 2 or -2, 4*r² = 16. I will be assuming that r is positive for this question.
Given the common ratio, we can find x₆ as x₅ * r, x₇ as x₅*r², and all the way up to x₁₀ = x₅*r⁵. We don't know the general term, but can still find the tenth term of the sequence
the point a(2,-5) is reflected over the origin and its image is point b. what are the coordinates of point b
Answer:
b(-2,-5)
Step-by-step explanation:
If f(x)=-4x-5 and g(x)=3-x whats is g(-4)+f(1)
Answer: -2
Step-by-step explanation:
g(-4) = 3 - (-4) = 3 + 4 = 7f(1) = -4(1) - 5 = -4 - 5 = -9g(-4) + f(1) = 7 + (-9) = 7 - 9 = -2
Chris is buying new wood flooring for his house. The cost depends on the area of the floors.
Which is the dependent variable, and which is the independent variable?
Answer:
strong and fexible .
variable
look at the image below forr the question plz
Answer:
[tex]308 \ m^3\\[/tex]
Step-by-step explanation:
The volume of a three-dimensional shape is the amount of space the figure takes up. This can be found by multiplying all of the dimensions of a figure together. In essence, the following formula can be used to find the volume.
[tex]A=l*w*h[/tex]
Where (l) represents the figure's length; (w) is the width: and (h) the height. Substitute the given values into the formula and solve for the volume.
[tex]A=l*w*h[/tex]
[tex]A=7*4*11[/tex]
Simplify,
[tex]A=7*4*11[/tex]
[tex]A=28*11[/tex]
[tex]A=308[/tex]
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 421 gram setting. It is believed that the machine is underfilling the bags. A 43 bag sample had a mean of 414 grams. Assume the population standard deviation is known to be 19.
Required:
a. Is there sufficient evidence at the 0.1 level that the bags are underfilled?
b. Find the P-value of the test statistic.
Answer:
a) The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.
b) 0.0078.
Step-by-step explanation:
Question a:
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 421 gram setting.
At the null hypothesis, it is tested if the mean is of 421, that is:
[tex]H_0: \mu = 421[/tex]
It is believed that the machine is underfilling the bags.
At the alternative hypothesis, it is tested if the mean is of less than 421, that is:
[tex]H_a: \mu < 421[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
421 is tested at the null hypothesis:
This means that [tex]\mu = 421[/tex]
A 43 bag sample had a mean of 414 grams. Assume the population standard deviation is known to be 19.
This means that [tex]n = 43, X = 414, \sigma = 19[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{414 - 421}{\frac{19}{\sqrt{43}}}[/tex]
[tex]z = -2.42[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean below 414, which is the p-value of z = -2.42.
Looking at the z-table, z = -2.42 has a p-value of 0.0078.
The p-value of the test is 0.0078 < 0.1, which means that there is sufficient evidence at the 0.1 level that the bags are underfilled.
b. Find the P-value of the test statistic.
As found above, the p-value of the test statistic is 0.0078.
Find two consecutive even numbers whose sum is 758.
Answer:
378 and 380
Step-by-step explanation:
The two even consecutive numbers that add up to 758 are going to be very close to half of 758. This is because two half of 758 are going to be the most similar addends of 758. This is important because the answers will be consecutive and therefore, must also be very similar. To solve, first, divide 758 by 2. This is 379, which is not an even number. So, to find the needed addends subtract and add 1 to 379. Both of these will be even and consecutive. These two numbers are 378 and 380. Then, to check you, can add them and see that they do sum 758.
Answer:
Step-by-step explanation:
Let the first number = x
Let the second number = x + 2
x + x + 2 = 758 Collect like terms
2x + 2 = 758 Subtract 2
2x = 758 - 2 Combine
2x = 756 Divide by 2
2x/2 = 756/2
x = 378
The first number is 378
The second number 380
If your teacher is really fussy, you can do it this way.
Let the first number = 2x
Let the second number = 2x + 2
The reason for this is to guarantee that both numbers were even to start with.
2x + 2x+2 = 758 Combine like terms
4x + 2 = 758 Subtract 2
4x = 756 Divide by 4
x = 756/4
x = 189
Therefore 2x = 378
2x + 2 = 380 Just as before.
I need help guys thanks so much
Answer:
A. 243
Step-by-step explanation:
[tex] 81^\frac{5}{4} = (3^4)^\frac{5}{4} = 3^{4 \times \frac{5}{4}} = 3^5 = 243 [/tex]
Answer: A
I just simplified it to 3^5, and that is also 243.
Last question guys! Help help help
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Answer:
slope 125, annual dues paymentStep-by-step explanation:
The two given points can be used to find the slope:
m = (y2 -y1)/(x2 -x1)
m = (650 -400)/(4 -2) = 250/2 = 125
The vertical axis is cost, and the horizontal axis is years, so the slope is the ratio of these: cost per year.
The slope of $125 per year is the yearly membership dues cost.
The graph of [tex]y = ax^2 + bx + c[/tex] is a parabola. The axis of symmetry is [tex]x = -b/2a[/tex]. What are the coordinates of the vertex?
The vertex can be written as:
(-b/2a, b^2/(4*a) - b^2/2a + c)
For a general parabola:
y = a*x^2 + b*x + c
We can write the vertex as:
(h, k)
The x-value of the vertex is the value of the axis of symmetry.
Then we have:
h = x = -b/2a
Now we need to find the y-value of the vertex.
To do that, we just replace the variable "x" by the x-value of the vertex in our equation, so we get:
k = y = a*(-b/2a)^2 + b*(-b/2a) + c
k = b^2/(4*a) - b^2/2a + c
Then the coordinates of the vertex are:
(h, k) = (-b/2a, b^2/(4*a) - b^2/2a + c)
If you want to read more:
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the binomial quadratic expressions with their factored form.
Answer:
x²-36 and (x-6)(x+6)
9x-1 and(3x-1)(3x+1)
4x² -16 and 4(x-2)(x+2)
Step-by-step explanation:
when you multiply(x+6)(x-6)
you get x²-36,this is known as difference of two squares ie (a+b)(a-b)=(a²-b²)=0
x(x-6)+6(x-6)
x²-6x+6x-36
x² -36
the second the same explanation as the first
for the third, multiply (x+2)(x-2) it will give x²-4
then multiply this by 4 which is = 4x² - 16
14 80 tiles of side 30cm were used to cover a counter top. Calculate the area of the counter top in square metres.
Answer:
Step-by-step explanation:
1,480 is a lot of tiles. Did you mean 80 tiles?
30 cm = 0.3 m
Area of one tile = 0.3² m² = 0.09 m²
Multiply the number of tiles by 0.09 m².
Jared works at a clothing store and is listening to a customer complain about a shirt he purchased that's damaged. Which behavior can Jared exhibit to show good communication skills with the customer? O a) Stopping the customer to quickly explain the store's return policy b) Repeating back what he has heard once the customer is done speaking Od Asking the customer how the shirt was damaged O d) Promising the customer a full refund even though it's against policy
Answer:
C
Step-by-step explanation:
in my point of view, my choice is C (asking the customer how the shirt was damaged) because when he finds out the reason why the shirt was damaged, he will explain whether or not that fault is in the store's return policy
another reason:
A) stopping the customers when they are talking, it's impolite behavior and i ensure that that customer will feel disatified.
B) i guess that customer doesnt waste of time because it
D) a full refund without finding the reason, i dont think it's a good idea
A researcher conducts an ANOVA analysis and reports no differences in average certification exam test scores for nurses identified as Baby Boomers, Millennials or Generation X. You would expect to see:
Answer:
"Type II error" is the right answer.
Step-by-step explanation:
A type II mistake would be that a fake null hypothesis also isn't rejected. It's also called false negatives.It happens whenever an investigator does not eliminate a truly wrong null hypothesis. Here quite a scientist determines that whenever it genuinely exists, that there's no substantial consequence.Thus the above is the right answer.
In the past, Alpha Corporation has not performed incoming quality control inspections but has taken the word of its vendors. However, Alpha has been having some unsatisfactory experience recently with the quality of purchased items and wants to set up sampling plans for the receiving department to use. For a particular component, X, Alpha has a lot tolerance percentage defective of 52 percent. Zenon Corporation, from which Alpha purchases this component, has an acceptable quality level in its production facility of 20 percent for component X. Alpha has a consumer's risk of 10 percent and Zenon has a producer's risk of 5 percent. a. When a shipment of Product X is received from Zenon Corporation, what sample size should the receiving department test
Answer:
The answer is "28"
Step-by-step explanation:
[tex](LTPD) = 52\%\\\\(AQL) = 20\%\\\\\to \frac{LTPD}{AQL} = \frac{52\%}{20\%}= 2.6\\\\[/tex]
The value of [tex]\frac{LTPD}{AQL} = 2.6[/tex] that value of [tex]\frac{LTPD}{AQL} = 2.618[/tex]
Acceptance number, [tex]c = 9[/tex]
Value of [tex]n\times AQL = 5.426[/tex]
Sample size [tex]n = n\times \frac{AQL}{AQL} =\frac{5.426}{20\%} = 27.13=28[/tex]
