Answers
Answer:
5. LA = 301.6 sq. cm., SA = 402.1 sq. cm.
6. LA = 377.0 sq. in., SA = 603.2 sq. in.
7. LA = 113.1 sq. cm., SA = 169.6 sq. cm.
8. LA = 502.7 sq. cm., SA = 603.2 sq. cm.
9. 396 sq. in.
Step-by-step explanation:
The lateral area is the area of all the faces, except the base(s). The surface area is the area of ALL the faces of the shape.
5.
The lateral area of a cylinder is given by the formula:
LA = 2πrh
where r is the radius and h is the height of the cylinder
So, lateral area would be 2π(4)(12) = 301.6 sq. cm.
The surface are would be the lateral area (301.6) PLUS the area of 2 of the circular bases. Circle has an area of πr^2.
So 2 bases would have area of (π(4)^2)*2=100.5
Thus, the surface area = 301.6 + 100.5 = 402.1
6.
The lateral area would be LA = 2πrh
The radius is given as 6 and height as 10. Plugging it would give us:
LA = 2πrh = 2π(6)(10) = 377.0 sq. in.
For the surface area, we would need to add the top and bottom (which are 2 identical circles with area πr^2 each) with the lateral area. So we have:
2 * (π(6)^2)
=226.2
Surface area = 377.0 + 226.2 = 603.2 sq. in.
7.
The radius of the cylinder is 3 and height is 6. We will plug them into the respective formulas.
lateral area:
LA = 2πrh = 2π(3)(6) = 113.1
surface area:
area of 2 circles (top and bottom) = (πr^2)*2 = (π(3)^2)*2 = 56.5
Surface area = 113.1 + 56.5 = 169.6
8.
diameter is given as 8, so radius is half of it. Hence, radius is 4 and height given as 20.
Plugging these values into the respective formula we will get the answer.
lateral area:
LA = 2πrh = 2π(4)(20) = 502.7
surface area:
area of both the circles (top and bottom) PLUS the lateral area of 502.7.
So, surface area = 502.7 + (πr^2)*2 = 502.7 + (π(4)^2)*2 = 603.2
9.
The frosting area of area of two rectangles (left and right) + area of two rectangles (back and front) + area of rectangle (top).
So, surface area of the frosting part = 2 (4*15) + 2(4*12) + (12)(15) = 396
Related Questions
can anyone Explain in words why these are equivalent expressions.
10(b + 4c) is equivalent to 10b + 40c
Answers
Answer:
The distributive property says that when there is a number outside of parenthesis, this means it should be distributed (or multiplied) to the values inside the parenthesis.
So in this situation, 10 x b = 10b
and 10 x 4c = 40 c
so 10(b + 4c) becomes 10b + 40c once the 10 is distributed within the parenthesis.
I hope this helps!
Answer:
They are equivalent expressions because if you use distributive property and multiply 10*b, then multiply 10*4c, you get 10b+40c
Step-by-step explanation:
A basketball coach claims that the team's players commit, on average, no more than 10 fouls per game. Let µ represent the team's average number of fouls per game. Another coach thinks that these players create more fouls.
What is the null hypothesis, H0, for this situation?
(B) u ≤ 10
What is the alternative hypothesis, Ha, for this situation?
(B) u > 10
What type of significance test should be used for this situation?
A right-tailed test
These are the correct answers but I don't know the explanations for them someone help me out
Answers
Answer:
H0: u ≤ 10
Ha: u > 10
A right-tailed test
Step-by-step explanation:
In hypothesis testing there are two types of hypotheses;
The null hypothesis, H0 and the alternative hypothesis, Ha. The null hypothesis is the hypothesis of no difference and as such it always has an equality sign;
=, ≤, ≥
On the other hand the alternative hypothesis complements the null hypothesis meaning that if the null hypothesis is rejected then we take the alternative hypothesis to be true.
In order to identify the null and alternative hypothesis we look out for specific key words that will provide us with information on the type of inequality sign. In this scenario, the coach claims that the average number of fouls committed per game is no more than 10. Since µ represents the team's average number of fouls per game, this statement can be written in mathematical symbols as;
u ≤ 10, that is u is no more than 10; average number of fouls committed per game is no more than 10.
This statement will be our null hypothesis since it contains an equality sign.
H0: u ≤ 10
The complement of this statement will enable us deduce the alternative hypothesis. The complement of this statement can be found in the claim of the second coach who thinks that these players create more fouls, to be specific more than 10 fouls. In mathematical notation this claim can be written as;
u > 10, more than 10 fouls.
This statement will be our alternative hypothesis since it complements the null hypothesis;
Ha: u > 10
The type of significance test to be carried out in hypothesis testing emanates from the inequality sign of the alternative hypothesis. The following are the key points to note, if the alternative hypothesis contains;
≠, then this automatically becomes a two tailed test
<, then this automatically becomes a left tailed test since the inequality sign is pointing towards the left.
>, then this automatically becomes a right tailed test since the inequality sign is pointing towards the right.
Our alternative hypothesis contains >, hence this will be a right-tailed test .
Answer:
Answer is B
Step-by-step explanation:
what is the value of x, 6x +2=180
Answers
Answer: [tex]x=\frac{89}{3}[/tex] or [tex]26\frac{2}{3}[/tex]
[tex]\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\6x+2-2=180-2\\6x=178[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}6\\\frac{6x}{6}=\frac{178}{6}\\[/tex]
[tex]x=\frac{89}{3}[/tex]
Hope this helps and have a great day!!!
Answer: there are three answers. the exatct, decimal, and mixed. i will give them all!
exact: X= 89/3
decimal: x= 29.6
mixed: x= 29 2/3
Step-by-step explanation:
Write a general formula to describe the variation: x varies jointly with the inverse of the sum of y and z
Answers
Answer:
x = k/(y+z)
Step-by-step explanation:
We need to write a general formula to describe the variation: x varies jointly with the inverse of the sum of y and z
it can be written as
x ∝ 1/(y+z)
or can be written as
x = k/(y+z)
where k is the constant of variation introduced when we remove the ∝ sign.
144 divided by 12 what is the answer
Answers
Answer:
12
Step-by-step explanation:
12 times 12 is 144
Answer:
12.
Step-by-step explanation:
If you were to divide 144 into 12 parts, each part would have 12 pieces. Another way to imagine it would be setting up a fraction (144/12) and then simplifying until you get 12/1.
Divide and answer in simplest form: 5 3 ÷ 3
Answers
Answer: 17.7 (rounded)
Step-by-step explanation:
53/3= 17.6 ..
17.6 rounded is 17.7
Answer:
result is 17.7
Step-by-step explanation:
3.7 ÷ 1.1 = ? Round to the nearest hundredth. A. 4.8 B. 0.297 C. 4.07 D. 3.36
Answers
The answer is D.
Hope this helps!
Answer:
D. 3.36
Step-by-step explanation:
Just by intuition, we can see that 3.7 / 1.1 will give a result somewhere around 3.3 (forget the decimal point, think 37 / 11). That automatically allows you to zoom in on the correct answer, based on the other choices.
But let's verify it too.
3.7 / 1.1 = 3.363636
They ask to round to the nearest hundredth, so 3.363636 becomes 3.36
Convert z = 8cos72° + 8isin72° from polar form to rectangular form.
Answers
Answer:
The rectangular form of z = 8 cos72° + 8 sin72° is z = (2.5 , 7.6)
Step-by-step explanation:
* Lets revise how to change from polar form to rectangular form
- Cartesian Coordinates (x , y) and Polar Coordinates (r , θ)
- Where x = r cosФ , y = r sinФ
* To convert from Polar Coordinates (r , θ) to Cartesian Coordinates (x , y)
# x = r × cos( θ )
# y = r × sin( θ )
* In the problem
∵ z = 8 cos72° + 8 sin72°
∴ r = 8
∴ Ф = 72°
∵ x = r cosФ
∴ x = 8 cos72° = 2.5
∵ y = r cosФ
∴ y = 8 sin72° = 7.6
* The rectangular form of z = 8 cos72° + 8 sin72° is z = (2.5 , 7.6)
I haven’t done area in a while and now we have to do with algebra, can anyone please help me with this? Thanks!
Answers
Answer: The area of the triangle is:
____________________________________________________
→ " (4x² + 6x) cm³ " .
____________________________________________________
Step-by-step explanation:
____________________________________________________
The formula for the "Area, "A" ; of a triangle is:
A = (1/2) * (baselength) * (perpendicular height) ;
→ that is:
→ A = (1/2) * b * h ;
____________________________________________________
The Area, "A" ; should be in "cubic units" ; in our case, "cubic centimeters" ;
or; " cm³ " .
____________________________________________________
Given: baselength: "b" = " 4x " ;
perpendicular height: " h = (2x + 3) " ;
____________________________________________________
Plug in these values into the equation/formula:
A = (1/2) * b * h ;
→ A = (1/2) * (4x) * (2x + 3) ;
→ (1/2) * 4x = 2x ;
→ A = 2x (2x + 3) cm³
____________________________________________________
→ 2x (2x + 3) = ?
____________________________________________________
Note the "distributive property" of multiplication:
→ a(b + c) = ab + ac .
____________________________________________________
As such:
→ 2x (2x + 3) = 2x(2x) + (2x)(3) ;
= 4x² + 6x ; ____________________________________________________
The area of the triangle is: " (4x² + 6x) cm³ " .
________________________________________________
Hope this helps!
Best wishes in your academic endeavors
— and within the "Brainly" community!
____________________________________________________
A survey asked two age groups which summer sport they most preferred. The results are shown in the table below.
Age 10-19 Age 20-29 Total
Ski 12 15 27
Swim 102 88 190
Kayak 35 42 77
Hike 23 123 146
Total 172 268 440
Of the total people surveyed, what is the relative frequency of 10-19 year olds who preferred to ski?
2.73%
6.98%
12%
44.44%
Answers
Answer:
6.98%
Step-by-step explanation:
To find relative frequency we divide frequency with the total number participants in that age bracket
Total number of participants age 10-19=172.....................given in the table
The frequence for those who ski at age 10-19=12---------------given in table
Relative frequency= 12/172 = 0.0697
Expressed as a percentage= 0.06976×100 =6.98%
Answer:
The correct answer option is 6.98%.
Step-by-step explanation:
We are given the results of a survey which asked two age groups which summer sport they most preferred.
We are to find the relative frequency of 10-19 year old who preferred to ski.
For that, we will divide the number of kids aged 10-19 years who prefer to ski by the total number of people who prefer to ski and multiply by 100.
Relative frequency = 12/172 * 100 = 6.98%
One serving of vegetables has 60 calories. Write the unit rate as a ratio. Then write an equivalent ratio.
Answers
Answer:
1:60, 2:120
Step-by-step explanation:
In one serivng there are 60 calories, i.e. 60 calories per serving. This is 1:60, an equivalent is 2:120
1:60, 9:540
Hope this helps!
suppose the probability of success in a binomial event is 0.15. what is the probability of failure
Answers
Answer:
Step-by-step explanation:
85
Let g(x) = 2x2 - 11x. Find g(1).
A) -13
B) -9
C) 9
D) 11
Answers
Answer:
(B) -9
Step-by-step explanation:
g(x) = 2x² - 11x
To find g(1), we substitute x = 1 into g(x).
g(x) = 2x² - 11x
g(1) = 2(1)² - 11(1) = 2 - 11 = -9
ANSWER
B) -9
EXPLANATION
The given function is
[tex]g(x) = 2 {x}^{2} - 11x[/tex]
Put x=1 into the given function to obtain;
[tex]g(1) = 2 {(1)}^{2} - 11(1) [/tex]
Simplify to get:
[tex]g(1) = 2 (1) - 11(1) [/tex]
[tex]g(1) = 2 - 11 = - 9[/tex]
The correct choice is B.
Use the bar graph. Describe how the amount of practice time changed from Week 1 to Week 4
Answers
there is no bar graph here
expand 2(x+3) plss coukd u expand it
Answers
Answer:
2x + 6
Step-by-step explanation:
Each term in the parenthesis is multiplied by the 2 outside, that is
2(x + 3)
= (2 × x) + (2 × 3)
= 2x + 6
What would be the expression?
Answers
6*6-(3*3)-(2*2) is the answer
in the triangles, gk=pn and hg=mp. which statement correctly compares the angles
Answers
Answer:
Angle G is smaller than angle P
Step-by-step explanation:
In this problem we know that
MN > HK
therefore
∠P > ∠G
The measure of angle P is greater than the the measure of angle G
Rewrite
∠G < ∠P
The measure of angle G is smaller than the the measure of angle P
Answer:
Angle G is smaller than angle P
Step-by-step explanation:
Vito buys a twin mattress that is 39 inches wide and 75 inches long. He wants to buy a quilt to cover the top of the mattress. Which expression can he use to find the area of the top of the mattress?
39 + 75
2(39) + 2(75)
39 × 75
39(75) + 39(75)
Answers
Answer:b 2(39) +2(75)
Step-by-step explanation:
Because there are four corners of a mattress your going to take the length and width of the mattress and multiply each time to then add them to get the exact size your needing
Answer:
39 × 75
Step-by-step explanation:
Since, the shape of the twin mattress is rectangular,
Given,
The length of the mattress = 75 inches,
Width of the mattress = 39 inches,
Now, the the area of the top of the mattress( which is covered by the quilt) = Area of the mattress
We know that,
The Area of a rectangle = Length × Width
Hence, the area of the top of the mattress = 75 × 39
= 39 × 75
Third option is correct.
Please help me!!! Geometry question.
Answers
Answer:
The volume of the figure is [tex](\frac{l^{3}}{3})[\frac{\pi }{2}-1]\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the figure is equal to the volume of the cone minus the volume of the square pyramid
step 1
Find the volume of the cone
The volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]r=\frac{l\sqrt{2}}{2}\ units[/tex] ----> the diagonal of the square base of pyramid is equal to the diameter of the cone
[tex]h=l\ units[/tex]
substitute
[tex]V=\frac{1}{3}\pi (\frac{l\sqrt{2}}{2})^{2}(l)[/tex]
[tex]V=\frac{1}{6}\pi (l)^{3}\ units^{3}[/tex]
step 2
Find the volume of the square pyramid
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base
h is the height of the pyramid
we have
[tex]h=l\ units[/tex]
[tex]B=l^{2}\ units^{2}[/tex]
substitute
[tex]V=\frac{1}{3}l^{2}(l)[/tex]
[tex]V=\frac{1}{3}l^{3}\ units^{3}[/tex]
step 3
Find the volume of the figure
[tex]\frac{1}{6}\pi (l)^{3}\ units^{3}-\frac{1}{3}l^{3}\ units^{3}=(\frac{l^{3}}{3})[\frac{\pi }{2}-1]\ units^{3}[/tex]
the 7 in 72 represents how many times the value of the 7 in 78
Answers
Answer:
1
Step-by-step explanation:
Knowing what place values are, we know that since both of those numbers have the 7 in the tens place, it represents 70. So both of those number are 70 plus another number (under 10)
Answer:
1
Step-by-step explanation:
1
Please help me!! Or can you just tell me why the statement is false
Answers
Answer:
Because 0 is basically nothing. This would only change if X=-9. In that case , |x| < 0.
Step-by-step explanation:
Im just a sixth grader so..........
A kite store has a kite tethered to the top of a 6 foot pole at the beach. The kite is flying at a height, H, of 186 ft above the ground. The angle between the string and the ground is 60°. What is the length of the kite string, L?
Answers
See the attached picture for the solution.
Round the answer as needed.
Answer:
211.8 feet.Step-by-step explanation:
This problem models a right triangles, where the hypothenuses is the length of the string, and one leg would be 180ft, which is the difference between the total height from the ground and the pole height (186-6=180). Also, the angle in front of the knowing leg is 60.
As, based on all given values, we can apply trigonometric reasons to the hypothenuse, which is L.
[tex]sin60=\frac{180}{L}\\ L=\frac{180}{sin60}\\ L=\frac{180}{\frac{\sqrt{3} }{2} }\\ L=\frac{360}{\sqrt{3}}=\frac{360}{1.7} \approx 211.8ft[/tex]
Therefore, the length of the kite string is around 211.8 feet.
The angles of a triangle are 30,60,and 90 ls this a unique triangle?Justify your answer.
Answers
A triangle with angles of 30, 60, and 90 degrees is a unique and special type of right triangle known as a 30-60-90 right triangle, which has consistent properties and side ratios in Euclidean geometry.
Yes, a triangle with angles of 30, 60, and 90 degrees is a unique triangle, known as a 30-60-90 right triangle. This classification is based on the fact that in Euclidean geometry, the sum of the angles in any triangle is exactly 180 degrees. Since one of the angles is given as 90 degrees, this indicates it is a right triangle, and the remaining angles must add up to 90 degrees. Given that the other two angles are 30 and 60 degrees, this satisfies the requirement exactly, making it a specific type of right triangle with consistent properties.
For example, the sides of a 30-60-90 triangle are always in the ratio 1:√3:2. The side opposite the 30-degree angle is the shortest; the side opposite the 60-degree angle is √3 times longer; and the hypotenuse, opposite the 90-degree angle, is twice as long as the shortest side. These proportions and the angles create the unique properties of the 30-60-90 triangle, and they can be applied in trigonometric calculations and proofs. This distinct set of angles and side ratios is what makes the 30-60-90 triangle a special and unique case in geometry.
What should I type here? Will give Brainliest and 25 points Help ASAP!
Answers
Answer:
6+10=16 That is your length.
Step-by-step explanation:
Answer:
POINTSS
Step-by-step explanation:
I WANT POIITNS
Please need help very badly.
Find the area of the shaded area.
Round to the nearest tenth
Answers
Answer:
192.5 ft²
Step-by-step explanation:
Area of the sector
= (360-100)/360 x π(8.35)²
= 158.195 ft²
Area of the triangle
= 1/2 (8.35)(8.35) sin (100)
= 34.3316 ft²
Area of the shaded part
= 158.195 + 34.3316
= 192.5 ft²
Select whether the number is rational, irrational, or imaginary.
3/11
rational
irrational
imaginary
Answers
Irrational because it can not be a whole number
Need Help ASAP!!
What’s the future value of a $1,000 investment compounded at 8% semiannually for five years?
Answers
Answer:
$1480.24
Step-by-step explanation:
This will be solved by the formula:
[tex]FV=I(1+r)^t[/tex]
Where
FV is the future value (what we are looking for)
I is the initial amount (which is $1000)
r is the rate of interest per period (8% is annual interest, but the period is SEMI-ANNUAL, that's 6 months, half of yearly. So r would be half of 8%, which is 4% or r = 0.04)
t is the times compounding occurs in the whole time (The whole time period is 5 years, but compounding occurs semi-annually, so 5*2 = 10 times. Thus, t = 10)
plugging the info into the formula we will get our answer.
[tex]FV=I(1+r)^t\\FV=1000(1+0.04)^{10}\\FV=1000(1.04)^{10}\\FV=1480.24[/tex]
Answer:
C. $1,480
Step-by-step explanation:
Plato
Distributive property 7(2n+3)
Answers
its 14n+21. 7×2n is 14n, and 3×7 is 21
Answer:
[tex]7(2n+3)=14n+21[/tex]
Step-by-step explanation:
[tex]7(2n+3)=(7*2n)+(7*3)\\\\ 7*2n=14n\\ 7*3=21\\ \\ 7(2n+3)=14n+21[/tex]
What is the total perimeter of this figure in inches?
Answers
Answer:
12
Step-by-step explanation:
My basketball team plays four games per week. During the first four weeks, we lost all 16 of our games. During week 5, we won three games and lost one game, bringing us to 3 wins and 17 losses for the season so far. Each week after that, we win 3 games and lose 1 game. At the end of which week will my team have won at least 65% of its games total for the first time in the season?
Answers
Answer:
You need 30 total weeks to win at least 65% games
Step-by-step explanation:
Team have played = 20 games
Number of winning games = 3
Let x represents the number of additional weeks.
You have won 3 games per week. Therefore you will win 3x additional games.
We know that 65% = 0.65
Therefore,
3+3x/20+4x = 0.65
By cross multiplication:
3+3x= 0.65(20+4x)
3+3x = 13+2.6x
Combine the like terms:
3x-2.6x = 13-3
0.4x=10
4x/10 =10
4x = 10*10
4x=100
Divide both sides by 4
4x/4 = 100/4
x = 25
since you have already played 5 weeks...you need to play 25+5 = 30 weeks.
Therefore you need 30 total weeks to win at least 65% games....