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.
Find the unknown measures. Round lengths to the nearest tenth and angle measures to the nearest degree.
AC =
BC=
∡C=
degrees
Answer:
AC= 6.3 units (nearest tenth)
BC= 2.8 units (nearest tenth)
∠C= 64°
Step-by-step explanation:
Please see attached picture for full solution.
Solve 2 - x= -7.
O A. x=-9
O B. x= 5
O C. x= -5
O D. x= 9
Answer:
x = 9
Step-by-step explanation:
2 - x= -7
Subtract 2 from each side
2- 2 - x= -7-2
-x = -9
Multiply by -1 on each side
x = 9
2.5(2z + 5) = 5(z + 2.5)
Answer:
z is any real number
Step-by-step explanation:
2.5(2z + 5) = 5(z + 2.5)
Distribute
5z + 12.5 = 5z +12.5
Subtract 5z from each side
5z -5z + 12.5 = 5z-5z +12.5
12.5 = 12.5
This is always true so z can be any real number
Answer:
All Real Numbers
Step-by-step explanation:
We are considering the following equation - 2.5(2z + 5) = 5(z + 2.5),
[tex]2.5 * (2z + 5) = 5 * (z + 2.5) - Apply Distributive Property,\\\\2.5 ( 2z ) + 2.5 ( 5 ) = 5z + 5 ( 2.5 ) - Multiply Like Terms,\\5z + 12.5 = 5z + 12.5 - Subtract Terms From Either Side,\\\\0 = 0,\\Conclusion ; z - All Real Numbers[/tex]
Solution; All Real Numbers
What happens when you see 42 (17 – 15) / (3 + 1) – 5 ? What do you do first? The mnemonic PEMDAS or Please Excuse My Dear Aunt Sally can help you remember the order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. If your expression doesn't have every type of operation, the order of operations is still the same. If it is missing one, just skip it and move on to the next operation. Which operation is done first to evaluate this expression: 5 + 7 x 2 - 9
Answer:
The operations done first are:
a) 42 (17 – 15) / (3 + 1) – 5 ; (17 -15) or (3 + 1) (parenthesis) are done first
b) 42 (17 – 15) / (3 + 1) – 5 ; 7 × 2 (multiplication) is done first
Step-by-step explanation:
from the mnemonic PEDMAS, the order of operations are: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
hence in the first expression : 42 (17 – 15) / (3 + 1) – 5, the parenthesis (bracket is simplified first as follows:
(17 - 15) = (2) ; and (3 + 1) = (4) ; hence the expression will be simplified as follows: 42 (2) / (4) - 5.
Next, since there is no exponent in the expression, Multiplication follows:
42 (2) = 42 × 2 = 84 ; hence he expression becomes: 84 / 4 - 5
Next division follows : 84/4 = 21, therefore the expression becomes
21 - 5.
Finally, subtraction follows : 21 - 5 = 16
b) 5 + 7 x 2 - 9;
first, multiplication is done: 7 × 2 = 14, hence the expression becomes :
5 + 14 - 9.
Next in the order is addition : 5 + 14 = 19, hence, the expression becomes:
19 - 9.
Finally, subtraction follows: 19 - 9 = 10
Answer:
multiply
Step-by-step explanation:
Choose the kind(s) of symmetry: point, line, plane, or none.
(A)
none
plane
point
line
it would be a Line
The line would be vertical right through the middle
can i get brainliest?
12) The sum of two natural numbers is 30. If one of the numbers is one-
fifth of the other, then what is the product of both the numbers?
a) 5
b) 25
c) 30
d) 125
Answer:
D.) 5 x 25 = 125
Step-by-step explanation:
The two numbers are 25 and 5. If you take 1/5 of 25, or simply divide by 5, you will get 5.
Answer:
A) X + Y = 30
B) X = .2Y OR X - .2Y = 0
We subtract B) from A)
1.2Y = 30
Y = 25 X = 5
X * Y = 125
Answer is d.) 125
Step-by-step explanation:
What’s the cosine of U?
Step-by-step explanation:
The cosine of U is equal to the adjacent side divided by the hypotenuse.
cos(U) = 28/53
You can simplify it from there.
Jeff needs to rent a car for one day, so he shops around to find a car rental company with the lowest overall price. He finds a national rental car company that charges a 12$ daily fee plus .30 per mile, he also find a rental car company that charges a 10$ daily fee, plus a .40 per mile under what conditions would it be less expensive to rent from the national car company?
Answer:
When Jeff travels more than 20 miles
Step-by-step explanation:
Let 'x' be the number of miles traveled by Jeff.
In order for the national car company to be less expensive, then the following condition must be met:
[tex]12+0.30x < 10+0.40x\\12-10 < 0.4x-0.3 x\\2 <0.1x\\20<x[/tex]
This means that when Jeff travels more than 20 miles, it is cheaper to rent from the national car company.
What is the equation in slope-intercept form of the line?
Answer:
y = 1x - 500
Step-by-step explanation:
b is were the line crosses the y axis so its -500
and to find slope you do -200-(-400) over 300-100 and it equals 1
hope this helps:)
Q 1: There are n boxes in a large bag and m toys in each box. What is the total number of toys in the bag? Q 2 :The length of a rectangle is given by x + 2 and its width is equal to 3. Give a simplified expression of the area of this rectangle.
Answer:
Q1: n*m
Q2: A = 3x+6
Step-by-step explanation:
Q1: The total number of toys in the bag is given by the number of boxes (n) in the bag multiplied by the number of toys in each box (m):
[tex]T = n*m=nm[/tex]
Q2: The area of a rectangle is given by the product of its height by its length:
[tex]A = (x+2)*3\\A=3x+6[/tex]
The area of this rectangle is given by the expression A = 3x+6.
Grace orders groceries worth $49.65. About how much should she spend for 12% home delivery charges?
Answer:
$5.96
Step-by-step explanation:
To find 12% of 49.65 you multiply 49.65*0.12 (decimal equivalent of 12%) = 5.958. Since it's money, you need to round to the nearest cent.
f(n) = 9+ 5n; 64
determine which term produces the given answer?
Answer:
the 11th term
Step-by-step explanation:
f(n) = 9+ 5n;
Let f(n) =64
64 = 9+5n
Subtract 9 from each side
64-9 = 9+5n-9
55 = 5n
Divide each side by 5
55/5 = 5n/5
11= n
PLEASE HELP ASAP the question is in the picture
can you please rotate the picture
Jade buys a blouse and a skirt for 3/4 of their original price. Jade pays a total of $31.50 for the two items. If the original price of the blouse is $18, what is the original price of the skirt?
Answer:
The skirt was originally 24 dollars
Step-by-step explanation:
3/4 ( b+s) = 31.50
where b is the original price of the blouse and s is the original price of the skirt
b = 18
3/4 ( 18+s) = 31.50
Multiply each side by 4/3
4/3 * 3/4 ( 18+s) = 31.50 *4/3
18+s =42
Subtract 18 from each side
18+s-18 = 42-18
s =24
The skirt was originally 24 dollars
Use the method of cylindrical shells to find the volume of the solid generated by rotating the region bounded by the curves y=cos(πx/2), y=0, x=0, and x=1 about the y-axis
Answer:
1,45 cubic units
Step-by-step explanation:
The method of cylindrical shells demands that the volume of the solid is given by:
[tex]V=2\pi\int_a^b xf(x)dx[/tex] (1)
In this case you have that f(x) is:
[tex]f(x)=cos(\frac{\pi}{2}x)[/tex]
a = 0
b = 1
First, you solve the integral, by parts:
[tex]\int xf(x)dx=\int xcos(\frac{\pi}{2}x)dx=x(\frac{2}{\pi})sin(\frac{\pi}{2}x)-\int (\frac{2}{\pi})sin(\frac{\pi}{2}x)dx\\\\=(\frac{2}{\pi})xsin(\frac{\pi}{2}x)+(\frac{2}{\pi})^2cos(\frac{\pi}{2}x)+C[/tex]
Next, you calculate the volume of the solid, by replacing the solution to the integral in the equation (1):
[tex]V=2\pi[(\frac{2}{\pi})xsin(\frac{\pi}{2}x)+(\frac{2}{\pi})^2cos(\frac{\pi}{2}x)]_0^1\\\\V=2\pi[(\frac{2}{\pi})-(\frac{2}{\pi})^2]=1,45u^3[/tex]
hence, the volume of the solid generated is 1,45 cubic units
How do I find the arc of a circle?\
Answer:
Step-by-step explanation:
Step-by-steP
LA FÓRMULA ES:
arc = πrΘ/180
Picture attachment is below
Answer:
0.04
Step-by-step explanation:
Answer:0.04
Step-by-step explanation:4/100
HELPP I don’t get this at all. I originally got c but my teacher said it was incorrect. This is about volume and cylinders. Explanation needed
Answer:
B
Step-by-step explanation:
The formula for the volume of a cylinder is [tex]\pi r^2 h[/tex], where r is the radius of the base and h is the height of the cylinder.
[tex]\pi \cdot 3.25^2 \cdot 10=105.625\pi \text{ cm}^3[/tex]
Therefore, the correct answer is choice B. Hope this helps!
Answer:
I believe it is b
Find the 11th term from the end of the A.P 10,7,4.... -62.
Term 11=a+10d
Here
a=10
d= 7-10= -3
Term 11;
=10+(10×-3)
=10+(-30)
= -20 is the answer
Thank you Hope it helps dear
Answer: -32
Step-by-step explanation:
a=10, d = 7-10 = -3
First find which term is -62
an = -62
a = (n-1) d= -62
Putting values
10 + (n-1)(-3) = -62
10 + (n(-3) -1 (-3) = -62
10 - 3n + 3 = -62
13 - 3n = -62
-3n = -62-13
n = 75/3 = 25
We need to find out 11th term from the last term ie., 25 - 10 = 15th term
So we need to find a14
an = a +(n-1) d
a15 = 10+ (15-1) (-3)
= 10 + 14 (-3)
= 10 -42
= -32
So the 11th term from the 15th term from the first = -32
What is the final amount if 1442 is increased by 9% followed by a 6% decrease?
Answer:
1,485.26
Step-by-step explanation:
100% is 1442
1% is 14.42
10% is 144.2
9% is 10 - 1 so its 129.78
1442 add 129.78 is 1 571.78
5% is 72.1
so add 72.1 and 14.42 86.52 and take it from 1571.78
answer is 1,485.26
How many revolutions must be made by a wheel of diameter 2.8m in order to cover a distance of 484km?
A wheel is a circle.
Given diameter of wheel = 2.8 m
Then radius of the wheel = 2.8/2 = 1.4 m
Now we know that , circumference of circle =[tex]2\pi r[/tex]
Then,Circumference of wheel = 2 × 22/7 × 1.4
Circumference of wheel = 8.8 m
From the above we can conclude that ;
1 revolution = 8.8 m
x revolution = 484 km = 484000 m
Thus,[tex]x = \frac{1}{8.8} \times 484000 \\ \\ x = 55000[/tex]
Therefore, total of 55,000 revolutions are made by the wheel.write as an algebraic expression
Answer:
13) x=n-11
15) x=3*10
Step-by-step explanation:
I used x as the variable. The questions are pretty straightforward. They are asking you to put the terms in the description on the right side of the equation. The questions = x. That was probably confusing, but it is correct. I hope this helped!
Product of 3 and 10 and12
1/3 of 6 1/2 multiply 3/4 (56 divide by 7) pls help me
Answer:
13
Step-by-step explanation:
1/3 of 6 1/2 multiply by 3/4 (56 divided by 7)
1/3* 13/2 * 3/4 * 56/7= 1*13*3*56/3*2*4*7= 13*3*56/3*56= 13
Simplify the expression
12x^-6 y^10 •3x^7y
At the corner store near Billy’s
house, loose mixed nuts cost
$1.75 per 100 g. Write an
equation to represent the amount
of mixed nuts, n, he can buy if he
has d dollars. Then, use your
equation to determine how many
grams of mixed nuts Billy can buy
if he has $5.
Answer:
d = 0.0175n ---> required equation
Billy can buy 285.714 gram nut with $5
Step-by-step explanation:
cost of 100g loose nut = $1.75
dividing LHS and RHS by 100
cost of 100/100g loose nut = $1.75
Thus, cost of 1 gm loose nut = $0.0175
let the weight of loose nut be n gm
Multiplying LHS and RHS by n
cost of x g loose nut = $0.0175*n = $0.0175n
It is given that Billy spent d dollars to buy n gm nuts
thus,
d = 0.0175n ---> required equation
________________________________________________
He spent $5 to buy nuts
substituting value of d as 5 we have
0.0175n = 5
=>n = 5/0.0175 = 285.714
Thus, Billy can buy 285.714 gram nut with $5.
Jenna wants to wrap a shipping box shaped like a rectangular prism. The box is 30 inches tall and has a square base with sides that each measure 3 inches. How much paper will she use?
Expand and simplify . 5(3m+6n)-4(11m-8n) PLEASE HELP. BEST ANSWER RECIEVES A BRIANLIEST
Answer:
-29m+62n
Step-by-step explanation:
5 (3m+6n)-4 (11m-8m)
15m+30n-44m+30n
15m-44m +32n+30n
-29m +62n
Which of the following is this?
-A balanced budget
-A budget deficit
-A budget surplus
The sum of the digits of a two-digit number is 14. If the number formed by reversing the digits is less than the original number by 18. Find the original numbers.
Answer: Dear friend my answer for this question is 86.
Step-by-step explanation:Let the two digits of two digit number be, 10s digit x and 1s digit y.
x + y = 14
x = 14 - y…..Eq..1
The nuber formed is 10x + y
If the number formed by reversing the digits is 18 less than the original number, what is the original number
On reversing the digit the number will be 10y + x
10y + x + 18 = (10x + y)
10y + x = 10x + y - 18
10y - y + x - 10x = - 18
9y - 9x = -18…Eq..2
Now substituting the value of x from Eq..1 to Eq..2
9y - 9 (14 - y) = - 18
9y - 126 + 9y = - 18
18y = 126 - 18
18y = 108
y = 108/18
y = 6
Thus 1s digit if the number is 6
Substituting the derived value of y in Eq..1 to derive value of x.
x = 14 - y
x = 14 - 6
x = 8
The 10s digit if two digit number is 8.
The original number formed is 86.
On reversing the digits, the number transform to 68, which is 18 less than original number
Answer the original number is 86.
What is the value of this discriminant?
Answer:
The answer is A.
Step-by-step explanation:
The formula of discriminant is D = b² - 4ac using ax² + bx + c. In this question, a is 1, b is -4 and c is 4. Then substitute the values into the formula :
D = b² - 4ac
D = (-4)² - 4(1)(4)
= 16 - 16
= 0