Answer: [tex]47,916\pi \ cm3[/tex]
Step-by-step explanation:
You need to use the formula for calculate the volume of a sphere. This is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Where "r" is the radius.
You know that the radius of the exercise ball is 33 centimeters, then, you must substitute the valueof this radius into the formula [tex]V=\frac{4}{3}\pi r^3[/tex].
Therefore, the volume of the exercise ball is:
[tex]V=\frac{4}{3}\pi (33cm)^3[/tex]
[tex]V=47,916\pi \ cm3[/tex]
At the start of 2014 Lucy's house was worth £200,000.
The value of the house increased by 5% every year.
Work out the value of her house at the start of 2017.
To find the value of Lucy's house at the start of 2017, calculate a 5% increase each year from the initial £200,000 value in 2014. The compound value over the three years results in a house value of £231,525 at the start of 2017.
To calculate the value of Lucy's house at the start of 2017, we need to apply a 5% annual increase to the initial value of the house for three consecutive years (2014 to 2017).
Find the increase for the first year:
Initial value for 2014: £200,000
5% increase: £200,000 * 0.05 = £10,000
Value at the start of 2015: £200,000 + £10,000 = £210,000
Calculate the increase for the second year:
Value at the start of 2015: £210,000
5% increase: £210,000 * 0.05 = £10,500
Value at the start of 2016: £210,000 + £10,500 = £220,500
Calculate the increase for the third year:
Value at the start of 2016: £220,500
5% increase: £220,500 * 0.05 = £11,025
Value at the start of 2017: £220,500 + £11,025 = £231,525
Therefore, the value of Lucy's house at the start of 2017 would be £231,525.
how to simplify 2(3-4a)+5(a-7)
Multiply the first bracket by 2
Multiply the second bracket by 5
6-8a+5a-35
6-35-8a+5a ( just rearranging)
-29-3a or -3a-29 same answer just rearranging.
Answer is -29-3a or -3a-29
Answer:
2(3-4a)+5(a-7)
=6-8a+5a-35
=-3a-29
Step-by-step explanation:
Find the height of a rectangular prism if the surface area is 868, the width is 7 and the length is 31.
A.) 434
B.) 2.85
C.) 76
D.) 5.7
Answer:
D
Step-by-step explanation:
[tex]\rm\red{\overbrace{\underbrace{\tt\color{orange}{\:\:\:\:\:\:\:\:Question \: and \: Choices:\:\:\:\:\:\:\:\:\:}}}}[/tex]
Find the height of a rectangular prism if the surface area is 868, the width is 7 and the length is 31.
A.) 434
B.) 2.85
C.) 76
D.) 5.7
[tex]\rm\red{\overbrace{\underbrace{\tt\color{orange}{\:\:\:\:\:\:\:\:Answer:\:\:\:\:\:\:\:\:\:}}}}[/tex]
[tex]\huge\colorbox{pink}{\color{black}{\boxed{D.) 5.7}}}[/tex]
[tex]\large\purple{ChaEunWoo2009}[/tex]
#CarryOnLearning
IfH = 80° and J = 45°, then HJ ___ HG
Choose the correct symbol to put in the blank.
<
=
>
Answer:
c for sure
Step-by-step explanation:
(I got the question correct on my assignment)
The correct symbol to fill in the blank is: c. > (greater than)
Therefore, HJ < HG is the relationship between the angles HJ and HG based on the given angle measures.
To determine the relationship between the angles HJ and HG based on the given information, which states that angle H equals 80° and angle J equals 45°, we can utilize the properties of angles in a triangle.
Considering the angles in a triangle, the sum of the interior angles equals 180°. Therefore, if we have the measures of angles H and J in triangle HJG, we can find the measure of angle HG.
Given:
Angle H = 80°
Angle J = 45°
Let's calculate angle HG:
In a triangle, the sum of all angles is 180°.
So, angle HG = 180° - (angle H + angle J)
= 180° - (80° + 45°)
= 180° - 125°
= 55°
Therefore, angle HG measures 55°.
Now, to determine the relationship between HJ and HG:
Angle HJ is opposite angle HG within triangle HJG, and since angle H is greater than angle J, which implies that angle HG is greater than angle HJ.
Hence, the correct symbol to fill in the blank is:
c. > (greater than)
Therefore, HJ < HG is the relationship between the angles HJ and HG based on the given angle measures.
Complete Question:
IfH = 80° and J = 45°, then HJ ___ HG
Choose the correct symbol to put in the blank.
a.<
b.=
c.>
given that sin r= 28/53, what is cos R?
Answer:
45/53
Step-by-step explanation:
SinR is opposite side's length divided by the hypotenuse. That means that the hypotenuse is 53 units, and the opposite side (the shorter-looking) is 28 units.
By the pythagorean theorem, that means the longer-looking one is √(53² - 28²) = 45 units long.
CosR is the adjacent side'd length divided by the hypotenuse. That means that is is 45/53.
The value of the cosR is 45/53 if the value of sinR= 28/53 after applying the Pythagoras theorem.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
sinR = 28/53
Sin is the ratio of opposite to hypotenuse.
The length of the adjacent side from the Pythagoras theorem:
Adjacent side length = √(53²-28²) = 45 units
corR = 45/53
Because, cos is the ratio of adjacent to hypotenuse.
Thus, the value of the cosR is 45/53 if the value of sinR= 28/53 after applying the Pythagoras theorem.
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What is the point slope equation of a line with slope -4 that contains the point (-2,7)?
Answer: [tex](y-7)=-4(x+2)[/tex]
Step-by-step explanation:
The equation of a line in point slope form with slope m and passing through point (a,b) is given by :-
[tex](y-b)=m(x-a)[/tex]
Given : The slope of the line : m= -4
The point from which line is passing : (a,b) =(-2,7)
Then , the point slope equation of a line with slope -4 that contains the point (-2,7) will be :-
[tex](y-7)=-4(x-(-2))\\\\\Rightarrow\(y-7)=-4(x+2)[/tex]
Solve the equation for x.
the square root of the quantity x minus 8 end quantity plus 2 equals 7
A. x=1
B. x=13
C. x=17
D. 33
Answer:
D. 33
Step-by-step explanation:
√(x-8) + 2 = 7
subtract 2 from both sides
√(x-8) = 5
square both sides
(√(x-8))² = 5²
x-8 = 25
add 8 to both sides
x = 33
ANSWER
D. 33
EXPLANATION
The given radical equation is
[tex] \sqrt{x - 8} + 2 = 7[/tex]
Group similar terms,
[tex]\sqrt{x - 8} = 7 - 2[/tex]
[tex]\sqrt{x - 8} = 5[/tex]
Square both sides:
[tex] {(\sqrt{x - 8})}^{2} = {5}^{2} [/tex]
Simplify
[tex]x - 8 = 25[/tex]
Solve for x
[tex]x = 25 + 8 = 3[/tex]
The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 247 cubic units.
What is the height of the cylinder?
A. 2 units
B. 4 units
C. 6 units
D. 8 units
Answer:
8.91 units.
Step-by-step explanation:
If the height = h then the radius = h/3.
The volume = 247 = π r^2 h
247 = π (h/3)^2 h
(h/3)^2 h = 247/π
h^3 / 9 = 247 /π
h^3 = 9*247/ π
h= 8.91 units.
The value of height of the cylinder is,
⇒ 13.14 units.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We know that;
The volume of the cylinder is,
⇒ V = πr²h,
Where V is the volume, r is the radius, and h is the height.
Given that;
The volume of the cylinder is 247 cubic units,
Also, we are told that the height of the cylinder is 3 times the radius of the base.
Hence, We get;
⇒ 247 = πr²h
And, Mathematically expressed, h = 3r.
Hence, Substituting value of h in the above equation,
247 = πr²(3r)
Simplifying further, we get:
247 = 3πr³
Dividing both sides by 3π,
r³ = 82.33
Taking the cube root of both sides,
r ≈ 4.38
Now, use the value of r and find the height of the cylinder, using the equation h = 3r.
Therefore, the height of the cylinder is:
h = 3 × r
h = 3 × 4.38
h ≈ 13.14
So, The value of height of the cylinder is 13.14 units.
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What is the slope of the line that passes through the points (3, -4) and (7, 4)?
Answer:
The slope m = 2Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (3, -4) and (7, 4). Substitute:
[tex]m=\dfrac{4-(-4)}{7-3}=\dfrac{8}{4}=2[/tex]
find the sum of the angle measures in the figure below
Answer:
540°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5, hence
sum = 180° × 3 = 540°
Four points from a line are shown in the table below.
INPUT OUTPUT
10 -8
2 -6
4 -4 |
6 -2
Use the table to determine the slope-intercept form of the equation of the line.
A.
y = x - 8
B.
y = x + 8
C.
y = -8x + 1
D.
y = -8x - 1
Reset
Sulit
Answer:
Correct choice is A. [tex]y=x-8[/tex].
Step-by-step explanation:
pick any two points from the table say (0,-8) and (2,-6)
Now we we can use both points to find the equation of line.
slope [tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-6--8}{2-0}=\frac{2}{2}=1[/tex]
now plug slope m=1 and any point say (0,-8) into point slope formula
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y--8=1\left(x-0\right)[/tex]
[tex]y+8=1\left(x\right)[/tex]
[tex]y+8=x[/tex]
[tex]y=x-8[/tex]
Hence correct choice is A. [tex]y=x-8[/tex].
Let
x^2−12x=61
.
What values make an equivalent number sentence after completing the square?
Enter your answers in the boxes.
x2−12x+_____=______
Answer:
Step-by-step explanation:
Add the square of half the x-coefficient to both sides.
x² -12x +(-6)² = 61 +(-6)²
x² -12x +36 = 97Answer:
x² - 12x + 36 = 97
Step-by-step explanation:
Given
x² - 12x = 61
To complete the square
add (half the coefficient of the x- term)² to both sides
x² + 2(- 6)x + (- 6)² = 61 + (- 6)², so
x² - 12x + 36 = 61 + 36
x² - 12x + 36 = 97
Match each pair of polynomials to their sums.
Answer:
12x^2+3x+6 and -7x^2-4x-2 -> 5x^2-x+4
2x^2-x and -x-2x^2-2 -> -2x-2
x^3+x^2+2 and x^2-2-x^3 -> 2x^2
x^2+x and x^2+8x-2 -> 2x^2+9x-2
hope this helps :)
A study estimates that the cost of tuition at a university will increase by 2.8% each year. The cost of tuition at the University in 2015 was $33,741 the function b(x) , models the estimated tuition cost , where x is the number of years since 2015.
finds the expression that completes the function b(x)
so, the cost will increase 2.8% per annum... so that simply means is a compound interest rate, so let's use the compound interest formula for this one.
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$33741\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=\textit{years after 2015}\dotfill &t \end{cases} \\\\\\ A=33741\left(1+\frac{0.028}{1}\right)^{1\cdot t}\implies b(x)=33741(1.028)^x[/tex]
The complete expression for the compounding tuition fee function is [tex]b(x) = 33741(1.028) {}^{x} [/tex]
Using the compound interest relation :
[tex] b = P(1 + \frac{r}{n} ) {}^{nx} [/tex]
Where ;
b = final amount after x years P = Initial amount = 33741 r = rate = 2.8% = 0.028x = number of years since 2015 n = number of compounding times per period = 1 (yearly)The function b(x) can be written as :
[tex]b(x) = 33741(1 + \frac{0.028}{1} ) {}^{x} [/tex]
Therefore, the expression for the function b(x) is :
[tex]b(x) = 33741(1.028) {}^{x} [/tex]
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Select all that apply.
A point located at (3, -2) undergoes a transformation. Its image is at (-3, -2). What was the transformation?
The point was reflected over the y-axis.
The point was translated left 6 units.
The point was reflected over the x-axis.
The point was translated right 6 units.
Answer:
The point was reflected over the y-axis.
The point was translated left 6 units
Step-by-step explanation:
step 1
we know that
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite
In this problem
If you apply a reflection across the y-axis
(x.y)------> (-x,y)
(3,-2) ------> (-3,-2)
step 2
If you apply a translation to the left 6 units
The rule of the translation is equal to
(x,y)------> (x-6,y)
(3,-2) ------> (3-6,-2) ----> (-3,-2)
Christine is riding her bicycle. She rides for 11.2 kilometers at a speed of 7 kilometers per hour. For how many hours does she ride?
Answer:
[tex]1.6\ hours[/tex]
Step-by-step explanation:
we know that
She rides for 11.2 kilometers at a speed of 7 kilometers per hour
Using proportion
Find how many hours does she ride
[tex]\frac{7}{1}\frac{km}{h} =\frac{11.2}{x}\frac{km}{h}\\ \\x=11.2/7\\ \\x=1.6\ hours[/tex]
The system of linear equations -2x+y=8 and -3x-y=7 is graphed below. What is the solution to the system of equations? (–3, 2) (–2, 3) (2, –3) (3, 2)
answer is
-3,2
Answer:
x = -3 , y = 2
Step-by-step explanation:
Solve the following system:
{y - 2 x = 8 | (equation 1)
{-3 x - y = 7 | (equation 2)
Swap equation 1 with equation 2:
{-(3 x) - y = 7 | (equation 1)
{-(2 x) + y = 8 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{-(3 x) - y = 7 | (equation 1)
{0 x+(5 y)/3 = 10/3 | (equation 2)
Multiply equation 2 by 3/5:
{-(3 x) - y = 7 | (equation 1)
{0 x+y = 2 | (equation 2)
Add equation 2 to equation 1:
{-(3 x)+0 y = 9 | (equation 1)
{0 x+y = 2 | (equation 2)
Divide equation 1 by -3:
{x+0 y = -3 | (equation 1)
{0 x+y = 2 | (equation 2)
Collect results:
Answer: {x = -3 , y = 2
The solution to the system of equations -2x + y = 8 and -3x - y = 7 is (x, y) = (-3, 2). The correct answer is option A.
Let's use the elimination method:
-2x + y = 8
-3x - y = 7
By adding the two equations together, we can eliminate the y variable:
(-2x + y) + (-3x - y) = 8 + 7
-2x - 3x + y - y = 15
-5x = 15
Dividing both sides by -5, we get:
x = -3
Now, substitute this value of x back into one of the original equations. Let's use -2x + y = 8:
-2(-3) + y = 8
6 + y = 8
y = 8 - 6
y = 2
Therefore, the solution to the system of equations -2x + y = 8 and -3x - y = 7 is (x, y) = (-3, 2).
Therefore, the correct answer is option A.
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The complete question is as follows:
The system of linear equations -2x+y=8 and -3x-y=7 is graphed below. What is the solution to the system of equations?
A. (–3, 2)
B. (–2, 3)
C. (2, –3)
D. (3, 2)
What is the r-value of the following data, to three decimal places
Option: A is the correct answer.
A. -0.903
Step-by-step explanation:The formula to calculate correlation coefficient r is given by:
[tex]r=\dfrac{n\sum xy-(\sum x)(\sum y)}{\sqrt{n(\sum x^2)-(\sum x)^2}\sqrt{n(\sum y^2)-(\sum y)^2}}[/tex]
x y xy x² y²
4 23 92 16 529
5 12 60 25 144
8 10 80 64 100
9 9 81 81 81
13 2 26 169 4
-------------------------------------------------------------------------
∑ 39 56 339 355 858
Also n=5 ( as there are 5 data points )
Hence, we get:
[tex]r=\dfrac{5\times 339-39\times 56}{\sqrt{5\times 355-(39)^2}\times \sqrt{5\times 858-(56)^2}}\\\\\\r=\dfrac{-489}{\sqrt{254}\times \sqrt{1154}}\\[/tex]
[tex]r=-\dfrac{489}{541.40188}=-0.9032[/tex]
Hence, the r-value of the following data, to three decimal places is:
A. -0.932
Answer: A. -0.903
Step-by-step explanation: I just did this on A P E X and got it right
Increasing on intervals
Decreasing on the intervals
The function is constant on the intervals
What is the domain of function.
Step-by-step explanation:
Look at the picture.
[tex]\text{The function is increasing on the intervals:}\ \left<-3,\ 0\right>\ \text{and}\ \left<4,\ 9\right>\\\\\text{The function is decreasing on the interval:}\ \left<-6,\ -3\right)}\\\\\text{The function is constant on the interval:}\ \left<1,\ 4\right>\\\\\text{The domain of the function:}\ \left<-6,\ 0\right>\ \cup\ \left<1,\ 9\right>[/tex]
In Mathematics, analyzing whether function intervals are increasing, decreasing, or constant involves checking the derivative. Positive derivatives indicate increasing intervals, negative derivatives indicate decreasing intervals, and a derivative of zero signifies constant intervals. The domain of a function comprises all possible input values.
Explanation:The subject of your question falls under Mathematics, specifically the topic of functions. Where a function is increasing, decreasing, or constant on an interval depends upon the derivative of the function on that interval. For an increasing interval, the derivative is positive. For a decreasing interval, the derivative is negative. For a constant interval, the derivative is zero. As for the domain of a function, it refers to all possible input values (x-values) the function can have. For example, for the function f(x) = 1/x, all real number except for 0 are in the domain because you cannot divide by 0.
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Is anybody good at algebra?
Answer:
Which question do you need help on
Step-by-step explanation:
91) (5, 4) is a solution to which of the following
systems of linear equations?
A) x + 6y = 18 B) 4x + 2y = 12
3x-27=-6
3x - y = -15
C) 2x - 3y = -2 D) 8x + 5y = 40
4x + y = 24
x-7y=-14
Answer:
2x - 3y = -2 AND 4x + y = 24
Step-by-step explanation:
Simply plug in the coordinates into each answer choice, evaluate them, and you will have your answer.
I hope this helps you out, and as always, I am joyous to assist anyone at any time.
Simplify this expression using the distributive property.
8(9 + w)
A. 72w
B. 17 + 8w
C. 72 + 8w
D. 17w
the answer is c: .... 72+8w
Answer:
The answer is option C.
Step-by-step explanation:
8(9+w)
Distribute the 8 to the 9 and the w:
9(8)+w(8)
Simplify:
72+8w
This cant be simplified further.
hope this helps :)
Suppose Q and R are independent events. Find P(Q and R). P(Q) = 0.87, P(R) = 0.51
Answer:
0.4437
Step-by-step explanation:
First we will define independent events.
Two events are said to be independent when the occurrence of one event doesn't affect the probability of occurrence of second event.
Given
P(Q)=0.87
and
P(R)=0.51
The probability of independent events is given as:
P(Q∩R)=P(Q)*P(R)
=0.87*0.51
=0.4437
So the probability of Q and R is 0.4437 ..
A farmer wants to build a new grain silo. The shape of the silo is to be a cylinder with a hemisphere on the top, where the radius of the hemisphere is to be the same length as the radius of the base of the cylinder. The farmer would like the height of the silo’s cylinder portion to be 4 times the diameter of the base of the cylinder. What should the radius of the silo be if the silo is to hold 35,500pie cubic feet of grain?
Answer:
[tex]r=16\ ft[/tex]
Step-by-step explanation:
we know that
The volume of the silo is equal to the volume of a cylinder plus the volume of a hemisphere
so
[tex]V=\pi r^{2}h+\frac{4}{6}\pi r^{3}[/tex]
In this problem we have
[tex]V=35,500\pi\ ft^{3}[/tex]
[tex]h=4D=8r[/tex] ----> 4 times the diameter is equal to 8 times the radius
substitute in the formula and solve for r
[tex]35,500\pi=\pi r^{2}(8r)+\frac{4}{6}\pi r^{3}[/tex]
Simplify pi
[tex]35,500=8r^{3}+\frac{4}{6}r^{3}[/tex]
[tex]35,500=r^{3}[8+\frac{4}{6}][/tex]
[tex]35,500=r^{3}[\frac{52}{6}][/tex]
[tex]r^{3}=35,500/[\frac{52}{6}][/tex]
[tex]r=16\ ft[/tex]
Tamika has two bags of trail mix. Each has a combination of 60 pieces of fruit and nuts.
Ratio of fruit to nuts in the first bag: 3/5
Ratio of fruit to nuts in the second bag: 7/10
Which bag has more fruit? Use the ratios to justify your answer.
A. The first bag, because the ratio is greater.
B. The first bag, because the ratio is smaller.
C. The second bag, because the ratio is greater.
D. The second bag, because the ratio is smaller.
Answer:
C
Step-by-step explanation:
The ratio of nuts is .60 in the first bag and .7 in the second bag. Therefore C would be the answer.
Answer:
StepJust found the answer it was C.
-by-step explanation:
Which number is written in scientific notation?
Answer:
0.2 x 10 ^ 5
Option C is correct. The number is written in scientific notation is,0.2×10⁵.Because the number is written in the decimal form.
What is scientific notation?Scientific notation is a method of describing numbers that are either too large or too little to be expressed in decimal form.
Out of all, the number C is written in the decimal form.
Hence, the number is written in scientific notation is,0.2×10⁵
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I’m having trouble finding angle DCE, I figured out the angles in the kite (I hope), how do I find the angle next to it, it doesn’t equal 180, does it?
Answer:
180 -angle BCD
Step-by-step explanation:
if you've found angle BCD you should be able to find angle DCE as angles on a straight line equal 180°
38. The volume of a cylinder is 97 ft3. If the dimensions are doubled, what will be the new volume?
Volume is cubed. If the dimensions are doubled, cube the scale factor:
2^3 = 8
The volume will increase by a scale of 8.
The new volume would be 97 x 8 = 776 ft^3
Which characteristic is correct for the function?
A. Both even and odd
B. Neither even or odd
C. Odd
D. Even
Answer:
D. Even
Step-by-step explanation:
Given function is [tex]f\left(x\right)=-2x^4+3x^2[/tex].
Now we need to check if the given function is Even/Odd.
we know that if f(-x)=f(x) then function is called Even.
we know that if f(-x)=-f(x) then function is called Odd.
[tex]f\left(x\right)=-2x^4+3x^2[/tex]
[tex]f\left(-x\right)=-2(-x)^4+3(-x)^2[/tex]
[tex]f\left(-x\right)=-2x^4+3x^2[/tex]
[tex]f\left(-x\right)=f\left(x\right)[/tex]
Hence given function is an Even function.
So the correct choice is D. Even.
9. What is the solution to the
equation log4 (5x + 9) = 3?
Answer:
11
Step-by-step explanation:
The solution to the equation [tex]\rm log_4 (5x + 9) = 3\\\\[/tex] is x = 11.
What is the logarithmic equation?In mathematics, the logarithmic function is an inverse function to exponentiation.
The given equation is;
[tex]\rm log_4 (5x + 9) = 3\\\\[/tex]
The solution to the equation is determined in the following steps given below.
[tex]\rm log_4 (5x + 9) = 3\\\\ Taking \ exponetital \ on \ both \ sides\\\\5x+9 =4^3\\\\5x+9=64\\\\5x=64-9\\\\5x=55\\\\x=\dfrac{55}{5}\\\\x=11[/tex]
Hence, the solution to the equation [tex]\rm log_4 (5x + 9) = 3\\\\[/tex] is x = 11.
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