With the function given as y = |x|, and the value of x on the graph is -5, when translated it becomes
[tex]y+3=|x+5|[/tex]Because when x = -5, then y + 3 = 0 (that is, y = -3)
prove that the sum of the lengths of the diagonals of a quadrilateral is less than the perimeter but greater than the half of the perimeter of this quadrilateral
Let us consider a quadrilateral ABCD (as shown in the figure below) such that AC and BD are the two diagonals of ABCD.
Now, in triangle ABC and triangle ADC, by using the properties of triangle inequality we have-
AB +BC > AC .... (1)
and AD + CD >AC .... (2)
adding equations (1) and (2) we get-
AB+ BC+CD+AD > 2AC .... (3)
Similarly for diagonal BD we get-
AB+BC+CD+AD > 2BD .... (4)
Adding equations (3) and (4) we get-
2(AB+BC+CD+AD) > 2(AC+BD)
⇒ (AB+BC+CD+AD) > AC+BD
here (AB+BC+CD+AD) = perimeter of quadrilateral.
Hence, we have proven that the sum of the length of the diagonals of a quadrilateral is less than the perimeter.
Now the 2 diagonals divide the quadrilateral into 4 quadrilaterals
Therefore, AO+OD > AD
OD+OC > CD
OC+OB > BC
and OA+OB > AB
Adding all these equations-
2(AC+BD)>AB+BC+CD+AD
⇒AC+BD > 1/2(AB+BC+CD+AD)
Hence, we've proven that the sum of the length of the diagonals is greater than the half of the perimeter of this quadrilateral.
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How to simplify the 6th root of y^21
The simplified expression is [tex]y^{\frac{7}{2} }[/tex]
How is the given expression simplified?
[tex]6\sqrt{y^{21} } \\\\= [(y)^{21} ]^{\frac{1}{6} } \\\\[/tex]
By applying power rule of exponents ,
[tex]6\sqrt{y^{21} } =[/tex] [tex]y^{\frac{7}{2} }[/tex]
What is power rule of exponents?
The exponent power rule is [tex](a^{m} )^{n} = a^{mn}[/tex]Exponent times power is how you raise a number with an exponent to a power.When a base is raised to a power and then the entire expression is raised to another power.An algebraic expression can be made simpler by using the power of a power rule in exponents.To learn more about power rule, refer:
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The abbreviated form is
How is the expression that is given simplified?
by using the exponents' power rule.
What is the exponents power rule?
Exponent power rule states that
You increase a number with an exponent to a power by multiplying the exponent by the power.when the expression as a whole is raised to a higher power after raising a base to that powerThe power of a power rule in exponents can be used to simplify an algebraic expression.To learn more about power rule refer to:
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On a number line, the coordinates of X, Y, Z, and W are -7, -3, 1, and 5, respectively. Find the lengths of the two segments below. Then tell whether they are congruentXY and ZWThe length of XY isThe length of ZW is(Type an integer or a decimal.)(Type an integer or a decimal.)
The Solution:
Given:
[tex]\begin{gathered} X=-7 \\ Y=-3 \\ Z=1 \\ W=5 \end{gathered}[/tex]Required:
Determine whether segment XY is congruent to segment ZW.
Step 1:
Find the length of segment XY.
[tex]XY=-3-(-7)=-3+7=4[/tex]Step 2:
Find the length of segment ZW.
[tex]ZW=5-1=4[/tex]Since:
[tex]\begin{gathered} XY=ZW=4 \\ It\text{ follows that XTY and ZW are congruent.} \end{gathered}[/tex]Answer:
XY = 4
ZW = 4
They are congruent.
Write this equation in Y=MX+B form: 3x+4y=8
the initial expression is:
[tex]3x+4y=8[/tex]So to write it in the form slope intercept we can rest 3x in bout sides of the equation so:
[tex]\begin{gathered} -3x+3x+4y=-3x+8 \\ 4y=-3x+8 \end{gathered}[/tex]now we divide by 4 so:
[tex]\begin{gathered} \frac{4y}{4}=-\frac{3}{4}x+\frac{8}{4} \\ y=-\frac{3}{4}x+2 \end{gathered}[/tex]No M is equal to -3/4 and B is equal to 2e
Answer:
y = -3/4x + 2
Step-by-step explanation:
Given:
Write this equation in "y=mx+b form"
Equation given: 3x+4y=8
Solve:
3x + 4y = 8
⇒ 3x -3x + 4y = 8 -3x ⊂ Subtract 3x from both side ⊃
⇒ 4y = -3x + 8
⇒ 4y/4 = -3x/4 +8/4 ⊂ Divide all by 4 ⊃
⇒ y = -3/4x + 2
Hence, this equation ( 3x + 4y = 8) in y = mx+b is y = -3/4x + 2
Lenvy~♡
what number do I need to add -5 to get -7
- 5 - 2 = - 7
The number that you need to add to - 5 to get - 7 is - 2
This can be ssen on the number line. If you are adding, you move towards the right but since we are adding a negative number, the - sign makes the plus sign to become - sign. So we would subtract by moving 2 points to the left of -5 and that gives - 7
What is the perimeter of STUV?* STUV – XYZW T Z 20
The perimeter of the figure is the addition of the segments so in this case we have to find the sides so:
[tex]\frac{35}{21}=\frac{25}{TU}=\frac{20}{UV}=\frac{20}{SV}[/tex]So:
[tex]\begin{gathered} TU=\frac{25\cdot21}{35}=15 \\ UV=\frac{20\cdot21}{35}=12 \\ SV=\frac{20\cdot21}{35}=12 \end{gathered}[/tex]So the perimeter will be:
[tex]\begin{gathered} P=21+15+12+12 \\ P=60 \end{gathered}[/tex]do you think you'd be able to help me out here
1) Let's make a graph for that round trip with stops.
2) Continuing the graph, on the way back
Considering that every time the plane stops, its altitude goes down to 0, i.e. a point in the x-axis, then we can count 4 stops, 1 in the Chicago-NY and 3 on the way back. Considering that the graph touches the x-axis when it lands then the graph touches 6 times
Find the area swept by the door. Note: Enter your answer in terms of \piπpi.
We are asked to determine the area swept by the door. We notice that the area forms a sector of a circle. The area of the sector of a circle is given by:
[tex]A=\frac{1}{2}r^2\theta[/tex]Where:
[tex]\begin{gathered} A=\text{ area} \\ r=\text{ radius} \\ \theta=\text{ angle in radians} \end{gathered}[/tex]To convert the given angle into radians we use the following conversion factor:
[tex]\pi\text{ radians = 180 degr}ees[/tex]Now, we multiply by the conversion factor:
[tex]45\times\frac{\pi}{180}=\frac{\pi}{4}[/tex]Now, we plug in the values in the formula for the area:
[tex]A=\frac{1}{2}(80cm)^2(\frac{\pi}{4})[/tex]Solving the operations:
[tex]A=800\pi cm^2[/tex]Therefore, the area is 800 pi square centimeters.
how do you find slope?1?!
Answer:
Pick two points on the line and determine their coordinates.
Answer:
Step-by-step explanation:
Rise over Run
1. Find 2 points
2. Count the Y distance .then the X distance
3.Y/X
EX. (0,0) and (4,4)
0 to 4 of the y-axis is 4
0 to 4 on the x-axis is 4
4/4= 1 slope 1
Kennedy's car used 16 gallons to travel 288 miles. How many miles can the car go for
each gallon of gas?
Answer:
18 miles
Step-by-step explanation:
The car needs 16 gallons to travel 288 miles. We can divide by 16, kind of like dividing on both sides of an equation, to get that with 1 gallon, the car can travel 288/16=18 miles.
Write the transformed equation for f(x) -5, calling it h(x)
The image of the function after the translation is h(x) = 6x - 3
How to determine the equation of h(x)?The given parameters are:
f(x) = 6x + 2
The transformation is given as
f(x) - 5
This implies that we translate the function f(x) 5 units down
Mathematically, this transformation can be represented as
(x, y) = (x, y - 5)
When represented as a function, we have
h(x) = f(x) - 5
Substitute the equation f(x) = 6x + 2 in the equation h(x) = f(x) - 5
So, we have the following equation
h(x) = 6x + 2 - 5
Evaluate the like terms
h(x) = 6x - 3
Hence, the equation of h(x) is h(x) = 6x - 3
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Possible question
Given that the equation of f(x) is f(x) = 6x + 2
Write the transformed equation for f(x) -5, calling it h(x)
Which of the following values are solutions to th I. 2 II. – 6 None O I only Submit Ang O II only O III only I and II I and III O II and III I, II and III
ok, but the inequality is not complete in the picture
[tex]\begin{gathered} \text{ 1 }\leq\text{ 1 - 2x} \\ \text{ 1 - 1 }\leq\text{ -2x} \\ \text{ 0 }\leq\text{ -2x} \\ \text{ 0/-2 }\ge\text{x} \\ \text{ 0 }\ge\text{ x} \end{gathered}[/tex]for choose one you have to tell me what kind of angle it is.
Part 1
By angle addition property
m<4+m<5+m<1=180 degrees
m<4=39 degrees
m<5=45 degrees
substitute
39+45+m<1=180
m<1=180-39-45
m<1=96 degreesPart 2
we see that
m<4 and m<3 are alternate interior angles
and since lines, l and k are parallel, <4 and <3 are congruent
so
m<3=39 degreesPart 3
we see that <2 and <5 are alternate interior angles
and since lines, l and k are parallel, < 2 and <5 are congruent
so m<2=45 degrees
Part 4
therefore m<1+m<2+m<3=180 degrees
The relationship between <1, <2 and <3 is an example of the following rule
The sum of the interior angles measures of a triangle is 180 degrees
Select the correct answer.The Junior and senior classes at Central High School were asked to choose a destination for a field trip. The results are shown in the giventwo-way frequency table.JuniorsSeniorsTotalCentral High School Field Trip DestinationAmusement Park5764121OA 38.55%B. 19.93%OC 47.50%OD. 42.31%ntum. All rights reserved.Museum Broadway Show214465What percentage of surveyed students chose the amusement park?4258100Total120166286
The probability that the subject is physics if an assignment is submitted on time is 89.7%.
Given that,
The table is
Subject: On-time Assignment: On-time Arrival to Class:
PHYSICS 89.7% 82.3%
MATH 88.2% 88.7%
CHEMISTRY 89.4% 83.1%
BIOLOGY 90.1% 82.4%
TOTAL 88.5% 84.7%
What is probability?
The characteristic or state of being probable; the probability that something will occur or be the case:
If an assignment is turned in on time, there is an 89.7% chance that the subject will be physics.
If an assignment is turned in on time, there is an 88.2% probability that the subject is math.
If an assignment is turned in on time, there is an 89.4% probability that the subject is chemistry.
If an assignment is turned in on time, the probability that the subject is biology is 90.1%.
Therefore, the chance that the subject is physics if an assignment is submitted on time is 89.7%.
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A pizza parlor offers a choice of 12 different toppings. How many 2-topping pizzas are possible? (no double-orders of toppings are allowed)
==========================================================
Explanation:
There are 12 choices for the first topping and 11 for the next topping. The decrease is to account for the fact we cannot select a repeat topping.
That gives 12*11 = 132 permutations. If order of toppings mattered, then this would be our final answer.
However, the topping order doesn't matter. So we need to divide by 2 to correct for the double counting.
There are 132/2 = 66 combinations.
------------
Alternative Method:
n = 12 toppings are available and r = 2 selections are allowed
Order doesn't matter so we use the nCr combination formula
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\12 C 2 = \frac{12!}{2!*(12-2)!}\\\\12 C 2 = \frac{12!}{2!*10!}\\\\12 C 2 = \frac{12*11*10!}{2!*10!}\\\\ 12 C 2 = \frac{12*11}{2!}\\\\ 12 C 2 = \frac{12*11}{2*1}\\\\ 12 C 2 = \frac{132}{2}\\\\ 12 C 2 = 66\\\\[/tex]
There are 66 combinations
Notice the 2nd to last step involves 132/2 which was mentioned in the previous section.
A pharmaceutical company makes the capsule below. Find the volume of the capsule
Find an equation for the line that bisects QII and QIV. Write your answer in general form.
Consider the equation y= mx+b
he line bisects two Quadrants II and IV,It passes through the origin.
the y intercept is =0
thus, the equation will be y=x
but the line is from the II to IV quadrants
the equation is y=-x.
A jewelry store sells a necklace at $365 that was original purchased at $240, what is the markup? Round your answer to the nearest whole percent.
We are given a selling price of $365 and a purchase cost of $240, we are asked to find the markup. The formula for calculating the mark up is the following:
[tex]\text{markup}=\frac{sale\text{ price-cost}}{\cos t}[/tex]we have that the sale price is 365 and the cost is 240. Replacing in the formula:
[tex]\text{markup}=\frac{365-240}{240}[/tex]solving the operations we get:
[tex]\text{markup}=\frac{125}{240}=0.52[/tex]This can be expressed as a percentage like this:
[tex]\text{markup}=52\text{ percent}[/tex]the markup is 52%
PLEASE HELP FOR 20 POINT! The area model shows 3 and one-fourth. What is 3 times 3 and one-fourth?
An area model has 4 shaded rectangles. An area model has 4 shaded rectangles. An area model has 4 shaded rectangles .An area model has 1 shaded rectangle and 3 unshaded rectangles.
3 and one-fourth
3 and three-fourths
9 and one-fourth
9 and three-fourths
The multiplication of the mixed number 3 1/4 by 3 has a result given as follows:
9 and three-fourths.
Mixed numbersA mixed number is modeled as follows:
a b/c.
In which the integer and the fractional parts are given as follows:
a is the integer part of the number.b/c is the fractional part of the number.To apply multiplication involving mixed numbers, we convert these numbers to fractions, as follows:
a b/c = (ac + b)/c
In this problem, the mixed number is given as follows:
3 1/4.
Hence the fraction is given as follows:
(3 x 4 + 1)/4 = 13/4
The multiplication by 3 is given as follows:
3 x 13/4 = 39/4.
The division of 39 by 4 has a quotient of 9 and a remainder of 3, hence the mixed number that represents the division is:
9 and three-fourths.
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TWO tailors, Aisha and Debbie, sit down to do some embroidery. Alsha can embroider 4 shirtsper hour, and Debbie can get through 6 shirts per hour. In addition, the tailors had previouslyfinished some shirts. Aisha has already completed 20 shirts, and Debbie has completed 10shirts. Aisha and Debbie decide to take a break when they have finished the same totalnumber of shirts. How long will that take?Write a system of equations, graph them, and type the solution
For the information given in the statement you have
[tex]\begin{gathered} t=4h+20\Rightarrow\text{ shirts embroidered by Aisha} \\ t=6h+10\Rightarrow\text{ shirts embroidered by Debbie} \end{gathered}[/tex]Suppose you have an experiment where you toss a fair coin 3 time you didn't count the number of heads observe over those 3 tosses use this experiment to address each of the falling question round solution to 3 destiny places
a) In order to complete the table for the probability distribution for the variable X:
X = the number of heads observed when you flip a coin three times,
b) we create a list of all the possible outcomes. We use the notation: H = heads, T = tails.
The possible outcomes after tossing the coin three times are:
[tex]HHH,HHT,HTH,THH,TTT,TTH,THT,HTT[/tex]From the list above we see that we have 8 equiprobable events. Now, we classify the events according to the number of Heads included.
- Events with x = #H = 0: TTT
- Events with x = #H = 1: HTT, THT, TTH
- Events with x = #H = 2: HHT, HTH, THH
- Events with x = #H = 3: HHH
Using the data above we compute the probabilities for each x, we simply compute the quotient between the number of outcomes of each case by N = 8 (the total number of possible outcomes):
[tex]\begin{gathered} P\mleft(x=0\mright)=\frac{1}{8}=0.125 \\ P(x=1)=\frac{3}{8}=0.375 \\ P(x=2)=\frac{3}{8}=0.375 \\ P(x=3)=\frac{1}{8}=0.125 \end{gathered}[/tex]c) Shape of the probability disribution. The probability distribution of x is: Symmetric.
d) Using the data above, we can compute the mean number of heads for the distribution:
[tex]\begin{gathered} E(x)=\sum ^3_{n=0}x_n\cdot P(x_n_{}) \\ E(x)=0\cdot P(x=0)+1\cdot P(x=1)+2\cdot P(x=2)+3\cdot P(x=3) \\ E(x)=0+1\cdot0.375+2\cdot0.375+3\cdot0.125 \\ E(x)=\frac{3}{2}=1.5 \end{gathered}[/tex]So the mean number of heads for this distribution is 1.5
Three people travel by car to San Diego, a distance is 380 miles. Thetrip takes 6 hours. Daily cost for meals is $20 per person and gas costs$3.59 per gallon and their vehicle gets 15 mpg. Calculate the cost perperson for this trip to the nearest dollar.A) $85B) $70C) $50D) $90E) $105
Given:
• Distance = 380 miles
,• Time = 6 hours
,• Daily cost for meals = $20 per person
,• Cost of gas = $3.59 per gallon
,• Vehicle gets 15 miles per gallon.
Let's calculate the cost per person for this trip.
We have the following:
To find the total cost of gas they used for this trip, we have:
[tex]\frac{380}{15}*3.59=90.95[/tex]The total cost of gas for this trip is $90.95
The cost of gas per person will be:
[tex]\frac{90.95}{3}=\text{ \$30.32}[/tex]Cost of gas per person is $30.32
Therefore, the cost per person for this trip will be:
Cost per person = Cost of gas per person + Cost of meal per person
Cost per person = $30.32 + $20 = $50.32 ≈ $50
Therefore, the cost per person for this trip to the nearest dollar is $50
ANSWER:
C) $50
Angel Sanchez has 6 books on a shelf; 2 mysteries, 3 science fiction books, and 1 biography. Determine the probability of each situationla) Selecting one mystery and then one science fiction, with replacementb) Selecting one mystery and then one science fiction, without replacementa) The probability of selecting one mystery and then one science fiction, with replacement is
It is given that there are 6 books in total, with 2 mysteries, 3 science fiction books, and 1 biography.
Recall that the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.
(a) It is required to find the probability of selecting one mystery and then one science fiction, with replacement.
The probability of selecting one mystery is:
[tex]P(M)=\frac{1}{6}[/tex]The probability of selecting one science fiction next with replacement is:
[tex]P(S)=\frac{1}{6}[/tex]The probability of independent events is the product of their respective probabilities.
Hence, the probability of selecting one mystery and then one science fiction, with replacement is:
[tex]P(M)\cdot P(S)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36}[/tex]The answer is 1/36.(b) It is required to find the probability of selecting one mystery and then one science fiction, without replacement.
Since there is no replacement, the probability of selecting one science fiction next without replacement is:
[tex]P(S)=\frac{1}{6-1}=\frac{1}{5}[/tex]Hence, the probability of selecting one mystery and then one science fiction, without replacement is:
[tex]P(M)\cdot P(S)=\frac{1}{6}\cdot\frac{1}{5}=\frac{1}{30}[/tex]The answer is 1/30.How many years are there in 467 days?
Answer:
there are approximately 1.28 years in 467 days
Step-by-step explanation:
1 yr = 365 days
467/365 = 1.28
Answer: 1 year and 102 days.
Step-by-step explanation:
There are 365 days in a year.
ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST (also please show how you got answer)
only giving brainlyest for correct answer
The slope of the line is 125.
The slope in the context represent the change in price with respect to the sizes of the houses.
The line won't pass through the point (5, 650)
How to find the slope of a line?The slope of a line is the change in y with respect to change in x.
Therefore,
slope = m = y₂ - y₁ / x₂ - x₁
using (0, 0)(2, 250)
m = 250 - 0 / 2 - 0
m = 250 / 2
Therefore,
m = 125
The slope simply implies the change in price with respect to the change in sizes of the houses.
Using the slope intercept equation we can know if the line passes through (5, 650).
Therefore,
y = 125x + 0
625 = 125(5)
Therefore, the line won't pass through the point (5, 650).
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A fashion photographer needs to hire a stylist to prepare her models. Emmet charges $177 for showing up, plus $75 per hour. Pam charges $187 plus $70 per hour. The photographer realizes that, given the expected duration of her photo shoot, either stylist would cost her the same amount. What would the duration be? What would the cost be?
Emmet charges $177 for showing up, plus $75 per hour
Total charge = Show up charge + Per hour charges
Pam charges $187 plus $70 per hour
either stylist would cost her the same amount
i.e the total cost of photographer and stylist
Let x be the time taken in shoot
so, the charge of Emmet is 177 + 75x
The charge of palm = 187+70x
Since the charge is equal so,
[tex]\begin{gathered} 177+75x=187+70x_{} \\ 75x-70x=187-177 \\ 5x=10 \\ x=2 \end{gathered}[/tex]we get x= 2
i.e. 2 hours
The duration at which the cost of palm and emmet is equal is 2 hours
for the cost
substitute the value of x in the cost equation :
Emmet = 177 + 75x
Emmet cost=177+75(2)
Emmet cost = 327
Since the cost is same so,
The cost of emmet and palm is $327
Answer: 2 hours & $327
A club consists of 15 people including Ali, Kendra,
Ted, Alice, Marie, Dan, Linda and Frank. From the 15
members, a president, vice president and treasurer
will be selected at random. An advisory committee
of 5 other individuals will also be selected at
random.
Determine the probability that Ali is selected
president, Kendra is selected vice president, Ted is
named the treasurer and the other 5 individuals
named form the advisory committee.
The required probability of the random event is 0.273.
The probability is estimated by dividing the total number of possible outcomes by the number of possible ways the event could occur.The probability and chances of that happening are two distinct ideas. Odds are calculated by dividing the probability of an event by the likelihood that it won't.Keep in mind that a president, vice president, and treasurer will be chosen at random from the 15 members. The number of options to choose from to fill these spots is thus:
[tex]_{15}P_3=\frac{15!}{(15-3)!} =2730[/tex].
The required probability of the random event is 0.273.
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To "double" a number means to multiply by two. It is often useful to be able to estimate the double of a number using mental math (without a calculator).
For example, a shirt costs $59. Estimate the cost to buy 2 shirts (disregard the tax).
Double the number $59 is $118 after applying the mental math, the answer is $118.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that:
To "double" a number means to multiply by two.
From the definition of the arithmetic operation, the operation in which we do the addition of numbers, subtraction, multiplication, and division.
Using mental math it can be easy to determine the double a number.
The number is $59
To double:
= 59 + 59
= 50 + 9 + 50 + 9
= 100 + 18
= $118
Thus, double the number $59 is $118 after applying the mental math, the answer is $118.
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Identify all the sets to which the number belongs. Choose from rational number, irrational number, whole number, and itenger. 0.62478916532
0.62478916532 is an irrational number
This is because it cannot be expressed as a rational number except in surd form which is also known to be irrational. it is neither a whole number nor an integer too
ANSWER => Option B
Kristen gets a full scoop of frozen yogurt in a cone. The scoop is aperfect sphere with the same radius as the cone. She wonders if theentire volume of the frozen yogurt could fit completely inside thecone. What is the relationship between the volume of the coneand the volume of frozen yogurt? Is the volume of the cone greatenough to fit all of the frozen yogurt? Explain. (Use 3.14 for (pie) andround your answer to the nearest whole number)
The volume of a sphere is calculated as follows:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r is the radius of the sphere.
Substituting with r = 5 cm, we get:
[tex]\begin{gathered} V=\frac{4}{3}\cdot\pi\cdot5^3 \\ V=\frac{4}{3}\cdot\pi\cdot125 \\ V=523.3\operatorname{cm}^3 \end{gathered}[/tex]The volume of a right circular cone is calculated as follows:
[tex]V=\pi r^2\frac{h}{3}[/tex]where h is the height of the cone.
Substituting with r = 5 cm, and h = 11 cm, we get:
[tex]\begin{gathered} V=\pi\cdot5^2\cdot\frac{11}{3} \\ V=\pi\cdot25\cdot\frac{11}{3} \\ V=287.8\operatorname{cm}^3 \end{gathered}[/tex]The volume of the cone is less than the volume of the sphere, then the
entire volume of the frozen yogurt cannot fit completely inside the
cone.
