Answer:
using [tex]\pi[/tex]: 65.45 in³ (nearest hundredth)
using [tex]\pi =3.14[/tex]: 65.42 in³ (nearest hundredth)
Step-by-step explanation:
The radius of the sphere is half the side length of the cube (see attached diagram). Therefore, the side length of the cube = 2r
Given:
volume of the cube = 125 in³side length of cube = 2r[tex]\textsf{Volume of a cube}=x^3\quad \textsf{(where}\:x\:\textsf{is the side length)}[/tex]
[tex]\implies 125=(2r)^3[/tex]
[tex]\implies \sqrt[3]{125}=2r[/tex]
[tex]\implies 5=2r[/tex]
[tex]\implies r=\dfrac52[/tex]
Substitute the found value of r into the volume of a sphere equation:
[tex]\begin{aligned}\textsf{Volume of a sphere} & =\dfrac43 \pi r^3\\\\ & =\dfrac43 \pi \left(\dfrac52\right)^3\\\\ & =\dfrac43 \pi \left(\dfrac{125}{8}\right)\\\\ & =\dfrac{500}{24} \pi\\\\ & =\dfrac{125}{6} \pi\\\\ & =65.45\:\sf in^3\:(nearest\:hundredth) \end{aligned}[/tex]
What is a rewritten form of the radical?
A.
-8816
B.
C.
D.
-90.75
-98616
-2.904
A rectangular dance floor has an area of 96 square feet and a length of 8 feet. What is the width of the dance floor?
Answer:
The answer is 12ft
Step-by-step explanation:
96/8 = 12
Area = length x width
100 POINTS ANSWER ASAP
George's living room is a square that is 33 ft long on each side. He knows the diagonal of the ceiling from corner to corner must be longer than 33 ft.
(a) He thinks that because a square cut in half forms a special right triangle with the diagonal as the hypotense, so he multiples the side length by two to get 66 feet.
What is George's mistake?
(b) What is the correct length of the diagonal of George's ceiling using the correct special right triangle shortcut? (give exact answer, do not round)
(c) Use either the pythagorean theorem OR the correct trigonometry ratios to solve for the length of the diagonal (round to the nearest tenth of a foot)
Make sure to show all your work.
Answer:
47
Step-by-step explanation:
a)
a^2 + b^2 = c^2
33^2+33^2=c^2
2178=c^2
c=(nearest is 47)
b)
If you cut the square in half diagonally, it forms two right triangles with angle measures 90-45-45. You can use sin (opposite over hypotenuse) to find the length of the hypotenuse. sin (45) would be 33/(hypotenuse length). From a trig chart, you can find that sin (45) is 1/sqrt(2), meaning that 33/x = 1/sqrt(2). This means that x=33sqrt(2), which is around 47.
what is the greatest prime number less than 50?
Answer:
The greatest prime number less than 50 is 47
Please help and explain this to me!! I am confused and would like to know how to solve!!
Answer:
13. C) The sum of the numerators is incorrect.
14. B) [tex]-\frac{5}{8}+\frac{1}{8}=\frac{-5+1}{8}=\frac{-4}{8} =-\frac{1}{2}[/tex]
Step-by-step explanation:
13. The reason why it's incorrect.
When dealing with the sum of fractions, denominators must be the same. So allows us to do the sum of the numerator. The image displayed is the incorrect sum of the numerator.
14. [tex]-\frac{5}{8}+\frac{1}{8}=\frac{-5+1}{8}=\frac{-4}{8} =-\frac{1}{2}[/tex]
write an inequality for this situation
Embiid scored at least 31 points
A, E > 31
B, E < 31
Answer: [tex]E \ge 31[/tex]
Reason:
"at least 31 points" means "31 or more".
So either E = 31 or E > 31 (meaning Embiid scored 31 points or he scored more than 31 points).
Choice A looks like the closest match assuming the inequality sign is [tex]\ge[/tex]
Saying E > 31 instead of [tex]E \ge 31[/tex] would be false because it leaves out the case E = 31.
Please help me with this math question. Thank you.
Answer:
D
Step-by-step explanation:
We want to find the values of x such that:
[tex]\displaystyle -x^2 + 7x + 5 = 0[/tex]
We can use the quadratic formula. Recall that:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = -1, b = 7, and c = 5. Substitute and evaluate:
[tex]\displaystyle \begin{aligned} x & = \frac{-(7)\pm\sqrt{(7)^2-4(-1)(5)}}{2(-1)}\\ \\ & = \frac{-7\pm\sqrt{49+20}}{-2} \\ \\ & = \frac{-7\pm\sqrt{69}}{-2}\end{aligned}[/tex]
In conclusion, the answer is D.
Please help on math.
Answer:
The median is 45
Step-by-step explanation:
The median is also referred to as "the middle" value, so you want to take all the values in order and find the middle number. that will be the median. It's the same either box plots.
A quicker way to find it with box plot is to look at the line inside the of the box (line is not always in center of box) on the plot. that is where you'll find the median on questions like these.
hope this helps! :)
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
Answer:
the answer is in the picture
I need help solving this math problem. The teacher wants us to fill in three things using this math equation: 2x - 3√x + 1 = 0
(1) u=_
(2) u^2=_
(3) _u^2+_u+1=0
The teacher wants us to accomplish this using the U-Substitution method.
I'm not sure for my awnser but I thing 30
help me with this pls
Answer:
sure I'll help u with this as this question required to have a and asuch a being used to review with an associate with you in the comment of the item that you used in the comment is the only one that was a good one to review the product and details about the refund
Find the missing dimension of the triangle.
Area = 30 mm squared
6 mm = height
b = mm
Answer:
b = 10 mm
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex]bh ( b is the base and h the height )
given A = 30 and h = 6 , then
[tex]\frac{1}{2}[/tex]b × 6 = 30 , that is
3b = 30 ( divide both sides by 3 )
b = 10
henry had charged 847 dollars to his credit card. the cost of his next purchase caused him to exceed his credit limit of 1000
Answer:
The purchase is greater than $153
Step-by-step explanation:
What is z in the context of the problem that’s at hand?
Answer:
The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean
Step-by-step explanation:
i dont know if i am correct tho, please like if i am correct
Suppose you play a game in which 5 dice (6-sided) are rolled simultaneously.
If a "4" is rolled, then you win $2 for each "4" showing.
If all the dice are showing "4", you win $1000.
If none of the dice are showing "4", then you lose $5.
What is the expected value of this game. (Show work)
If you want to you can take a photo of the work and upload it.
The expected value of the game in which 5 dice (6-sided) are rolled simultaneously is -0.2094.
How to find the mean (expectation) and variance of a random variable?Supposing that the considered random variable is discrete, we get:
Mean = [tex]E(X) =[/tex] [tex]\sum_{\forall x_i} f(x_i)x_i[/tex]
Here, [tex]x_i; \: \: i = 1,2, ... ,[/tex] n is its n data values and [tex]f(x_i)[/tex]is the probability of [tex]X = x_i[/tex]
Suppose you play a game in which 5 dice (6-sided) are rolled simultaneously.
If a "4" is rolled, then you win $2 for each "4" showing.If all the dice are showing "4", you win $1000.If none of the dice are showing "4", then you lose $5.Let Y is the amount of money player won. The value of X can be,
[tex]Y=2,4,6,8,1000,-5[/tex]
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials. Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np\\ Var(X) = np(1-p)[/tex]
Put the values as 5 trials for each time 4 appears.
[tex]P(X =0) = \: ^5C_1(\dfrac{1}{6})^0(1-\dfrac{1}{6})^{5-0}=0.4018 \:\\P(X =1) = \: ^5C_1(\dfrac{1}{6})^1(1-\dfrac{1}{6})^{5-1}=0.402\\P(X =2) = \: ^5C_2(\dfrac{1}{6})^2(1-\dfrac{1}{6})^{5-2}=0.162\\P(X =3) = \: ^5C_3(\dfrac{1}{6})^3(1-\dfrac{1}{6})^{5-3}=0.032\\P(X =4) = \: ^5C_4(\dfrac{1}{6})^4(1-\dfrac{1}{6})^{5-4}=0.0032\\P(X =5) = \: ^5C_5(\dfrac{1}{6})^5(1-\dfrac{1}{6})^{5-5}=0.00013\\[/tex]
The probability of loosing $5 equal probability of 0 success.
[tex]P(Y=-5)=P(x=0)[/tex]
Similarly, for probability of getting profit are,
[tex]P(Y=2)=P(x=1)\\P(Y=4)=P(x=2)\\P(Y=6)=P(x=3)\\P(Y=8)=P(x=4)\\P(Y=1000)=P(x=5)[/tex]
Expected value of game,
[tex]E(Y)=\sum y .P(Y=y)\\E(Y)=-5.P(X=0)+2.P(X=1)+4.P(X=2)+6.P(X=3)+8.P(X=4)+1000.P(X=5)\\E(Y)=-0.2094[/tex]
Thus, the expected value of the game in which 5 dice (6-sided) are rolled simultaneously is -0.2094.
Learn more about expectation of a random variable here:
https://brainly.com/question/4515179
Learn more about binomial distribution here:
https://brainly.com/question/13609688
#SPJ1
What is the answer to3/8 + 3/4=?
Use ABC to find the value of tan B 41/9 40/9 41/40 9/41
Answer:
tanB =40/9
Step-by-step explanation:
tan B = opposite/adjacent
where the opposite is 40 and the adjacent is 9
therefore, tanB =40/9
8. The expression below is evaluated when x = 9, y = 3,
and z = 2. What is the value of the expression?
8x - 72 + 2y
Answer:
64
Step-by-step explanation:
First of all substitute the values to where ever you see their corresponding variables to make them multiply.
x = 9
y = 3
z = 2
so we get
8x as 8(9),
7z as 7(2)
2y as 2(3)
then the it's will be
8(9) - 7(2) + 2(3)
which is
72 - 14 + 6
finally we get
64
Which equation does NOT represent a linear function? A. y = 5 B. 4 y = 2 x − 8 C. y = x + 2 x 2 D. y = − 2 3 x − 1
What are all possible values of x if 10x + 7 ≥ 67
[tex]~~~~10x+7\geq 67\\\\\implies 10x \geq 67 -7\\\\\implies 10x \geq 60\\\\\implies x \geq \dfrac{60}{10}\\\\\implies x \geq 6[/tex]
1. Find the volume of the figure.
4 cm
2 cm
10 cm
10 cm
1 cm
3 cm
1 cm 1 cm
some one help me solve this asap pls and thx!!
Answer:
x = 14
Step-by-step explanation:
Knowing that this figure is a vertical angle.
Define vertical angles ⇒ a pair of opposite angles formed by intersecting lines
Thus, if the left side = 122
then the other side must equal 122
The equation is:
8x + 10 = 122
Subtract 10 from both sides
8x + 10 - 10 = 122 -10
8x = 122
Divide both sides by the same factor
8x/8 = 122/8
Simplify
x = 14
Thus, x = 14.
Kavinsky
Write an equation in slope-intercept form of the line shown.
An equation is
Answer:
y = -x - 4
hope this helped :)
A table of values for the quadratic function f is shown below. If 3 is one solution to f(x) = 0, what is the value of the other solution?
Record your answer and fill in the bubbles on your answer document.
Answer:The answer to this oroblem would be -7
Step-by-step explanation:We can see this by when f(x) is 0 right next to it is -7
The value of the other solution for f(x)=0 is -7. This is obtained by taking the general form of the quadratic equation f(x)=y.
Quadratic function:A function is represented by an equation f(x)=ax²+bx+c where a≠0 and b, c are any real numbers.This can be generalized into f(x)=y where x is an independent variable and y is a dependent variable.Given data:In the table, x values range from -8 to 1
So, we can write using the general form f(x)=y for these values
For x=-8, f(-8)=-2.75
x=-7, f(-7)=0
x=-6, f(-6)=2.25
x=-5, f(-5)=4
x=-4, f(-4)=5.25
x=-3, f(-3)=6
x=-2, f(-2)=6.25
x=-1, f(-1)=6
x=0, f(0)=5.25
x=1, f(1)=4
And 3 is one of the solution to f(x)=0.
Calculating solution for f(x)=0:It is given that f(x)=0 when x=3
Thus,
f(3)=0
From the table,
f(-7)=0
So, the other solution for the function f(x)=0 is -7.
Learn more about quadratic function here:
https://brainly.com/question/12275667
#SPJ2
Solve for x=?
a. 1.5(x+t)=9
Answer:
1.5x1.5t=9
Step-by-step explanation:
because i am learning this topic
Please help me answer this! Thank you! No links!
Answer:
139
Step-by-step explanation:
why does thsi always happen
Answer:
It always happens because you asked the question
Step-by-step explanation:
The angle of elevation to the top of a Building in New York is found to be 3 degrees from the ground at a
distance of 2 miles from the base of the building. Using this information, find the height of the building.
Your answer is in feet
Answer:
The height of the building is about 553.4 feet.
Step-by-step explanation:
tan (3°) = h/2
h = 2 tan (3°) = .10481 miles = 553.4 feet
Two angles are supplementary. The larger angle is
150
∘
larger than the smaller angle. Find the measure of both angles, and separate your answers with a comma.
Answer:
x = 165, y = 15
Step-by-step explanation:
1. Well, what does supplementary mean? - The angles add up to 180°.
2. Let's form an equation: x + y = 180°
3. Let's say x is the larger angle and y is the smaller angle.
4. Let's form another equation: x = 150 + y
5. Put the two equations next to each other:
x + y = 180
x = 150 + y
6. We know what x is equaled to, so let's plug it into the first equation!
150 + y + y = 180
150 + 2y = 180
-150 -150
2y = 30
y = 15
7. Now, we know what y is, let's find x!
x + 15 = 180
-15 -15
x = 165
The measure of both angles are 15 degrees and 165 degrees.
What is Angle?An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle
Given that the two angles are supplementary.
we know that supplementary angles are the angles whose sum is added to 180 degrees.
Let the smaller angle is x.
The larger angle is 150∘ larger than the smaller angle.
y=x+150
Now add both the angles which makes 180 degrees
x+x+150=180
2x+150=180
Subtract 150 on both sides
2x=30
Divide both sides by 2
x=15
So the smaller angle is 15 and the larger angle is 165 degrees
Hence, the measure of both angles are 15 degrees and 165 degrees.
To learn more on Angles click:
https://brainly.com/question/28451077
#SPJ2
where can I get study guide help for algebra 2 thank you
Answer:
Stay after school more often with your math teacher or come early to school to practice math or to see what your stuggling at.