The height of the right pyramid is 48.53 cm.
What is the height of the pyramid?A rectangle pyramid is a 3-dimensional shape that is made up of a rectangular base and 4 triangular faces.
Height = ( 3 x Volume of a pyramid) /( area)
Height = (3 x 21452) / 1326 = 48.53 cm
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
1.The center of the circle lies on the x-axis
2.The radius of the circle is 3 units.
3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
90°
Find mZR.
A. 30°
B. 60°
C. 120°
D. 180°
(2x)
to
P
90°
S
Answer:
120°
Step-by-step explanation:
Angles in a quadrilateral add to 360°, so
90+90+x+2x=360
180+3x=360
3x=180
x=60
So, angle R measures 120°.
Ashley deposits $10 000 at the end of each month for 6 times at rate of 5% compounded monthly. How much will be in her account
a. at the end of 6th month?
b. 3 months after her last deposit if rate of interest have remained level?
c. at the end of 6th months if she misses the deposit in 3rd month?
d. at the end of 6th months if she deposit $20 000 at the beginning of 1st month
e. at the end of 6th months if the rate growth to 6% from 4th months
f. Construct the deposit table for each of the above questions
The future values of Ashley's periodic deposits under the five scenarios are stated in the deposit table as follows:
Deposit Table:Item Initial Periodic Deposit Interest Future Value Interest
Deposit Deposit Period Rate ($)
a. $10,000 $10,000 6 months 5% $61,774.51 $1,774.51
b. $10,000 $10,000 3 months 5% $30,502.78 $502.78
c. $10,000 $10,000 6 months 5% $51,774.51 $1,522.42
d. $20,000 $10,000 6 months 5% $72,201.71 $2,201.71
e. $10,000 $10,000 6 months 5%/6% $60,803.78 $803.78
What is the future value?The future value of a periodic investment represents the present value of cash flows compounded at an interest rate into the future.
The future value is computed using the FV formula or factor.
It can also be computed using an online finance calculator as follows:
Data and Calculations:Periodic Deposit = $10,000
Investment period = 6 months
Interest rate = 5% compounded monthly
a) for illustration:N (# of periods) = 6 months
I/Y (Interest per year) = 5%
PV (Present Value) = $0
PMT (Periodic Payment) = $10,000
Results:
FV = $61,774.51
Sum of all periodic payments = $60,000 ($10,000 x 6)
Total Interest = $1,774.51
Other Special Cases:c) Interest on $10,000 for 3 months is $1,522.42 ($1,774.51 - $252.09).
d) Future Value Interest
5% with $20,000 $82,285.04 $2,285.04
5% with $10,000 (10,083.33) (83.33)
Total for 6 months $72,201.71 $2,201.71
e) Future Value Interest
5% for 3 months $30,502.78 $502.78
6% for 3 months $30,301.00 $301.00
Total for 6 months $60,803.78 $803.78
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Mohinder needs to create a 5 character password. He wants each of the first, third, and fifth characters in the password to be one of the letters A to E and second and fourth characters to be one of the numerals 0 through 9. If each of the characters in the password must be unique how many passwords are possible
The number of unique passwords is 5400
How to determine the number of unique passwords?The characteristics of the password are given as:
Number of characters = 5First, third, and fifth characters in the password = One of the letters A to ESecond and fourth characters = one of the numerals 0 through 9Since the characters in the password must unique, we have the following possibilities
First character = Any of 5 charactersSecond characters = Any of 10 digitsThird character = Any of remaining 4 charactersFourth characters = Any of remaining 9 digitsFifth character = Any of remaining 3 charactersSo, the number of unique passwords is
Password = 5 * 10 * 4 * 9 * 3
Evaluate the product
Password = 5400
Hence, the number of unique passwords is 5400
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Using the slope and the y-intercept, graph the line represented by the following equation. Then select the correct graph. x - y - 3 = 0
The graph that represents the given line with slope and y-intercept is as attached below.
How to interpret Linear Graphs?
We are given the equation;
x - y - 3 = 0
Now, the standard way we should put the equation would be in slope intercept form which is; y = mx + c
where;
m is slope
c is y-intercept
Thus, our equation can be rearranged to get;
y = x - 3
Thus, y-intercept is c = -3
The graph that represents the given line is as attached below.
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Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise unless otherwise indicated. Integrate c ln(x+y)dx-x^2 dy where C is the rectangle with vertices (1,1), (3,1), (1,4), and (3,4).
Using Green's Theorem to evaluate the given line integral with the given conditions and vertices gives us; -30
How to evaluate an Integral with Green's Theorem?
The line integral of a vector-valued function along the edges of a rectangle or any other closed curve can be found by converting the line integral into a double integral. We apply Green's theorem to do this. The resulting double integral is integrated over the two-dimensional region bounded by the same closed curve.
Green's Theorem can be applied as follows:
∮_c (P.dx + Q.dy) = ∫∫_R ((dQ/dx) - (dP/dy))dA
The vertices of the rectangle (1,1), (3,1), (1,4), and (3,4).
Applying Green's Theorem to the given function gives;
∮_c (ln x + y) dx - x² dy
= ∫14∫13 Dx(-x2) -Dy(ln(x) +y) dx dy
= ∫₁⁴∫₁³ (-2x - 1) dx dy
= -3·[x² +x]₁³
= -30
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18. Which TWO linear inequalities are shown in the
graph below?
y
A.
B.
C.
D.
E.
F.
G.
H.
y> -2
y < -2
x<-2
X > -2
x+y<1
x-y<-1
x+y>1
x-y> -1
Answer: A and H
Step-by-step explanation:
y=x+1 is shaded below and dotted, so [tex]y < x+1 \implies x-y > -1[/tex].
Also, y=-2 is dotted and shaded above, so it represents [tex]y > -2[/tex]
Split [tex](4ax-a^2)/(x^2+ax-2a^2)[/tex] into partial fractions.
The decomposition of the partial fraction is [tex]\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}[/tex]
How to split the fraction?The expression is given as:
[tex]\frac{4ax-a^2}{x^2+ax-2a^2}[/tex]
Expand the denominator
[tex]\frac{4ax-a^2}{x^2- ax+2ax-2a^2}[/tex]
Factorize
[tex]\frac{4ax-a^2}{x(x- a)+2a(x-a)}[/tex]
Factor out x - a
[tex]\frac{4ax-a^2}{(x+ 2a)(x-a)}[/tex]
The denominator of the partial fraction is a product of two linear factors.
So, the decomposition can be represented as:
[tex]\frac{4ax-a^2}{(x+ 2a)(x-a)} = \frac{A}{x + 2a} + \frac{B}{x - a}[/tex]
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Find cos B, sinB,tanb
Using right triangle relations, we will get:
tan(B) = 1.05sin(B) = 0.735cos(B) = 0.7How to find the value of the trigonometric equations?
We assume that bot triangles are equivalent, then the angle B will be the same as the angle Z.
Now remember the relations:
tan(θ) = (opposite cathetus)/(adjacent cathetus).sin(θ) = (opposite cathetus)/(hypotenuse)cos(θ) = (adjacent cathetus)/(hypotenuse).If we step on angle B, we have:
opposite cathetus = 29.4adjacent cathetus = 28hypotenuse = 40.6Replacing that, we get:
tan(B) = 29.4/28 = 1.05sin(B) = 29.4/40.6 = 0.735cos(B) = 28/40.6 = 0.7If you want to learn more about trigonometric functions:
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f(x) = |2x +1| +3
g(x) = −2
Find (ƒ + g)(x).
Hello!
We are going to solve the question with our given functions.
We were given:
f(x) = |2x +1| + 3g(x) = -2Those are our two given functions, we will use those to solve for (f + g)(x).
Keep in mind that (f + g)(x) could also be written as f(x) + g(x)
With this knowledge, we can solve our question.
Solve:
(ƒ + g)(x) = f(x) + g(x)
Plug in our f(x) and g(x) functions and solve.
f(x) + g(x) = |2x +1| + 3 - 2
Simplify.
|2x +1| + 3 - 2
|2x +1| + 1
Since we can't simplify this any further, the above will be our answer.
(f + g)(x) = |2x +1| + 1
Answer:
|2x +1| + 1
What is the product?
Sr-203r-40
O 157-8
0157-8
O 15/+14-8
0152²-140-8
Off the production line, there is a 2.2% chance that a candle is defective. If the company selected 40 candles off the line, what is the standard deviation of the number of defective candles in the group?
The standard deviation of the number of defective candles in the group is 0.9277.
When a random variable X follows a binomial distribution, with the sample size n, and the proportion of success is p, then the standard deviation is calculated as:
σ = √{np(1-p)}.
In the question, we are given that off the production line, there is a 2.2% chance that a candle is defective.
We are asked if the company selected 40 candles off the line, then what is the standard deviation of the number of defective candles in the group.
Assuming the occurrence of a defective bulb as success, we get the proportion of success, p = 2.2% or 0.022, and the sample size, n = 40.
Thus, we can calculate the standard deviation of the number of defective candles in the group as:
σ = √{np(1-p),
or, σ = √{40*0.022*(1 - 0.022)} = √0.86064 = 0.9277.
Thus, the standard deviation of the number of defective candles in the group is 0.9277.
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Find the missing length indicated. need help
Step-by-step explanation:
the formula for the height in a right-angled triangle is
h = sqrt(p×q)
p and q being the segments of the Hypotenuse left and right from the point, where the height intersects with the Hypotenuse.
so, in our case
12 = sqrt(16×(x-16))
let's square this to eliminate the square root :
144 = 16×(x - 16) = 16x - 256
400 = 16x
x = 25
If a diameter of a circle has endpoints (-3,5) and
(5, 7), then the center of the circle is
Answer:
(1 , 6)
Step-by-step explanation:
the center of the circle is the midpoint of the diameter
Which is the point of coordinates:
[tex](\frac{-3+5}{2} ,\frac{5+7}{2} )[/tex]
Then the center is the point :
[tex](1 , 6)[/tex]
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:
[tex]\longrightarrow\bold{(-3,5)}[/tex]
[tex]\longrightarrow\bold{(5, 7)}[/tex]
Calculate the average value between the x-coordinates of the diameter and do the same for the y-coordinates:
[tex]\longrightarrow\sf{C_x=\dfrac{-3+5}{2} = \dfrac{2}{2} =1}[/tex]
[tex]\longrightarrow\sf{C_y= \dfrac{5+7}{2} = \dfrac{12}{2} = 6 }[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex]\longrightarrow\sf{=(1,6)}[/tex]
answer me with step by step details please
Answer:
31 3/4 %
Step-by-step explanation:
There are 100 squares so each square is a percent. There at 31 full squares colored and it looks like 3/4 of 1 square.
Johnny is starting a zoo. His favorite animals are lions, tigers and snakes. These are the only animals in the zoo and he has them in the ratio of 5 : 3 : 2. If he has a total of 50 animals in the zoo, how many snakes does he have?
*
The total number of snakes in the zoo is 10.
How to use ratio to find the number of snake?The number of snake can be found using ratio as follows:
The animals in the zoo are lions, tigers and snakes and he has them in the ratio of 5 : 3 : 2. The total animal is 50 animals.
Therefore,
total snakes = 2 / 10 × 50
total snakes = 100 / 10
total snakes = 10
Therefore, the total number of snakes in the zoo is 10.
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find RY if RV=8 and VW=12
Solve for x. Round your answer to the nearest tenth if necessary. Figures are
not necessarily drawn to scale.
T
63°
72°
18
19
45
630
37
72°
W
45°
X
X
Answer:
18/19= X/37 because 18 and x are both between 72 and 45 degrees
Multiply 18 and 37 then divide by 19 to get answer
Step-by-step explanation:
Q, Fixed a system of coordinates in the plane, conficer the curve C having equation y = (x-2)^2. The line x + y - 2 = 0 intersects C in:
(A)1 poin
(B) no point
(C) 2 points
(D) infinitely many points
3 points
Answer:
C
Step-by-step explanation:
y = (x - 2)² = x² - 4x + 4 → (1)
x + y - 2 = 0 → (2)
substitute y = x² - 4x + 4 into (2)
x + x² - 4x + 4 - 2 = 0
x² - 3x + 2 = 0
(x - 1)(x - 2) = 0
equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 2 = 0 ⇒ x = 2
substitute these values into (2) and solve for y
x = 1 : 1 + y - 2 = 0 ⇒ y - 1 = 0 ⇒ y = 1 ⇒ (1, 1 )
x = 2 : 2 + y - 2 = 0 ⇒ y + 0 = 0 ⇒ y = 0 ⇒ (2, 0 )
the line intersects curve C at 2 points (1, 1 ) and (2, 0 )
Gabrielle is 12 years younger than Mikhail. The sum of their ages is 38. What is Mikhail’s age?
Use the permutation formula below to find the number of outcomes when n = 5 and r = 2.
[tex]nPr = \frac{n!}{(n - r)!} [/tex]
[tex]5P2 = \frac{5!}{(5 - 2)!} = \frac{5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} = 20[/tex]
The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts (a) through (d) below.
a. Find the probability of getting exactly 6 girls in 8 births.
b. Find the probability of getting 6 or more girls in 8 births.
c. Which probability is relevant for determining whether 6 is a significantly high number of girls in 8 births: the result from part (a) or part (b)?
d. Is 6 a significantly high number of girls in 8 births? Why or why not? Use 0.05 as the threshold for a significant event.
Number of Girls x P(x)
0 0.002
1 0.016
2 0.109
3 0.199
4 0.348
5 0.199
6 0.109
7 0.016
8 0.002
The answers to the questions are
0.1090.127b is a relevant factor6 is not highHow to solve for the probabilitya. From the table the probability of having 6 girls in 8 birth is given as
0.109.
b. The probability of 6 or more girls in 8 births
p(6) + p(7) + p(8)
= 0.109 + 0.016 + 0.002
= 0.127
c. The result from b is the relevant factor given that it includes the probability of getting 6, 7 and 8 girls.
D. No six is not a significantly high number of girls in 8 births. This conclusion is from the fact that 0.109 is greater than 0.05.
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What is the range of the function graphed below? A bidirectional arrow rises steeply through (negative 2, negative 8), (negative 1 point 5, negative 4), (negative 1, 0), (0, 2) and extends linearly through (2, 2), (3, 2), (4, 2), (5, 2), (6, 2) and (8, 2) on the x y coordinate plane. A. B. C. D.
Answer:
A. -∞ < y < 2
Step-by-step explanation:
The range is the vertical extent of the graph.
Lower limitThe arrow pointing down tells you the graph extends toward -∞.
Upper limitThe arrow pointing right suggests that y=2 is a horizontal asymptote. A graph will approach, but never cross, an asymptote. Thus, we can conclude y < 2.
RangeThe range is the set of values that lie between the limits:
-∞ < y < 2
Suppose that, for a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 9. The teacher wishes to give A's to the top 7% of the students and F's to the bottom 7%. The next 17% in either direction will be given B's and D's, with the other students receiving C's. Find the bottom cutoff for receiving an A grade. (You may need to use the standard normal distribution table. Round your answer to the nearest whole number.)
The bottom cutoff for receiving an A grade is 88.
What is the bottom cutoff for receiving an A grade?The bottom cutoff for receiving an A grade is found as follows:
The mean of the distribution = 75
The standard deviation = 9
The z-score for the 93% = 1.476
The score for an A grade, x = mean + z-score * standard deviation
Score for an A grade, x = 75 + 1.476 * 9
Score for an A grade, x = 88
In conclusion, the minimum score for an A grade is obtained from the mean, the z-score and the standard deviation.
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2 qts for every 50 gal of water i just want to use 15 gal of water so how much do i use
The amount of qts to use for 15 gals is 0.6qts
Proportion and ratio
Ratio are written as quotient of 2 integers
Given that 2 qts for every 50 gal of water, this is written as;
2qts = 50 gals
In order to calculate for 15gal, we will have:
x = 15gals
Take the ratio
2/x = 50/15
50x = 30
x = 3/5
x = 0.6qts
Hence the amount of qts to use for 15 gals is 0.6qts
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Solve the following equation for y to find the slope and the y-intercept: 2y - x = 6
Step-by-step explanation:
2y - x = 6
2y = x + 6
y = (x + 6) / 2
the slope is 1 and the y int is 3
A ribbon is 4 m long. How many pieces each 30 cm long can be cut from the ribbon?
Answer:
13 pieces
Step-by-step explanation:
First we convert 4m into cm :
1m = 100cm
4m = 400cm
Now we need to figure out how many 30s go into 400 :
400 ÷ 30 = 13 remainder 10
So 13 pieces can be cut from the ribbon
Hope this helped and have a good day
Answer:
13
Step-by-step explanation:
4 meters is equal to 400 centimeters.
400/30 = 13 1/3
You don't want partial pieces, so your answer is 13
I need help with this
Answer:
361
Step-by-step explanation:
discriminant = b² - 4ac
= (21)² - 4(1)(20)
= 441 - 80
= 361
please help....title of the work assignment...WHERE DOES THE DECIMAL GO USING ESTIMATION WHEN DIVIDING DECIMALS.....
146÷0.7. SOLUTION AND REASONING...
The correct equation of 146 ÷ 7 = 20857 is 146.0 ÷ 7.0 = 20.857
How to divide the decimals?The equation is given as:
146 ÷ 7 = 20857
The above equation is wrong.
The equation can be rewritten as:
146.0 ÷ 7.0 = 20857
The significant digits in 146.0 and 7.0 are 3 and 1, respectively.
3 - 1 = 2
This means that
So, the decimal place in the result must be after the second digit.
So, we have:
146.0 ÷ 7.0 = 20.857
Using the above highlights, we have:
146 ÷ 0.7 = 208.57
1.46 ÷ 7 = 0.20857
14.6 ÷ 0.7 = 20.857
1460 ÷ 70 = 20.857
The reasoning behind the above equations is that the decimal position in the results is dependent on the decimal positions in the dividend and divisor
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Choose the two answers that are solutions to the equation. (X+7)^2=121
A. x=4
B. x=-18
C. x=18
D. x=-4
Answer: A. x = 4
Step-by-step explanation:
Substituting 4 for x..
(4+7)^2 = 121
(11)^2 = 121
11 * 11 = 121