Answer:
8 cm.
Step-by-step explanation:
We have been given that an ice cream cone that is 4 cm across the top is topped with a single scoop of ice cream (spherical) that is 4 cm in diameter.
To find the minimum height of cone we will use volume of cone formula and volume of sphere as we are told that when the ice cream melts, the ice cream does not overflow out of the cone. This means that volume of sphere will be equal to volume of cone.
[tex]\text{Volume of cone}=\frac{1}{3} \pi r^2h[/tex]
[tex]\text{Volume of sphere}=\frac{4}{3} \pi r^3[/tex]
Since diameter of both cone and sphere is 4 cm, so radius will be half the diameter, that is 2 cm.
Let us substitute r=2 in both equations and equate the volumes of cone and sphere to find the height of cone.
[tex]\frac{4}{3} \pi\times 2^3=\frac{1}{3} \pi\times 2^2\times h[/tex]
[tex]\frac{4}{3} \pi\times 8=\frac{1}{3} \pi\times 4\times h[/tex]
Multiply both sides of equation by 3.
[tex]3\times \frac{4}{3} \pi\times 8=3\times \frac{1}{3} \pi\times 4\times h[/tex]
[tex]4 \pi\times 8= \pi\times 4\times h[/tex]
[tex]32 \pi= 4\pi\times h[/tex]
[tex]h=\frac{32 \pi}{4\pi}[/tex]
[tex]h=8[/tex]
Therefore, the minimum height of cone must be 8 cm.
Natasha is observing the growth of a population of bacteria. She started out with 250 bacteria cells. The population of bacteria quadruples every hour. Use x to represent the number of hours and y to represent the population of the bacteria. Enter an equation that represents this scenario in the box.
Answer:
[tex]y=250(5)^x[/tex]
Step-by-step explanation:
The growth of a population of bacteria can be represented by exponential growth function,
[tex]y=a(1+r)^x[/tex]
where,
y = the population of the bacteria after x hours,
x = the number of hours,
a = initial population of bacteria,
r = rate of growth,
At the beginning the number bacteria was 250 and the population of bacteria quadruples every hour i.e rate of growth is 400% or 4 per hour.
Putting all the values,
[tex]y=250(1+4)^x[/tex]
[tex]\Rightarrow y=250(5)^x[/tex]
Considering only functions with a greater rate of change than that of the function represented on the graph, which function has the lowest rate of change? (only one answer)
A) y = 13/7x - 7/3
B) y = 7/5x + 2/5
C) y = 11/8x + 3/8
D) y = 5/4x + 13/4
E) y = 5/3x - 8/3
Answer:
C (1.38)
Step-by-step explanation:
The graphed function has the slope 4/3, which is obvious: As x increases from 0 to 1.5, y increases from -2 to 0. Thus, m = rise / run = 2/1.5 = 4/3.
Which of the given functions have greater rates of change than 4/3? These include A (1.86), B (1.4), C (1.38), E (1.67). Of these, C has the lowest rate of change (1.38).
The lowest rate of change of the function is y = 11/8x + 3/8. The correct option is C.
What is a function?
The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
The graphed function has a slope of 4/3, which is obvious: As x increases from 0 to 1.5, y increases from -2 to 0. Thus, m = rise / run = 2/1.5 = 4/3.
Which of the given functions has greater rates of change than 4/3? These include A (1.86), B (1.4), C (1.38), E (1.67). of these, C has the lowest rate of change (1.38).
Therefore, the lowest rate of change of the function is y = 11/8x + 3/8. The correct option is C.
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Which is an equation of the line that is perpendicular to 3x+y=-5 and passes through the point (3, -7)?
Answer:
y+7=1/3(x-3) in point slope
y=1/3x-8 in slope intercept form
Step-by-step explanation:
First put 3x+y=5 in slope-intercept form (y=mx+b)
y=-3x+5
Give that the slope is -3 the perpendicular slope would be 1/3
now using the points (3.-7)
y+7=1/3(x-3) in point slope
y=1/3x-8 in slope intercept form
Put it in Slope - Intercept Form:
3x + y = -5
-3x -3x
y = -3x - 5
Now plug in the ordered pair that is given:
(3, -7)
y = -3x - 5
-7 = -3(3) - 5
-7 = -9 - 5
-7 = -14
NO, it's false....
Hi, really really sorry if I am incorrect...
At the art fair, 95 artists exhibited their work. Of those 95 artists, 25 showed sculptures and 48 showed paintings. If 12 showed both sculptures and paintings, how many artists showed only sculptures or paintings?
To determine the number of artists who showed only sculptures or paintings at the art fair, we use the formula for the principle of inclusion-exclusion, resulting in 61 artists.
Explanation:To find out how many artists showed only sculptures or paintings at the art fair, we apply the principle of inclusion-exclusion. First, we add the number of artists who showed sculptures (25) to those who showed paintings (48), which gives us a total of 73 artists. However, this counts the 12 artists who showed both sculptures and paintings twice, so we subtract 12 from this total to correct for the double counting. Therefore, the number of artists who showed only sculptures or paintings is 73 - 12, which equals 61 artists.
Alicia runs for exercising falicia runs 8 Miles and 6 days how many days will it take for her to run 36 miles
Alicia runs 8 miles in 6 days. By setting up a proportion, it's calculated that it will take her 27 days to run 36 miles at the same rate.
Calculating Days Needed to Run a Total Distance:
Alicia runs 8 miles in 6 days. To find out how many days it will take her to run 36 miles, we can set up a proportion. Since the number of days is directly proportional to the miles run, we can use the equation:
8 miles / 6 days = 36 miles / x days
By cross-multiplying, we get:
8 miles * x days = 6 days * 36 miles
x = (6 days * 36 miles) / 8 miles
The miles cancel out, leaving us with:
x = 216 / 8
x = 27 days
Therefore, it will take Alicia 27 days to run a total of 36 miles if she continues running at the same rate.
The function p(t) represents the population of a certain town t years after 2010.
p(t)=3476(0.97)t
What does the value 3476 represent in this situation?
Every year after 2010, the population decreases by 3476.
Every year after 2010, the population increases by 3476.
The population of the town in 2010 is 3476.
The population t years after 2010 is 3476.
Answer:
Population of town in Year 2010 is 3476.
Step-by-step explanation: Formula for the Population after t years is given by P(t) = P (1-i/100)^n
where P is initial population.
Here in question P is initial population.
If we compare the equation given in the question to the problem equation
we have P = 3476 , which is initial population.
Answer:
The population of the town in 2010 is 3476.
Step-by-step explanation:
Jasmine arrives at school at 7am. She starts the day with 9 sharpened pencils. She asks Kim to sharpen pencils. Kim sharpens eleven pencils every minute for the next seven mins. What was the number of sharpened pencils at 7:07 am?? Plz I will give you 100 points
Answer:
should be about 86
Step-by-step explanation:
multiply 11 by seven and then add nine because thats what you had originally.
we multiply because in those seven minutes we're constantly adding more pencils so instead of adding, multiplication is the easiest to do
9+(7x11)
7/8 & -8/7 are these line slope perpendicular or parallel or neither
Answer:
Perpendicular!
Step-by-step explanation:
If they were parallel they would have the exact same slope. If they are perpendicular their slopes would be opposite reciprocals of each other... which they are. Another trick to tell if two slopes are perpendicular is to multiply them by each other and if the answer equals -1 they are perpendicular:
7/8 • -8/7 = -1/1 = -1
How many batches of soup can Marcia make
Answer:
400 divided by 5 is how you get the answer.
Step-by-step explanation:
400 / 5 = 80
80 batches of soup.
Easy question.
Pia, Gauri, Zarna and Yasmin have EQUAL number of pencils.
Each of them ties their pencils in bundles with each bundle containing the same
number of pencils.
- Pia ties 10 pencils together as a bundle.
- Gauri ties 12 pencils together as a bundle.
- Zarna ties 15 pencils together as a bundle.
- Yasmin ties 20 pencils together as a bundle.
Who has the maximum number of bundles?
a) Yalan b) Pia c) Gauri d) Zarna
One line reasoning
Answer:
Pia
Step-by-step explanation:
The smaller the number of pencils in a bundle the greater the number of bundles.
For example if the number of pencils each has is 60,
Then the number of bundles for Pia = 60/10 = 6,
and ...................................................Gauri = 60/12 = 5,
and .....................................................Yasmin = 60/20 = 3.
Answer:
Pia
Step-by-step explanation:
A plane travels at a constant speed. It takes 6 hours to travel 3,360 miles
To find the average speed of the plane, divide the total distance traveled, which is 3,360 miles, by the total time of the journey, which is 6 hours, resulting in an average speed of 560 miles per hour.
Explanation:The student's question involves calculating average speed, which is a concept in Physics, specifically within the topic of kinematics. To find the average speed of the plane you would use the formula:
average speed = total distance / total time
In this case, the plane travels 3,360 miles in 6 hours, so the calculation would be:
average speed = 3,360 miles / 6 hours = 560 miles/hour
This calculation demonstrates how to determine the average speed of an object in motion when given the total distance traveled and the total time taken. This concept is analogous to determining the average speed in other examples, such as a car journey or a train trip.
PLEASE HELP!!!!! THANK YOU!
Answer:
The slope is found by the change in Y over the change in x.
Using the given points:
The change in Y = -8 - 4 = -12
The change in x = 2 - -6 = 2 +6 = 8
The slope is -12/8
Both the numerator and denominator can be divided by 4
-12/4 = -3
8/4 = 2
The slope = -3/2
Given JKL : XYZ, find the scale factor DO NOT find x
Answer:
2/3
Step-by-step explanation:
find the leagth of x
Answer:
As a fraction, the answer is 5/2
In decimal form, the answer is 2.5
=====================================
Explanation:
The triangles are similar (AA similarity property) so we can solve the proportion below
x/3 = 5/6
6*x = 3*5
6x = 15
x = 15/6
x = 5/2
x = 2.5
in the equation m = k + 3, m is the:
In the equation m = k + 3, m represents a dependent variable. Hence the correct option is 2.
In an equation, a variable is a placeholder for an unknown value.
"Dependent" means that its value depends on the value of another variable.
In this case, the value of m depends entirely on the value of k.
If you know the value of k, you can solve the equation for m and find its specific value.
k is the independent variable in this equation because its value is not determined by any other variable in the equation.
Hence the correct option is 2.
Complete question:
In the equation m = k + 3, m is the:
Independent variable
Dependent variable
333.333 Which statements are true? Choose all answers that are correct. The 3 in the hundredths place is 110 times the value of the 3 in the tenths place. The 3 in the ones place is 10 times the value of the 3 in the tenths place. The 3 in the thousands place is 10 times the value of the 3 in the hundredths place. The 3 in the thousandths place is 110 times the value of the 3 in the hundredths place. Assessment navigation
Answer:
The only correct answer is the second one, that the three in the tenths place is 10 times the amount in the 100ths place.
Step-by-step explanation:
The others are all wrong because the further the place, the less the value, so they cannot be ANY times the amount of a place closer to the decimal.
Write an algebratic expression for "six more than the quantity d times two."
Answer:
6+2d
Step-by-step explanation:
An algebraic expression for 'six more than the quantity d times two' is written as 2d + 6, which represents the multiplication of d by two, followed by the addition of six.
To write an algebraic expression for "six more than the quantity d times two," you first perform the multiplication and then add six.
The quantity d times two is expressed as 2d. Then, to represent "six more" than this quantity, you add six to the product, which is written as [tex]2d + 6[/tex].
Divide (x^3-8x^2+17x-10)/(x-5)
Answer:
(x - 2)*(x - 1) is the answer
Step-by-step explanation:
We have to divide the polynomial f(x) = x^{3}-8x^{2}+17x-10 by (x-5).
Now, after dividing f(x) gets simplified into (x-5)*(x^{2}-3x+2).
So, we need to factorize the quadratic equation x^{2}-3x+2.
i.e. x^{2} - 3x + 2 = x^{2} - x - 2x + 2 = x(x-1) - 2(x-1) = (x - 2)*(x - 1)
Therefore, f(x) again gets simplified into (x-5)*(x - 2)*(x - 1)
Now eliminating the common factor (x-5).
We get, [tex]\frac{x^{3}-8x^{2}+17x-10}{x-5}[/tex] = (x - 2)*(x - 1)
Answer:
[tex]x^{2}-3x+2[/tex]
Step-by-step explanation:
Use synthetic division.
Reverse the sign of -5 and write the coefficients of the polynomial.Multiply the coefficient by the divisor, then add to the next coefficient.Continue through the last coefficient.5 | 1 -8 17 -10
+ 5 -15 10
1 -3 2 0
The quotient is [tex]x^{2} -3x+2[/tex].
Two runners start 30 kilometers apart and run toward each other. They meet after 3 hours. One runner runs 2 kilometers per hour faster than the other runner. What rate do they run?
2 km/hr and 4 km/hr
3 km/hr and 5 km/hr
5 km/hr and 7 km/hr
4 km/hr and 6 km/hr
Answer: 4 km/hr and 6 km/hr
Step-by-step explanation:
A runner = 4km/hr
A runner covered distance after 3 hours = 12 km
B runner = 6km/hr
B runnet covered distance after 3 hours = 18 km
Total distance = 12 + 18 = 30km
PLZZZ HELP ASAP!!!!!!!
Marie mixes 16 liters of 18% acid solution with a 27% acid solution, which results in 21% acid solution. Let x represent the number of liters of 27% solution used and let y represent the number of liters of mixture. Which system of equations can be used to find the number of liters of 27% acid solution in the mixture?
1. y = x + 16; 0.27y = 0.21x + 2.88
2. y = x + 16; 0.21y = 0.27x + 2.88
3.y = x + 16; 0.21y = 0.27x + 4.32
4. y = x + 16; 0.27y + 2.88x = 0.21
Answer:
2. y = x + 16; 0.21y = 0.27x + 2.88
Step-by-step explanation:
You have two conditions:
Volume of 18 % + volume of 27 % = volume of 21 % Mass of acid in 18 % + mass of acid in 27% = mass of acid in 21 %For the first condition,
16 + x = y Transpose
(1) y = x + 16
=====
For the second condition
V₁c₁ + V₂c₂ = V₃c₃
16×0.18 + 0.27x = 0.21y
2.88 + 0.27x = 0.21y Transpose
(2) 0.21y = 0.27x + 2.88
The system of equations is y = x + 16; 0.21y = 0.27x + 2.88
crate a list of steps, in order, that will solve the following equation. 2(x+3/4)^2 -5 =123
Answer:
x = -8.75; x = 7.25
Step-by-step explanation:
2(x + ¾)² - 5 = 123
Add 5 to each side: 2(x+ ¾)² = 128 Divide each side by 2: (x+ ¾)² = 64 Take the square root of each side: x + ¾ = 8 x + ¾ = -8 Subtract ¾ from each side: x = 8 - ¾ x = -8 - ¾ Convert to decimal fraction: x = 8 - 0.75 x = -8 – 0.75 Subtract: x = 7.25 x = -8.75The graph of your equation is a parabola with x-intercepts at x = -8.75
and x = 7.25.
The list of steps, in order, that will solve the equation is:
Addition of 5 to both sides to eliminate the value of -5Division of both sides of the equation by 2 to eliminate the coefficient of 2 from the left-hand sideTaking the square root of both sidessubtract 3/4 from each sideConvert the answer to decimalThe given expression is raised to a power of 2, so we can say that the given expression is a quadratic equation.
What is a quadratic equation?A quadratic equation is a form of an algebraic expression in which the variable is usually raised to the power of its second degree.
From the parameters given:
[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 = 123 }[/tex]
Addition of +5 to both sides[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 +5 = 123+5 }[/tex]
[tex]\mathbf{2(x + \dfrac{3}{4})^2 = 128}[/tex]
Division of both sides by 2[tex]\mathbf{\dfrac{2(x + \dfrac{3}{4})^2 }{2} =\dfrac{ 128}{2}}[/tex]
[tex]\mathbf{(x + \dfrac{3}{4})^2 = 64}[/tex]
Taking the square root of both sides[tex]\mathbf{\sqrt{(x + \dfrac{3}{4})^2} =\sqrt{ 64}}[/tex]
[tex]\mathbf{(x + \dfrac{3}{4})} =\pm8}[/tex]
Subtract 3/4 from both sides[tex]\mathbf{(x + \dfrac{3}{4} - \dfrac{3}{4}) }\mathbf{= \pm 8-\dfrac{3}{4}}[/tex]
[tex]\mathbf{x= \pm 8-\dfrac{3}{4}}[/tex]
[tex]\mathbf{x= +8-\dfrac{3}{4} \ \ OR \ \ x= -8-\dfrac{3}{4}} [/tex]
[tex]\mathbf{x=7.25 \ \ OR \ \ -8.75} [/tex]
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a jewelry store makes 5 dollar profit for each 1 dollar they spend on jewelry. a jewelry store owner made a profit of 95 dollars on a necklace. what was the original cost of the necklace? solve by using equivalent ratios.
Three boxes of candy canes cost 23.97 how many much does each box cost?
Answer:
So you are going to take the total cost and divide it by the amount
Step-by-step explanation:
23.97/3=7.99
Hope that helps feel free to ask more questions
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What is the measure of angle c in the diagram below?
A. 105°
B. 137°
C. 16°
D. 121°
Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours. How long, to the nearest tenth of an hour, will it take them to paint the room together?
Answer:
It will take 1.5 hours to paint the room together
Step-by-step explanation:
Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours.
Work done by Martha in 1 hour = [tex]\frac{1}{2}[/tex]
Work done by Jamie in 1 hour = [tex]\frac{1}{6}[/tex]
Work one together in 1 hour = [tex]\frac{1}{2}+\frac{1}{6}[/tex]
Now take common denominator to add both fractions
LCD = 6, Multiply the first fraction by 3
[tex]\frac{1*3}{2*3}+\frac{1}{6}[/tex]
[tex]\frac{3}{6}+\frac{1}{6}[/tex]
Now add the numerators
[tex]\frac{4}{6}[/tex]
[tex]\frac{2}{3}[/tex]
To find total hours of painting together, we take reciprocal of 2/3
Time taken to paint together = [tex]\frac{3}{2}= 1.5[/tex]
It will take 1.5 hours to paint the room together
The nearest tenth of an hour, will it take them to paint the room together is 1.5 hours.
Given data:
Time taken by Martha to paint a room is, 2 hours.
Time taken by Jamie to pain the same room is, 6 hours.
Then work done by each of Martha and Jamie in 1 hour is given as,
[tex]W_{Martha}=\dfrac{1}{2}\\\\W_{Jamie}=\dfrac{1}{6}[/tex]
Total work done in 1 hour is given as,
[tex]W_{total}=W_{Martha} + W_{Jamie}\\\\W_{total}=\dfrac{1}{2} + \dfrac{1}{6}\\\\W_{total}=\dfrac{6+2}{12} \\\\W_{total}=\dfrac{8}{12}\\\\W_{total}=\dfrac{2}{3}[/tex]
To find total hours of painting together, we take reciprocal of 2/3.
Then, time taken to paint together is, 3/2 = 1.5 hours.
Thus, we can conclude in the nearest tenth of an hour, will it take them to paint the room together is 1.5 hours.
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I need the answer ASAP
Answer: He would have 20
Step-by-step explanation:
well first you do 15/3=5 which means it was 5 per week =. Then, you multiply 4 x 5=20 to know how much he had over 4 weeks.
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What is the complete factored form of the polynomial 25ab^2+5ab
Answer:
5 a b (5 b + 1)
Step-by-step explanation:
Factor the following:
25 a b^2 + 5 a b
Hint: | Factor common terms out of 25 a b^2 + 5 a b.
Factor 5 a b out of 25 a b^2 + 5 a b:
Answer: 5 a b (5 b + 1)
Three snacks bars contain 1/5,0.22, and 19 percent of their Calories from fat. Which snack bar contains the least amount of calories from fat?
Answer:
19 percent
Step-by-step explanation: First we need to convert them all the a similar format. Fractions would be easiest.
.22 = 22/100
1/5 = 20/100
19% = 19/ 100
The one that contains the least is 19/100 or 19%.
How do u write 10 x10x10x10 using exponents
Answer: I'm not really sure how to shrink the number to the top but in word form it would be 10 to the power of 4.
Brian works 40 hours a week. He spends 40% of his time helping customers, 13% doing paperwork, and the remainder performing other store tasks. What percentage of Brian's time is spent on other store tasks?
40% helping customers + 13% doing paper work = 53% of his time.
This means 100% - 53% = 47% of his time he is doing other tasks.