Answer:
288π or 904.78
Step-by-step explanation:
We know that the diameter of this beach ball is 12 inches and we want to determine how much air it can hold using the formula for the volume of a sphere which is [tex]\frac{4}{3}[/tex] × π × r³ where 'r' is the radius. In the question we are given the diameter not the radius but we can half the diameter to find the radius so 12 ÷ 2 = 6. The radius of the beach ball is 6 inches so let's work out how much air it can hold.
Volume = [tex]\frac{4}{3}[/tex] × π × r³
→ Let's substitute in the values
Volume = [tex]\frac{4}{3}[/tex] × π × 6³
→ Simplify
Volume = [tex]\frac{4}{3}[/tex] × π × 216
→ Simplify further
Volume = 288π or 904.78
The amount of air can the sphere shape beach ball hold is 208π or 904.78 inches.
What is sphere?
The "set of all points in 3 dimensional space is lying the same distance from the given points or center" is called sphere.
According to the question,
Diameter of sphere shape beach ball is 12inches
Radius of sphere shape beach ball is 12/2 = 6inches
Volume of sphere = [tex]\frac{4}{3}[/tex] × π × r³
= [tex]\frac{4}{3}[/tex] × [tex]\frac{22}{7}[/tex] × (6)³
= 904.78inches
Hence, the amount of air can the sphere shape beach ball hold is 208π or 904.78 inches.
Learn more about sphere here
https://brainly.com/question/20377790
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similarity statements between triangles
Answer:
Two triangles are said to be similar if any two corresponding sets of angles are equal and the corresponding sides are in the same ratio.
Wich is a factor of x^2+ 5x-24?
Answer:
(x−3)(x+8)
Step-by-step explanation:
Let's factor x2+5x−24
x2+5x−24
The middle number is 5 and the last number is -24.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 5
Multiply together to get -24
Can you think of the two numbers?
Try -3 and 8:
-3+8 = 5
-3*8 = -24
Fill in the blanks in
(x+_)(x+_)
with -3 and 8 to get...
(x-3)(x+8)
Answer:
(x−3)(x+8)
Hope this helps.
Find an equation of the tangent line to the graph of
y = g(x) at x = 4 if g(4) = −3 and g'(4) = 2.
(Enter your answer as an equation in terms of y and x.)
Answer:
[tex] y- y_o = m(x-x_o) [/tex]
For this case m represent the slope and is given by [tex]m= g'(4) = 2[/tex] and from the other condition given we know that [tex] x_o = 4, y_o =-3[/tex]. And replacing we got:
[tex] y -(-3) = 2 (x-4)[/tex]
And if we reorganize the terms we have:
[tex] y+3 = 2x -8[/tex]
And subtracting 3 in both sides we got:
[tex] y = 2x -11[/tex]
Step-by-step explanation:
For this case we have the following function y=g(x) and we want to find the tangent line to this function using the conditions: [tex] g(4) =-3, g'(4)=2[/tex]
So we need a function like this one:
[tex] y- y_o = m(x-x_o) [/tex]
For this case m represent the slope and is given by [tex]m= g'(4) = 2[/tex] and from the other condition given we know that [tex] x_o = 4, y_o =-3[/tex]. And replacing we got:
[tex] y -(-3)=2(x-4)[/tex]
And if we reorganize the terms we have:
[tex] y+3 = 2x -8[/tex]
And subtracting 3 in both sides we got:
[tex] y = 2x -11[/tex]
9. For the following vectors, x and y, calculate the indicated similarity or distance measures. a. (a) x : (0,0,1,1), y : (2,2,2,2) cosine, correlation, Euclidean b. (b) x : (0,1,0,1), y : (0,1,0,1) cosine, correlation, Euclidean, Jaccard c. (c) x : (1,1,0,1), y : (-1,0,-1,0) cosine, correlation, Euclidean d. (d) x : (1,0,0,1,0,1), y : (0,1,1,0,0,1) cosine, correlation, Jaccard e. (e) x : (2,1,0,2,0,3), y : (1,1,1,0,0,1) cosine, correlation
Answer:
The answer to this question can be defined as follows:
a)
cosine: 0.707
correlation: 0
Euclidean: 3.16
b)
cosine: 1
correlation: 1
Euclidean: 0
Jaccard: 1
c)
cosine: -0.4082
correlation: 0.5774
Euclidean: 2.64
d)
cosine: -0.333
correlation: -0.3333
Jaccard: 0.5
e)
cosine: -0.7075
correlation: 0.2132
Step-by-step explanation:
a) cosine:
[tex]x \times y( 0 \times 2+ 0 \times 2 +1 \times 2+1 \times 2) = 4\\\\ x= \sqrt{2} = 1.414\\\\y= \sqrt(16)=4\\\\\cos (x\times y) = \frac{x\times y}{x\times y}\\\\\cos (x\times y) = \frac{4}{1.414\times 4}\\\\= 0.707[/tex]
correlation:
[tex]\ corr(x,y) =[\frac{covariance (x,y)}{standec(x) \times standdev(y)}]\\X \ mean = 0.5\\Y \ mean = 2\\covariance (x,y) = 0\\standdev(x) = 0.5774\\standdev(y) = 0\\corr(x,y) = 0[/tex]
Euclidean:
[tex]d(x,y) = \sqrt((0-2)^2+(0-2)^2+(1-2)^2+(1-2)^2)\\d(x,y) = 4+4+1+1\\d(x,y)= \sqrt(10)\\d(x,y)= 3.16\\[/tex]
by applying above formula we get all the values.
b)
cosine: 1
correlation: 1
Euclidean: 0
Jaccard: 1
c)
cosine: -0.4082
correlation: 0.5774
Euclidean: 2.64
d)
cosine: -0.333
correlation: -0.3333
Jaccard: 0.5
e)
cosine: -0.7075
correlation: 0.2132
Let A, P, and D by n x n matrices. Mark each statement true or false. Justify each answer.
a. A is diagonalizable if A = PDP^-1 for some matrix D and some invertible matrix P. Choose the correct answer below.
O The statement is true because the columns of P are the n linearly independent eigenvectors of A.
O The statement is false because A must have n distinct eigenvalues for the matrix D and P to exist.
O The statement is true because if A = PDP^-1, then A is diagonalizable by definition.
O The statement is false because the symbol D does not automatically denote a diagonal matrix.
Answer:
Correct answer is the 4th answer.
Step-by-step explanation:
By definition, a matrix is called diagonalizable if there exists some invertible matrix P and a diagonal matrix D such that AP = PD, which is equivalent to having A = PDP^-1.
We are not told that D is a diagonal matrix, hence, it could be any matrix. If A=PDP^-1 for some matrix D that is not diagonal, it doesn't imply that A is diagonalizable. Consider the following case: Let us take A a non diagonalizable matrix. Take D = A and P = identity matrix of size n. Then, this equation holds, but A is still not diagonalizable.
una mulita está atada a un aranjo la mulita aburrida ha dado vueltas y vueltas alrededor del árbol manteniendo estirada la cuerda sin que ésta Se enrolle si la distancia que hay de la mulita al centro del árbol es de 5 metros qué distancia habrá recorrido después de dar 150 vueltas
Answer:
[tex]\Delta s_{T} = 4712.4\,m[/tex]
Step-by-step explanation:
(This exercise is written in Spanish and for this reason the response will be presented in such language).
La distancia recorrida por la mulita tras una vuelta es:
[tex]\Delta s = 2\pi\cdot (5\,m)[/tex]
[tex]\Delta s \approx 31.416\,m[/tex]
Ahora, la distancia recorrida total es directamente proporcional a la cantidad de vueltas invertidas. Este indicador se determina por regla de tres simple:
[tex]\Delta s_{T} = \frac{150}{1}\times (31.416\,m)[/tex]
[tex]\Delta s_{T} = 4712.4\,m[/tex]
How are the functions f (x) = 16 Superscript x and g (x) = 16 Superscript one-half x related
Answer:
g(x) is f(x) expanded horizontally by a factor of 2
Step-by-step explanation:
Given:
f(x) = 16^x
g(x) = 16^(x/2)
__
Replacing x in a function with x/k expands the graph horizontally by a factor of k. Here, it seems we have ...
g(x) = f(x/2)
so g(x) is a horizontal expansion of f(x) by a factor of 2.
Answer:
c). The output values of g(x) are the square root of the output values of f(x) for the same value of x.
Step-by-step explanation:
slope of the line with points (4,-2) and (24,-17)
Answer:
-3/4
Step-by-step explanation:
y2-y1/x2-x1
-17+2 divided by 24-4
-15/20
-3/4
Answer:
-3/4
Step-by-step explanation:
The slope of a line is given by
m = (y2-y1)/(x2-x1)
= (-17- -2)/(24-4)
= (-17+2)/(20)
= -15/20
=-3/4
Which is the best estimate of -3/5
Answer:
-0.6
Step-by-step explanation:
3/5 is 0.6 and the negative makes it -0.6.
Answer:
-0.6
Step-by-step explanation:
An automobile battery manufacturer offers a 31/54 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated-credit period. Under this warranty, if a battery fails within 31 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 31 months but within 54 months, the manufacturer provides a prorated credit toward the purchase of a new battery. The manufacturer assumes that X, the lifetime of its auto batteries, is normally distributed with a mean of 45 months and a standard deviation of 5.6 months.
1. If the manufacturer's assumptions are correct, it would reed to replace _______ of its batteries free.2. The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect. A standard deviation of ____ results in a 1.07% replacement rate.3. Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?
Answer:
1) If the manufacturer's assumptions are correct, it would reed to replace 0.621% of its batteries free
2) The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect. A standard deviation of 6.084 results in a 1.07% replacement rate
3) Using the revised standard deviation for battery life, the percentage of the manufacturer's batteries that don't qualify for free replacement but do qualify for the prorated credit = 92%
Step-by-step explanation:
This is a normal distribution problem with
Mean = μ = 45 months
Standard deviation = σ = 5.6 months.
Batteries that fail within the first 31 months get a free replacement and batteries that fail after 31 months but within 54 months get a prorated credit toward the purchase of a new battery.
1) Percentage of batteries that'll qualify for a replacement are the batteries that fail within 31 months. That is, P(X ≤ 31)
To obtain this, we first normalize or standardize 31 months.
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (31 - 45)/5.6 = - 2.50
The required probability
P(X ≤ 31) = P(z ≤ -2.50)
We'll use data from the normal probability table for these probabilities
P(X ≤ 31) = P(z ≤ -2.50) = 0.00621 = 0.621%
2) The company finds that the percentage of free batteries replaced is actually 1.07%
P(X ≤ 31) = 1.07% = 0.0107
Let the z value of 31 months under this new normal distribution be z'
P(X ≤ 31) = P(z ≤ z') = 0.0107
From the normal distribution table,
z' = -2.301
z' = (x - μ)/σ
-2.301 = (31 - 45)/σ
σ = (-14) ÷ (-2.301) = 6.084 months
3) Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?
That is, P(31 < X ≤ 54)
We first normalize 31 and 54 using the revised standard deviation
For 31
z = (x - μ)/σ = (31 - 45)/6.084 = - 2.30
For 54
z = (x - μ)/σ = (54 - 45)/6.084 = 1.48
The required probability = P(31 < X ≤ 54)
= P(-2.30 < z ≤ 1.48)
Using the normal distribution tables
P(31 < X ≤ 54) = P(-2.30 < z ≤ 1.48)
= P(z ≤ 1.48) - P(z < -2.30)
= 0.93056 - 0.0107
= 0.91986 = 91.986% = 92% to nearest whole number.
Hope this Helps!!!!
You are paid $10.65/hr. Your deductions are FICA (7.65%), federal tax withholding (9.9%), and state tax withholding (7.35%). Your housing and fixed expenses are $493.68/month. How many hours per month must you work to be sure those expenses are paid?
62 hours
64 hours
68 hours
66 hours
Answer:
The first option; You must work about 62 hours.
Step-by-step explanation:
The total percent that you pay in taxes is 24.9%.
That means that you keep 75.1% of the money that you earn. We can write the following equation to determine the number of hours, h, that it will take to earn 493.68.
0.751(10.65)h = 493.68
Just divide by 0.751 and 10.65 and you will get the number of hours needed.
Answer:
A.) 62 hours
Step-by-step explanation:
I took the consumer math test :)
Please answer this correctly
Solve the system of equations by elimination.
2x + 2y = -2
3x - 2y = 12
5x = 10
x = 2
2(2) + 2y = -2
4 + 2y = -2
2y = -6
y = -3
The function F(c)=log0.5x is decreasing true or false
Answer:
true
Step-by-step explanation:
We assume you intend your function to be ...
[tex]F(x)=\log_{0.5}x[/tex]
A logarithm with a base less than 1 is a decreasing curve. Here, the base appears to be 0.5, a value less than 1. Hence the curve is decreasing.
What is the domain of the given function?
{(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
A shop has the following offers. Fig rolls (125g packet) Normal price £1.08. Buy one, get 2nd half price
Step-by-step explanation:
Fig rolls = 1.08
Half price = 1.08 ÷ 2 = 0.54
Total price = 1.08 + 0.54 = 1.62
Answer:
£8.52
Step-by-step explanation:
Fig rolls: £1.08+£1.08=£2.16
Crisps: £1.59+£1.59=£3.18 £3.18x2=£6.36
Total price= £2.16+£6.36=£8.52
Someone please help!!!! I’ll give most brainliest
Answer:
252 inches squared
Step-by-step explanation:
(6 x 9) + (6 x 15) + (9 x 12) = 252
If f(x) = 3x² + 1 and g(x) = 1 - X, what is the value of (f -9)(2)?
Answer:
(f -g)(2) = 14
Step-by-step explanation:
You can write the expression for the composite function as ...
(f -g)(x) = f(x) -g(x) = (3x² +1) -(1 -x)
(f -g)(x) = 3x² +x
Then for x = 2 ...
(f -g)(2) = 3(2²) +2
(f -g)(2) = 14
show work 1/4 ÷ 3/8 simplest form
Answer:
2/3
Step-by-step explanation:
1/4 ÷ 3/8 = 1/4 x 8/3 = 8/12 = 2/3
Answer:
2/3
Step-by-step explanation:
to divide make sure to use the reciprocal of the 3/8 which is
1/4*8/3
reduce the numbers with the greatest common factor divisor of 4
8/4=2 then 1*3 equals 3 which is 2/3
so it is 2/3
Which of the following choices describes volume?
a
The amount of juice a carton can hold.
b
The weight of a bowling ball.
c
How tightly the molecules in a glass of water are packed together.
d
The temperature that must be reached for ice to melt.
Answer:
C. How tightly the molecules in a glass of water are packed together
Step-by-step explanation:
Volume of a substance is different according to the state of the matter.
So for a water molecule, the volume of the the water is definite and can be measured by the container which is the glass cup
So volume can be the measure of how tight the molecule of that substance ate together.
Use angles shown to make other angles
Answer:
angle ABC and angle KLM
Step-by-step explanation:
Angle ABC equals to 35 degrees and KLM equals to 95 degrees. Their sum equals 135 degrees.
Answer:
The answer is B and C.
Step-by-step explanation:
When these 2 angles are added together, they form 130° :
∠ABC + ∠KLM = 35° + 95°
= 130°
The volume of the prism shown is 84 cubic yards. What is the Height of the prism
Answer:
4 yd
Step-by-step explanation:
If l×w×h=v, then v÷l÷w=h
84÷7÷4=h
12÷3=h
h=4
The height of the prism is 4 yards.
In a certain Algebra 2 class of 23 students, 11 of them play basketball and 13 of them play baseball. There are 8 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answer:
9/23
Step-by-step explanation:
Of the 23 students, 9 play both baseball and basketball. The probability of choosing one of those is 9/23.
___
Let A represent basketball, and B represent baseball. Then ...
P(A or B) = P(A) +P(B) -P(A and B)
Since 8 students play neither sport, we have ...
1 -8/23 = 11/23 +13/23 -P(A and B)
15/23 = 24/23 -P(A and B)
P(A and B) = (24 -15)/23
P(A and B) = 9/23
there are 7 row of 9 people how many people in all
Answer:
63
Step-by-step explanation:
You simply just multiply the 7 and 9.
James invests $100 at the beginning of each quarter in stock ABC. According to the table below, how many shares of ABC will James own at the end of the year?
A.
44 shares
B.
37 shares
C.
38 shares
D.
41 shares
Answer:
ABC | Stock price
Q1 | $10.50
Q2 | $11.50
Q3 | $9.00
Q4 | $10.50
Step-by-step explanation:
Answer is 37 shares on AP3X
10^xy=1000, where x and y are positive integers and x > y, what is one possible value of x?
Answer:
hey
Step-by-step explanation:
Lisa is packing a set of cubic inch blocks into the box shown below How many blocks will fit in the box8 in.5 in.3 in.A.16B. 32C. 120D. 180
Answer:
120 Blocks or letter C
Step-by-step explanation:
I did 8x5x3, because lxwxh so i got 120
if X/4 = x+1/5, then x =
Answer:
as written, -4/15with parentheses, 4Step-by-step explanation:
As the problem is written, you have ...
[tex]\dfrac{x}{4} =x+\dfrac{1}{5}\\\\5x=20x+4\qquad\text{multiply by 20}\\\\-15x=4\\\\x=-\dfrac{4}{15}[/tex]
__
If you add parentheses to include x in the numerator, then you have ...
x/4 = (x +1)/5
[tex]5x=4(x+1)\qquad\text{multiply by 20}\\\\5x -4x = 4\qquad\text{eliminate parentheses, subtract 4x}\\\\x=4[/tex]
__
Additional comment
We include the second working because it is a fairly common mistake to neglect to put parentheses around a numerator or denominator. The solutions to such problems are not often fractions, so we suspect you intend the latter form.
put this on order from greatest to least pls
Answer:
0.497 < 1/2 < 0.55 < 3/5 < 6/7
Step-by-step explanation:
Order from Least to Greatest
1: Using the given inputs
2: Rewriting these inputs as decimals
3: Sorting this table by decimal values in order from least to greatest
4: Therefore, the sorted inputs in order from least to greatest is
Answer: 0.497 < 1/2 < 0.55 < 3/5 < 6/7
Hope this helps.
Write a 3×3 matrix A which A^2 is diagonal while A is not diagonal ?
Consider the matrix
[tex]A=\begin{bmatrix}0&1&0\\1&0&0\\0&0&1\end{bmatrix}[/tex]
Multiplying A by itself has the effect of swapping the first and second rows:
[tex]A^2=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}[/tex]
which is diagonal, while A itself is not.