Answer:
Step-by-step explanation:
This is an exponential function:
[tex]y=16(\frac{2}{3})^x[/tex] that tells us that the initial height of the ball is 16 feet and that after each successive bounce the ball comes up to 2/3 its previous height. We are looking for y when x = 2, so
[tex]y=16(\frac{2}{3})^2[/tex] and
[tex]y=16(\frac{4}{9})[/tex] and
[tex]y=\frac{64}{9}[/tex] so
y = 7.1 feet
Two friends entered a contest jointly and won; however, there is only one prize and it cannot be split. Some methods of selecting who receives the prize are given below. A: Place both names in equal amounts into a hat and draw one without looking. B: Ask a stranger to flip a coin. C: Roll a die and evaluate the outcome as either even or odd. D: Throw a stone closest to an object. E: Play a hand of blackjack. F: Ask a random stranger to select. The methods that are fair include _____ because _____ is flawed due to increased chances of winning based on one's skill, ______ is flawed due to poor randomization, and ______ is flawed due to unequal probabilities of winning and losing.
Answer:
The methods that are fair include __A, B and C__ because __D__ is flawed due to increased chances of winning based on one's skill, ___F___ is flawed due to poor randomization, and ___E___ is flawed due to unequal probabilities of winning and losing.
Step-by-step explanation:
A. Place both names in equal amounts into a hat and draw one without looking:
If you place both names in equal amounts into a hat, then the probability of picking any one of the names would be equal.
For example, if you put 20 pieces of paper containing each name in a hat, then,there will be 40 names in the hat. The probability of picking any one or the other randomly would be:
P = 20/40 =1/2
B. Ask a stranger to flip a coin:
A coin has only two faces, head and tail. Hence, if one person picks head and the other picks tail, the probability of landing on either head or tail is given as:
P = 1/2
C. Roll a die and evaluate the outcome as either even or odd:
A die has 6 faces with equal number of faces with equal number of even numbers and odd numbers, 3. Hence, the probability of rolling an even or odd number is given as:
P = 3/6 = 1/2
D. Throw a stone closest to an object:
This method is not fair because then it depends solely on who can throw the farthest i.e. the physical ability of the throwers.
E. Play a hand of blackjack
This method is flawed because it has unequal probabilities of winning and losing.
F. Ask a random stranger to select:
This method is unfair because it then depends solely on the random picker. The picker could have personal preferences or a bias based on maybe height, beauty, weight, basically anything characteristic. Hence, it is unfair.
Final answer:
Fair methods for deciding who gets the prize include placing both names in a hat, flipping a coin, and rolling a die as they provide equal chances of winning, while throwing a stone, playing blackjack, or asking a stranger can introduce bias or skill, making them unfair.
Explanation:
The methods that are fair include placing both names in a hat, asking a stranger to flip a coin, and rolling a die because these methods provide equal probabilities of winning or losing. Method D: Throwing a stone closest to an object is flawed due to increased chances of winning based on one's skill, which means it's not random. E: Playing a hand of blackjack is flawed due to poor randomization, as the cards dealt can create significantly different chances of winning. F: Asking a random stranger to select is flawed due to unequal probabilities of winning and losing if the stranger holds a bias, even if unintended.
Tossing a coin is a fair way to decide because both outcomes (heads or tails) have equal chances of occurring, which is a 50% chance each way. This is consistent with the principle of randomness and independent events, where the outcomes of past coin tosses do not influence the results of future tosses.
Orange juice, a raisin bagel, and a cup of coffee from Kelly's Koffee Kart cost a total of $3.60. Kelly posts a notice announcing that, effective the following week, the price of orange juice will increase 50% and the price of bagels will increase 20%. After the increase, the same purchase will cost a total of $4.50, and the orange juice will cost twice as much as coffee.
A. Find the price of each item before the increase.
B. What was the cost of a glass of orange juice before the increase?
C. What was the cost of a raisin bagel before the increase?
D. What was the cost of a cup of coffee before the increase?
Answer:
A
Step-by-step explanation:
what is the segment of AD?
A) 5
B) 6
C) 4.5
D) 3
Answer:
i am pretty sure it is B
Step-by-step explanation:
8. Find the inverse of the function.
Y=-3/x+4
Yo sup??
y=-3/x+4
cross multiply
x+4=-3/y
x=-3/y-4
f(y)=-3/y-4
or
f(x)=-3/x-4
=-4x-3/x
The correct answer is option 4
Hope this helps.
Answer:
It is -4x-3/x.
True or false? All occurrences of the letter u in "Discrete Mathematics" are lowercase. Justify your answer
The given statement "All occurrences of the letter u in "Discrete Mathematics" are lowercase" is true.
Here's why:
There are no occurrences of the letter "u" in "Discrete Mathematics" at all.
Therefore, the question of whether they are uppercase or lowercase becomes irrelevant due to the absence of the letter itself.
Because the statement involves a vacuous quantification, meaning it deals with an empty set, it automatically becomes true.
In such cases, it doesn't matter what property is being attributed to the empty set because there are no elements for that property to be true or false for.
Joel has a goal to practice his clarinet for 4 1/2 per week. The list below shows the number of hours Joel has a practiced so far for the week. Monday 1 1/2 hours Wednesday 1 1/4 hours Thursday 1 hour How many more hours does he need to practice this week to meet his goal
0.75 hours more is needed to practice to meet his goal
Solution:
Given that,
Goal per week of Joel = [tex]4\frac{1}{2} = \frac{2 \times 4 + 1}{2} = \frac{9}{2}[/tex]
From given,
The list below shows the number of hours Joel has a practiced so far for the week
[tex]Monday = 1\frac{1}{2}\ hours = \frac{3}{2}\ hours[/tex]
[tex]Wednesday = 1\frac{1}{4}\ hours = \frac{5}{4}\ hours\\\\Thursday = 1\ hour[/tex]
How many more hours does he need to practice this week to meet his goal
Find the difference
Hours needed = Goal per week of Joel - (monday + wednesday + thursday)
[tex]Hours\ needed = \frac{9}{2} - (\frac{3}{2} + \frac{5}{4} + 1)\\\\Hours\ needed = 4.5-(1.5+1.25+1)\\\\Hours\ needed = 4.5 - 3.75 = 0.75\\\\Hours\ needed = 0.75 = \frac{3}{4}[/tex]
Thus 0.75 hours more is needed to practice to meet his goal
Joel needs to practice \( \frac{3}{4} \) hours more this week to meet his goal.
First, we need to calculate the total number of hours Joel has practiced so far. We will add the hours practiced on Monday, Wednesday, and Thursday.
[tex]Monday: \( 1 \frac{1}{2} \) hours = \( 1 + \frac{1}{2} \) hours = \( \frac{3}{2} \) hours[/tex]
[tex]Wednesday: \( 1 \frac{1}{4} \) hours = \( 1 + \frac{1}{4} \) hours = \( \frac{5}{4} \) hours[/tex]
[tex]Thursday: \( 1 \) hour = \( \frac{4}{4} \) hours (to keep the denominator consistent)[/tex]
Now, let's add these hours together:
[tex]\( \frac{3}{2} + \frac{5}{4} + \frac{4}{4} = \frac{6}{4} + \frac{5}{4} + \frac{4}{4} = \frac{15}{4} \) hours[/tex]
Joel's goal is to practice [tex]\( 4 \frac{1}{2} \)[/tex] hours per week, which is [tex]\( 4 + \frac{1}{2} \) hours = \( \frac{8}{2} + \frac{1}{2} \) hours = \( \frac{9}{2} \) hours.[/tex]
To find out how many more hours Joel needs to practice, we subtract the total hours he has already practiced from his goal:
[tex]\( \frac{9}{2} - \frac{15}{4} \)[/tex]
To subtract these fractions, we need a common denominator, which is 4:
[tex]\( \frac{18}{4} - \frac{15}{4} = \frac{3}{4} \) hours[/tex]
Therefore, Joel needs to practice [tex]\( \frac{3}{4} \)[/tex] hours more to meet his weekly goal.
Statistics encompasses all scientific disciplines in which random occurrences are analyzed. In addition, statistics references any random occurrence which is reported using percentages or proportions. True or false?
Answer: FALSE
Step-by-step explanation: Statistics is the Science of collecting, organising,sumarising,analysing information to reach at a reasonable conclusion or outcome. Statistics also helps to measure levels of confidence in any conclusion or outcome.
Statistics has been applied in several fields like Medicine, pharmacy, Engineering,Biology etc it helps in determining especially in numerical representation the impact of certain conditions or activities or information.
FUNCTIONS: In the space provided, type the answer in descending order as it applies without any spaces between the letters, numbers, or symbols.
Type the composition (fog)(x) of the given functions:
f(x) = x^2 + 2x − 6 and g(x) = x + 5.
Answer:
Hence The composition [tex](fog)(x)[/tex] of the given function is [tex]x^2+12x+29[/tex].
Step-by-step explanation:
Given:
[tex]f(x) = x^2+2x-6[/tex]
[tex]g(x)=x+5[/tex]
We need to find [tex](f o g)(x)[/tex].
Solution:
Now we can say that;
[tex](f o g)(x)[/tex] = [tex]f(g(x))[/tex]
[tex](fog)(x) = (x+5)^2+2(x+5)-6[/tex]
Now Applying distributive property we get;
[tex](fog)(x) = (x+5)^2+2\times x+2\times5-6\\\\(fog)(x) = (x+5)^2+2x+10-6\\\\(fog)(x) = (x+5)^2+2x+4[/tex]
Now Solving the exponent function we get;
[tex](fog)(x) = x^2+2\times x\times 5+5^2+2x+4\\\\(fog)(x) = x^2+10x+25+2x+4\\\\(fog)(x) = x^2+12x+29[/tex]
Hence The composition [tex](fog)(x)[/tex] of the given function is [tex]x^2+12x+29[/tex].
George's sandbox requires 32 cubic feet of sand to fill how many bags of sand does he need to fill the sand box if each bag holds 2/3 cubic feet of sand
Answer:
48 bags are needed by George to fill his sandbox.
Step-by-step explanation:
Given:
Total capacity of the sandbox (V) = 32 cubic feet
Capacity of each bag = (B) = [tex]\frac{2}{3}[/tex] cubic feet
Now, number of bags required (N) = ?
The formula to find the total number of bags required to fill the sandbox is given as:
[tex]Number\ of\ bags=\frac{Total\ capacity\ of\ sandbox}{Capacity\ of\ each\ bag}\\\\N=\frac{V}{B}[/tex]
Now, plug in the given values and solve for 'N'. This gives,
[tex]N=32\div\frac{2}{3}[/tex]
In order to multiply a whole number with a fraction, we replace the division sing by multiplication and take the reciprocal of the fractional number. This gives,
[tex]N=32\times \frac{3}{2}\\\\N=\frac{32\times 3}{2}\\\\N=16\times 3=48[/tex]
Therefore, 48 bags are needed by George to fill his sandbox.
George needs 48 bags of sand, each holding 2/3 cubic feet, to fill his sandbox that requires 32 cubic feet of sand.
To determine how many bags of sand are required to fill George's sandbox that has a volume of 32 cubic feet, when each bag holds 2/3 cubic feet of sand, we need to perform a division operation. We divide the total volume (32 cubic feet) by the volume each bag holds (2/3 cubic feet).
The calculation is as follows:
Find the inverse of 2/3 which is 3/2.
Multiply the total volume by the inverse. 32 × (3/2) = 32 × 1.5 = 48.
Thus, George would need 48 bags of sand to fill his sandbox.
If a chain of 30 identical short springs linked end-to-end has a stiffness of 450 N/m, what is the stiffness of one short spring?
The stiffness of one short spring is 13500 N/m
Solution:
We are given a chain with number of spring N = 30 and linked end to end ( in series) and stiffness of this chain is 450 N/m
We have to find the stiffness of one short spring
The springs are identical, which means they have same stiffness
The stiffness of one spring in series is given as:
[tex]k_i = N \times k_s[/tex]
Where,
N is the number of springs
[tex]k_i[/tex] is the stiffness of one spring
[tex]k_s[/tex] is the stiffness of this chain
Substituting,
[tex]N = 30\\\\K_s = 450[/tex]
Therefore,
[tex]k_i = 30 \times 450\\\\k_i = 13500[/tex]
Thus the stiffness of one short spring is 13500 N/m
If a chain of 30 identical short springs linked end-to-end has a stiffness of 450 N/m , The stiffness of one short spring is 13500 N/m
Given : Stiffness = 450 N/m,
To find : the stiffness of one short spring
According to the given question,
A chain with number of spring N = 30 Chain is linked end to end Stiffness of this chain is 450 N/m
We knows that,
The springs are identical, by which means they have the same stiffness
Hence, The stiffness of one spring will be given as:
[tex]\rm k_i=N \times k_s[/tex]
Where,
N = number of springs [tex]\rm k_i[/tex] = Stiffness of one spring. [tex]\rm k_s[/tex] = Stiffness of given chain.On substituting the values in the formula we will get,
N = 30
[tex]\rm k_s[/tex] = 450
Then,
[tex]\rm k_i =30 \times450\\\\k_i = 13500[/tex]
Therefore, The stiffness of one short spring is 13500 N/m
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The present above is a 10 in by 10 in by 10 in cube. How many square inches of wrapping paper do you need to wrap the box?
Answer:
600 in^2.
Step-by-step explanation:
There are 6 faces on a cube so the area we need is:
6 * 10 * 10
= 600 in^2.
Anna wants to estimate the mean number of siblings for each student in her school. She records the number of siblings for each of 75 randomly selected students in the school. What is the statistic?a. the specific number of siblings for each randomly selected student
b. all the students in the school
c. the mean number of siblings for all students in the school
d. the mean number of siblings for the randomly selected students
e. the 75 randomly selected students
Final answer:
The statistic concerning the number of siblings would be the mean number of siblings for the randomly selected students, not the entire school population.
Explanation:
The question posed by the student pertains to determining the mean number of siblings for students in a school. Anna collected data by randomly selecting 75 students and recording the number of siblings for each student. The statistic in this context is d. the mean number of siblings for the randomly selected students. This is because the statistic refers to a summary measure that is calculated from a sample of data. Therefore, the statistic is the calculated average number of siblings from just those 75 students and not the entire school population.
When discussing sampling methods, one could use a completely random method or use systematic sampling with a tool such as a random number generator for selection. Regardless of the method, the primary criterion is that every member of the population has an equal chance of being included in the sample.
Final answer:
The statistic refers to the mean number of siblings for the randomly selected students, computed by dividing the sum of siblings reported by the 75 students by 75.
Explanation:
The statistic in this scenario is the mean number of siblings for the randomly selected students. The mean, or average, will be calculated by adding up the total number of siblings reported by the 75 students and then dividing that sum by 75. This statistic will serve as an estimate for the mean number of siblings for each student in the whole school. Although option b attempts a similar approach with systematic sampling by selecting every 50th student, the actual calculated mean from the 75 randomly selected students (which is the result of the random sampling method described in option a) is the statistic we are referring to. Option c is asking for a different kind of statistic related to stress scores.
Three brothers Charlie Robert and Nicholas have 21 video games Charlie has twice as many games as Robert. Robert has 5 fewer games than Nicholas what would be the equation
Answer:
The equation would be [tex]4x-15=21[/tex].
Step-by-step explanation:
Given;
Total Number of Video games = 21
Let the number of video game Nicholas has be 'x'.
Now Given:
Robert has 5 fewer games than Nicholas.
so we can say that;
number of video game Robert has = [tex]x-5[/tex]
Also Given:
Charlie has twice as many games as Robert.
so we can say that;
number of video game Charlie has = [tex]2(x-5)=2x-10[/tex]
we need to write the equation.
Solution:
Now we can say that;
Total Number of Video games is equal to sum of number of video game Nicholas has, number of video game Robert has and number of video game Charlie has.
framing the equation we get;
[tex]x+x-5+2x-10=21\\\\4x-15=21[/tex]
Hence The equation would be [tex]4x-15=21[/tex].
On Solving we get;
Adding both side by 15 we get;
[tex]4x-15+15=21+15\\\\4x=36[/tex]
Dividing both side by 4 we get;
[tex]\frac{3x}{4}=\frac{36}{4}\\\\x=9[/tex]
Hence Nicholas has = 9 video games
Robert has = [tex]x-5= 9-5=4[/tex] video games
Charlie has = [tex]2x-10 = 2\times9-10=18-10=8[/tex] video games
Answer:
The equation would be [tex]4x-15=21.[/tex]
Step-by-step explanation:
Given:
Three brothers Charlie Robert and Nicholas have 21 video games Charlie has twice as many games as Robert. Robert has 5 fewer games than Nicholas.
Now, to find the equation.
Let the games Nicholas has be [tex]x.[/tex]
Robert has games [tex]x-5.[/tex]
And Charlie has [tex]2(x-5).[/tex]
Now, the equation is:
[tex](x)+(x-5)+2(x-5)=21.[/tex]
[tex]x+x-5+2x-10=21\\2x-5+2x-10=21\\4x-15=21[/tex]
[tex]4x-15=21.[/tex]
Therefore, the equation would be [tex]4x-15=21.[/tex]
What’s the Value for k?
Answer:
Step-by-step explanation:
The sum of the angles on a straight line is 180 degrees. Therefore,
Angle XYZ + angle MYZ = 180
Angle XYZ + 115 = 180
Angle XYZ = 180 - 115 = 65 degrees
The sum of the angles in a triangle is 180 degrees. It means that
Angle XZY + angle YXZ + angle MYZ = 180
Therefore,
4k + 5 + 6k + 10 + 65 = 180
4k + 6k + 5 + 10 + 65 = 180
10k + 80 = 180
10k = 180 - 80 = 100
Dividing the left hand side and the right hand side of the equation by 10, it becomes
10k/10 = 100/10
k = 10
Need help with #1 #4 #7 plz giving 15 points
Answer:
Q1: p = - 33
Q2: d = - 99
Q3: t = - 13
Step-by-step explanation:
Q1: [tex]$ \textbf{-} \frac{\textbf{p}}{\textbf{3}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{8} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{3}[/tex]
We solve this taking LCM.
We get: [tex]$ \frac{-p - 24}{3} = 3 $[/tex]
[tex]$ \implies - p - 24 = 9 $[/tex]
[tex]$ \implies \textbf{p} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 33} $[/tex]
Q4: [tex]$ \frac{\textbf{d}}{\textbf{11}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{4} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 13} $[/tex]
Again we proceed like Q1 by taking LCM.
We get: [tex]$ \frac{d - 44}{11} = - 13 $[/tex]
[tex]$ \implies d - 44 = - 13 \times 11 = - 143 $[/tex]
[tex]$ \implies d = - 143 + 44 $[/tex]
[tex]$ \implies \textbf{d} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 99} $[/tex]
Q7: 5t + 12 = 4t - 1
We club the like terms on either side.
[tex]$ \implies 5t - 4t = - 1 - 12 $[/tex]
[tex]$ \implies (5 -4)t = - 13 $[/tex]
[tex]$ \implies \textbf{t} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 13} $[/tex]
Hence, the answer.
Janine is saving money to buy a car. She has a total of $1400 left to save, and she plans to save a certain percentage of $1400 each month: In August, Janine will save 25% of $1400. In September, Janine will save 40% of $1400. In October, Janine will save 15% of $1400. In November, Janine will save the remaining amount. Which option correctly explains what Janine plans to save each month?
Answer:
August=$350
September=$560
October=$210
November= $280
Step-by-step explanation:
Total amount left to save $1400.
We calculate the amount save each mount since we are already given the percentages.
For the month of August she saves 25% of $1400, we convert the percentage to equivalent cash
[tex]\frac{25}{100}*1400\\=350[/tex]
for the month of August, she saved $350,
Next For the month of September she saves 40% of $1400, we convert the percentage to equivalent cash
[tex]\frac{40}{100}*1400\\=560[/tex]
for the month of September, she saved $560,
Next For the month of October she saves 15% of $1400, we convert the percentage to equivalent cash
[tex]\frac{15}{100}*1400\\=210[/tex]
for the month of October, she saved $210,
total amount saved by October = $350+$560+$210=$1120
Amount saved by November=1400-1120=$280
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.
cot x sec4x = cot x + 2 tan x + tan3x
(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x
1 + sec2x sin2x = sec2x
sine of x divided by one minus cosine of x + sine of x divided by one minus cosine of x = 2 csc x - tan2x + sec2x = 1
Answer:
Step-by-step explanation:
1.
cot x sec⁴ x = cot x+2 tan x +tan³x
L.H.S = cot x sec⁴x
=cot x (sec²x)²
=cot x (1+tan²x)² [ ∵ sec²x=1+tan²x]
= cot x(1+ 2 tan²x +tan⁴x)
=cot x+ 2 cot x tan²x+cot x tan⁴x
=cot x +2 tan x + tan³x [ ∵cot x tan x [tex]=\frac{ \textrm{tan x }}{\textrm{tan x}}[/tex] =1]
=R.H.S
2.
(sin x)(tan x cos x - cot x cos x)=1-2 cos²x
L.H.S =(sin x)(tan x cos x - cot x cos x)
= sin x tan x cos x - sin x cot x cos x
[tex]=\textrm{sin x cos x }\times\frac{\textrm{sin x}}{\textrm{cos x} } - \textrm{sinx}\times\frac{\textrm{cos x}}{\textrm{sin x}}\times \textrm{cos x}[/tex]
= sin²x -cos²x
=1-cos²x-cos²x
=1-2 cos²x
=R.H.S
3.
1+ sec²x sin²x =sec²x
L.H.S =1+ sec²x sin²x
=[tex]1+\frac{{sin^2x}}{cos^2x}[/tex] [[tex]\textrm{sec x}=\frac{1}{\textrm{cos x}}[/tex]]
=1+tan²x [tex][\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}][/tex]
=sec²x
=R.H.S
4.
[tex]\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}} = \textrm{2 csc x}[/tex]
L.H.S=[tex]\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}}[/tex]
[tex]=\frac{\textrm{sinx(1+cos x)+{\textrm{sinx(1-cos x)}}}}{\textrm{(1-cos x)\textrm{(1+cos x})}}[/tex]
[tex]=\frac{\textrm{sinx+sin xcos x+{\textrm{sinx-sin xcos x}}}}{{(1-cos ^2x)}}[/tex]
[tex]=\frac{\textrm{2sin x}}{sin^2 x}[/tex]
= 2 csc x
= R.H.S
5.
-tan²x + sec²x=1
L.H.S=-tan²x + sec²x
= sec²x-tan²x
=[tex]\frac{1}{cos^2x} -\frac{sin^2x}{cos^2x}[/tex]
[tex]=\frac{1- sin^2x}{cos^2x}[/tex]
[tex]=\frac{cos^2x}{cos^2x}[/tex]
=1
A frustum is made by removing a small cone from a similar large cone.Work out the frustum radius of cone=4.5cm radius of frustum=3cm height of the frustum =3cm height of the cone=9cm
The radius of the cone is found by comparing the ratios of heights and radii in a similar triangle. By applying the given values, the radius of the cone is found to be 9 cm.
Explanation:In mathematics, problems related to finding the dimensions of cones and frustums are common. As the problem mentions, a frustum is created when a smaller, similar cone is removed from a larger cone. To calculate the dimensions of the frustum, we use the properties of similar triangles.
For similar triangles:
Base ratios are equal to height ratios.
Therefore:
Height ratio (height of frustum/height of cone) = Base ratio (radius of frustum/radius of cone)
Applying the given values, it becomes:
3/9 = 3/Radius of cone
Hence, the radius of the cone is 9 cm.
Learn more about Frustum here:
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Final answer:
The volume of a frustum can be calculated using the formula [tex]\(V = \frac{1}{3}\pi h (r_{1}^{2} + r_{2}^{2} + r_{1}r_{2})\)[/tex]. Given the dimensions provided for the frustum with the larger cone having a radius of 4.5 cm, the frustum a radius of 3 cm, and height of 3 cm, the volume of the frustum is approximately 134.25π cubic centimeters.
Explanation:
To work out the volume of a frustum that is formed by removing a small cone from a larger, similar cone, you can make use of the formula for the volume of a frustum:
V = [tex]\(\frac{1}{3}\pi h (r_{1}^{2} + r_{2}^{2} + r_{1}r_{2})\),[/tex]
where:
h is the height of the frustum,
r₁ is the radius of the larger base (radius of the original cone),
r₂ is the radius of the smaller base (radius of frustum).
Given:
Radius of the large cone (r₁) = 4.5 cm,
Radius of the frustum (r₂) = 3 cm,
Height of the frustum (h) = 3 cm.
The height of the original cone (9 cm) is not needed to calculate the volume of the frustum. Plugging the given values into the formula:
[tex]\(V = \frac{1}{3}\pi \times 3 \times (4.5^{2} + 3^{2} + 4.5 \times 3)\)[/tex]
[tex]\(V = \pi (20.25 + 9 + 13.5)\)[/tex]
[tex]\(V = \pi (42.75)\)[/tex]
[tex]\(V = 134.25\pi \text{cm}^{3}\)[/tex]
Therefore, the volume of the frustum is approximately 134.25π cubic centimeters.
Sandra earned $8,000.00 from a summer job and put it in a savings account that earns 3% interest compounded continuously. When Sandra started college, she had $8,327.00 in the account which she used to pay for tuition. How long was the money in the account? Round your answer to the nearest month.
____ years and ____ months
Answer: 1 year and 4 months
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 8000
r = 3% = 3/100 = 0.03
A = 8327
Therefore,
8327 = 8000 x 2.7183^(0.03 x t)
8327/8000 = 2.7183^(0.03t)
1.040875 = 2.7183^(0.03t)
Taking log of both sides, it becomes
Log 1.040875 = log 2.7183^(0.03t)
0.0174 = 0.03tlog2.7183
0.0174 = 0.03t × 0.434 = 0.01302t
t = 0.0174/0.01302
t = 1.336
0.336 × 12 = 4.032
Therefore, the money waa in the account for 1 year and 4 months
Kwame's team will make two triangular pyramids to decorate the entrance to the exhibit. They will be wrapped in the same metallic foil. Each base is an equilateral triangle. If the base has an area of about 10.8 square feet, how much will the team save altogether by covering only the lateral area of the two pyramids? The foil costs $0.24 per square foot.
Answer:
Therefore the team saves $5.18.
Step-by-step explanation:
i) there are two triangular pyramids
ii) the base of each pyramid is an equilateral triangle with an area of 10.8 square feet.
iii) the base of the pyramids are not covered with foil.
iv) since there are two pyramids the total area not covered
= 10.8 [tex]\times[/tex] 2 = 21.6 square feet
v) the cost of foil = $0.24 per square foot.
vi) the team save altogether by covering only the lateral area of the two pyramids
= 21.6 [tex]\times[/tex] 0.24 = $5.18
Therefore the team saves $5.18.
Does the graph represent a function ? Why or Why not ?
Answer:yes
Step-by-step explanation: the answer does represent a function because if you were to put points in the line wherever, and connect them by drawing a line vertically, it would not cross two points.
Given: △ABC; AB=BC, m∠BDA = 60°, BD=4 cm, BD ⊥ BA . Find: DC, AC.
Answer:
DC = 10.93 cm , AC = 9.8 cm
Step-by-step explanation:
From trigonometry;
⇒ Tan 60 = AB/BD
⇒AB = BD Tan 60 ( where BD = 4 cm )
⇒ AB = 6.93 cm
Also, AB=BC , therefore;
⇒ BC = 6.93 cm
⇒ Cos 60 = BD/AD
⇒ AD = BD/ Cos 60 = 4/Cos 60
⇒ AD = 8 cm
From Pythagoras theorem;
⇒ [tex]AC^{2}[/tex] = [tex]AB^{2}[/tex] + [tex]BC^{2}[/tex] = [tex](6.93)^{2}[/tex] + [tex](6.93)^{2}[/tex]
⇒ AC = [tex]\sqrt{96.05}[/tex] = 9.80 cm
⇒ DC = BD + BC = 4 + 6.93
⇒ DC = 10.93 cm
The U.S. Post Office is interested in estimating the mean weight of packages shipped using the overnight service. They plan to sample 300 packages. A pilot sample taken last year showed that the standard deviation in weight was about 0.15 pound. If they are interested in an estimate that has 95 percent confidence, what margin of error can they expect?A. Approximately 0.017 pounds B. About 0.0003 pounds C. About 1.96 D. Can't be determined without knowing the population mean.
Answer: A. Approximately 0.017 pounds
Step-by-step explanation:
Formula to find the margin of error :
[tex]E=z^*\dfrac{s}{\sqrt{n}}[/tex] , where z* = critical value for confidence interval , s= standard deviation , n= sample size.
As per given , we have
s= 0.15 pound
n= 300
Critical value for 95% confidence = 1.96
Then, Margin of error for 9%% confidence interval will be :
[tex]E=(1.96)\dfrac{0.15}{\sqrt{300}}\\\\=0.0169740979142\approx0.017[/tex]
Hence, they can expect a margin error of 0.017 pound (approximately.)
Thus , the correct answer is A. Approximately 0.017 pounds
A wheelchair ramp is to be built from ground level to a platform that is 9 feet above the ground. The angle that the ramp makes with the ground is 11 degrees. What is the length of the ramp?
The answer is in the attachment
Answer: the length if the ramp is 47.17 feet
Step-by-step explanation:
The wheelchair ramp makes an angle of 11 degrees with the ground and forms a right angle triangle. The length of the ramp becomes the hypotenuse of the right angle triangle.
The distance of the platform from the ground level forms the opposite side of the right angle triangle.
To determine the length of the ramp, h, we would apply the Sine trigonometric ratio. It is expressed as
Sin θ = opposite side/hypotenuse
Therefore,
Sin 11 = 9/h
h = 9/Sin 11 = 9/0.1908
h = 47.17 feet
A square is 3 inches on each side. A small square, x inches on each side, is cut out from each corner of the original square. Represent the area of the remaining portion of the square in the form of a polynomial function A(x)
Here's the polynomial function representing the area of the remaining portion of the square:
A(x) = 9 - 4x + x^2
1. **Initial area:** The original square has a side length of 3 inches, so its initial area is 3 * 3 = 9 square inches.
2. **Removing squares:** When small squares of side length x are cut out from each corner, the remaining shape becomes a smaller square with a side length of (3 - 2x) inches.
3. **New area:** The area of this smaller square is (3 - 2x) * (3 - 2x) = 9 - 6x + 4x^2 = 4x^2 - 6x + 9.
4. **Simplifying:** We can rearrange this expression to get a simpler polynomial function: A(x) = 9 - 4x + x^2.
Therefore, A(x) = 9 - 4x + x^2 represents the area of the remaining portion of the square after the small squares are cut out, as a function of the side length x of the removed squares.
In Don's congruence flowchart for problem 6-29, one of the ovals "AB/FD= 1". In Phil's flowchart, one of the ovals said, "AB=FD". Discuss with with your team whether these ovals say the same thing. Can equality statements like Phil's always be used in congruence flowcharts?
Yes, they are saying the same thing. In fact, if a ratio equals one, it means that numerator and denominator are equal.
This is the reason why you can always use A=B or A/B, as they are totally equivalent.
Jaylan and casper are equal partners in J&C racoon hats. Jaylan contributed 12000 and casper contributed inventory with a FMV of 12000 and an adjusted basis of 10000. What is each partnership basis
Answer:
The question continues ; Which of the following is true ;
Jaylan basis in the partnership is $12,00 and Caspers is 10,000
Jaylan and Casper each have a basis in the partnership of 12,000
Jaylan will have a larger share of the profits than Casper
The first and third answers are both correct
Answer ; Jaylan and Casper each have a basis in the partnership of 12,000
Step-by-step explanation:
Both Jaylan and casper will have a partnership basis of $12,000 , it was mentioned initially in the question that (Jaylan and casper are equal partners in J&C racoon hats), equal partners implies both Jaylan and casper with have equal profit and equal losses as the case maybe Irrespective of the amount each contributed. Hence Jaylan and Casper each have a basis in the partnership of 12,000.
Tyler has two savings accounts that his grandparents opened for him. The two accounts pay 10% and 12% in annual interest; there is $400 more in the account that pays 12% than there is in the other account. If the total interest for a year is $158, how much money does he have in each account?
Answer: the amount of money in the account that earns 10% interest is $500
the amount of money in the account that earns 12% interest is $900
Step-by-step explanation:
Let x represent the amount of money in the account that earns 10% interest.
Let y represent the amount of money in the account that earns 12% interest.
There is $400 more in the account that pays 12% than there is in the other account. This means that
y = x + 400
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering the account that earns 10% interest.
P = x
R = 10
T = 1 year
I = (x × 10 × 1) = 0.1x
Considering the account that earns 12% interest.
P = y
R = 12
T = 1 year
I = (y × 12 × 1) = 0.12x
If the total interest for a year is $158, it means that
0.1x + 0.12y = 158 - - - - - - - - - - -1
Substituting y = x + 400 into equation 1, it becomes
0.1x + 0.12(x + 400) = 158
0.1x + 0.12x + 48 = 158
0.22x = 158 - 48 = 110
x = 110/0.22 = 500
y = x + 400 = 500 + 500
y = 900
Juan wants to paint somthing in the shape of a right rectangle prism. The prism is 17 in long 11 in wide and 9 in high. He had enough paint to cover 850 sq in. Dose he have enough paint? Explain your reasoning
Juan does not have enough paint to cover shape of a right rectangle prism
Solution:
Given that,
Juan wants to paint something in the shape of a right rectangle prism
From given,
Length = 17 inches
Width = 11 inches
Height = 9 inches
The surface area of prism is given as:
[tex]A=2(wl+hl+hw)[/tex]
Where, "l" is the length and "w" is the width and "h" is the height
Substituting the values we get,
[tex]A = 2(11 \times 17 + 9 \times 17 +9 \times 11)\\\\A = 2(187+153+99)\\\\A = 2 \times 439 \\\\A = 878[/tex]
Thus surface area of prism is 878 square inches
Given that,
He had enough paint to cover 850 sq in
No he cannot paint since surface area is 878 square inches which is greater than 850 square inches
So, he does not have enough paint
Leon wants to estimate the height of a building. Leon's eyes are 6 feet above ground. He stands 25 feet from the building and sights the top of the building at a 77° angle of elevation. What is the building's height to the nearest tenth of a foot?
Answer:
114.29 ft
Step-by-step explanation:
tan ∅ = Opp/Adj
tan 77 = x/25
x = 25 tan 77
x = 108.29ft
Plus 6ft = 114.29 ft