Question 4) Identify the surface area of the composite figure.
The surface area of the composite figure is 714 sq. in.
What is formula of surface area of cube ?
Let, a be the edge of the cube.
Then, surface area of the cube = 6a² square unit
What is formula of surface area of cuboid ?Let, length of the cuboid = l unit
Width of the cuboid = w unit
Height of the cuboid = h unit
Then, surface area of the cuboid = 2(lw+lh+hw) square unit
What is the required surface area ?Given, edge of cube = 4 in.
∴ Surface area of cube = (6×4²) sq. in. = 96 sq. in.
Now, given, length of cuboid = 15 in.
Width of the cuboid = 10 in. & height of the cuboid = 7 in.
∴ Surface area of the cuboid = 2{(15×10)+(15×7)+(10×7)} sq. in.
= 2{150+105+70} sq. in.
= 2{325} sq. in. = 650 sq. in.
Here, we have to find the surface area of the composite figure.
We have to subtract the surface area from both of cube & cuboid, where they are attached.In that case, we have to subtract (4×4) from both.
So, we have to subtract 2(4×4) sq. in. = 32 sq. in.
∴ The surface area of the composite figure = (650+96-32) sq. in.
= 714 sq. in.
Learn more about composite figure here :
https://brainly.com/question/27915109
#SPJ10
1/3 · (-3x + 4y - 5z)
(1/3 Is A Fraction)
(Write Explanation)
The value of expression is -(x- 4y/3 + 5z/3)
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts.
Given:
1/3 · (-3x + 4y - 5z)
= 1/3(-3x) + 1/3 *4y + 1/3* (-5z)
= -x +4/3*y -5/3 *z
=-(x- 4y/3 + 5z/3)
Hence, 1/3 · (-3x + 4y - 5z)= -(x- 4y/3 + 5z/3)
Learn more about this concept here:
https://brainly.com/question/9655268
#SPJ1
Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and F C intersects A D at H. image If m ∠ B = 126 ° and m ∠ A H C = 142 ° , determine and state m ∠ G F H .
A quadrilateral in which opposite sides are parallel is called a parallelogram. The measure of the ∠GFH is 16°.
What is a parallelogram?A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
For a parallelogram and a rhombus opposite sides are parallel, therefore, the sides that are parallel are,
AB║DC║ED║FG
Since the sides are parallel,
∠ABC = ∠FGH = 126°
Also, ∠AHC and ∠GHF lie on the same line, therefore,
∠AHC + ∠GHF = 180°
∠GHF = 180° - 142° = 38°
Now, in ΔGHF
∠GHF + ∠HFG + ∠GFH = 180°
∠GFH = 180° - 126° - 38°
∠GFH = 16°
Hence, the measure of the ∠GFH is 16°.
Learn more about Parallelogram:
https://brainly.com/question/1563728
#SPJ1
Two players take turns removing a ball from a jar that initially contains m white and n black balls. The rst player to remove a white ball wins. Find the probability that the starting player wins.
½×½ which will be ¼
Step-by-step explanation:
because
Probability that the starting player wins:
[tex]P_{n} =[/tex] m /n + m + n(n-1) /(n + m)(n+m -1) × [tex]P_{n-2}[/tex]
Let us say that the probability that the first player wins is [tex]P_{n}[/tex]. Then this can be happen in two ways:
If the first player wins in the first move which has a probability: m /n + m
If the first player wins after the second move which has a probability :
n(n-1) /(n + m)(n+m -1) × [tex]P_{n-2}[/tex]
Therefore by the law of probability,
[tex]P_{n} =[/tex] m /n + m + n(n-1) /(n + m)(n+m -1) × [tex]P_{n-2}[/tex]
This will allow us to find out the probability of first player winning the game recursively.
Know more about probability,
https://brainly.com/question/31828911
#SPJ2
A water sample shows 0.033 grams of some trace element for every cubic centimeter of water. Marques uses a container in the shape of a right cylinder with a diameter of 13.2 cm and a height of 19.7 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Marques collected? Round your answer to the nearest tenth.
Answer:
89.0 grams of trace element
Step-by-step explanation:
Step 1Find the volume of the sample container.
Given:
Container is a right cylinder with d = 13.2 cm and h = 19.7 cmVolume formula:
V = πr²h = πd²h/4Substitute to get:
V = π(13.2)²(19.7)/4 = 2695.9 cm³ (rounded)Step 2Find the volume of the trace element, using the given proportion:
2695.9*0.033 = 89.0 grams (rounded)Here are the dimensions of some rectangles. Which rectangle has an area of 12 square units and a perimeter of 14 units?
a length of 1 unit and a width of 12 units
a length of 6 units and a width of 1 unit
a length of 6 units and a width of 2 units
a length of 3 units and a width of 4 units
Considering the formulas for the area and the perimeter of the rectangle, the one with the desired measures is given as follows:
a length of 3 units and a width of 4 units.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that:
A = lw.P = 2(l + w).For a rectangle with a length of 3 units and a width of 4 units, we have that:
A = 3 x 4 = 12 square units.P = 2(3 + 7) = 14 units.Hence it is the correct option.
More can be learned about the area and the perimeter of a rectangle at https://brainly.com/question/10489198
#SPJ1
You spin the spinner twice.
What is the probability of landing on a 7 and then landing on a number less than 9?
Write your answer as a fraction or whole number.
Answer:
1/3
Step-by-step explanation:
the answer is 1/3 because the probability of landing on a 7 is 1/3 and the probability of landing on any number less than 9 is 2/3. Then, you multiply the probabilities: 1/3 * 2/3 = 2/9 = 1/3
(X^2-16)/(x^2)-x-12
I know the answer is x+4/x+3
but i don't understand how x^2 -x - 12 simplifies into (x+3) (x-4)
Please help! What is 7 days 8 hours 20 minutes - 4 days 10 hours 30 minutes?
Answer:
2 days 21 hours and 50 minutes
Step-by-step explanation:
There are a couple of ways to solve this. Here is my approach
Convert everything to the lowest unit ie minutes, find the difference and then find the equivalent days, hours and minutes
Note
1 hour = 60 minutes
1 day = 24 hours * 60 minutes/hour = 1440 minutes
So,
7 days, 8 hours, 20 minutes = 7 * 24 * 60 + 8 * 60 + 20 = 10580 minutes
4 days, 10 hours, 30 minutes = 4 * 24 * 60 + 10 * 60 + 30 = 6390 minutes
Difference(elapsed time) = 10580 - 6390 = 4190 minutes
Convert 4190 to days, minutes and hours. This is a process of using whole division to find the quotient and remainder successively
For days, divide by 1440 which is the number of minutes in a day:
4190 minutes ÷ 1440 minutes = 2 whole days with remainder of 1390 minutes
For hours divide by 60 which is the number of minutes in an hour:
the remainder 1390 minutes ÷ 60 minutes = 21 whole hours with remainder of 50 minutes
So 4190 minutes == 2 days, 21 hours and 50 minutes
Out of a population of 1,000 students, 80 were asked by a random sampling what color they would prefer for their first car. Their responses are shown in the table below.
Car Color
Favorite Color
Number of Students
Blue
5
Red
18
Gray
27
Silver
14
White
16
Using proportional reasoning, how many students out of the 1,000 would you expect to prefer a silver car?
There are 175 students out of the 1,000 would you expect to prefer a silver car.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
We have to given that;
Out of a population of 1,000 students, 80 were asked by a random sampling what color they would prefer for their first car.
Now, We have there are 14 students out of 80 prefer silver car for their first car.
Hence, By using proportion, we get;
⇒ 14/80 = x / 1000
⇒ 14 × 1000 / 80 = x
⇒ x = 175
Thus, There are 175 students out of the 1,000 would you expect to prefer a silver car.
Learn more about the proportion visit:
https://brainly.com/question/1496357
#SPJ1
Answer:
175
（￣︶￣）↗
Step-by-step explanation:
Six less than the product of
twice a number and ten is
twenty.
[tex]\text{First I'd recommend replacing the number with just n.}\\\text{Now, multiply this number by 2:: 2n}\\\text{Multiply 10 by it:: 2n*10}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{6 is subtracted from (2n*10):: (2n*10)-6}[/tex]
[tex]\text{This gives a total of 20}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\text{(2n*10)-6=20}[/tex]
15. What is 5¹/4 ÷ 2²/7 ?
A. 2 ¹⁹/64
B. 12
C. 2
D. 12 ¹⁹/64
Please help it's urgent... I'll mark brainlist if you answer and get it right
Answer:
A 2 19/64
Step-by-step explanation:
change the proper fractions into mixed fractions then remember to reciprocate the number at your right hand then calculate good day.
if f (x) = 3x + 5/x , what is f(a+2)?
Answer:
f(a+2)=3a+11/a+2
Step-by-step explanation:
9.25(18.4-2.1.2)
Please hurry I need to Finnish 2 more pages today
Step-by-step explanation:
9.25( 18.4 - 2.12)
9 × 25 ( 18×4 - 2× 1.2) (multiply)
9.25 ( 72 - 2.4) ( calculate)
9×25×69.5 (calculate)
(answer) 1566
What is the area of a circle with a radius of 11 meters? Round your answers to the nearest tenth.
A. 34.6 m2
B. 121.0 m2
C. 380.1 m2
D. 760.3 m2
Answer:
380.1
Step-by-step explanation:
A=[tex]\pi[/tex]r^2
A=[tex]\pi[/tex]*11*11
A~ 380.13 m^2
nearest tenth: 380.1
Sarah is y years old now. How could you represent her age 5 years ago? (pls help me)
1. y-5
2. 5 y
3. y divided by 5
4. y + 5
Answer:
so y represents her age right now so if we go back we are subtracting so he age would be y-5
a
Hope This Helps!!!
Given cos theta = √3/3 and sin theta < 0. What is the value of sin theta?
The value of the sin theta will be equal to [tex]Sin\theta =\sqrt{\dfrac{2}{3}}[/tex]
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
Given that:-
Cos[tex]\theta[/tex] = √3/3 Sin[tex]\theta[/tex] <0The value of Sin will be calculated as:-
[tex]Sin^2\theta +Cos^2\theta = 1\\\\Sin^2\theta + \dfrac{\sqrt{3}}{2}=1\\\\Sin^2\theta = 1 -\dfrac{1}{3}\\\\Sin\theta = \sqrt{\dfrac{2}{3}}[/tex]
We can see that the value of sin is less than zero therefore
To know more about Trigonometry follow
https://brainly.com/question/24349828
#SPJ1
8. A group of teenagers were surveyed to find out whether they like to drink coffee or tea. The result is shown below. •21 teenagers like to drink coffee or tea •3 teenagers like to drink coffee and tea. •2 teenagers do not like to drink coffee or tea. Based on the information, calculate (a) the total number of teenagers in the group. (b) the number of teenagers who like to drink coffee only or tea only.
a) 26 teenagers are in the group. 21+3+2=26
b) 21 like to drink coffee or tea only. (3 like both and 2 like neither, so 21 enjoy one or the other)
Based on the details in this excerpt, which word best describes the garage?
Answer:The end of immigration quotas in the 1960s led to
a significant decrease in safe places for refugee immigrants.
a significant increase in discrimination against immigrants.
a significant increase in the number of Asian immigrants.
a significant decrease in the number of Asian immigrants.
Step-by-step explanation:
Help please this is khan academy
Answer:
9800 cm^2
Step-by-step explanation:
The area of a square is just the length of one of the sides squared. In the first image it's given that one of the sides is 70 cm and the shape is also a square pyramid so the base is going to be a square. So the area the base is (70 cm) ^ 2 = 4,900 cm^2. The area of a triangle is 1/2 bh. The base is given in the first image which is 70 cm and the height is also given which is 140 cm. This gives you the equation 0.5 * 140 cm * 70 cm = 4900 cm^2. Adding these two values gives you 9800 cm^2
four students drew four different triangles in math class Anna triangle Yuna triangle Carly triangle saki triangle
The question was incomplete. Below you will find the missing image.
Only the Saki's triangle can be solved using law of cosines.
Law of cosines formula is used to find missing including angle or missing side.
It is used in SAS and SSS triangles.
If a, b & c are three sides and C be the vertices opposite to side c then,
c²=a²+b²-2ab×CosC
Here in the given image we see that,
In Anna's triangle, there is one side and one angle.
So, it is not possible to solve with law of cosines.
In Yuna's triangle, there are two angles and one side.
So, also it is not possible to solve with law of cosines.
In Carley's triangle, there are three angles.
Also in this case, law of cosines it not possible to use.
In Saki's triangle, there are three sides are given. So, it is a SSS triangle.
We can apply the law of cosines here in this triangle.
Learn more about law of cosines here :
https://brainly.com/question/4372174
#SPJ10
which of the following is a Monomail
Reason:
sorry but here is no options so I am giving you a example so that you can understand by your own!
Answer;
5r+3
2x-6
X4+10
4y-1
Step by step answer;
So the method of identifying the Monomail is if you see a variable in a constant so it is a Monomail !
Mark as brainlest answerWhich of the following is a true statement about the rhombus shown? A) m angle STP=90^ B) overline ST cong overline PT C) m angle SPQ=90^ D) overline SQ cong overline PR
Answer:
A
Step-by-step explanation:
.......STP=90°........
Andy spent $55 in all to purchase 20 two-dollar and five-dollar toys. How many two-
dollar toys did he buy? How many five-dollar toys did he buy?
Use the figure to decide the type of angle pair that describes <5 and <6.
3
5
1
4
2
6
Answer:
A. Corresponding Angles
Step-by-step explanation:
1. ∠4 and ∠6 = 180°
2. ∠3 and ∠5 = 180°
3. So, ∠5 and ∠6 are the same angles.
A thin silver disc of diameter 10 cm costs # 3 300. What is the cost per m²
Answer:
The diameter is 10 cm. the radius is 5 cm. the area is πr² = π x 5² = 78.5 cm².
1 m² = 10,000 cm².
78.5/10,000 = 3,300/n n is the cost per square meter.
78.5n = 10,000 x 3300
n = 420,382.1656
The cost per square meter is $420,382.17.
What can each term of the equation be multiplied by to eliminate the fractions before solving?
1/2x-5/4+2x=5/6+x
Answer:
12
Step-by-step explanation:
Scalar and Matrix Multiplication
Answer:
multiply 1/2 by each element in the matrix
Step-by-step explanation:
6. 32
39 15
Kierran is trying to find the circumference of a circle. He knows that the radius (r) of the circle is 6 feet and that the diameter,
=2
. Which formula should he use?
a. =3.14(2)2
b. =3.14(2)
c. =3.142
d. =3.14(2)
The formula should he use willl be 3.14(2). Option B is correct.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
Given data;
Radius,r = 6 feet
Diameter,d=2
Circumfererenc,C
The circumferrence of the circle is;
C=πD
C= 3.14 × 2
The formula should he use willl be 3.14(2).
Hence, option B is correct.
To learn more about the area, refer to the link;
https://brainly.com/question/11952845
#SPJ1
A rectangular parallelepiped has dimensions a, b and c. The volume is 100cm3. A second parallelepiped has dimensions α, β, γ, where α is 50% of a, β is 20% of b and γ is 10% of c. What is the volume of the second parallelepiped in cubic meters?
The volume of the second parallelepiped will be 1 cm³. According to the given conditions, α is 50% of a, β is 20% of b and γ is 10% of c.
What is volume?The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.
Given condition;
α is 50% of a, β is 20% of b and γ is 10% of c
α = a/2
β = b/5
γ = c/10
The volume of the first parallelepiped:
V = abc
100cm³=abc
The volume of the second parallelepiped:
[tex]\rm V'= \alpha \times \beta \times \gamma \\\\ \rm V'= \frac{a}{2} \times \frac{b}{5} \times \frac{c}{10} \\\\ V' = \frac{abc}{100} \\\\ V'=\frac{100}{100} \\\\ V' = 1 cm^3[/tex]
Hence, the volume of the second parallelepiped willl be 1 cubic meter.
To learn more about the volume, refer to https://brainly.com/question/1578538
#SPJ1
