Answers
Answer:
Step-by-step explanation:
b = 21 is the base, a is the height
area = 0.5ab = 210
ab = 420
a = 420/b = 420/21 = 20 ft
length of hypotenuse = √(a²+b²) = √(20²+21²) = √841 = 29 ft
Related Questions
An advertiser claims that 74% of people stream their TV, 12% have cable, and the rest do not watch TV. A test is conducted to evaluate the claim and the conclusion is fail to reject
using alpha = 0.1. What is your interpretation of the test result?
Answers
Considering the hypothesis tested, the interpretation is that there is not enough evidence to conclude that the percentages are different at a significance level of 0.1.
What are the hypothesis tested?At the null hypothesis, we test if the percentages are as advertised.At the alternative hypothesis, we test if the percentages are different than advertised.We fail to reject the null hypothesis, hence the interpretation is that there is not enough evidence to conclude that the percentages are different at a significance level of 0.1.
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what is the measure of this
Answers
Answer:
60
Step-by-step explanation:
140-80=60
Asphalt roofing shingles are typically sold by the square, with a square covering 100 square feet. A contractor must shingle a roof that measures 65.5'x 35'. How many squares will be required to cover this roof?
Question content area bottom
Part 1
A 23
B 26
C 33
D 25
Answers
Step by step
First find the square feet you will be shingling
65.5 x 35 = 2292.5 sq feet
Now divide by the 100 sq feet in a “square” of shingles
2292.5 / 100 = 22.92 squares of shingles
Round up to a full square = 23
Problem solved
PLEASE NEED HELP
A machine at a food-distribution factory fills boxes of rice. The distribution of the weights of filled boxes of rice has an approximately Normal distribution, with a mean of 28.2 ounces and a standard deviation of 0.4 ounces. Boxes are often weighed before shipping, and any box with a weight of at most 27.5 ounces is considered underweight and is rejected for distribution. What percentage of filled boxes of rice are rejected for distribution?
Find the z-table here.
4.0%
24.2%
75.8%
96.0%
Answers
Answer:
D) 96%
Step-by-step explanation:
If you take 96% of 28.6 you get 27.6 so it fits
Write the recursive rule for the 5th term of the sequence: -7, -3, 1, 5, 9
Answers
Answer:
Step-by-step explanation:
Let [tex]x_{n}[/tex] represent the nth term in the sequence. Then [tex]x_{n-1}[/tex] represents the previous term
The first term, [tex]x_{1}[/tex] = -7
Each consecutive term is obtained by adding 4 to the previous term.
So the recursive relation is
[tex]\left \{ {{x_{1}= -7} \atop {x_{n}= x_{n-1} + 4}} \right.[/tex]
A role-playing game uses an 11-sided die that displays the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 What is the probability that someone throws the 11-sided die one time and rolls a number 9 or higher? Express your answer as a percentage rounded to one decimal place
Answers
Using it's concept, it is found that there is a 27.3% probability that someone throws the 11-sided die one time and rolls a number 9 or higher.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 11 numbers, 3 of which are 9 or higher, hence the probability is:
p = 3/11 = 0.273 = 27.3%.
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In the triangle below M, Z, and P are the midpoints of the sides. Name a segment that is parallel to the one given. Pay attention to the order of the points used in the given side.
Answers
Based on the triangle midsegment theorem, the midsegments and the sides they are parallel to are:
MP is parallel to XY
PZ is parallel to WX
MZ is parallel to WY
What is the Triangle Midsegment Theorem?The segment that connects the midpoints of two sides of a triangle is referred to as the midsegment of the triangle. All triangles possess three midsegments. According to the triangle midsegment theorem, the third side of the triangle that is directly opposite the midsegment is twice the size of the midsegment and it is parallel to it.
In the diagram showing triangle WXY with midpoints at points M, Z, and P, the midsegments are:
MP which is parallel to XY, also, MP = 1/2(XY)
PZ which is parallel to WX, also, PZ = 1/2(WX)
MZ which is parallel to WY. also, MZ = 1/2(WY)
Thus, the midsegments and the sides they are parallel to are:
MP is parallel to XY
PZ is parallel to WX
MZ is parallel to WY
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According to the Rational Root Theorem, which function has the same set of potential rational roots as the function g(x) = 3x5 – 2x4 + 9x3 – x2 + 12?
f(x) = 3x5 – 2x4 – 9x3 + x2 – 12
f(x) = 3x6 – 2x5 + 9x4 – x3 + 12x
f(x) = 12x5 – 2x4 + 9x3 – x2 + 3
f(x) = 12x5 – 8x4 + 36x3 – 4x2 + 48
Answers
Option A, The option that has the same potential roots according to the rational root theorem is 3x5 – 2x4 – 9x3 + x2 – 12.
How to solve for the rootsWe have p, this is the factors of the number 12.
The factors are ±(1, 2, 3, 4, 6, 12)
We have factors of q = 3
= ±(1, 3)
The rational roots are the roots that have the same factors that are contained in the question.
Hence the answer is A.
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Answer:
The Answer is A
Step-by-step explanation:
Did it on edge :)
12 ft
8 ft
8 ft
Find the area of the kite
Answers
The area of the kite exists 48 sq. ft.
How to estimate the area of kite?The area of a kite exists half the outcome of the lengths of its diagonals. The formula to define the area of a kite exists:
Area = ½ × p × q.
Given that a kite contain diagonals of lengths 12 ft and 8 ft.
We know that the area of a kite having diagonals of length 'p' units and 'q' units exists
Area of kite = ½ (p × q)
Here, p = 12 ft and q = 8 ft.
Area of kite = ½ (p × q)
= (12 × 8)/2
= 96/2 = 48
Therefore, the area of the kite will be 48 sq. ft.
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Find a polynomial function of degree 7 with -1 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 1 as a zero
of multiplicity 1.
Answers
The polynomial function is P(x) = x^3(x + 1)^3(x -1)
How to determine the polynomial function?The zeros of the polynomial and the multiplicities are given as:
-1 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, 1 as a zero of multiplicity 1The degree is given as
Degree = 7
The polynomial is represented as:
P(x) = (x - zero)^multiplicity
Using the above format, we have
P(x) = (x + 1)^3(x - 0)^3(x -1)
This gives
P(x) = x^3(x + 1)^3(x -1)
Hence, the polynomial function is P(x) = x^3(x + 1)^3(x -1)
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Mandy used the graph to write the equation of the line it represents. She took these steps. 1. y−intercept = (0, 2) 2. Slope = rise run = − 2 4 = − 1 2 3. Substituting values into y = mx + b y = x +
Answers
Based on the information given about the equation, y will be 0.5x + 2.
How to illustrate the equation?From the information given, it should be noted that the equation of the line it represents was given and the y intercept is = (0, 2).
The function to represent y will be:
y = mx + b
y = (1/2)x + 2
y = 0.5x + 2
In conclusion, y = 0.5x + 2.
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DATE PAGE No. Demand 10 a) A ratio of two number is equal to 3:8. If the smaller number is 12, find the greater number:
Answers
From ratio concept, the greater number number is 32 .
What is the greater number from concept of ratio ?A ratio exists as an ordered pair of numbers a and b, written a / b where b does not equivalent to 0. A proportion exists in an equation in which two ratios stand set equal to each other. For example, if there exists 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there exist 3 girls)
Let the greater number be x .
The ratio given is 3:8 .
Thus, by the concept of ratio -
⇒ 3/8 = 12/x
⇒ x = (8/3 * 12)
∴ x = 32
Therefore, from ratio concept, the greater number number is 32 .
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The figure shows two parallel lines PQ and ST cut by the transversals PT and QS:
Answers
Answer:
triangle PQR is similar to triangle TSR because the measure of angle 3 is congruent to the measure of angle 4 and the measure of angle one is congruent to the measure of angle 5
Step-by-step explanation:
angle 3 and angle 4 are congruent because they are vertical pairs.
Angles 1 and five are congruent because they are alternate interior angles
Lesson Review
Directions: Factor the following trinomials containing negative numbers. Follow the rules for operations with signed numbers to identify the correct binomial factors.
1. x2 + 6x - 7
2. x2 - 5x + 6
3. x2 - 6x - 7
4. x2 + 5x - 6
5. x2 + x - 12
6. x2 - 2x - 8
7. x2 - 4x - 5
8. x2 + 2x - 3
9. x2 - 16
10. x2 - x - 12
11. x2 -9x + 18
12. x2 -5x - 14
13. x2 - 7x + 10
14. x2 -11x + 24
15. x2 - x - 30
Answers
Factorization implies the obtaining of the common factors in an expression.
What is factorization?The term factorization implies the obtaining of the common factors in an expression.
The factors of the expressions are as follows;
1) (x−1)(x+7)
2) (x−2)(x−3)
3) (x+1)(x−7)
4) (x−1)(x+6)
5) (x−3)(x+4)
6) (x+2)(x−4)
7) (x+1)(x−5)
8) (x−1)(x+3)
9) (x+4)(x−4)
10) (x+3)(x−4)
11) (x−3)(x−6)
12) (x+2)(x−7)
13) (x−2)(x−5)
14) (x−3)(x−8)
15) (x+5)(x−6)
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In what statistical measurement would you be most interested when considering housing prices in a particular city?
Answers
Answer:
Median
Explanation:
Real estate prices are virtually usually biased to the right. If we estimate the price of a typical home in a city at $500,000. We would have no trouble locating properties for $2 million and $3 million, and perhaps even some $5 or $6 million residences. However, you won't find houses for under $1.5 million. Because of this, the mean value is pulled toward the high end more than the median value.
Which equation could possibly represent the graphed function?
Answers
Answer: A
Step-by-step explanation:
The polynomial has roots at [tex]x=-4, -2, 4[/tex].
So, the equation should have factors of [tex](x+4), (x-2), (x-4)[/tex].
This eliminates everything except for A.
write the whole number as an equivalent fraction with the given denominator.
3= 4
Answers
Answer: 12/4
Step-by-step explanation: whole number = 3. given denominator = 4. 4/4 = 1. 1 times 3 = 3. 4 plus 4 plus 4 = 12. therefore answer is 12/4
On a recent trip to the convenience store, you picked up 2 gallons of milk, 6 bottles of water, and 7 snack-size bags of chips. Your total bill (before tax) was $25.65. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.90 more than a bottle of water, how much does each item cost?
Answers
Answer:
The water costs $1.90, the chips are $.95 and the milk is $3.80.
Step-by-step explanation:
Let m = milk
Let w = water
Let c = chips
2m+6w+7c =25.65 w = 2c m = w + 1.90
For the first equation, substitute w for 2C and m for w + 1.90 to get:
2(w+1.90) +6(2c) + 7c = 25.65
2w+3.8+12c+7c=25.65
2w+19c = 21.85
Now substitute 2c for w:
2(2c)+19c =21.85
4c + 19c = 21.85
23c = 21.85
c = .95 Now that we know the cost of the chips we can use that to find the water and the milk for the original equations that we wrote at the top.
w = 2c
w=2(.95) = 1.90
m = w + 1.90 = 1.90+1.90 = 3.80
Craig decides to purchase a property that has been valued at $475,000. He has $80,000 available as a deposit and will require a mortgage for the remaining amount. The bank offers him a 25 year mortgage at 2% interest. Calculate the total interest he will pay over the life of the loan, assuming he makes monthly payments. Give your answer in dollars to the nearest ten dollars. Do not include commas or the dollar sign in your answer.
THE REAL ANSWER IS $107, 270
First, we note that Craig requires a mortgage on $475,000−$80,000=$395,000. To calculate the monthly repayments we must apply the formula for P0 and solve for d, that is,
P0=d(1−(1+rk)−Nk)(rk).
We have P0=$395,000,r=0.02,k=12,N=25, so substituting in the numbers into the formula gives
$395,000=d(1−(1+0.0212)−25⋅12)(0.0212),
that is,
$395,000=235.9301d⟹d=$1,674.22.
Therefore the total interest payable is
I=$1,674.22×25×12−$395,000=$107,266
which is $107,270 to the nearest $1
Answers
The total interest is $107,270
What is monthly payment formula?
The formula for monthly payment is:
[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]
We can find total interest as shown below:
Value of property = $475,000
Money available as a deposit = $80,000
P = 475,000-80,000
= 395000
t = 25 year
r = 2% = 0.02
n = 25*12 = 300
[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]
Putting the value of P, t, r, and n in the above formula
[tex]=\frac{395000(\frac{0.02}{12} )(1+\frac{0.02}{12}) }{(1+\frac{0.02}{12})^{300}-1}[/tex]
after solving the above expression
M = $1674.22
Interest = M*n-P
Putting the value of P, n and M
= 1674.22*300-395000
= 502266-395000
= 107,266
Rounding to nearest ten dollar
= $107,270
Hence, the total interest is $107,270.
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Answer:
Step-by-step explanation:
How do u solve for X?
Answers
Answer:
x = 70
Step-by-step explanation:
x and 2x - 30 are supplementary angles , sum to 180° , then
x + 2x - 30 = 180 ( add 30 to both sides )
3x = 210 ( divide both sides by 3 )
x = 70
Answer:
2x - 30 and x degrees should add up to 180 degrees
2x - 30 + x = 180
3x = 210
x = 70 degrees
The correct answer would be D
Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.
What is the value of y?
3 StartRoot 3 EndRoot units
6 StartRoot 3 EndRoot units
9 StartRoot 3 EndRoot units
12 StartRoot 3 EndRoot units
Answers
The value of y in the triangle is B. 6✓3.
How to calculate the value?From the information given,
NU = 9
UM = 3
MN = 3 + 9 = 12
NT² = 9 × 12 = 108
NT = ✓108
NT = 6✓3
Therefore, y is 6✓3.
The value of y in the triangle is 6✓3.
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Answer:
B
Step-by-step explanation:
Please answer fast!
Ted practices two types of swimming styles for a total of 50 minutes every day. He practices the breaststroke for 20 minutes longer than he practices the butterfly stroke.
Write a pair of linear equations to show the relationship between the number of minutes Ted practices the butterfly stroke every day (x) and the number of minutes he practices the breaststroke every day (y). (5 points)
Answers
Answer:
x = 15 & y = 35
Step-by-step explanation:
[tex]y = x + 20[/tex]
[tex]x + y = 50 \\ x + (x + 20) = 50 \\ 2x + 20 = 50 \\ 2x = 50 - 20 \\ 2x = 30 \\ x = \frac{30}{2} = 15[/tex]
[tex]y = x + 20 = (15) + 20 = 35[/tex]
The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 57.5% of their carbon-14. How old were the bones at the time they were discovered?
Answers
Therefore, the bones were 6612.5 years old at the time they were discovered.
Half lifeGiven that the radioactive element carbon-14 has a half-life of 5750 years, and a scientist determined that the bones from a mastodon had lost 57.5% of their carbon-14, to determine how old were the bones at the time they were discovered, the following calculation must be made:
50 = 5750100 = 1150057.5 = X57.5 x 11500 / 100 = X6612.5 = XTherefore, the bones were 6612.5 years old at the time they were discovered.
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Answer:Therefore, the bones were 6612.5 years old at the time they were discovered.
Step-by-step explanation:
I need some help please
Answers
The values of x and y that can represent the equation is illustrated.
How to illustrate the information?The equation given us 32 = xy + 16
The table will be:
x. y
4. 4
16. 1
2. 8
32. 0.5
For example, when x and y are 4. This will be:
= xy + 16
= (4 × 4) + 16
= 32
Other values of x and y will also give 32.
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Ivy is running errands for her mother. She bikes along straight paths to the supermarket, the bank, and then back home.Find the distance between Ivy's house and the supermarket and the distance between the supermarket and the bank. Each distance is rounded to the nearest meter.
Answers
The distance between Ivy's house and the supermarket and the distance between the supermarket and the bank:
H&S = 1,014 M; and S&B = 854m. This is resolved using the Sine Theorem.
Notice that the Angles of a Triangle add up to 180° That is
∠A + ∠B + ∠C = 180°
Thus,
∠C = 180° - 32° - 109°
= 39°
Recall the Sine Theorem which indicates;
a/SinA = b/SinB = c/SinC
thus given that
AC = 1,523m
We have
AC/SinB = BC/SinA
BC = AC/SinB * SinA
= 1523/Sin109° * Sin32°
BC =854m
Therefore
AC/SinB = AB/SinC
Thus,
AB = AC/SinB * SinC
= 1523/Sin109° * Sin39°
AB ≈ 1,014m
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which quantity is scalary
Answers
Step-by-step explanation:
find the greatest number which divides 225 and 1029 leaving remainder of 5 in each case
Rewrite as an exponential equation.
In 5 = y
Answers
The equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]
How to rewrite the expression?The natural logarithm equation is given as:
ln 5 = y
Rewrite as:
ln(5) = y
Take the exponent of both sides
[tex]e^{ln(5)} = e^y[/tex]
Evaluate the expression
[tex]5 = e^y[/tex]
Rewrite as:
[tex]e^y = 5[/tex]
Hence, the equation ln 5 = y as an exponential equation is [tex]e^y = 5[/tex]
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Express the formula in terms of the height, Use that formula to find the height when the volume is and the radius is
Answers
The formula to find the height of the Cylinder is; h = V/(πr²) and at V = 45π and r = 3, we have; h = 5
How to change the subject of the formula?We are given the formula for volume of a cylinder as;
V = πr²h
where;
h is height
r is radius
To make h the subject, let us divide both sides by πr² to get;
V/(πr²) = h
At V = 45π and r = 3, we have;
h = 45π/(πr²)
h = 45/3²
h = 5
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We know for a fact that the equation:
[tex]|z+z'| \leqslant |z|+|z'|[/tex]
holds for any 2 complex numbers
I came up with the conclusion that:
[tex]|z+z'|=|z|+|z'|[/tex]only holds when z and z' are pure imaginary or pure real numbers of the SAME sign.
How can i prove this algebraically/geometrically?
Note: Irrelevant answers will be reported
Answers
They don't need to be pure real or imaginary. Any "mixed" complex number works so long as [tex]z=z'[/tex].
Let [tex]z=z'=a+bi[/tex]. Then
[tex]|z+z'| = |2a+2bi| = 2 \sqrt{a^2+b^2}[/tex]
[tex]|z| + |z'| = 2|a+bi| = 2 \sqrt{a^2+b^2}[/tex]
so [tex]|z+z'|=|z|+|z'|[/tex].
The geometric interpretation is essentially identical. [tex]|z+z'|=2|z|[/tex] is a complex number twice the distance away from the origin in the complex plane as [tex]z[/tex], which is exactly [tex]|z|+|z|[/tex].
The function h(t) = −5t2 + 15t shown in the graph models the supporting structure of a bridge:
graph of parabola starting at zero comma zero, rising from the left to about one and one half comma 11, and falling to the right, ending at 3 comma zero
What is the domain of h(t)?
All real numbers
0 ≤ x ≤ 11
0 ≤ x ≤ 3
x ≥ 0
Answers
Since the function is h(t) = −5t² + 15t, the domain of the function h(t) is 0 ≤ t ≤ 3
What is the domain of a function?The domain of a function is the range of input values that make the function have real values.
Now given the function h(t) = −5t² + 15t, it will have real values when
h(t) ≥ 0
So, h(t) ≥ 0
⇒ −5t² + 15t ≥ 0
Factorizing, we have
-5t(t - 3) ≥ 0
5t(t - 3) ≤ 0
t(t - 3) ≤ 0
t ≤ 0 and t - 3 ≤ 0
t ≤ 0 and t ≤ 3
For t ≤ 0, say -1, t(t - 3) = -1(-1 - 3) = -1(-4) = 4 ≥ 0
For 0 ≤ t ≤ 3, say 2, t(t - 3) = 2(2 - 3) = 2(-1) = -2 ≤ 0
For t ≥ 3, say 4, t(t - 3) = 4(4 - 3) = 4(1) = 4 ≥ 0
Since we require t(t - 3) ≤ 0, the domain of t is thus 0 ≤ t ≤ 3
So, the domain of the function h(t) is 0 ≤ t ≤ 3
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