Answer:
15Step-by-step explanation:
In the question it is given that the volume of a sphere is 4,500π cubic yards. And we have to find the radius.
We know that,
4/3πr³ = Volume of a sphereNow, Substituting the values in the fomulae :
⇒ 4/3πr³ = 4500π
Cancelling π from both sides :
⇒ 4/3r³ = 4500
⇒ 4r³ = 4500 × 3
⇒ 4r³ = 13500
⇒ r³ = 13500/4
⇒ r³ = 3375
Taking cube root on both sides we get :
⇒ r = 15
Therefore,
The radius of the sphere is 15 yardsAnswer:
15 yardsStep-by-step explanation:
In this question we have provided volume of sphere that is 4500π cubic yards . And we are asked to find the radius of the sphere .
We know that ,
[tex] \qquad \: \frak{Volume_{(Sphere)} = \dfrac{4}{3}\pi r {}^{3} } \quad \bigstar[/tex]
Where ,
r refers to radius of circleSolution : -
As in the question it is given that volume of sphere is 4500π . So equation it with volume formula :
[tex] \dashrightarrow \: \qquad \: \dfrac{4}{3} \pi r {}^{3} = 4500\pi[/tex]
Step 1 : Cancelling π as they are present on both sides :
[tex]\dashrightarrow \: \qquad \: \dfrac{4}{3} \cancel{\pi }r {}^{3} = 4500 \cancel{\pi}[/tex]
We get ,
[tex]\dashrightarrow \: \qquad \: \dfrac{4}{3} r {}^{3} = 4500[/tex]
Step 2 : Multiplying with 3/4 on both sides :
[tex]\dashrightarrow \: \qquad \: \dfrac{ \cancel{4}}{ \cancel{ 3}} r {}^{ 3} \times \dfrac{ \cancel{3}}{ \cancel{4}} = \cancel{ 4500} \times \dfrac{3}{ \cancel{4} }[/tex]
On further calculations, We get :
[tex]\dashrightarrow \: \qquad \: r {}^{3} = 1125 \times 3[/tex]
[tex]\dashrightarrow \: \qquad \:r {}^{3} = 3375[/tex]
Step 3 : Applying cube root on both sides :
[tex]\dashrightarrow \: \qquad \: \sqrt[3]{r {}^{3} } = \sqrt[3]{3375} [/tex]
We get :
[tex]\dashrightarrow \: \qquad \: \purple{\underline{\boxed{\frak{r = 15 \: yards}}}}[/tex]
Therefore , radius of sphere is 15 yards .#Keep Learning9,15,21 find the 38th term
Answer:
231
Step-by-step explanation:
The pattern is add 6. But it is more easier to use the linear function: 6x+9. Since this starts with 0, we plug in 37 for x instead of 38.
simplify the given expressions and then write your answer in standard form.
1.456×100000000
Answer:
145600000
Step-by-step explanation:
Please mark as branliest !
During second period, Cora completed a grammar worksheet. She got 28 out of 40 questions correct. What percentage did Cora get correct?
Answer:
%70
Step-by-step explanation:
percentage can be found by dividing the values than multiplying the values by 100
Formula: (value/totalvalue)100
plug in the formula with what we have;
28/40(100)
→ First step; dividing our value by total value (28/40)
28/40 = 0.7
→ Second step; multiplying our value by 100 (0.7)
0.7 * 100 = 70
Therefore cora got %70 correct on her grammar sheet
Answer:
70% correct
Step-by-step explanation:
We know that there are 40 questions on her grammar worksheet.
Out of those 40 questions, she got 28 right so 28/40 equals 0.7
What is the geometric mean 2 and 7?
Answer: [tex]\sqrt{14}[/tex]
Work Shown:
[tex]\text{x} = \text{geometric mean of A and B}\\\\\text{x} = \sqrt{A*B}\\\\\text{x} = \sqrt{2*7}\\\\\text{x} = \sqrt{14}\\\\[/tex]
30 books = 45kg
45 books = ?
Answer:
67.5 kg
Step-by-step explanation:
To determine the weight of 45 books, we need to determine the weight of one book, using the equation (30 books = 45 kg). This can be done by dividing 30 to both sides of the equation. Therefore,
⇒ 30 books/30 = 45/30 kg⇒ 1 book = 45/30 kg = 3/2 kg = 1.5 kgWe obtained the following equation;
⇒ 1 book = 1.5 kgNow, multiply both sides by 45 to determine the weight of 45 books.
⇒ 1 book × 45 = 1.5 kg × 45⇒ 45 books = 67.5 kgTherefore, the weight of 45 books is 67.5 kg.
Answer:
[tex]\huge\boxed{\bf{45books = 67.5kg}} [/tex]
Step-by-step explanation:
Given:-
30 books = 45kgTo find:-
45 books = ?Ans:-
30books = 45kg
45books = y kg
Let's find 45 books (y)
[tex]\sf \to \frac{30}{45} = \frac{45}{y}[/tex]
[tex]\sf \to 45*45 = 30*y[/tex]
[tex]\sf \to 2,025 = 30*y[/tex]
[tex]\sf \to y = \frac{2,025}{30}[/tex]
[tex]\sf \to y = 67.5kg[/tex]
~therefore 45books = 67.5kg
[tex]\:[/tex]
[tex]\huge\colorbox{red}{BlackPain}[/tex]
At a certain intersection, the light for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds. What is the probability that the light is red? Using the binomial distribution, what is the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light?
a)P(red)=.15,P(exactly3getstopped)=.08
b)P(red)=.15,P(exactly3getstopped)=.97
c)P(red)=.3,P(exactly3getstopped)=.8
d)P(red)=.3,P(exactly3getstopped)=.25
The Probability of red light is 0.3
P(red) = 0.3
The probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light be 0.25.
P(exactly three get stopped by red light)=0.25
The correct option is (d) P(red)=.3,P(exactly 3 get stopped)=.25
What is Binomial distribution?
A binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times.
The occurrence,
Red light= 15 sec, Yellow light= 5 sec, Green light= 15 secp= probability of a red light
=[tex]\frac{15}{15+5+30}[/tex]
= [tex]\frac{15}{50}[/tex]
= 0.3
Hence, Probability of getting red light be,
P (red)= 0.3
Now, the Binomial distribution formula,
Probability=( [tex]_r^nC[/tex])[tex]\;p^{r} \;q^{n-r}[/tex]
where, r = number of times for a specific outcome within n trials
[tex]_r^nC[/tex] = number of combinations
p = probability of success on a single trial
q = probability of failure on a single trial
n = number of trial
According to question,
r= 3 (Exactly three)n=8 (eight eastbound)p(red) =0.3q= 1 -p= 1- 0.3
= 0.7
Now using the formula, ( [tex]_r^nC[/tex])[tex]\;p^{r} \;q^{n-r}[/tex]
P( exactly 3 get stopped) = ( [tex]_3^8C[/tex])[tex]\;(0.3)^{3} \;(0.7)^{8-3}[/tex]
= [tex]\frac{8!}{3!(8-3)!}[/tex] [tex](0.027) \; (0.7)^{5}[/tex]
= [tex]\frac{8!}{3!(5)!}[/tex][tex](0.027) \; (0.16807)[/tex]
= [tex]\frac{8 * 7 * 6 }{3 * 2}[/tex] x 0.027 x 0.16807
= 56 x 0.00453789
= 0.25412184
≈ 0.25
Hence, Probability of next eight eastbound so that exactly three will stopped by a red light be 0.25.
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Write the equation of this line in slope-intercept form.
Answer:
Slope-Intercept Form: [tex]y = 2*x -3[/tex]
or
Point-intercept form: [tex]y-(-3)=2(x-0)[/tex]
Step-by-step explanation:
Method 1: Start from 1 point and then count the rise overrun.Slope-Intercept Form: [tex]y=mx+b[/tex]
Start from the Y-axis where [tex]b=-3[/tex] then rise/run to the next point. making that our slope.
Method 2: Using the point-intercept formPoint-intercept form: [tex]y-y_0=m(x-x_0)[/tex]
Solve the slope using the two points.
[tex](0,-3)[/tex] and [tex](2,1)[/tex] plug those values into the formula. Make [tex](x,y)=(0,-3)[/tex] and [tex](x_0,y_0)=(2,1)[/tex]
[tex]-3-1=m(0-2)[/tex]
[tex]-4=m(-2)[/tex]
[tex]m=-2[/tex]
[tex]y-(-3)=-2(x-0)[/tex]
Which of the following is an equivalent expression to the expression a1/3 / a1/4
A. A1/12
B. A7/12
C. 1/1/1/a12
D. 1/7/a12
Answer:
Option A :- [tex] \sf {a}^{\frac{1}{12}} [/tex]
Step-by-step explanation:
[tex] \hookrightarrow \sf \: \frac{ {a}^{ \frac{1}{3} } }{ {a}^{ \frac{1}{4} } } [/tex]
Simplify the expression
[tex] \hookrightarrow \sf \: {a}^{ \frac{1}{3} - \frac{1}{4} }[/tex]
Transform the Expression
[tex] \hookrightarrow \sf \: {a}^{ \frac{4 - 3}{12} }[/tex]
Calculate
[tex] \hookrightarrow \sf {a}^{\frac{1}{12}} [/tex]
Answer:
Option A
Step-by-step explanation:
Exponent Law: In exponent division, if base are same, subtract the powers
[tex]\sf \dfrac{a^m}{a^n}=a^{m-n}[/tex]
[tex]\sf \dfrac{1}{3}-\dfrac{1}{4}=\dfrac{1*4}{3*4}-\dfrac{1*3}{4*3}[/tex]
[tex]\sf =\dfrac{4}{12}-\dfrac{3}{12}\\\\=\dfrac{1}{12}[/tex]
[tex]\sf \dfrac{a^{\frac{1}{3}}}{a^{\frac{1}{4}}}=a^{\frac{1}{3}-\frac{1}{4}}[/tex]
[tex]=a^{\frac{1}{12}}[/tex]
PLEASE HELP!!
BRAINLIEST
Answer: 26 + 13 + 26 + 13 + x =180
Step-by-step explanation:
People with heart arrhythmia are known to have a resting pulse rate of 110 with a standard deviation of 5. With a new
experimental treatment, a group of 100 patients who suffer from heart arrhythmia has a resting pulse rate lowered to
108. Does this provide significant evidence that the experimental medication is effective at reducing resting pulse rate?
A. Yes, the test value is in the rejection region
B. No, the test value is not in the rejection region
C. Yes, the test value is not in the rejection region
OD. No, the test value is in the rejection region
The answer will be option A Yes, the test value is in the rejection region.
What is Z-score?A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
here the formula will be
[tex]Z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt {n}}}[/tex]
[tex]Z=\dfrac{100-110}{\dfrac{5}{\sqrt{100}}}[/tex]
[tex]Z=-20[/tex]
Z critical value =-1.645
Z calculated> Z critical value so we will reject.
Hence the answer will be option A Yes, the test value is in the rejection region.
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A student read a 303 –page book in 7 days. The table shows the total number of pages the student had read at the end
of each day for the 7 days. What was the average number of pages the student read per day from the end of day 2 to the end of day 6
To find the average number of pages the student read from day 2 to day 6, add the total pages in these days and divide by 5 days.
What is the average?This is a very common word used in mathematics and stadistics to refer to the mean value in a set of values.
How to calculate the average from day 2 to day 6?Add the pages the person read these days and then divide by 5 (total of days).
For example:
35 + 45 + 10 +25 + 20 = 135 / 5 = 27 pages
Note: This question is incomplete because the table is missing; due to this, the answer is based on general knowledge.
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Evaluate e3/2 to one decimal place
Answer:
Assuming you mean e to the power of 3/2, your answer should be 4.5. (4.482 rounded to the tenth.)
Step-by-step explanation:
"e" is simply 10 with an exponent. "e" to the power of 3/2 means [tex]10^{3/2}[/tex].
Plugging this in comes up with approximately 4.482 which can be rounded to 4.5.
Answer:
4.5
Step-by-step explanation:
Which equation best represents the relationship between x and y in the graph?
Answer:
A is the answer
Step-by-step explanation:
Here is one way pick two easy points (-4,0) and (0,-3)
and sub into each of the equations until you find the one that 'fits'
To convert temperature between degrees Fahrenheit to degrees Celsius, we use the formula C = 5/9(F-32).
What is 10° Celsius in degrees Fahrenheit?
A. 40°
B. 45°
C. 50°
D. 55°
HELP PLEASE!!!
f(0)=4, f(n)=2f (n-1) write the first six terms of the sequence
Answer:
n
=
1
→
a
1
=
−
2
←
given value
n
=
2
→
a
2
=
−
2
+
4
=
2
n
=
3
→
a
3
=
−
2
+
4
+
4
=
6
n
=
4
→
a
4
=
−
2
+
4
+
4
+
4
=
10
Step-by-step explanation:
brainlist me
find the value of x. 2x 20
Answer:
X = 10
Step-by-step explanation:
Since 2x = 20
we can divide 2 from both sides giving us x = 20/2
Therefore , x = 10 because 20 divided by 2 is 10
Answer:
X= 10
Step-by-step explanation:
2X=20
Then Divide both sides by 2 in order to find the value of X
2X/2=20/2
X= 10
What is the area of a rectangle that measures 4 meters wide and 6 meters long?
Answer:
The area of the rectangle is 24.
Step-by-step explanation:
To find the area it is Legth x Width
Therefore, 4 * 6 is 24
jim has a dog. jim buys 6 bags of dog biscuits. there are 27 biscuits in each bag of dog biscuits. jims dog eats 5 dog biscuits each day. has jim brought enough dog biscuits for 4 weeks. you must show how you got your answer
Answer:
i will give it to you
Step-by-step explanation:
that's it for you dear
The relationship between food purchased and food eaten by dogs can be written as, 162 biscuits ≥ 80 biscuits
What is multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.
First, let's calculate the total number of dog biscuits that Jim has bought:
= 6 bags × 27 biscuits per bag
= 162 biscuits
Next, let's calculate how many biscuits the dog will eat in 4 weeks:
= 4 weeks × 5 biscuits per day
= 20 biscuits per week
20 biscuits per week × 4 weeks = 80 biscuits
So, Jim has bought 162 biscuits and his dog will eat 80 biscuits in 4 weeks. This means that Jim has brought enough dog biscuits for his dog for 4 weeks.
162 biscuits ≥ 80 biscuits
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( what’s the better deal ) please help me with this, i’ve been trying for a long time
Answer:
Brand A is the better deal!
Step-by-step explanation:
Let's start by comparing.
We know brand B has the following cost: 5 ounces = $3.75
10 ounces $7.50 and 16 ounces = $12
Now check the graph.
6 ounces cost $3
12 ounces cost $6
20 ounces cost $10
I don't think we need to look any further but brand A is the better deal!
Suppose the length and width of the box double. Does the surface area S double? Complete the explanation.
Answer:
No, it will quadruple.
Step-by-step explanation:
If a figure is scaled up by some amount x(by multiplying), while still being the same shape, the surface area will scale up by x^2, and the volume will scale up by x^3.
Help!! I need the answer quick. Im really bad at fractions-
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]
Let's evaluate ~
[tex]\qquad \tt \dashrightarrow \:6 \frac{5}{8} + 4 \frac{3}{4} [/tex]
[tex]\qquad \tt \dashrightarrow \: \frac{53}{8} + \frac{19}{4} [/tex]
[tex]\qquad \tt \dashrightarrow \: \frac{53 + 38}{8} [/tex]
[tex]\qquad \tt \dashrightarrow \: \frac{91}{8} [/tex]
[tex]\qquad \tt \dashrightarrow \: 11\frac{3}{8} [/tex]
[tex]6 \frac{5}{8} + 4 \frac{3}{4} [/tex]
to find:the simplest form.
solution:[tex] \frac{53}{8} + \frac{19}{4} [/tex]
[tex] = \frac{(53 \times 4) + (19 \times 8)}{8 \times 4} [/tex]
[tex] = \frac{212 + 152}{32} [/tex]
[tex] = \frac{364}{32} [/tex]
[tex] = 11 \frac{3}{8} [/tex]
Find the measure of <1
Please answer ASAP, in desperate need will mark as brainliest
Answer:
m<1=32
Step-by-step explanation:
Just do 102-38÷2 to get the measure
Please please help, I will mark brainliest if correct!!!!!!!
Find the measure of the arc or angle indicated.
A. 108°
B. 36°
C. 72°
Answer: l08
Step-by-step explanation: It's becuase 36 x 3 is 108
Which formula can be used to find the centripetal acceleration of an orbiting object? ac = startfraction the square root of v over t endfraction. ac = startfraction v superscript 2 baseline over t endfraction ac = startfraction v superscript 2 baseline over r endfraction. ac = startfraction the square root of v over r endfraction.
The formula which can be used to find the centripetal acceleration is:
ac = startfraction v superscript 2 baseline over r endfraction
What is centripetalacceleration?This is simply the acceleration of an object moving in a circulation motion.
The centripetal acceleration can be expressed mathematically as
a꜀ = v² / r
Where
a꜀ is the centripetal acceleration v is the velocity of the object r is the radiusWith the above formula, we can conclude that the correct answer to the question is:
ac = startfraction v superscript 2 baseline over r endfraction
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Answer:
(c)
Step-by-step explanation:
I took the test
Just need the answer fast pls help
Answer:
Answer is D. [tex]\frac{121}{49}a^8b^2[/tex]
Step-by-step explanation:
We expand the powers.
[tex]\frac{11}{7}^2*(a^4)^2*(b)^2\\\frac{11}{7}*\frac{11}{7}*(a^4)(a^4)*(b*b)\\\frac{121}{49}*(a^8)*(b^2)[/tex]
when doing variable power you add them together.
a^4*a^4=a^(4+4) , b^1*b^1=b^(1+1)
Write an equation for a function whose graph has exactly two x-intercepts, one at x=-6 and the other at x=3.
Answer:
y = x^2 + 3x - 18
Step-by-step explanation:
A parabola with zeroes at x = - 6 and 3 would look like this:
(x+6)(x-3) = x^2 + 3x -18
Two Dimensional Shapes: Area
I really need help with this!!!
Answer:
area of the rectangle will be 175 square feet
m+ 7 = 3 + m+4
A. m =1/4
B. m =-7
C. no solution
D. infinite solutions
Answer:
D. infinite solutionsStep-by-step explanation:
Given equation
m + 7 = 3 + m + 4Simplify it to get
m + 7 = m + 7We have both sides equal, if we simplify further it will result in correct equation
0 = 0Regardless the value of m, the equation remains correct. It means it has infinite solutions
Correct choice is D
Both sides are equal equation has infinite solutions
Option DThe equation v=68t represents the number of views v for a video after t hours. Identify the independent and dependent variables.
Answer(s):
Dependent variable: vIndependent variable: tWhat is the dependent variable of an equation?
The dependent variable of an equation is the variable that is completely isolated on one side.
What is the independent variable of an equation?
The independent variable is the variable that is not isolated. The independent variable can either have a cooeficient or has some operation (+ - × ÷) included on that side of the equation.
Determining the independent and dependent variable
In this equation, we can see that "v" is completely isolated on one side and "t" has a cooeficient of 68. Thus, the dependent variable is "v" and the independent variable is "t".
If x - 10 is a factor of x2 - 8x - 20, what is the other
factor?
Answer:
(x + 2)
Step-by-step explanation:
x² - 8x - 20
consider the factors of the constant term (- 20) which sum to give the coefficient of the x- term (- 8)
the factors are - 10 and + 2 , since
- 10 × + 2 = - 20 and - 10 + 2 = - 8 , then
x² - 8x - 20 = (x - 10)(x + 2)
Answer:
(×+ 2)
Step-by-step explanation:
just did that trust me