Answer:
As Per Provided Information
Lateral area of cone is 9.81 in Radius of cone is 1.4 inWe have been asked to determine the slant height of the cone .
Formula used to calculate the lateral area of a cone is
[tex] \boxed{\bf \: \purple{ Lateral \: Area _{(Cone)} \: = \pi\:rl}}[/tex]
here
l denote slant height
r denote radius
Substituting the value we obtain
[tex] \longrightarrow\tt \: 9.81 = 3.14 \times 1.4 \times l \\ \\ \\ \longrightarrow\tt \:9.81 = 4.396 \times l \\ \\ \\ \longrightarrow\tt \: \cfrac{9.81}{4.396} = l \\ \\ \\ \longrightarrow\tt \: \: l \: = \cfrac{9.81}{4.396} \\ \\ \\ \longrightarrow\tt \: \: l \: = \cancel\cfrac{9.81}{4.396} \\ \\ \\ \longrightarrow\tt \: \: l \: = 2.23 \:inch \: \: (approx)[/tex]
Therefore,
Slant height of the cone is 2.23 in .Repost bc I forgot something.
You throw a football and it leaves your hand of 5 feet. Its initial velocity is 20 feet per second. What is the maximum height the ball will reach? Also, how long will it take the ball to hit the ground? (Equation used: h(t)= -16t^2 + v0t + h0.)
Please show work
Answer:
The max height is 11.25 feet and the ball will take 1.464 seconds to hit the ground
Step-by-step explanation:
The quickest way to solve this equation is by using the equation that you gave, which is h(t)= -16t^2 + v0t + h0. This equation models the trajectory of the football, which means that at the equation's vertex, we can model what the height of the ball is. Along with that, by finding the positive root of where h(t) = 0, we can find how long it will take for the ball to hit the ground.
First, lets find h0 and v(0)
h0 is the initial height of the ball. So we know that the ball leaves your hand of 5 feet, so h0 = 5. Similarly, the initial velocity is 20 ft/sec, so v0 = 20.
Plugging 5 in for h0 and 20 for v0, we get h(t) = -16t^2 + 20t + 5.
Second, find max height.
To find the vertex of a parabola, use -b/2a to find the time, and plug that into h(t) to get the height.
b=20
a=-16
t = -b/2a = -20/2(-16) = .625 seconds
h(.625) = 11.25 feet
The max height is 11.25 feet
Third, find how long.
To find this, we need to find the t-intercepts of the equation.
set h(t) = 0
-16t^2 + 20t + 5 = 0
Use quadratic formula to find t
t = (- 20 ± [tex]\sqrt{20^{2} - 4(-16)(5)}[/tex])/2(-16)
t = {1.464}, -.214
The ball will take 1.464 seconds to hit the ground.
I need help with D, i’m confused on it.
Answer:
Step-by-step explanation:
[tex]A=P(1+\frac{r}{n})^{nt[/tex]
A = future value ($)
P = principal (orignal amount - $400)
R = rate (written as a decimal - 3%/100= 0.03)
N = compound (yearly - 1)
T = number of years (0, 5, 10, 15)
Now, substitute each number into the formula and record them in the table.
0 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*0}\\\\A=400(1+\frac{0.03}{1})^0 < ==any\ number\ raised\ to\ zero=1\\\\A=400(1)\\\\A=\$400[/tex]
5 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*5}\\\\A=400(1+\frac{0.03}{1})^{5}\\\\A=400(1+{0.03})^{5}\\\\A=400({2.03})^{5}\\\\A=400({1.1593})\\\\A=\$463.72 < ==round\ to\ the\ nearest\ dollar\\\\A=\$464[/tex]
10 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*10}\\\\A=400(1+\frac{0.03}{1})^{10}\\\\A=400(1+{0.03})^{10}\\\\A=400({1.03})^{10}\\\\A=400({1.3439})\\\\A=\$537.56 < ==round\ to\ the\ nearest\ dollar\\\\A=\$538[/tex]
15 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*15}\\\\A=400(1+\frac{0.03}{1})^{15}\\\\A=400(1+{0.03})^{15}\\\\A=400({1.03})^{15}\\\\A=400({1.5579})\\\\A=623.16 < ==round\ to\ the\ nearest\ dollar\\\\A=\$623[/tex]
20 years:
[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*20}\\\\A=400(1+\frac{0.03}{1})^{20}\\\\A=400(1+{0.03})^{20}\\\\A=400({1.03})^{20}\\\\A=400({1.8061})\\\\A=722.44 < ==round\ to\ the\ nearest\ dollar\\\\A=\$722[/tex]
Note that since we are rounding, answers may vary by a dollar or two.
Hope this helps!
What is the median of the data set represented by the dot plot?
Enter the answer in the box.
A number line with line with two dots above the number 10, one dot above the number 12, one dot above the number 13, one dot above the number 14, one dot above the number 15, one dot above the number 18, and two dots above the number 19.
Answer:
Median is 14Step-by-step explanation:
The median is the middle number (or average of middle two numbers if data set has even number of elements) of the data set.
According to the graph, the data set has 9 elements.
The 5th number in the set is the median, which is 14
14
Step-by-step explanation:Step-1: Prepare a table that represents the number of dots above a specific number:
[tex]\text{Dots above 10}: || \\ \text{Dots above 12}: | \\ \text{Dots above 13}: | \\ \text{Dots above 14}: | \\ \text{Dots above 15}: | \\ \text{Dots above 18}: | \\ \text{Dots above 19}: ||[/tex]
Step-2: Put the values in ascending or descending upon your choice:
[tex]10, 10, 12, 13, 14, 15, 18, 19, 19[/tex]
Step-3: Determine wether the total number of digits in the data is even or odd. This will help us find the median.
[tex]\text{9 digits in total}\\\\\text{The number of digits is \underline{odd}}[/tex]
Since the number of digits is odd, we will use the formula (a + 1)/2
(where a is the number of digits in the data)
Step-4: Substitute the number of digits in the formula.
⇒ (a + 1)/2th
⇒ (9 + 1)/2th
⇒ (10)/2th
⇒ 5th digit is median
Step-5: Look for the 5th digit in the data. That digit is your median.
[tex]10, 10, 12, 13, \underline{\underline{14}}, 15, 18, 19, 19[/tex]
The median of the dot plot is 14.
There are 15 students on the debate team. Four will attend the debate. How many groups of four can be selected from the 15 students?
Answer: 1365
Step-by-step explanation:
What additional information could be used to prove that the triangles are congruent using AAS?
Select two options
Answer:
Step-by-step explanation:
We have two congruent angles, so we need a pair of congruent sides. This is satisfied by options 2 and 3.
if a town with a population of 10,000 doubles in size every 17years wat will population be 68 years from now
Answer:
20,000×17 gives 340,000
340,000×68 which gives 23,120,000
When Brooklyn runs the 400 meter dash, her finishing times are normally distributed with a mean of 76 seconds and a standard deviation of 3 seconds. Using the empirical rule, what percentage of races will her finishing time be between 70 and 82 seconds?
Using the Empirical Rule, it is found that her finishing time will be between 70 and 82 seconds in 95% of her races.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, the mean is of 76 seconds and the standard deviation is of 3 seconds, then:
76 - 2 x 3 = 70.
76 + 2 x 3 = 82.
Which means that values between 70 and 82 seconds are within 2 standard deviations of the mean, hence the percentage is of 95%.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
Ill give brainliest please help .
Answer:
443.14
Step-by-step explanation:
A=6ah+33a2
=6·4·15+3·3·42
≈443.13844
Answer:
I believe the answer is 88 if correct please consider brainliest
<3
Step-by-step explanation:
A square pyramid is shown. What is the surface area of the pyramid? Enter your answer in the box. 100 points
Answer:
33 cm²
Step-by-step explanation:
Formula
Surface Area = 4 x Area (triangle) + Area (square)S.A. = 4 x 1/2 x bh + b²Solving
Given that h = 4 cm and b = 3 cmS.A. = 2 x 4 x 3 + 3²S.A. = 24 + 9 = 33 cm²Answer:
33 cm²
Step-by-step explanation:
Since the pyramid has a square base, the area of each of the triangular sides will be the same.
Therefore, to calculate the total surface area, find the area of one triangle, multiply it by 4, then add it to the area of the square base.
Formulae
Area of a square = x³ (where x is the side length)
Area of a triangle = 1/2 × base × height
Calculation
area of the square base = 3² = 3 × 3 = 9 cm²
area of one triangle = 1/2 × 3 × 4 = 6 cm²
Solution
Total area = area of the square base + 4 × area of one triangle
= 9 + (4 × 6)
= 9 + 24
= 33 cm²
Write a two-column proof on a space provided
Answer:
Step-by-step explanation:
Can you guys help me do today.
Answer:
Down Below
Step-by-step explanation:
b=0.5
g=0.8
1. 3b + 5g = ?
3×0.5+5×0.8=?
1.5+4= 5.5 cm
2. 6(3b+5g) = ?
18b + 30g
18×0.5+30×0.8
9+24= 33 cm
3. 2b + 3g
2×0.5+3×0.8
1+2.4=3.4 cm
4. 7(2b+3g)
14b + 21g
14×0.5+21×0.8
7+16.8= 23.8 cm
5. Add number 2 and 4 together
14b+21g+18b+30g= 32b+ 51g
Take numbers and add them from problems 2 and 4
23.8+33=56.8 cm
Please help me????22pts
Answer:
[tex]\mathrm{1 \dfrac{ 1 }{ 6 }\:cups}[/tex]
Step-by-step explanation:
Given from the graph:
There is [tex]\frac{1}{2}[/tex] cups of paint for one jar
There are 3 cups of paint for three jars
There is 1 [tex]\frac{1}{2}[/tex] cups of paint for one jar
There is 2 cups of paint for one jar
total amount of jars = 6
But since we need to find the amount of cups in each jar, we do:
[tex]\dfrac{ 1 }{ 2 } +3+1 \dfrac{ 1 }{ 2 } +2[/tex]
Add [tex]\frac{1}{2}[/tex] and 1 [tex]\frac{1}{2}[/tex]
[tex]2+3+2[/tex]
Add 2 and 3
[tex]5+2[/tex]
Add 5 and 2
[tex]7[/tex]
total cups of paint = 7
Then we need to find how much paint could be splitted equally among the 6 jars, so we do the following:
total amount of jars = 6
total cups of paint = 7
We divide the total amount of jars by the total cups of paint
7 ÷ 6
Divide 7 by 6
[tex]\dfrac{ 7 }{ 6 }[/tex]
[tex]= 1 \dfrac{ 1 }{ 6 }[/tex]
[tex]\mathrm{Answer: 1 \dfrac{ 1 }{ 6 }\:cups}[/tex]
What are the zeros of the following function?
Answer:
-4 and 2
Step-by-step explanation:
the graph intersects the x-axis only at the points (-4,0) and (2,0) so the only zeroes of the graph are going to be -2 and 2
Mark chose two cards randomly from a deck. What is the probabity of getting an Ace or King?
Answer:
50/50
Step-by-step explanation:
Answer:
depends on how many there are in a deck. But going from the usual, it would be 2/52
Step-by-step explanation:
(52 is how many cards there are, if theres a different amount then change it to that)
The sum of two numbers is 30 and their difference is 10. What are the two numbers?
Answer:
20 and 10
These are the only two possible numbers who match those descriptions.
Which construction uses the compass for only one step in addition to drawing the circle itself?
A) an equilateral triangle inscribed in a circle
B) a square inscribed in a circle
C) a regular hexagon inscribed in a circle
D) a diameter of a circle
Answer: A) an equilateral triangle inscribed in a circle
Step-by-step explanation:
In the mathematical world, a compass is a mathematical tool used for drawing and constructing precise shapes. You have likely seen one of these before, I have attached a visual example of what one might look like.
Out of these given options, the only one that utilizes a compass for one step in addition to drawing the circle itself is A:
A) an equilateral triangle inscribed in a circle
Read more about using a compass here: https://brainly.com/question/27490907
Which expression is equivalent to
Answer:
First option
Step-by-step explanation:
The expression can be simplified to:
[tex]\frac{8g^{15} }{64h^6}[/tex] = [tex]\frac{g^{15} }{8h^{6} }[/tex]
You can't simplify this further since the indices if you think about it is g 15 times or h 6 times so you can't simply them further.
PLEASE ANSWER QUICKLY!
The figure shows a right prism.
1. What is the volume of the figure?
2. If the dimensions of the prism are decreased by a factor of 1/4, how will the volume of the new prism compare to the volume of the original prism? (ANSWER IN A SIMPLIFIED FRACTION).
The volume of the prism is decreased by a factor of: ______
What is the difference between the two fractions explain in full detail. Type out answer
Answer:
Step-by-step explanation:
There is no difference between the two fractions. I can show you this in the following way, assuming you understand the distributive property. We can write the fraction -7/2 in the following way:
[tex]-\frac{7}{2} =-1(7*2^-^1)[/tex]
Hopefully you agree with me that we can bring the 2 into the numerator if we switch the signs of the exponent. And hopefully you agree that a negative sign is equivalent to multiplying by -1. Therefore, this negative 1 can distribute to the 7 or the 2. It really does not matter. To sum this up:
[tex]-\frac{7}{2} =\frac{-7}{2} =\frac{7}{-2}[/tex]
Examine the following piecewise function.
Which statements are true?
Select all that apply.
1.The function is increasing over the interval 2≤x≤3.
2.The function is increasing over the interval −2≤x≤2.
3.The function is increasing over the interval −8≤x≤−2.
4.The function is decreasing over the interval 3≤x≤7.
5.The function is constant over the interval −2≤x≤2.
A piecewise function is a function that's simply built from pieces of different functions over several intervals.
What is a piecewise function?Your information is incomplete as the function isn't given. Therefore, an overview will be given. It should be noted that a piecewise function simply means a function that's defined by multiple sub functions.
In this case, each sub-function applies to different interval in the domain as it's way of expressing the function.
Learn more about piecewise function on:
https://brainly.com/question/17966003
Maria bought a laptop computer for $850. The value of the computer depreciates about 25% each year. After 3 years, she decides to sell it to her younger brother. What is a fair price for the computer?
Using the depreciation formula:
start value x percent of value^time
850 x 0.75^3 = $358.59
answer: $358.59
Answer: $358.59
Step-by-step explanation:
[tex]$$After one year the laptop computer's price is:$$\begin{aligned}&=\$ 850-\$ 850 \times 25 \% \\&=\$ 850-\$ 212.5 \\&=\$ 637.5\end{aligned}$$[/tex]
[tex]$$ Again two year the computer's price is:$$\begin{aligned}&=637.5-25 \% \text { of } 637.5 \\&=637.5-159.375 \\&=\$ 478.125\end{aligned}$$[/tex]
[tex]\bold{\text { So a fair price for the computer is } \$ 358.59}[/tex]
[tex]\begin{aligned}\\\bold{Or}\text { Simply Calculate as } &=(\text { Purchase price }) \times(1-25 \%)^\text{time} \\&=850 \times(1-0.25)^{3} \\&=850 \times(0.75)^{3} \\\bold{&=\$358.59}\end{aligned}[/tex]
Who burned down Constantinople?
O barbarians
O crusaders
o Egyptians
o Turks
Answer:
The Turks burned down Constantinople
Donnie ran 6.24 kilometers in a race last weekend. How many meters did he run?
he ran 10meters last weekend
2. A baby weighs 8 pounds, 1 ounce. How much does she weigh in ounces?
Answer:
97 oz
Step-by-step explanation:
12 oz per pound
8 pounds + 1 oz
(12 · 8)+ 1
97 oz
Hope this helps!
Simplify the expression.
3.8m + 7 - 2.8m
(Use the operation symbols in the math palette as needed. Simplify your answer. Use whole numbers or decimals for any numbers in the expression.)
Answer:
m + 7
Step-by-step explanation:
→ Collect like terms
3.8m - 2.8m + 7
→ Simplify
m + 7
CAN SOMEONE HELP ME PLEASE ASAP!?
Answer:
3:10
Step-by-step explanation:
3:10 is the ratio form of 3/10
Help!! I’m so stuck!
Giving away all of my points in 100 point bursts. I have 1700 points. How people can I give to?
Total times can give:-
1700/10017One question can be answered by 2
Total persons=17(2)=34
simplify l(m-n) + m (n-l) + n (m-l)
Step-by-step explanation:
Multiplying :-l(m-n) + m (n-l) + n (m-l)lm - ln + mn - ml + nm - nlSolve the like terms :-lm - ml - ln - nl + mn + nm2mn - 2nlTake common :-2n(m - l)...simplified Hope it helps you !!Answer:
-2ln + 2mn
Step-by-step explanation:
Simplify l(m-n) + m(n-l) + n(m-l)
Step 1 : Distribute and multiply
l(m-n) + m(n-l) + n(m-l)
l(m) + l(-n) + m(n) + m(-l) + n(m) + n(-l)
lm - ln + mn - lm + mn - ln
Step 2: Combine like terms
lm - ln + mn - lm + mn - ln
lm - lm - ln - ln + mn + mn
0 -2ln + 2mn
Solution:
-2ln + 2mn
Hope this helps!
The speed of the jet Alyssa flew on from Boston to London was 480 mph. On her return flight, the speed of the jet was 600 mph with a tailwind. What was Alyssa's average speed on the round trip? Round your answer to one decimal place.
P.S: The answer is not 540
Answer:
533.3
Step-by-step explanation:
x/480+x/600
2x/18x
4800/9=533.333333
533.34
A street trader spent 550 on x article, each costing (2x -28) find x
Answer:
the x is 538
Step-by-step explanation:
sorry if im not right
