Answer:
The probability the student studies Art and Biology is 0.2143.
Step-by-step explanation:
Denote the events as follows:
A = a students studies Art
B = a students studies Biology
The information provided is:
N = 42
n (A ∩ B) = 9
n (A' ∩ B) = 10
n (A' ∩ B') = 7
Then the number of students who study Art but not Biology is:
n (A ∩ B') = N - n (A ∩ B) - n (A' ∩ B) - n (A' ∩ B')
[tex]=42-10-7-9\\\\=16[/tex]
The number of students who study Art but not Biology is 16.
Compute the probability the student studies Art and Biology as follows:
[tex]P(A\cap B)=\frac{n (A\cap B)}{N}[/tex]
[tex]=\frac{9}{42}\\\\=\frac{3}{14}\\\\=0.2143[/tex]
Thus, the probability the student studies Art and Biology is 0.2143.
What is the solution set of -|-x| = -12
Answer:
{-12,12}
Step-by-step explanation:
-|-x| = -12 multiply both sides by -1
|-x| = 12 apply rule for solving absolute value equations
-x = 12 and -x = -12 solve
x = -12 and x =12
*EASY GRADE 7 MATH*
BEST ANSWER WITH EXPLANATION WILL BE MARKED BRAINLIEST!
Evelyn wants to cover the top of a circular table with a price of cork board to protect it from spills. How much cork board will Evelyn need to completely cover the table if the diameter of the table is 48 inches?
Select ALL that apply. (possible answers on image)
Answer:
576π in² and 1,809 in².
Step-by-step explanation:
To find the answer, the formula for the area of a circle, or A = πr², will need to be used.
In this question, we are only given the diameter. Simply divide by 2 to calculate the radius:
48/2 = 24 inches.
Now, plugging this into the equation for the Area of a Circle, gets us:
A = π24²
A = 576π or 1808.64 in².
Looking at the answer choices, we can choose 576π in² and 1,809 in² (as 1808.64 ≈1809)
What is the gradient of the graph shown?
Answer:
-1/2
Because, for every one square, the line goes down by 1/2.
Answer:
- 0.5
Step-by-step explanation:
To find the gradient of a line,
divide the value of decrease by the value across.
So, count across from the extreme left toll the extreme right = 13
Where you completed in the extreme right, you have to count down till you reach the other end of the line = 6.5
Now, you divide: 6.5 divided by 13 = 0.5
Since we counted down, it is negative = -0.5
Please mark brainiest
Segment AB has length "a" and is divided by points P and Q into AP, PQ, and QB, such that AP = 2PQ = 2QB.
a) Find the distance between point A and the midpoint of segment QB
b) Find the distance between the midpoints of segments AP and QB
Answer:
a) 7a/8; b) 5a/8
Step-by-step explanation:
Given:
AP = 2PQ = 2QB
Calculations:
1. A to the midpoint of QB
a = AP + PQ + QB
If 2PQ = 2QB.
PQ = QB and
AP = 2PQ
∴ a = 2PQ + 2PQ = 4PQ
PQ = a/4
AP = 2PQ = a/2
Let M be the midpoint of QB.
AM = AP + PQ + QM
= a/2 + a/4 + a/8
= 7a/8
2. Midpoints of AP and QB
Let N be the midpoint of AP
NM = NP + PQ + QM
= a/4 +a/4 + a/8 =
= 5a/8
Write in standard form an equation for the line with slope 1/3 through
the point (2,-2).
Answer:
x - 3y = 8.
Step-by-step explanation:
Use the point-slope form of the equation of a line:
y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.
So substituting the given values:
y - (-2) = 1/3(x - 2)
y + 2 = 1/3x - 2/3 Multiply through by 3:
3y + 6 = x - 2
x - 3y = 6 + 2
x - 3y = 8 <---- Standard Form.
Each handful of cheese covers 21 sqaure inches. How much handful of cheese they need to cover 5 slices of cheese with a area of 125.7in
Answer: 30
Step-by-step explanation:
Hi, to answer this question, first we have to multiply the number of slices of cheese (5) by the area of each slice (125.7)
125.7 (5) = 628.5 in2
Finally we have to divide that result by the area that each handful of cheese covers (21 in2)
628.5 / 21 = 29.92 = 30 handful of cheese
Feel free to ask for more if needed or if you did not understand something.
Answer:
30
Step-by-step explanation:
Find the volume of a right circular cone that has a height of 8.1 in and a base with a diameter of 7.6 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
[tex]V=122.5in^3[/tex]
Step-by-step explanation:
The volume of a right circular cone can be found with the formula [tex]V=\pi r^2\frac{h}{3}[/tex] .
So, just plug in the values that are given (by the way, the radius is found by dividing the diameter by 2 since it's half the value of the diameter).
[tex]V=\pi r^2\frac{h}{3}\\V=\pi (3.8)^2(\frac{8.1}{3} )\\V=\pi (14.44)(2.7)\\V=122.484\\V=122.5in^3[/tex]
Answer:
122.5
Step-by-step explanation:
Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is 10,000cm^3 cubed. The base of the box is 25 cm by 10 cm.
Answer:
Complete question:
Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is 10,000 cm^3 cubed. The base of the box is 25cm by 10cm.
How tall is the box of cereal?
Answer: 40cm
Step-by-step explanation:
Given that :
A box is normally in the shape of a cube
formula of volume of a cube;
We want to find the height(tallness)
Volume=LengthxWidthxHeight
Volume = 10,000cm^3
Base of box = 25cm by 10cm,
Base of box = Length × width
Therefore:
Length = 25cm, Width = 10cm
Volume = Lengh × Width × Height
10,000cm^3 = 25cm × 10cm × Height
10,000cm^3 = 250cm^2 × Height
Height = 10,000cm^3 ÷ 250cm^2
Height = 40cm
The perimeter of a right triangle is 24 meters, and the area is 24 square meters. The lengths of the sides are each multiplied by 4. What is the area of the new triangle? help
Answer:
384m
Step-by-step explanation:
24 x 4 = 96
96 x 4 = 384
Answer:
the real answer is 96
Step-by-step explanation:
Anyone answer ASAP now plzz
Answer:
x = -0.189x= -15.810Step-by-step explanation:
I hope it helps
Can someone help me with this one I’m stuck please and thank you
Answer:
none of them it should be ac,cb,ab. From my point of view
I have worked the answer to a which is 301.6 but I’m not too sure how you work out b any help would be much appreciated!
Answer:
188.5 cm^2
Step-by-step explanation:
a) Your volume is correct.
b) The curved surface area of the cone is called the lateral area.
Its formula is:
LA = (pi)rs,
where pi is 3.14159...
r = radius of the base
s = slant height of the cone
Here, r = 6 cm, and s = 10 cm
LA = (3.14159)(6 cm)(10 cm)
LA = 188.5 cm^2
Will Mark Brainliest ! Here is a picture of a cube, and the net of this cube.
What is the surface area of this cube?
Enter your answer in the box.
Answer: [tex]726 cm^{2}[/tex]
Step-by-step explanation:
surface area(SA)= [tex]6s^{2}[/tex]
= [tex]6*(11)^{2}[/tex]
= [tex]6*121[/tex]
= [tex]726 cm^{2}[/tex]
s= the length of the side of the cube
Define surface area and volume. List an example of a situation where you would find surface area and a situation where you would find volume.
Answer:
Step-by-step explanation:
Surface area is the sum of the areas of the faces of a solid. It is measured in square units. Volume is the amount of space taken up by a solid. It is measured in cubic units. Surface area would be used to find the amount of wrapping paper for a gift, and volume would be used to find how much would fit into a box.
Answer: Surface area is the sum of the areas of the faces of a solid. It is measured in square units. Volume is the amount of space taken up by a solid. It is measured in cubic units. Surface area would be used to find the amount of wrapping paper for a gift, and volume would be used to find how much would fit into a box.
Step-by-step explanation:
Write in slope-intercept form an equation of the line that passes through the given points.
Answer:
y = x+5
Step-by-step explanation:
First we find the slope
m = (y2-y1)/(x2-x1)
m = (7-3)/(2 - -2)
=(7-3)/(2+2)
= 4/4
= 1
The slope intercept form is
y = mx+b
y = x+b
Substitute a point in
7 = 2+b
Subtract 2 from each side
5 =b
y = x+5
Answer:
y = x + 5
Step-by-step explanation:
m = (y2 - y1) / (x2 - x1)
= (7 - 3) / (2 - (-2))
= 4/4
= 1
Since y = mx + b and m = 1,
y = (1) * x + b
y = x + b
7 = 2 + b
b = 5
Putting b = 5 in y = x + b, we get:
y = x + 5
Hope this helps!
Find the length of side AB. Give your answer to 1 decimal place.
Answer:
Length of side AB = 5.6 cm
Step-by-step explanation:
From the figure attached.
In right triangle ABC,
m∠ABC = 62°
m(BC) = 12 cm
By applying Cosine rule in this triangle,
Cos62° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
Cos62°= [tex]\frac{AB}{BC}[/tex]
0.46947 = [tex]\frac{AB}{12}[/tex]
AB = 12 × 0.46947
AB = 5.63
≈ 5.6 cm
Therefore, length of side AB = 5.6 cm
Length of side AB = 5.6 cm.
Calculation of the length of side:Since In right triangle ABC,
m∠ABC = 62°
m(BC) = 12 cm
Here we used the cosine rule
So, it is
[tex]Cos 62 = AB\div BC\\\\0.46974 = AB\div 12[/tex]
So, AB = 5.6 cm
hence, Length of side AB = 5.6 cm.
Learn more about length here: https://brainly.com/question/21676565
Bess drew a rectangular prism that is 12 units long, 8 units wide, and 13 units tall. What is the volume of the rectangular prism? A. 109 cubic units B. 156 cubic units C. 970 cubic units D. 1,248 cubic units
Answer:
D. 1,248 cubic units
Step-by-step explanation:
the volume of the rectangular prism = length*width*height = 12*8*13 = 1248 cubic units
Answer: D. 1,248 cubic units
Step-by-step explanation:
The formula for a rectangular prism volume is: V = Length x Width x Height.
In this question it already gives us all of the sides that we need! So all we need to do is just multiply all the sides together to get the volume.
12 x 8 x 13 = 1,248. Therefore D is correct!
Hope this helped you!
Distance, Midpoint, Circles - What is the equation of the circle? WILL GIVE BRAINLIEST!
Answer:
(x-4)^2 + (y-3)^2 =8
Step-by-step explanation:
The midpoint of the diameter is (6+2)/2= 4, (5+1)/2 = 3
(4,3)
The radius is the distance from the midpoint to an endpoint
This is 2sqrt(8)
So the equation is
(x-4)^2 + (y-3)^2 =8
Please help me simplify these expressions
Answer:
4. -2s^9
7. 8b^10
Step-by-step explanation:
First, focus on the number part of the expression. For 4), multiply -2 x -1 x -1 = -2. Then, look at the exponents. When you're multiplying exponents with the same base (in number 4, the base is s), you can add the exponents.
2+3+4 = 9; which makes it s^9. Multiply -2 x s^9, which gives you -2s^9.
Same thing for 7). Multiply all the numbers first. this gives you 8. (Remember two negatives equals a positive). Add all of the exponents of b together, which gives you 10. (when a variable has no exponent, it means that the exponent is 1.) Multiplying 8 and b^10 should give you 8b^10.
It may help to brush up on exponent rules and sign rules.
Complete the sentence.
The bases of a circular cylinder are two ___
ao circles.
Answer:
congruent & parallel
Step-by-step explanation:
The bases of a circular cylinder are congruent and parallel to each other. If you need more explanation, reply to my answer.
Triangle FGH is equilateral. The midpoints of the sides are connected to form triangle XYZ. Line segment XY is parallel to line segment FH.
Triangle F G H is an equilateral triangle. Equilateral triangle X Y Z is inside of triangle F G H and the points are the midpoints of triangle F G H.
What type of figure is quadrilateral FXYH?
Answer:
Isosceles trapezoid
Step-by-step explanation:
The figure will look like one large triangle on the outside and four smaller triangles on the inside. you are only concerned with the inside triangle that is pointing to the line FH. Since XY and FH are parallel and the distance between FX and YH are equivalent (the midpoints of each side should be the same for all three sides of the larger triangle) the shape FXYH is an isosceles trapezoid.
Answer:
trapezoid
Step-by-step explanation:
A student is decorating a circular picture frame that has a diameter of 8 inches. How many inches of fabric will the student need to go completely around the outside of the frame?
Answer:
B
Step-by-step explanation:
Circumference is equal to [tex]\pi d[/tex]
[tex]C=\pi d[/tex]
[tex]C=\pi \times 8[/tex]
Answer:
there u go
Step-by-step explanation:
finding angle measures using triangles
In the given diagram ∠AJF or x comes to be 76°.
What are opposite angles?Opposite Angles are angles directly opposite to each other when two lines intersect in a plane.
We know that ∠JIH+∠JID=180°
107° +∠JID=180°
∠JID=180°-107°
∠JID=73°
∠JDI=31°(given))
In triangle JDI,
∠JDI+∠JID+∠IJD=180°
31° + 73° + ∠IJD =180°
∠IJD =76°
We know that ∠IJD and angle x° are opposite angles.
So, x=76°
Therefore, In the given diagram ∠AJF or x comes to be 76°.
To get more about angles visit:
https://brainly.com/question/25770607
The height of a tower on a scale is 14 centimeters. The scale is 2 cm: 13m. What is the actual height of the tower?
Answer: The actual height of the tower is 91m
[tex]\frac{14}{x}=\frac{2}{13} \\x=\frac{14\times13}{2} \\x=91 m[/tex]
The actual height of the tower is 91 m.
What is scale?An indication of the relationship between the distances on a map and the corresponding actual distances.
Given that, The height of a tower on a scale is 14 centimeters. The scale is 2 cm: 13 m.
Since, 2 cm = 13 m
1 cm = 13 /2 m
Therefore, 14 cm = 14 × 13/2 = 91 m
Hence, the actual height of the tower is 91 m.
Learn more about scales, click;
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Topic: Probability
Only complete question 9.
Answer:
see below
Step-by-step explanation:
a. H 1, H2 ,H3 T1 ,T2, H3
b 6 possible outcomes
c 2 outcomes for the coin ( h,T) 3 outcomes for the spinner
2*3 = 6
find the volume of prism
pls!! show how you got the volume
Answer:
7.5
Step-by-step explanation:
Add each number then divide at the end
Los lados de un triángulo rectángulo miden 6m, 8m y 10m. respectivamente. ¿Cuánto medirán los catetos de un triángulo semejante al primero si su hipotenusa mide 15m?
Answer: Los catetos medirán 12m y 9m.
Step-by-step explanation:
Bueno, sabemos que los lados de nuestro triangulo son 6m, 8m y 10m.
Podemos usar relaciones trigonométricas para encontrar los ángulos de este triangulo.
Cos(X) = cateto adyacente/hipotenusa
Si tomamos al cateto adyacente como 8m, tenemos:
Cos(X) = 8m/10m
X = Acos(8/10)
Esto nos dice que para que nuestro otro triangulo rectángulo sea equivalente al primero, entonces los nuevos catetos C1 y C2 tienen que ser tal que los cocientes entre los catetos y la hipotenusa se mantengan constantes:
C1/15m = 8m/10m
C1 = (8/10)*15m = 12m
C2/15m = 6m/10m
C2 = (6/10)*15m = 9m.
What is the 5th term of the linear sequence below?
−
-5,-2,1,4,7,
Answer:
The sequence has '+3' each time, so the next will be 10
Step-by-step explanation:
it is 10 cuz it goes from -5 adding 3
Identify whether the relationship between ∠a and ∠b in the image below is complementary, linear pair/supplementary, or vertical.
Answer:
see below
Step-by-step explanation:
Because there is the right angle symbol on the chart these angles are complementary meaning thety have a sum of 90°.
A diver needs to descend to a depth of 100 feet. She wants to do it in 5 equal descents. How far should she travel in each descent?
Answer:
20 feet
Step-by-step explanation:
5 descent =>100 feet
1 descent => 100÷5
= 20 descent
