radius -15
Surface Area of a sphere =4πr^2
=4x22/7x15x15
=19800/7
=2828.57
The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 96
cm ^2 , what is the length of the diagonal?
Thee diagonal of the rectangle is 13.86 cm long.
What is the length of the diagonal of rectangle?We are given that;
Width of a rectangle is 9 less than twice its length. Thus, if length is L, then;
W = 2L - 9
Area formula for a rectangle is;
A = Length * Width
We are given area of rectangle = 96 cm²
Thus;
L(2L - 9) = 96
2L² - 9L = 96
2L² - 9L - 96 = 0
Using online quadratic equation calculator gives;
L = 9.53 cm
Thus;
W = 2(9.53) - 9
W = 19.06 - 9
W = 10.06 cm
The diagonal of the triangle will be gotten from Pythagoras theorem;
D = √(9.53² + 10.06²)
D = √192.0245
D = 13.86 cm
Thus, we conclude that the diagonal of the rectangle is 13.86 cm long.
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The equation of the line passing through point _____ and point _____ plotted below in point-slope form is y+3 =-(x-4)
Answer:
The equation of the line passing through point __0___ and point __1___ plotted below in point-slope form is y+3 =-(x-4
Difference of Squares gives which complex factors for the expression +3?
A. (x+3i)(x-3i)
B. (x-i-√3)(x-i√3)
C. (x+3i)^2(x-3i)²
D. (x+i√3)(x-i√3)
The difference of squares is:
(x+i√3)(x-i√3)
So the correct option is the last one, D.
Which expression gives x^2 + 3?For a complex number:
[tex]Z = a + b*i[/tex]
We define the complex conjugate of Z as:
[tex]Z' = a - b*i[/tex]
Such that the product between the complex number and its complex conjugate gives:
[tex]Z*Z' = a^2 + b^2[/tex]
Now, of you look at option D, you can see we have the product of a number and its conjugate, then we can write the product and use the above rule to get:
[tex](x + i\sqrt{3} )*(x - i\sqrt{3} ) = x^2 + (\sqrt{3} )^2 = x^2 + 3[/tex]
Which is what we wanted to get, so that is the correct option.
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Suppose follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of so that the following is true.
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Answer:
c = 2.25
Step-by-step explanation:
The normal distribution function is symmetrical, so the area not in the central zone is split evenly between the lower and upper tails.
SolutionWe can find -c from ...
P(x < -c) = (1 - 0.9756)/2 . . . . . the area in the lower tail
The calculator tells us -c = -2.25.
c = 2.25
What is the domain of f(x)=(1/3)^x
Answer:
All Real Numbers
Step-by-step explanation:
The domain is all the x values for a function. As this function is not restricted in any way, the domain is all real numbers. You can put any number in for x and plot it on the graph.
Numbers from 1 to 50.
Find the probability of choosing
numbers with last digit 6.
0.1 or 10%
Step-by-step explanation:The numbers between 1 and 50 that end in 6 are as follows:
6, 16, 26, 36, 46
There are therefore 5 numbers between 1 and 50 that end in 6.
This means there are 5 out of 50, or 5/50.
5/50 is 0.1 as a decimal, or 10% in percentage form.
Donna has a $300 loan through the bank she is charged a simple rate The total interest she paid on the loan was $63 As a percentage what was the annual interest rate on her loan
Answer:
21%
Step-by-step explanation:
($63*100%) / $300 = 21%
On a map, 3 inches represents 50 miles. Which proportion can be used to find the actual distance represented by 5 inches on the map?
StartFraction 3 over 50 EndFraction = StartFraction x over 5 EndFraction
StartFraction 3 over 50 EndFraction = StartFraction 5 over x EndFraction
StartFraction 3 over x EndFraction = StartFraction 50 over 5 EndFraction
StartFraction x over 3 EndFraction = StartFraction 50 over 5 EndFraction
The correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
Given that 3 inches on a map represents 50 miles.
We are told to find the proportion which can be used to represent 5 inches.
Multiplication is basically finding the product of two numbers but it can be used to convert the units also.
If 3 inches represents 50 miles then,
1 mile=50/3
Multiply both sides by 5.
5 miles=5*50/3
If we see the options then we will get that the most appropriate and correct option which represents 5 inches is that start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
Hence the correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
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Answer:
B
Step-by-step explanation:
3/50 = 5/x
Find the measures of angles x and y
Find the exact value of x.
X =
11
X
00
8
Which of these tables represent a function
Answer: W
Step-by-step explanation: I remember learning this in school> you can tell it’s a function because no numbers repeat themselves etc .
Describe at least two differences between constructing parallel lines and constructing perpendicular lines
Answer:
Step-by-step explanation:
parallel lines are the same so they dont touch u-u
perpendicular lines do touch eachother and intersect
The required two differences between constructing parallel lines and constructing perpendicular lines are,
1) Constructing parallel lines never intersect each other while perpendicular lines intersect each other.
2) Constructing Perpendicular lines make an angle of 90° with each other at the point of the intersection. while parallel lines do not have angles with each other.
Parallel lines are defined as the pair of lines in which points on both the lines are equidistant from each other, and the line never intersects each other.
The differences between constructing parallel lines and constructing perpendicular lines are as follows.
1) Constructing parallel lines never intersect each other while perpendicular lines intersect each other.
2) Constructing Perpendicular lines make an angle of 90° with each other at the point of the intersection. while parallel lines do not have angles with each other.
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Wich solutions are correct
Answer:
Rhoda and Ming are both correct, but Ming's prediction is closer because the result is accurate to two decimal places.
Step-by-step explanation:
How many pairs of parallel faces does this shape have?
Answer: one
Step-by-step explanation:
parallel faces are the ones that are opposite to each other.
Answer:
one
Step-by-step explanation:
there is only one pair of parallel faces.
which table of ordered pairs represents a proportional relationship?
Answer:
B
Step-by-step explanation:
Every (x,y) pair is equal to each other, thus making them proportional :)
ILL GIVE BRAINLIEST
4. Multiply the following signed numbers:
a. (-42x)(+2x) =
b. (+8x)(-4x)(-3x) =
c. (+7)(-4)(-4) =
d. (+10)(-2)(-2)(+4) =
Explanation:(x)(x)=x^2 and(x)(x)(x)=x^3
2(−6c+3)+4c2, left parenthesis, minus, 6, c, plus, 3, right parenthesis, plus, 4, c
Answer:
[tex]-8c+6[/tex]
Step-by-step explanation:
[tex]2(-6c+3)+4c=-12c+6+4c=\boxed{-8c+6}[/tex]
Answer:
-8c + 6 and 3(-4c+2) + 4c
Step-by-step explanation:
khan
A rectangular box is designed to have a square base and an open top. The volume is to be 500in.3 What is the minimum surface area that such a box can have?
The minimum surface area that such a box can have is 380 square
How to determine the minimum surface area such a box can have?Represent the base length with x and the bwith h.
So, the volume is
V = x^2h
This gives
x^2h = 500
Make h the subject
h = 500/x^2
The surface area is
S = 2(x^2 + 2xh)
Expand
S = 2x^2 + 4xh
Substitute h = 500/x^2
S = 2x^2 + 4x * 500/x^2
Evaluate
S = 2x^2 + 2000/x
Differentiate
S' = 4x - 2000/x^2
Set the equation to 0
4x - 2000/x^2 = 0
Multiply through by x^2
4x^3 - 2000 = 0
This gives
4x^3= 2000
Divide by 4
x^3 = 500
Take the cube root
x = 7.94
Substitute x = 7.94 in S = 2x^2 + 2000/x
S = 2 * 7.94^2 + 2000/7.94
Evaluate
S = 380
Hence, the minimum surface area that such a box can have is 380 square
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A circle has a circumference of 50.24 units.
What is the radius of the circle?
Use 3.14 for π and enter your answer as a decimal.
units
Answer: 8 units
Step-by-step explanation:
Which rule describes the relationship between the x- and y- coordinates on the following graph? Choose 1 answer:
(Choice A)
A
y
=
2
x
y=2xy, equals, 2, x
(Choice B)
B
y
=
x
+
2
y=x+2
Answer:
A
Step-by-step explanation:
given the points
(0, 0 ) , (2, 4 ) , (4, 8 )
note that the y- coordinate is twice the value of the x- coordinate , so
y = 2x
ASAP help me with this question
Answer:
SAS and SSA
Kindly award branliest
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Congruency refers to the criteria of making two identical shapes that can hide each other properly when overlapped.
The criterias that guarantee congruence are :
SSSSASASAAAS[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct options are : b, c, d, eSuppose a stock qualifies as having moderate risk if the standard deviation of its monthly rate of return is less
than 10%. A stock rating agency randomly selects 36 months and decides the rate of return for a specific fund.
The standard deviation of the rate of return is computed to be 4.95%. Is there sufficient evidence to conclude
that the fund has moderate risk at the α=0.05 level of significance? A standard probability plot shows that the
monthly rates of return are typically distributed.
Test the claim using a hypothesis test.
What are the null and alternative hypotheses for the hypothesis test?
What is the conclusion based on the hypothesis test?
The conclusion of the Hypothesis Conclusion is; that there is sufficient evidence to support the claim that the fund has moderate risk.
How to test hypothesis claim?
We are given;
Sample size; n = 36
Population standard deviation; σ₀ = 10
Sample standard deviation; s = 4.95
Significance level; α = 0.05
Claim: Standard deviation less than 10
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis needs to contain an equality and the value mentioned in the claim. If the claim is the null hypothesis, then the alternative hypothesis states the opposite of each other. Thus;
Null Hypothesis; H₀: σ = 10
Alternative Hypothesis; H₁: σ < 10
Compute the value of the test statistic:
χ2 = [(n - 1)/(σ²)] * s²
χ2 = [(36 - 1)/(10²)] * 4.95²
χ2 = 8.576
The critical value of the left-tailed test is given in the row with df = n - 1 = 36 - 1 = 35 and in the column with 1 − α = 0.95 of the chi-square distribution table online, we have;
χ2_{1 - α} = 21.77
The rejection region then contains all values smaller than 21.77
If the test statistic is in the rejection region, then reject the null hypothesis:
8.576 < 13.848
Thus, we will reject H₀ and conclude that there is sufficient evidence to support the claim that the fund has moderate risk.
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1 gallon of paint covers 300 ft how many gallons I needed for a room 30 ft long 20 ft wide by 12 ft high
Answer:
6 gallons
Step-by-step explanation:
the total area to be painted :
= The total surface area - area of the floor
= area of the walls + area of the ceiling
area of the walls :
= [perimeter of the room] ×height
= [2 × (30+20)] × 12
= 1 200
area of the ceiling :
= length × width
= 30 × 20
= 600
the total area to be painted :
= 1200 + 600
= 1800
The number of gallon of paint needed to cover the room :
= 1800 ÷ 300
= 6
Write an inequality for the following statement, 1 is greater than x
The inequality suitable if 1 is greater than x is x<1.
Given that 1 is greater than x.
We are required to form an inequality which shows that 1 is greater than x.
Inequality is like an equation showing relationship between two or more variables.It is mostly not found in equal to form.
It shows the range of quantities.
When 1 is greater than x means the greater than sign will be used for 1 not x and the inequality will be as under:
x<1
We have not used equal to sign because 1 is greater than x not equal to x.
Hence the inequality suitable if 1 is greater than x is x<1.
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someone solve this question for me with detailed explanation and step by step so i can grasp the concept
Answer:
3rd grade
Step-by-step explanation:
Given that the values are different types (fractions, decimals, and percentages), it would be helpful to convert them to the same type of value.
Converting everything to percentages seems more convenient.
Since 61.24% is already a percentage, we simply have to convert 0.52, 25/36, and 0.5274444 (I wrote 0.5274 like this since the 4 is a repeating value).
To convert 0.52, we simply multiply by 100:
0.52 * 100 = 52%
For 25/36, we need to know its decimal form and multiply by 100 to find the percentage:
25 / 36 = 0.6944 * 100 = 69.44%
For 0.5274444, we also multiply by 100:
0.5274444 * 100 = 52.74444
Thus, we have 52% (2nd grade), 69.44% (3rd grade), 61.24% (4th grade), and 52.74444% (5th grade).
3rd grade has the highest portion of students
Solve for x
(please write work)
Answer:
x = -9
Step-by-step explanation:
12 + 2x + 24 = 27 + x
(12 + 24) + 2x = 27 + x
36 + 2x = 27 + x
subtract 27 from both sides
36-27 + 2x = 27-27 + x
9 + 2x = x
subtract x from both sides
9 + x = 0
subtract 9 from both sides
x = -9
(the steps could've been faster but that shows the most work)
check:
12 + 2(-9) + 24 = 27 + (-9)
36 - 18 = 18
18 = 18
True!
so -9 is correct
Answer:
Step-by-step explanation:
To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.
Suppose X, Y and Z are uncorrelated random variables with means 1, 2 and 3 and standard deviations 2, 4 and 5 respectively. If U = Y – X and V = Z – Y. Compute the correlation coefficient between U and V and comment on your result.
The correlation coefficient between U and V is -0.5587 and it illustrates to at there's a negative relationship between U and V.
How to illustrate the information?The data shows that:
E(x) = 1
E(y) = 2
E(z) = 3
Var(X) = 2² = 4
Var(Y) = 4² = 16
Var(Z) = 5² = 25.
Cov(U, V) = 16
Var(U) = Var(Z - Y)
= 25 - 0 + 16
= 41
The correlation coefficient will be:
= -16/✓(20 × 41)
= -0.5587
The correlation coefficient between U and V is -0.5587 and it illustrates to at there's a negative relationship between U and V.
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Follow the instructions for the following inequalities.
1. 4<7 Multiply both sides by 7 , then by 6, then by 3, then by 10
2. 11>-2 Add 5 to both sides, then add 3, then add (-4)
3. -4<-2 Subtract 6 from both sides, then 8, and then 2
4. -8<8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
Answer:
below
Step-by-step explanation:
1) 4 < 7
28 < 49
168 < 294
1680 < 2940
2) 11 > -2
16 > 3
19 > 6
15 > 2
3) -4 < -2
-10 < -8
-18 < -16
-20 < -18
4) -8 < 8
2 > -2
-1 < 1
5) When you multiply by a negative number, the inequality sign flips.
Choose the number (X) that should come next in this series (1, 2, 6, 15, X, 56, 92)
Answer:
31
Step-by-step explanation:
The numbers in the sequence increase by (n+1)^2. So the sequence is (1, 1+1^2 (which is 2), 2+2^2 , 6+3^2, 15+4^2, 31+5^2, 56+6^2) and the fifth term of that sequence is 15+4^2, which is 31
The unknown number(x) in the series is 31.
The given series 1, 2, 6, 15, x, 56, 92.
We need to find the value of x.
What is a series?In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, and mathematical analysis.
The numbers in the series increase by (n+1)².
So the sequence is 1, 1+1² (which is 2), 2+2², 6+3², 15+4², 31+5², 56+6² and the fifth term of that sequence is x=15+4²=31.
Therefore, the unknown number(x) in the series is 31.
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Goldie Gold Jewelry uses direct labor hours to apply overhead and estimated total overhead costs at $52,500 and direct labor hours at 12,500 for the second quarter. The direct labor quantity standard is 1.75 direct labor hours per unit, and the company produced 5,250 units in the second month of the second quarter. This required 2,625 direct labor hours. What was the overhead rate for the second quarter?
In the case above, the value of the overhead rate for the second quarter is $17,640.
What is the overhead rate about?Note that:
In the case above, for one to be able to calculate the predetermined overhead rate, a person need to divide the value of the estimated overhead costs which is $52,500 by that of the estimated direct labor hours .
Predetermined overhead rate=Estimated overhead costs/ estimated direct labor hours
Predetermined overhead rate=$52,500/ 12,500
Predetermined overhead rate=$4.20/DLH overhead rate
Hence: $52,500/ 12,500 = $4.20/DLH overhead rate.
Since the Overhead that was applied at standard hours was said to be allowed, then:
= $4.2 x 2,400 x 1.75
= $17,640.
Therefore, In the case above, the value of the overhead rate for the second quarter is $17,640.
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