Answer:
The funnel will fill the container in about 10 times
Step-by-step explanation:
To solve this question, the principal thing to do is to calculate the volumes of the cone-shaped funnel and the cylinder to actually know the number of times we will need to fill the funnel so as to fill the cylinder,
These number of times can simply be calculated by dividing the volume of the cylinder by the volume of the cone-shaped funnel.
Mathematically, we proceed as follows;
Volume of the cone funnel = 1/3 ×π× [tex]r^{2}[/tex]× h, where r and h represents the radius and height of the cone respectively.
From the question D = 6 inches, and mathematically r = D/2 = 6/2 = 3 inches and h = 7 inches
Plugging the values we have in the question, the volume = 1/3 ×π×[tex]3^{2}[/tex]×7 = 21π [tex]inches^{3}[/tex]
For the cylindrical receptacle, we have the volume calculated as π× [tex]r^{2}[/tex]× h
Where r = 4 inches and h = 13 inches.
Plugging these values we have ; π × [tex]4^{2}[/tex]× 13 = 208π [tex]inches^{3}[/tex]
Now the number of times is simply = volume of cylindrical container/volume of cone-shaped funnel
= 208π/21π = 208/21 = 9.9 which is approximately 10 times
What is the rate of change of the function shown in the table below
Answer: -3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
The original price of a shirt was $20. It was decreased to $15. What is the percent decrease of the price of this shirt?
Answer:
25%
Step-by-step explanation:
Price reduction = 20 - 15 = $ 5
Percent decrease of price = (5/20)*100 = 5*5 = 25%
Robert delivers papers every morning. On Sundays he has to deliver 57 papers and on each of the other days he only has to deliver 36 papers. How many papers does Robert deliver each week?
A.
309
B.
399
C.
345
D.
273
Reset Submit
Answer:
D. 273
Step-by-step explanation:
(36*6)+57
216+57
273
How is the graph of the parent quadratic function transformed to produce the graph of y=-(2x+6)? +3?
The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated up 3 units.
The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.
The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up 3 units.
The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.
Answer:
d
Step-by-step explanation:
Answer:
B on ed
Step-by-step explanation:
got D wrong on ed so it is B
A botanist is working with a sample of algae cells in a petri dish. The change in the population of algae cells can be modeled by this function, where I represents the time in minutes
f(t) = 0.89€
Which statement describes the population of algae cells in the sample?
The population is decaying at a rate of 89% per minute,
The population is decaying at a rate of 11% per minute.
The population is growing at a rate of 89% per minute.
The population is growing at a rate of 11% per minute.
Answer:
The population is decaying at a rate of 11% per minute.
Step-by-step explanation:
We have that € is the inicial sample of algae cells, and f(t) shows the sample after t minutes.
As € is multiplied by a number between 0 and 1, that means the sample will decrease it's size as the time passes.
The inicial sample is €, and after 1 minute the sample will be 0.89€, that is, it will decrease by 0.11€ or 11% of the previous sample.
So the correct option is:
The population is decaying at a rate of 11% per minute.
Answer:
The correct answer is b) The population is decaying at a rate of 11% per minute.
Step-by-step explanation:
Given the function
f(t) = 0.89€
We can see that every time the variable v grows 1, the population grows only 0.89. So the population is decreasing. And the percentage of decreasing we get it by discounting 1 -0.89= 11%
What is the slope of the line shown
Answer: The Option is A, slope is -1/3
Step-by-step explanation:
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 272 people entered the park, and the admission fees collected totaled 758.00 dollars. How many children and how many adults were admitted?
For which value of x is the equation 6 = 12x true?
Answer:
x = 0.5
Step-by-step explanation:
Ryan is building a ramp so he can easily move things in and out of an overhead storage area in his garage. The storage area is 8 feet off the ground, and Ryan has 15 feet of space along the ground to build the ramp.
A triangle with side lengths 15 feet, 8 feet, and an unlabeled hypotenuse.
What is the length of the ramp Ryan will build?
7 feet
10 feet
17 feet
23 feet
Answer:
17 feet
Step-by-step explanation:
c=the length of the ramp
a=8 ft
b=15 ft
Pythagorean Theorem
c²=a²+b²
c²=8²+15²
c²=64+225
c²=289
c=√289
c=17 ft
The length of the ramp of the triangular path is AC = 17 feet
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the base of the ramp is BC = 15 feet
The height of the ramp is AB = 8 feet
So , length of the ramp Ryan needs to build is AC is
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
AC = √ ( AB )² + ( BC )²
AC = √ ( 8 )² + ( 15 )²
AC = √ ( 64 + 225 )
AC = √289
AC = 17 feet
Therefore , the value of AC is 17 feet
Hence , the length of the ramp is 17 feet
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The heights (in cm) and arm spans (in cm) of 31 students were measured. The association between (height) and (arm span) is shown in the scatterplot below. The equation of the line of best fit modeling this relationship is given:
y=4.5+0.977x
Mike is 172 cm tall and George is 165 cm tall. Using the model, how many centimeters longer would we expect Mike's arm span to be than George's? Round your answer to the thousandths place.
Answer: Mike's arm span is 7.165 cm longer than the George's one.
Step-by-step explanation:
We have that the association between height and arm span is modeled by the equation
y = 4.5 + 0.977*x
where y is height and x is arm span.
Mike is 172 cm tall, so his arm span is:
172cm = 4.5 + 0.977*x
x = (172 - 4.5)/0.977 = 171.443 cm
and George is 165 cm tall, so his arm span is:
x = (165 - 4.5)/0.977 = 164.278 cm
Then the difference between their arm span is:
171.443cm - 164.278cm = 7.165 cm
So Mike's arm span is 7.165 cm longer than the George's one.
Takiya recorded the heights of two sets of plants, one set planted in the shade and one set planted in full sun. Her data are shown in the plots below. A dot plot. A number line going from 1.5 to 4.5 in increments of 0.5 is labeled Heights of Shaded plants (inches). There are 0 dots above 1.5, 4 above 2, 3 above 2.5, 2 above 3, 0 above 3.5 and 4, and 1 above 4.5. A dot plot. A number line going from 1.5 to 4.5 in increments of 0.5 is labeled Heights of Full Sun plants (inches). There are 0 dots above 1.5, 1 above 2, 0 above 2.5, 2 above 3, 0 above 3.5, 4 above 4, and 3 above 4.5. Which best explains the variability of the sets? The shaded plants set has greater variability because more data is clustered around the median. The sets are equally variable because the ranges of the data sets are equal. The full sun plants set has greater variability because the IQR for full sun plants is greater. The full sun plants set has greater variability because the median for full sun plants is greater.
Answer:
c
Step-by-step explanation:
its not a b or d so its c
Answer: C
Step-by-step explanation: on edge
The simplest cost function is the linear cost function C(x)=mx+b, where the y-intercept b represents the fixed cost of operating a business and the slope m represents the variable costs. Suppose that a small bicycle manufacturer has daily fixed costs of $1900 and each bicycle costs $40 to manufacture.a. Write a linear function that expresses the cost of manu. x bicycles in a day.C(x)=b. Graph the linear function.
Answer: C(x) = 40X + 1900
Step-by-step explanation: given from the question,
daily fixed costs = $1900 and
daily variable costs = $40
the linear cost function C(x)=mx+b, where the y-intercept b represents the fixed cost of operating a business and the slope m represents the variable costs
The cost of manufacturing x bicycle per day will be
C(x) = 40X + 1900
Is 17,22,29 a right triangle
Answer:
No!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
formula:
a^2+b^2=c^2
Answer:
No
Step-by-step explanation:
The only way that those side lengths formed a right triangle is if they formed a pythagorean triple. [tex]\sqrt{17^2+22^2}=\sqrt{773}\neq 29[/tex]. Therefore, that is not a right triangle. Hope this helps!
Is 28,45,53 a right triangle
Answer:
yes
Step-by-step explanation:
The numbers satisfy the Pythagorean theorem:
53^2 = 28^2 +45^2
2809 = 784 +2025
(28, 45, 53) is a Pythagorean triple. These lengths will make a right triangle.
A bakery sold 340 mocha cupcakes in a day, which was 85% of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
400
Step-by-step explanation:
Given:
Number of mocha cupcakes in a day = 340
Total number of cupcakes sold that day = [tex]85\%[/tex]
To find:
Total number of cupcakes sold by the bakery
Solution:
Let x denotes total number of cupcakes sold by the bakery.
According to question,
[tex]\frac{85}{100}x=340\\x=\frac{340}{85}\times 100=400[/tex]
So,
Total number of cupcakes sold by the bakery = 400
lena's coffee shop makes a blend that us a mixture of two types of coffee. Type A coffee costs Lena $5.70 per pound, and type B coffee costs $4.25 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $885.30. how many pounds of type A coffee were used?
Answer: 39 pounds of type A coffee were used.
Step-by-step explanation:
Let x represent the number of pounds of type A coffee that were used in the blend.
Let y represent the number of pounds of type B coffee that were used in the blend.
Type A coffee costs Lena $5.70 per pound, and type B coffee costs $4.25 per pound. The total cost of the mixture is $885.30. It means that
5.7x + 4.25y = 885.3- - - - - - - - - -1
This month's blend used four times as many pounds of type B coffee as type A. It means that
y = 4x
Substituting y = 4x into equation 1, it becomes
5.7x + 4.25 × 4x = 885.3
5.7x + 17x = 885.3
22.7x = 885.3
x = 885.3/22.7
x = 39
y = 4x = 4 × 39
y = 156
The weight of Type A coffee used was approximately 39 pounds. This is determined by setting up and solving an equation based on the provided costs per pound of the coffees and the total cost.
Explanation:In this problem, we need to solve for the amount of Type A coffee. Let's represent the weight of Type A coffee as x and the weight of Type B coffee as 4x, as it's mentioned the weight of Type B is four times Type A. We know that the combination of Type A and B coffee costs $885.30, so we can set up the equation using the costs per pound for each type: (5.70*x) + (4.25*4x) = 885.30.
Solving this equation, we have 5.70x + 17x = 885.30, or 22.7x = 885.3. Dividing both sides by 22.7, we get x = 38.97 pounds. So, approximately 39 pounds of Type A coffee were used.
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1. Krista is taller than Jan. Jan is shorter than Len, but taller than
Mick. Len is shorter than Krista. Who is the tallest?
After comparing the height of each person, we can confidently say that Krista is the tallest from all the given individuals.
Explanation:Krista is taller than Jan. Jan is shorter than Len, but taller than Mick. Len is shorter than Krist. The question provides information that allows us to compare the height of each individual. Based on given information we were provided, Krista is taller than Jan, Len is shorter than Krista but taller than Mick, and Jan is shorter than Len but taller than Mick. This means that Krista is taller than Len, Jan, and Mick, making Krista the tallest.
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deon buys candy that cost $6 per pound. he will buy at most 7 pounds.
Answer:
He will spend 42 dollars
Step-by-step explanation:
7 times $6
= $42
(If that's what you're asking)
Answer:
7 × $ 6 = $42 so it all equals to 42 dollars
As an estimation we are told £3 is €4.
Convert €91.30 to pounds.
Give your answer rounded to 2 DP.
Answer:
68.48 pounds
Step-by-step explanation:
€91.30 to pounds
€91.30 * (3 pounds/ 4€) = 68.475 pounds about 68.48 pounds
which cannot be a cross section of the figure? A cross section of the figure cannot be a ____
Answer: The answer is circle
Step-by-step explanation: The explanation is that you can see by looking at the shape you can easily make a rectangle, etc but you can not make a circle :).
Answer:
circle
Step-by-step explanation:
volume of a sphere with a radius of 10
Answer:
4189 cubic units
Step-by-step explanation:
Put the value in the volume formula and do the arithmetic. The formula for the volume of a sphere is ...
V = (4/3)πr³
Filling in 10 for r, we have ...
V = (4/3)π(10³) = 4000π/3 ≈ 4189 . . . cubic units
which of the following statements are correct? select all that apply
Answer:
sorry, but you need to show the selectings
Step-by-step explanation:
Answer:
we cant see the choices
Step-by-step explanation:
The combination of Wendell and Maggie’s ages is 33. Wendell’s age is 3 less than 3 times the age of Maggie. How old is Wendell?
Answer:
Wendell is 24 years old.
Step-by-step explanation:
First write an equation to represent the situation.
x=Maggie's age
x+(3x-3)=33
Then solve for x
x+3x-3=33
4x-3=33
4x-3+3=33+3
4x=36
4x/4=36/4
x=9
Then solve for Wendell's age
y=Wendell's age
y=3x-3
y=3(9)-3
y=27-3
y=24
Wendell is 24 years old.
By setting up and solving a system of equations based on the information given, we find that Wendell is 24 years old.
Explanation:In this question, we are asked to find out Wendell's age. First, we assume that Maggie's age is x. According to the problem, the sum of Wendell and Maggie's ages is 33, so we can write the first equation as Wendell's age + Maggie's age = 33. Next, we know that Wendell's age is three less than three times Maggie's age, so Wendell's age = 3*x - 3. Now, if we insert Wendell's age expression from the second equation into the first equation, we get 3*x - 3 + x = 33. When we solve this equation, we found that x equals to 9, hence, Maggie is 9 years old. That means, Wendell is 33 - 9 = 24 years old.
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Divide 45 in the ratio 7:8
Answer:
0.0195?
Step-by-step explanation:
Answer:
21 : 24
Step-by-step explanation:
Sum the parts of the ratio, 7 + 8 = 15 parts
divide 45 by 15 to find one part of the ratio
45 ÷ 15 = 3 ← value of 1 part of ratio, thus
7 parts = 7 × 3 = 21
8 parts = 8 × 3 = 24
45 divided in the ratio 7 : 8 is 21 : 24
A truangular bandana has an area of 42 square inches. The height of the triangle is 5 1/4 inches. Enter and solve an equation ti find the length of the base of the triangle.
Answer: The length of the base of the triangle is 16 inches.
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula
Area of a triangle (A) = base x height x 1/2
Replacing with the values given:
42 = b (5 1/4) 1/2
Solving for b (lenght of the base)
42 / (5 1/4) 1/2 = b
16 in = b
The length of the base of the triangle is 16 inches.
Feel free to ask for more if needed or if you did not understand something.
Final answer:
The length of the base of the triangle is 16 inches, calculated by using the area formula for a triangle and the given height.
Explanation:
To find the length of the base of the triangle, we use the formula for the area of a triangle, A = (b * h) / 2, where A is the area, b is the base, and h is the height. We know the area (A) is 42 square inches and the height (h) is 5 1/4 inches. Plugging these values into the formula gives us:
42 = (b*5.25) / 2
Multiplying both sides by 2 to isolate the term with b gives us:
84 = b* 5.25
Dividing both sides by 5.25 yields:
b = 84 / 5.25
Calculating this division, we get the length of the base (b):
b = 16 inches
What would be the coordinates at 315° if the coordinates at 135° are at (-square root 2/2, square root 2/2)?
Answer:
We choose C
Step-by-step explanation:
the coordinates at 135° are at ([tex]\frac{-\sqrt{2} }{2}[/tex], [tex]\frac{\sqrt{2} }{2}[/tex] )
As we can see, the x coordinate of the point is negative and the y coordinate of it is positive.
So this point is located at the quadrant ii
From 135 ° to 315°, it is rotated 180°
=> Each coordinate (x,y) is changed to (-x,-y)
= ([tex]\frac{\sqrt{2} }{2}[/tex], [tex]-\frac{\sqrt{2} }{2}[/tex] ) the new coordinate is located in quadrant iii
We choose C
Help pleas this late
Answer:
V = 282.10 cm³
Step-by-step explanation:
[tex]V= \pi r^2\frac{h}{3}[/tex] Use this equation to find the volume of the cone
[tex]V=3.14(3.5)^{2} \frac{22}{3}[/tex] Simplify the (3.5)²
V = 3.14(12.25)(22/3) Multiply
V = 282.10 cm³
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Jim had $2,052.24 in his checking account. He wrote a check to pay for
two airplane tickets. His account now has $1,084.12. How much did each
ticket cost? *
Answer:
$485.06
Step-by-step explanation:
Answer:
$484.06
Step-by-step explanation:
$2,052.24 - 1,084.12 = 916.12
916.12 divided by 2 = 484.06
Talulah is an ecologist who studies the change in the penguin population of Antarctica over time. She observed that the population decays by a factor of 8/9 every 4 months. The population of penguins can be modeled by a function, P, which depends on the amount of time, t (in months). When Talulah began the study, she observed that there were 27,000 penguins in Antarctica. Write a function that models the population of the penguins t months since the beginning of Talulah's study. P(t) =
Answer:
P(t) = 27000 * (8/9)^(t/4)
Step-by-step explanation:
The population of penguins in Antarctica decays by 8/9 every 4 months, starting from an initial count of 27,000. The function for the penguin population P(t) after t months is P(t) = 27,000 × (8/9)^(t/4).
Explanation:Talulah, an ecologist, has observed that the population of penguins in Antarctica decays by a factor of 8/9 every 4 months. To model this decay, we can use an exponential decay function. Given that the initial population (P0) is 27,000 penguins, the function P(t) that models the population at time t (in months) since the beginning of Talulah's study is:
P(t) = P0 × (decay factor)(t/rate period)
Where P0 is the initial population, the decay factor is 8/9, and the rate period is 4 months. Plugging in these values gives us:
P(t) = 27,000 × (8/9)(t/4)
This function allows researchers to predict the penguin population at any given time t months after Talulah's initial observation.
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Three bags of dog food cost $26.88, including tax. Jerry has $50.00. How many bags of dog food can Jerry buy?
Answer:
1 bag
Step-by-step explanation:
Jerry only has $50.00 if 1 bag costs $26.88, even without taxes, he can only buy 1 bag because 26.88+26.88=53.76