The wonderful waffle cone holds more ice cream than super sundae cone.
In this question,
The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.
Volume of ice cream cone = volume of hemisphere + volume of cone
Volume of ice cream cone = [tex]\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]
Volume of super sundae cone:
Radius of hemisphere = height of hemisphere = 0.5 in
Depth of the ice cream cone = 4 in
Volume of super sundae cone = [tex]\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)[/tex]
⇒ 0.2616+1.0466
⇒ 1.3082 ≈ 1.31 cubic in.
Volume of wonderful waffle cone:
Radius of hemisphere = height of hemisphere = 0.9 in
Depth of the ice cream cone = 3 in
Volume of wonderful waffle cone = [tex]\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)[/tex]
⇒ [tex]\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)[/tex]
⇒ 1.526+2.5434
⇒ 4.0694 ≈ 4.07 cubic in.
Thus volume of wonderful waffle cone > volume of super sundae cone.
Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.
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Find the inverse of the function.
y = 2x^2 -4
Answer:The inverse of the function y = 2x^2 –4 is;. y = √(x +4)/2To find the inverse of the function;We must first solve for x in the equation as follows;y = 2x² - 4y + 4 = 2x²x² = (y +4)/2x = √ (y +4)/2By swapping x and y; we then have;y = √(x +4)/2
Of the water lilies in the pond, 43% of them are yellow. The others are white.
A frog randomly jumps onto a lily.
round to the nearest hundredth place
Find the probability of the complement of the frog landing on a yellow lily.
Answer:
The probability of the frog landing on a complement of yellow lily is 0.57
Step-by-step explanation:
PLANTS Of the water lilies in the pond, 43% are yellow. The others are white.
It is given that 43% of plants are lilies it means the probability of a frog randomly jumping onto a lily is:
the probability of the frog landing on a complement of yellow lily is 0.57
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
[tex]Answer: \displaystyle\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .[/tex]
Step-by-step explanation:
[tex]D=12\ \ \ \ O(0;b)\\\displaystyle\\R=\frac{D}{2}\\R=\frac{12}{2} \\ R=6.\\Circle \ equation\ is:\\(x-a)^2+(y-b)^2=R^2.\\a=0\ \ \ \ \ R=6\\x^2+(y-b)^2=6^2\\x^2+(y-b)^2=36\\Henese:\\\displaystyle\\\left {{x^2+(y-3)^2=36} \atop {x^2+(y+8)^2=36}} \right. .[/tex]
The ratio of two numbers is 2/3, and their sum is 535. One of the numbers is:
(Select one)
A. 242
B. 321
C. 667
D. 408
One of the numbers would be 321. Hence option B is true.
Used the concept of the Number system that states,
A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.
Given that,
The ratio of the two numbers is 2/3, and their sum is 535.
Let us assume that,
The two numbers are x and y.
Hence we have;
[tex]\dfrac{x}{y} = \dfrac{2}{3}[/tex] .. (i)
And, [tex]x + y = 535[/tex] .. (ii)
From equation (i);
[tex]\dfrac{x}{y} = \dfrac{2}{3}[/tex]
[tex]x = \dfrac{2y}{3}[/tex]
Substitute the above value of x in (ii);
[tex]x + y = 535[/tex]
[tex]\dfrac{2y}{3} + y = 535[/tex]
[tex]2y + 3y = 535 \times 3[/tex]
[tex]5y = 1605[/tex]
[tex]y = 321[/tex]
From equation (i);
[tex]x = \dfrac{2y}{3}[/tex]
[tex]x = \dfrac{2\times 321}{3}[/tex]
[tex]x = 214[/tex]
Therefore, the number is 321. So option B is true.
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Is B equal to C in this geometry problem? I just need to know, that and then I can solve the rest.
In the right angled triangle ACD shown with isosceles triangle ABC and ADC, AB = AC = AD
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, equilateral and scalene.
In the diagram shown:
AB = AC = AD
In the right angled triangle ACD shown with isosceles triangle ABC and ADC, AB = AC = AD
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PLEASE HELP CORRECT ANSWER ONLY PLS
Answer:
y = -1x + 5
Step-by-step explanation:
y = mx + c
y = gradient(x intercept) + y intercept
y = -1x + 5
Triangle ABC was dilated using the rule Do,4. Triangle
A'B'C' is the result of the dilation.
3
A
B
C
A'
В'
C
What is OB'?
O 1.5 units
3 units
O4.5 units
O6 units
The value of OB based on the information given about the triangle is 3 units.
How to illustrate the information?It should be noted that dilation is the process of enlarging or shrinking of an object.
In this case, the triangle is dilated. Therefore, the length of OB will be:
= 3/4 × 4 = 3 units.
Therefore, the correct option is B.
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For the geometric series 1 - 2/3 + 4/9 - 8/27....
find s8
Answer:
Step-by-step explanation:
The sum of an alternating geometric series SUM((-1)^n*ar^n) = a/(1+r). The given series has r=2/3 and a=1. The sum will be 1/(1+2/3)= 3/5
Hello,
We have s0 = 1 and q = -2/3
[tex]S _{n} = S _{0} \times q {}^{n} = 1 \times ( - \frac{2}{3} ) {}^{n} [/tex]
[tex]S _{8} = ( - \frac{2}{3} ) {}^{8} = \frac{2 {}^{8} }{3 {}^{8} } = \frac{256}{6 561} [/tex]
PLEASE HELP! 20 Points!!
Shawn tried to define a reflection.
• For any point R on the line of reflection L, the image R’ is at the same point as R. • For any point P not on the line of reflection L, the image P’ is on the other side of L such that P and P’ are the same distance from L.
What mistake did Shawn make in his definition of a reflection?
Choose 1 answer from the options below.
The mistake that Shawn made in his definition of a reflection is that D. Shawn didn't make a mistake.
What's a reflection?It should be noted that reflection simply means ten transformation of the shape of an object.
In this case, for any point R on the line of reflection L, the image R’ is at the same point as R. Furthermore, for any point P not on the line of reflection L, the image P’ is on the other side of L such that P and P’ are the same distance from L.
Therefore, Shawn is right as no mistake was made.
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Answer:
PP' must be perpendicular to the line of reflection. Whatever the distance is between P and L, there are infinitely many points on the other side of L that are the same distance from L.
Step-by-step explanation:
A maker of folding tables estimates that 1 in 40 tables is returned due to a manufacturer's defect.
for each table not returned, the manufacturer makes a profit of $4.50, but for each table
returned, it loses $48. what is the manufacturer's long-term average profit on this product?
Answer:
$127.50
Step-by-step explanation:
The average profit is found by adding up the profits from both scenarios.
39(4.5) + 1(-48)
= $127.50
Brainliest, please :)
A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. during week 10 of the recall, the manufacturer fixed 200 cars. in week 15, the manufacturer fixed 175 cars. assume that the reduction in the number of cars each week is linear. write an equation in function form to show the number of cars seen each week by the mechanic. f(x) = 5x 250 f(x) = −5x 250 f(x) = 10x 200 f(x) = −10x 200
The linear function that shows that the number of cars seen each week by the mechanic is:
f(x) = -5x + 200.
What is a linear function?A linear function is modeled by:
y = mx + b
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 of the function.During the first week analyzed, the amount of cars was of 200, hence the y-intercept is of 200. In 5 weeks, the amount decayed by 25, hence the slope is given by:
m = -25/5 = -5.
Thus the linear function that shows that the number of cars seen each week by the mechanic is:
f(x) = -5x + 200.
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Answer:
f(x) = −5x + 250
Step-by-step explanation:
First, we must find the slope. We can take 2 points. (10, 100) and (15,175)
Using y2-y1/x2-x1=m, we find that the slope =-5. to find the y-intercept, we have to find that y= when x=0. Since 10 weeks passed since the begining, we can inverse the slope to find 5(cars)x10(weeks)=50.
so, 200(week10)+50(week 1)=250
f(x)=-5x+250.
If a line has a slope of 1/3 and passes through the point (1,-2) which ff points also lies on the line a) -2,-5 b) -2,1 c) 4,-1 d) 4,10
Answer: c
Step-by-step explanation:
The equation of the line is
[tex]y+2=\frac{1}{3}(x-1)\\\\y+2=\frac{1}{3}x-\frac{1}{3}\\\\y=\frac{1}{3}x-\frac{7}{3}[/tex]
To determine which point lies on the line, we can substitute in the x coordinate and see if the equation gives the same y-coordinate.
If x = 2, then the equation of the line gives that y = -5/3.If x = 4, then the equation of the line gives that y = -1.Therefore, the answer is c.
HELP pleeeeease, will give brainliest
Answer:The answer is A
Step-by-step explanation:
You select one red marble from the full bag in exercise 20. what is the probability that the next marble you select will be green without replacement of the first marble?
P(blue) = 1/3
Step-by-step explanation:
Probability for any event A is given by
p(A) = no of times of happening of event A/ total no of occurrence of all the events given under the situation.
A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles
So, total no of occurrences of all the events given under the situation
one can either pick blue, red, or 4 green marbles
Total no. of occurrence of all the event = 5 + 6 + 4 = 15
Now, no occurrence of selecting blue.
since there are 5 blue marbles, there is a chance of selecting blue as 5.
no occurrence of selecting blue = 5
Therefore,
P(blue) = no of occurrence of selecting blue /total no of occurrence of picking any color ball
P(blue) = 5/15 = 1/3.
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Find the missing side length in the image below.
Answer:
6 is the ?
Step-by-step explanation:
5[tex]5x-3y=34\\x-2y=4[/tex]
Laurel appears at Comedy Cafe at a random time between 1:00 and 2:00. Hardy turns up at a random time between 2:00 and 2:30. The probability that Laurel waits for no more than 40 minutes for Hardy can be expressed in the form $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m n$.
Answer:
i need more info please
Step-by-step explanation:
Select the correct answer. if 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactly 2 of the cards are spades? a. 0.038 b. 0.200 c. 0.315 d. 0.465 e. 0.747
Answer:
0.315
Step-by-step explanation:
To prove ABC is isosceles, which of the following
statements can be used in the proof?
Answer:
Angle CAB and angle CBA are congruent.
Step-by-step explanation:
Isosceles triangles have two sides of equal length as well as two congruent base angles.
Answer:
b
Step-by-step explanation:
A management consulting firm recommends that the ratio of middle-management salaries to management trainee salaries be 8:7. Using this recommendation, what is the annual middle-management salary if the annual management trainee salary is $17,000? (Round your answer to the nearest dollar.)
The management salary is $19,429
What is ratio?
Ratio is the quantitative relationship between two numbers which shows the number of times an amount or a number is contained within the other amount or number.
In this case, a ratio of 8:7 shows the number of times the management salaries is contained within the management trainee salary
The management salary has a value of 8 whereas the management trainee salary has a value of 7 as shown below:
salary ratio=management salary/management trainee salary
salary ratio=8/7
management salary=unknown(assume it is X)
management trainee salary=$17,000
8/7=X/$17,000
cross multiply
8*$17,000=7*X
X=8*$17,000/7
X=$19,429
The fact that annual management trainee salary is $17,000 means that the management salary is $19,429 annually.
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The probability that a professor in the business department is full time is 30%. If we randomly select 9 professors; What is the probability that 3 or fewer of them are FULL TIME
The probability that a professor in the business department is full time is [tex]30[/tex]%. If we randomly select [tex]9[/tex] professors; the probability that [tex]3[/tex] or fewer of them are FULL TIME is [tex]10[/tex]%
How can find the probability of full time ?
Probability of selecting [tex]3[/tex] from [tex]9[/tex]people = [tex]3/9[/tex]
Probability of selecting [tex]2[/tex] people= [tex]2/9[/tex]
Probability of selecting [tex]1[/tex] people=[tex]1/9[/tex].
Probability of selecting up to to 3 people is [tex]1/9+2/9+3/9 = 6/9[/tex].
Every person who got selected is full time person has probability [tex]0.3[/tex]
=> For selection of people up to [tex]3[/tex] is
[tex]=\frac{3}{9} *0.3\\=0.1\\[/tex]
[tex]=10[/tex]%
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The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x. Group of answer choices mean: 1.39; standard deviation: 0.80 mean: 1.18; standard deviation: 0.64 mean: 1.39; standard deviation: 0.64 mean: 1.18; standard deviation: 1.30
The value of the Mean & Standard deviation is 1.30 and 1.18.
According to the statement
we have a given that the random variable x represents the number of computers that families have along with the corresponding probabilities.
And we have to find the mean and standard deviation from the given data which is related to the probabilities values
So, according to the given data
The formula to compute the mean is:
Mean = summation [x*p(x)]
Compute the mean as follows:
Mean = summation [x*p(x)]
Mean = summation [0*0.49 + 1* 0.05 + 2*0.32 + 3*0.07 + 4*0.07]
Mean = 0 +0.05 + 0.64 + 0.21 + 0.28
Mean = 1.18
The mean of the random variable x is 1.18.
And after calculating the variance from the formula get
The value of standard deviation is 1.30
So, The value of the Mean & Standard deviation is 1.30 and 1.18.
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations that have the same solution as the given equation are 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
Writing equationsFrom the question, we are to determine the equations that have the same solution as the given equation
The given equation is
2.3p – 10.1 = 6.5p – 4 – 0.01p
Simplifying,
2.3p – 10.1 = 6.5p – 0.01p – 4
2.3p – 10.1 = 6.49p – 4
Thus, 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation
Also,
If we multiply both sides of the given equation by 100
That is,
100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)
230p – 1010 = 650p – 400 – p
∴ 230p – 1010 = 650p – 400 – p is equivalent to the given equation
Hence, the equations that have the same solution as the given equation are 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
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Write down the mathematical name of the shape made by each net.
a)
b)
How do I do the picture
Answer:
1. Cube
2. Square-based pyramid
Step-by-step explanation:
Answer:
Below.
Step-by-step explanation:
a) Cube
b Pyramid
A music website claims the mean length of their songs is 3.75 minutes. Suppose the length of songs from this website follows a Normal distribution with standard deviation 0.5 minutes. If 7 songs from this website are randomly selected, then there is about a 90% probability that the sample mean will fall in which interval
The confidence interval is from 3.44 to 4.06 minutes.
According to the statement
we have given that the mean length of songs is 3.75 minutes and standard deviation 0.5 minutes and the sample size n is 7. and the confidence interval is 90%
and we have to find the mean interval.
So, We know that the
A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.
And A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.
We know that the z value for 90% confidence interval is 1.64.
so, The formula to calculate margin of error is
MOE = Z*standard deviation/ (n)^1/2
put the values in it
MOE = Z*standard deviation/ (n)^1/2
MOE = 1.64*0.5/ (7)^1/2
MOE = 1.64*0.189
MOE = 0.310
And to find the interval the formula is
Confidence interval = sample mean ± margin of error
Confidence interval = 3.75 ± 0.310
Confidence interval = (4.06,3.44)
So, The confidence interval is from 3.44 to 4.06 minutes.
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Please help with these problems having trouble!!
The function f(x) is vertically compressed to form g(x) while the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
How to compare both functions?The functions are given as
f(x) =x^2
g(x) =3x^2
h(x) = -3x^2
Substitute f(x) =x^2 in g(x) =3x^2 and h(x) = -3x^2
g(x) =3f(x)
h(x) = -3f(x)
This means that the function f(x) is vertically compressed to form g(x)
Also, the function f(x) is vertically compressed and then reflected across the x-axis to form h(x)
See attachment for the functions g(x) and h(x)
Also, functions f(x) and g(x) have the same domain and range
While functions f(x) and h(x) have the same domain but different range
The complete table is:
x -2 -1 0 1 2
g(x) 12 3 0 3 12
h(x) -12 -3 0 -3 -12
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Use the graph that shows the solution to f(x)=g(x).
f(x)=1/x−2
g(x)=x−2
What is the solution to f(x)=g(x)?
Select each correct answer.
−1
1
2
3
The solution to the system of equations is given as follows:
x = 1 and x = 3.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the two equations are:
[tex]\frac{1}{x - 2} = x - 2[/tex]
Applying cross multiplication:
(x - 2)(x - 2) = 1
x² - 4x + 4 = 1
x² - 4x + 3 = 0
(x - 1)(x - 3) = 0
Hence the solutions are:
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Drag the tiles to the correct boxes to complete the pairs Match each inequality to the number line that represents its solution
Answer:
x ≤ 7 => [tex]- \frac{13x}{18}[/tex] + [tex]\frac{5}{9} \geq - \frac{9}{2}[/tex]
x ≤ 8 => -[tex]\frac{x}{10}[/tex] + [tex]\frac{1}{5}[/tex] ≥ -[tex]\frac{33}{55}[/tex]
x ≤ -5 => - [tex]\frac{50x}{3}[/tex] - [tex]\frac{11}{6}[/tex] [tex]\geq[/tex] [tex]\frac{163}{2}[/tex]
x ≤ -6 => [tex]\frac{3x}{2}[/tex] + 105 ≤ 96
Step-by-step explanation:
-[tex]\frac{x}{10}[/tex] + [tex]\frac{1}{5}[/tex] ≥ -[tex]\frac{33}{55}[/tex]
[tex]\frac{1}{5}[/tex] + [tex]\frac{33}{55}[/tex] ≥ [tex]\frac{x}{10}[/tex] / *10
2 + 6 ≥ x
8 ≥ x
- [tex]\frac{50x}{3}[/tex] - [tex]\frac{11}{6}[/tex] [tex]\geq[/tex] [tex]\frac{163}{2}[/tex] / *6
- 100x - 11 ≥ 489
-500 ≥ 100x
-5 ≥ x
[tex]\frac{3x}{2}[/tex] + 105 ≤ 96
[tex]\frac{3x}{2}[/tex] ≤ 96 - 105 / * [tex]\frac{2}{3}[/tex]
x ≤ -6
[tex]- \frac{13x}{18}[/tex] + [tex]\frac{5}{9} \geq - \frac{9}{2}[/tex] /*18
-13x + 10 ≥ - 81
-13x ≥ -91 /:-13
x ≥ 7
8.8÷4=8, point, 8, divided by, 4, equals
\text{ tenths}\div 4 tenths÷4start text, space, t, e, n, t, h, s, end text, divided by, 4
8.8 \div 4 =8.8÷4=8, point, 8, divided by, 4, equals
\text{ tenths} tenthsstart text, space, t, e, n, t, h, s, end text
8.8 \div 4 =8.8÷4=8, point, 8, divided by, 4, equals
The results of the given task 8.8 ÷ 4 is 2.2.
Division of Decimal8.8 ÷ 4
= 2.2
Therefore, 8.8 ÷ 4 = 2.2
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A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer. Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground.
The rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground is 1/20 degree/sec.
What is angle of elevation?It is described as a relationship between an oblique line from the observer's eye to an item above his eye and the horizontal plane. This angle eventually develops above the surface. The angle of elevation is made in such a way that it is above the observer's eye, as the name suggests.
Calculation for the rate of change of angle of elevation-
According to the question,
A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer.
The balloon is 100 feet above the ground.
Let the height of the balloon be 'h' ft.
Then tanØ = h/100
h = 100tanØ
Differentiate the above equation with respect to time.
dh/dt = 100 sec² Ø (dØ/dt)
We know dh/dt = 10 ft/sec.
when h = 100
tanØ = 100/100 = 1/1
tanØ = Perpendicular/Base
On comparing above two equations,
Perpendicular = 1; Base = 1.
By Pythagoras the hypotenuse is,
H² = P² + B²
= 1² + 1²
= 2
H = √2
Now, calculate the value of cosØ.
cosØ = B/H = 1/√2
Squaring both side
cos² Ø = 1/2
sec² Ø = 1/cos² Ø
sec² Ø = 2
The main equation was,
dh/dt = 100 sec² Ø (dØ/dt)
Substitute the values,
dØ/dt = (dh/dt )/100 sec² Ø
= (10)/(100×2)
dØ/dt = 1/20 degree/sec.
Therefore, the rate of change of the angle of elevation of the balloon from the observer is 1/20 degree/sec.
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