The volume of the chocolate is the amount of choclate used in the cherries
The amount of chocolate used is 17.24 cubic centimeters
How to determine the amoumt of chocolate?Start by calculating the volume of the cherries using:
V = 4/3 π(D/2)^3
The diameter of the cherry is 2.8 cm.
So, we have:
V = 4/3π(2.8/2)^3
Evaluate
V = 11.49
Next, calculate the volume of the cherry and the chocolate.
V = 4/3π(0.5+2.8/2)^3
V = 28.73
Calculate the difference (d) between both volumes
d = 28.73 - 11.49
d = 17.24
Hence, the amount of chocolate used is 17.24 cubic centimeters
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Which expression is equivalent to 7x2/2x4.62x12, if x # 0?
OA. 26 r22
B. 13.r12/2
O C. 84x10
D. 42x12/2
C
ЖStep-by-step explanationЖ
⇒ [tex]7x^2\sqrt{2x^4}\bullet\ 6\sqrt{2x^1^2}[/tex]
[tex]=7\sqrt{2}x^4\bullet 6\sqrt{2}x^6[/tex]
[tex]=84x^1^0[/tex]
[tex]So\ choose\ C[/tex]
[tex]\{square\ root\ \}.[/tex]
I hope this helps you
:)
Four friends are order pizza from a take away.
The amount of pizza each person eats is shown as a fraction below
Matthew eats 0.8of a pizza
Lily eats 3/4of a pizza
George eats 77%opizzas f a pizza
Sam eats 82%of a pizza
Which person eats the most pizza?
You must show your workings
Answer:
Sam ate the most pizza.
Step-by-step explanation:
Mathew: 0.8 is equal to 80%
To get a percentage, you need to move the decimal two places to the right.
Lily: 3/4 = 75%
George: 77%
Sam: 82%
In Exploration 5.4.2 Question 2, what conclusion can you make about the value of the derivative at
the maximum or minimum for a continuous function?
The value of the derivative at the maximum or minimum for a continuous function must be zero.
What happens with the derivative at the maximum of minimum?So, remember that the derivative at a given value gives the slope of a tangent line to the curve at that point.
Now, also remember that maximums or minimums are points where the behavior of the curve changes (it stops going up and starts going down or things like that).
If you draw the tangent line to these points, you will see that you end with horizontal lines. And the slope of a horizontal line is zero.
So we conclude that the value of the derivative at the maximum or minimum for a continuous function must be zero.
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Use the definition of the derivative as a limit to find the
derivative f′ where f(x)= √ x+2.
Step-by-step explanation:
If the equation is
[tex] \sqrt{x + 2} [/tex]
Then, here is the answer.
The definition of a derivative is
[tex] \frac{f(x + h) - f(x)}{h} [/tex]
Also note that we want h to be a small, negligible value so we let h be a value that is infinitesimal small.
So we get
[tex] \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} [/tex]
Multiply both equations by the conjugate.
[tex] \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} \times \frac{ \sqrt{x + h + 2} + \sqrt{x + 2} }{ \sqrt{x + h + 2} + \sqrt{x + 2} } = \frac{x + h + 2 - (x + 2)}{h \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{h}{h \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{1}{ \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]
Since h is very small, get rid of h.
[tex] \frac{1}{ \sqrt{x + 2} + \sqrt{x + 2} } [/tex]
[tex] \frac{1}{2 \sqrt{x + 2} } [/tex]
So the derivative of
[tex] \frac{d}{dx} ( \sqrt{x + 2} ) = \frac{1}{2 \sqrt{x + 2} } [/tex]
Part 2: If your function is
[tex] \sqrt{x} + 2[/tex]
Then we get
[tex] \frac{ \sqrt{x + h} + 2 - ( \sqrt{x} + 2) }{h} [/tex]
[tex] \frac{ \sqrt{x + h} - \sqrt{x} }{h} [/tex]
[tex] \frac{x + h - x}{h( \sqrt{x + h} + \sqrt{x}) } [/tex]
[tex] \frac{h}{h( \sqrt{x + h} + \sqrt{x} ) } [/tex]
[tex] \frac{1}{ \sqrt{x + h} + \sqrt{x} } [/tex]
[tex] \frac{1}{2 \sqrt{x} } [/tex]
So
[tex] \frac{d}{dx} ( \sqrt{x} + 2) = \frac{1}{2 \sqrt{x} } [/tex]
A bag contains 2 red marbles, 7 blue marbles and 5 green marbles. If two marbles are
drawn out of the bag, what is the exact probability that both marbles drawn will be
blue?
Answer:
1/2
Step-by-step explanation:
There are :-
⇒ 2 red marbles
⇒ 7 blue marbles
⇒ 5 green marbles
Probability (Blue)
= No. of blue marbles / No. of total marbles= 7 / (2 + 7 + 5)= 7/14= 1/2In the electric field [tex]{\vec{E}=3x\hat{i}-2y\hat{j}+5z\hat{k}}[/tex], find the potential difference between the points A(1,3,5) and B(3,2,7)
Let's recall that, the potential difference between any two points X(x,y,z) and Y(a,b,c) is given by ;
[tex]{\boxed{\bf{V_{Y}-V_{X}=\displaystyle \bf -\int_{X}^{Y}\overrightarrow{E}\cdot \overrightarrow{dr}}}}[/tex]So, here ;
[tex]{:\implies \quad \sf \overrightarrow{E}=3x\hat{i}-2y\hat{j}+5z\hat{k}}[/tex]
So, now our second component of the Integrand will just be ;
[tex]{:\implies \quad \sf \overrightarrow{dr}=dx\hat{i}+dy\hat{j}+dz\hat{k}}[/tex]
So, now the whole integrand will just be ;
[tex]{:\implies \quad \sf \overrightarrow{E}\cdot \overrightarrow{dr}=(3x\hat{i}-2y\hat{j}+5z\hat{k})(dx\hat{i}+dy\hat{j}+dz\hat{k})}[/tex]
[tex]{:\implies \quad \sf \overrightarrow{E}\cdot \overrightarrow{dr}=3xdx-2ydy+5zdz}[/tex]
Now, Let's move to the final answer ;
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\int_{X}^{Y}3xdx-2ydy+5zdz}[/tex]
As,X is the point (1,3,5) and Y being (3,2,7) , so seperate the integral into three integrals with limits as follows respectively;
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg(\int_{1}^{3}3xdx-\int_{3}^{2}ydy+\int_{5}^{7}zdz\bigg)}[/tex]
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg(3\int_{1}^{3}xdx-2\int_{3}^{2}ydy+5\int_{5}^{7}zdz\bigg)}[/tex]
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg\{3\bigg(\dfrac{x^2}{2}\bigg)\bigg|_{1}^{3}-2\bigg(\dfrac{y^2}{2}\bigg)\bigg|_{3}^{2}+5\bigg(\dfrac{z^2}{2}\bigg)\bigg|_{5}^{7}\bigg\}}[/tex]
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg\{2\bigg(\dfrac{9}{2}-\dfrac12\bigg)-2\bigg(\dfrac{4}{2}-\dfrac92\bigg)+5\bigg(\dfrac{49}{2}-\dfrac{25}{2}\bigg)\bigg\}}[/tex]
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\{3(4)-(-5)+5(12)\}}[/tex]
[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\{12+5+60\}}[/tex]
[tex]{:\implies \quad \displaystyle \boxed{\bf{V_{Y}-V_{X}=-77\:\: Volt}}}[/tex]
Hence, this is the required answer
Find angles B, E, C, and D, given that angle m A=140° and m F=130°.
*Picture is not drawn to scale*
Answer:
Angle B=40 degrees
Angle C= 90 degrees
Angle E=50 degrees
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these answer- I am sure they ar correct
A worker is getting a 4.5% raise. His current salary is $35,591. How much will his raise be?
His raise will be $
(Type an integer or decimal rounded to two decimal places as needed.)
Help me solve this
View an example
Get more help
Mr. Bartley is taking the theater club on a field trip to see the musical wicked. The school treasurer asked mr. Bartley for the groups total ticket cost. He wrote the following cost function for the school treasurer: total cost = 52(25+2)
Which of the following statements could describe the cost function? Select all that apply
Tickets cost $52 each, and there are 25 students and 2 teachers going n trip
Tickets cost $25 and each person must pay $2 for the bus. There are 52 people going
Mr. Bartley expression of the ticket cost function is an illustration of equations
The true statement is (a) Tickets cost $52 each, and there are 25 students and 2 teachers going n trip
How to determine the true statement?The equation of the total cost is given as:
Total Cost = 52 * (25 + 2)
The above can be rewritten generally as:
Total Cost = Cost per each * (Student + Teachers)
By comparison, we have:
Cost per each = $52
Students = 25
Teachers = 2
Hence, the true statement is (a) Tickets cost $52 each, and there are 25 students and 2 teachers going n trip
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-3/5m + 8 = 20
what is the answer of m
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m + 8 = 20[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m = 20 - 8[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ 3}{5} m =12[/tex]
[tex]\qquad \sf \dashrightarrow \: - \frac{ }{} m =12 \times \frac{5}{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: - m = 4 \times 5[/tex]
[tex]\qquad \sf \dashrightarrow \:m = - 20[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Help! 10 Points !!
A line passes through the point (-8. 5) and has a slope of -5/4
f(x) = x^2-3
What is the average rate of change on the interval [-5, 2] ?
Answer:
[tex](-3)[/tex].
Step-by-step explanation:
Over this interval, the change in the value of this function is:
[tex]f(-5) - f(2) = 22 - 1 = 21[/tex].
The corresponding change in the value of [tex]x[/tex]:
[tex](-5) - 2 = -7[/tex].
The average rate of change of function [tex]f[/tex] over this interval is equal to the change in the function value divided by the corresponding change in [tex]x[/tex]:
[tex]\begin{aligned}& (\text{average rate of change}) \\ =\; & \frac{(\text{change in function value})}{(\text{change in $x$})} \\ =\; & \frac{f(-5) - f(2)}{(-5) - 2} \\ =\; & \frac{22 - 1}{-7} \\ =\; & \frac{21}{-7} \\ =\; & -3\end{aligned}[/tex].
Thus, the average rate of change of [tex]f(x) = x^{2} - 3[/tex] over the interval [tex][-5,\, 2][/tex] would be [tex](-3)[/tex].
HELP ME ON THIS!!!!!
PLS ITS VERY IMPORTANT
Answer: 30 units^2
Step-by-step explanation:
[tex]\mathrm{From \ the \ figure \ we \ know \ this \ is \ a \ right \ triangle. \ The \ area \ of \ the \ triangle}:[/tex]
[tex]A = \frac{1}{2}bh \\= \frac{1}{2} \times 6 \times 10\\= 30 \ units^2[/tex]
(Formula for area of right triangle: Half of the product of two right edges)
Therefore, the area of the triangle is 30 units^2
In 1995 there were 501 computer viruses reported. Since then, the viruses have been replicating at a
rate of 57% per year. How many viruses are projected for the year 2021?
Therefore, there are projected to be approximately 1541 computer viruses in the year 2021.
What is exponential growth?Exponential growth is a pattern of growth where a quantity grows at a constant percentage rate per unit of time. In other words, the rate of growth is proportional to the current value of the quantity. This type of growth is often seen in natural phenomena such as population growth, the spread of diseases, and the growth of financial investments. Exponential growth can be described mathematically by an exponential function of the form y = abˣ, where a is the initial value, b is the growth factor, and x is the time variable.
Here,
To solve this problem, we can use exponential growth formula:
A = P(1 + r)ˣ
where:
A = final amount
P = initial amount
r = growth rate
t = time (in years)
Let's first calculate the number of years from 1995 to 2021:
2021 - 1995 = 26 years
Using the given information, we can plug in the values into the formula:
A = 501(1 + 0.57)²⁶
A = 501(3.08)
A = 1540.68
Rounding to the nearest whole number, we get:
A ≈ 1541
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Find the least common multiple of x2 – 2x – 15 and x2 + 2x – 3.
(x + 3)(x – 1)(x + 5)
(x – 5)(x + 3)(x – 1)
(x – 5)(x + 1)(x + 3)
(x + 5)(x + 3)(x + 1)
Step-by-step explanation:
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PLEASE HELP!!!!
Earth is about 1.5 x 10^8 kilometers away from the sun. Saturn is about 1.4 x 10^9 kilometers away from the sun. How many times closer to the sun is Earth than Saturn? Give answer is standard form and round to the nearest tenth.
If you can, please explain, or just show what you did
Answer:
8.33
Step-by-step explanation:
Answer: 8.33 minutes will it take to travel from the sun to the earth. Step-by-step explanation: Distance of the Earth from the Sun = d = 1 km = 1000 m.
Answer: 9.33
Step-by-step explanation: you divide Saturn by earth
Change 75m to decimeters
Answer:
750 decimeters
Step-by-step explanation:
1 meter is equal to 10 decimeters.
so 75 times 10 equals your answer: 750 decimeters
Hope that helps!
Someone pls
.
A
A
A
A
A
A
S
Answer:
7
Step-by-step explanation:
Degree of a polynomial is a variable's highest exponent
In this expression the degree is 7
Answer:
7
Step-by-step explanation:
If you used
P.E.M.D.A.S
Brainly please I worked so hard for this answer
What is the solution to the system of equation s x+y=4. X=y-1
Answer:
x = 3/2
y = 5/2
Step-by-step explanation:
x + y = 4
x = y - 1
substitute y - 1 in for x in the first equation, to find y
y - 1 + y = 4
2y - 1 = 4
add 1 on both sides
2y - 1 = 4
+1 +1
2y = 5
divide by 2 on both sides
2y/2 = 5/2
y = 5/2
subtitute y in for the second equation, to find x
x = 5/2 - 1
x = 5/2 - 2/2
x = 3/2
so x = 3/2 and y = 5/2
to double check, plug x and y in the first equation
3/2 + 5/2 = 4
8/2 = 4
4 = 4
2 points
Daria earns h dollars per hour at the grocery store. She works 9 hours per week. She writes the expression 9 • h • 4 to represent how much
money she earns in a four-week month. Daria's boss writes the expression 36h. Which person's expression tells you how many hours Daria
works per four-week month? EXPLAIN YOUR REASONING.
Answer:
Daria's boss expression
Step-by-step explanation:
Her boss expression because it's asking about the hours worked per four week month. Daria's expression represents the 9 hours she works per week for the 4 weeks in the month.
Her boss expression represents the total number of hours she works altogether in all the four weeks in the month.
Help help help hemp grko
Answer:
12
Step-by-step explanation:
x-4=2(x+8)/5
let's do my favorite strategy: distributive property!
x-4=(2x+16)/5
Now we can simplify.
x-4=(2/5)x+16/5
Let's solve for x!
Subtract 2/5 from both sides
3/5)x=36/5
Now multiply both sides by 5/3, the reciprocal.
You would get 12 as x!
A bedroom door in the house has the same dimension as the front door but the length is 30 inches rather than 36 inches how much greater is the volume of the front door than than the bedroom door
Answer:
6/5
Step-by-step explanation:
Calculate the volume by multiplying the measured length and width of the space together, then multiply the result by the height of the room. From the example, 10 * 25 feet = 250 square feet, and 5 * 10 feet = 50 square feet.
Can you be serious and more understanding about the home work
Answer:
yes
Step-by-step explanation:
is there a specific question?
Answer: All children should be doing homework. But the amount and quality should change." His basic prescription.
Step-by-step explanation:
Help picture below problem 16
Concept :-
⠀
We have studied the law which states that the sum of all angles in a triangle is 180°, this is known as angle sum property of a triangle. We can solve this question based on that property.
Solution :-
⠀
Let us assume the missing angle to be x,
Therefore,
→ 66° + 71° + x = 180° ( Angle sum property of a triangle )
→ 137° + x = 180°
→ x = 180° - 137°
→ x = 43°
Thus, the measure of the missing angle is 43°.
Hope that helps :)
Make an accurate drawing of two rectangles with the same perimeter, but different areas. Indicate the dimensions of the rectangles, as well as the perimeter and the area in each figure.
here.
Step-by-step explanation:
Help picture below problem 18
Solution :-
This triangle is a right angled triangle as we can see ∠POC, has a right angled sign. Now, we will assume the missing angle to be x, thus,
25° + 90° + x = 180° ( Angle sum property of a triangle )
115° + x = 180°
x = 180° - 115°
x = 65°
Thus, the measure of missing angle is 65°.
Hope that helps. :D
A large set of data was collected and analyzed for the majors of college seniors in the U.S. From the scatter plots produced the following associations were observed. The linear model P(t) 2,376 + 73,219 can be used to estimate the number of college seniors who graduated with a bachelor's degree in psychology, tyears after 2000 - The linear model B(t) = 2, 414t + 56, 545 can be used to estimate the number of college ( seniors who graduated with a bachelor's degree in biology, tyears after 2000. Which of the following statements are true? The number of psychology degrees increases by about 73,219 each year after 2000. The number of biology degrees increases by about 2.414 each year after 2000. About 73.000 students graduated with degrees in psychology in 2000. About 2.400 students graduated with degrees in biology in 2000. in 2000, more students graduated with psychology degrees than biology degrees
Using linear function concepts, it is found that the true statements are as follows:
The number of biology degrees increases by about 2.414 each year after 2000. About 73.000 students graduated with degrees in psychology in 2000.In 2000, more students graduated with psychology degrees than biology degrees.What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value.In this problem, for psychology, the model for the number of graduated students in t years after 2000 is:
P(t) = 2,376t + 73,219.
For biology, it is given by:
B(t) = 2,414t + 56, 545
Hence, the correct statements are:
The number of biology degrees increases by about 2.414 each year after 2000. About 73.000 students graduated with degrees in psychology in 2000.In 2000, more students graduated with psychology degrees than biology degrees.More can be learned about linear function concepts at https://brainly.com/question/24808124
When do you say that a given quadrilateral is a parallelogram?
Answer:
Theorem : If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Given : ABCD is a quadrilateral in which ∠A = ∠C and ∠B = ∠D. We know that the sum of the angles of a quadrilateral is 360o.
Step-by-step explanation:
hope that helps
Find the equation of a line that passes through the point (0,-4) and has a gradient of 2. Leave your answer in the form y=mx+c
Answer:
y=2x-4
Step-by-step explanation:
y-y1=m(x-x1)
y-(-4)=2(x-0)
y+4=2x-0
y=2x-0-4
y=2x-4
Consider the graph of the quadratic function. Which
interval on the x-axis has a negative rate of change?
-2 to -1
-1.5 to 0
0 to 1
1 to 2.5
The only interval with a negative rate of change is the last one:
[1, 2.5]
When the rate of change is negative?
For an interval (a, b) and a function f(x), the rate of change is defined as:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
So the rate of change is only negative when the function evaluated on the first value of the interval is larger than the function evaluated in the second one.
For example, on the interval [1, 2.5} we can see that:
f(1) = 3
f(2.5) = -1
Then on this interval, the rate of change will be negative, meaning that this is the correct option.
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Answer:
It's D: 1 to 2.5
Step-by-step explanation:
It's D: 1 to 2.5