The probability that a student is a female or major in civil engineering is 62%
Complete questionAt a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering. What is the probability that a randomly selected female student majors in civil engineering?
How to determine the probability?Let A represent Female and B represents civil engineering.
The above representation means that the given parameters are:
P(A) = 49%P(B) = 21%P(A and B) = 8%The required probability is calculated as:
P(A or B) = P(A) + P(B) - P(A and B)
This gives
P(A or B) = 49% + 21% - 8%
Evaluate
P(A or B) = 62%
Hence, the probability that a student is a female or major in civil engineering is 62%
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How would you apply the fundamental counting principle to a bike lock combination with 5 numbers?
1. 10+ 10+ 10+ 10+10
2. 10x5
3. 10x10x10x10x10
4.none of these
Answer:
3
Step-by-step explanation:
let A={1,2,3,4,5} and B={4,5,6} Let R is relation from A to B defined by R={(a,b):a+b ⊆ B} Then Find 1. R 2. Domain (R) 3. Range (R) 4.Inverse of R
1. Disregard my comment. Since R is said to be a relation from A to B, we take both a ∈ A and b ∈ A. Then the set R is the pairs (a, b) whose entries' sum belongs to B.
We have
• 4 = 1 + 3 = 2 + 2 = 3 + 1, so R contains (1, 3), (2, 2), and (3, 1)
• 5 = 1 + 4 = 2 + 3 = 3 + 2 = 4 + 1, so R contains (1, 4), (2, 3), (3, 2), and (4, 1)
• 6 = 1 + 5 = 2 + 4 = … = 5 + 1, so R contains (1, 5), (2, 4), …, (5, 1)
Then
R = {(1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4),
… (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)}
2. The domain of R is the set of all values a in the pairs (a, b) belonging to R :
dom(R) = {1, 2, 3, 4, 5}
3. The range of R is the set of all values b in those same pairs:
range(R) = {1, 2, 3, 4, 5}
4. The inverse of R is the set with the same elements as R, but the entries are swapped:
inv(R) = {(3, 1), (4, 1), (5, 1), (2, 2), (3, 2), (4, 2),
… (1, 3), (3, 2), (3, 3), (1, 4), (2, 4), (1, 5)}
In this case, we have R = inv(R).
What are the zeros of f(x) = x(x − 9)?
Answer:
x = 0 , x = 9
Step-by-step explanation:
to find the zeros let f(x) = 0 , that is
x(x - 9) = 0
equate each factor to zero and solve for x
x = 0
x - 9 = 0 ⇒ x = 9
Answer:
The X-intercepts are 0,0 and 9,0
If f(x) = 1-x, which value is equivalent to fi)?
Answer:
[tex]\sqrt 2[/tex]
Step-by-step explanation:
[tex]f(x) = 1-x\\\\|f(i)| = |1-i| = \sqrt{1^2 +1^2 } =\sqrt 2[/tex]
Solvex²= 12x-15 by completing the square. Which is the solution set of the equation?
-6- √51, -6 + √51)
1-6-√21, −6+ √21}
(6-√51, 6+ √51)
16-√21, 6+ √21}
Answer
B
Step-by-step explanation:
The solution to the equation by completing the square is (6 - √21, 6 + √21)
How to complete the square?The equation is given as:
x²= 12x-15
Rewrite as:
x² -12x = -15
Take the coefficient of x
k = -12
Divide by 2
k/2 = -6
Square both sides
k/4 = 36
Add 36 to both sides of x² -12x = -15
x² -12x + 36 = -15 + 36
Evaluate the sum
x² -12x + 36 = 21
Express the equation as a perfect square
(x - 6)² = 21
Take the square root of both sides
x - 6 = ±√21
Add 6 to both sides
x = 6 ± √21
Split
x = (6 - √21, 6 + √21)
Hence, the solution to the equation by completing the square is (6 - √21, 6 + √21)
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What are the solutions to the equation x^2+9x+12=6
Answer:
[tex]x= -\dfrac {9}2 +\dfrac{\sqrt{57}}{2},~~x = -\dfrac {9}2 - \dfrac{\sqrt{57}}{2}[/tex]
Step-by-step explanation:
[tex]~~~~~~~x^2 +9x +12 = 6\\\\\implies x^2 +9x = 6-12\\\\\implies x^2 +9x = -6\\\\\implies x^2 +2 \cdot \dfrac 92 \cdot x +\left(\dfrac 92\right)^2 -\left( \dfrac 92 \right)^2 = -6\\\\\implies \left(x+ \dfrac 92 \right)^2 -\dfrac{81}{4}= -6\\\\\implies \left(x +\dfrac 92 \right)^2 = -6 + \dfrac{81}4\\\\\implies \left(x + \dfrac92 \right)^2 = \dfrac{57}{4}\\\\\implies x+ \dfrac 92 = \pm\sqrt{\dfrac{57}4}\\\\\implies x = -\dfrac {9}2 \pm\dfrac{\sqrt{57}}{2}[/tex]
write a Pythagorean triplet whose smallest member is 6
Answer:
6, 8, 10
Step-by-step explanation:
Where:
a = 6
b = 8
c = 10
Pythagorean theorem: [tex]a^2 + b^2 = c^2[/tex]
[tex]6^2 + 8^2 = c^2[/tex]
[tex]36 + 64 = c^2[/tex]
[tex]100 = c^2[/tex]
c = [tex]\sqrt{100}[/tex]
c = 10
need help with this problem
Answer:
(28) 61.5, or $61,500
(29) 49.25, or $49,250
(30) the median
Step-by-step explanation:
(28) the mean can be calculated by adding together the values and then dividing by the total number of values.
(45 + 47 + 47.5 + 51 + 53.5 + 125) / 6 = 61.5
(29) the median can be calculated by crossing off the values from the outside in, alternating sides
45, 47, 47.5, 51, 53.5, 125
47, 47.5, 51, 53.5
47.5, 51
you will end with two middle values since there are six values in the set, so average these to find the median
(47.5 + 51) / 2 = 49.25
(30) The median will better reflect the value of the homes because it is not as much influenced by the outlier value, 125, as the mean is.
math
any help please
Step-by-step explanation:
the answer is true
the statement is true
Solve for x in the equation x squared minus 12 x + 59 = 0.
The value of x in the equation is -4.92
How to solve for x?The equation is given as:
12x + 59 = 0
Add -59 to both sides of the equation
12x = -59
Divide by 12
x = -59/12
Evaluate
x = -4.92
Hence, the value of x in the equation is -4.92
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[tex]x^2-12x+59=0\\x^2-12x+36+23=0\\(x-6)^2=-23\\x\in\emptyset[/tex]
This rectangle is composed of two parts, labeled 1 and 2.
5√2 in
3 in
1
3√2 in
2
What are the areas of each smaller rectangle and the large rectangle?
Drag each tile to the correct location on the image. Not all tiles will be used.
The area of part 1 is
square inches.
The area of part 2 is:
square inches.
The area of the entire rectangle is:
square inches.
The area of part 1 is 15√2 square in, the area of part 2 is 30 square in, and the area of the entire rectangle is (30 + 15√2) square in.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
The area of part 1 = 5√2×3 = 15√2 square in
The area of the part 2 = 5√2×3√2 = 15×2 = 30 square in
The area of the entire rectangle = area of part 1 + area of part 2
= (15√2 + 30) square in or
= (30 + 15√2) square in
Thus, the area of part 1 is 15√2 square in, the area of part 2 is 30 square in, and the area of the entire rectangle is (30 + 15√2) square in.
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Evaluate the series 12 + 6 + 3 + . .
A) 21
B) 1.5
C) 2
D) 24
All the numbers follow a pattern of division by 2
Therefore the next number is 3/2 which is equal to 1.5
in a circle H with m angle GKJ=27 find the m angle GHJ
In a circle H with a measure of angle ∠GKJ = 27°. Then the measure of angle ∠GHJ will be 54°
What is a circle?It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
In a circle H with a measure of angle ∠GKJ = 27°.
Then the measure of angle ∠GHJ will be
We know that a chord's slope in the centre is double that of the chord's slope at the perimeter.
Then we have
∠GHJ = 2 x ∠GKJ
∠GHJ = 2 x 27°
∠GHJ = 54°
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factorize that x^4+4y^4
Answer:
(x² + 2y² + 2xy)(x² + 2y² - 2xy)Step-by-step explanation:
Given binomial:x⁴ + 4y⁴
In order to factorize it, follow the steps:
Complete the square:x⁴ + 4y⁴ = (x²)² + 2*(x²)*(2y²) + (2y²)² - 2*(x²)*(2y²) = (x² + 2y²)² - (2xy)² = (x² + 2y² + 2xy)(x² + 2y² - 2xy)Used identities:
(a + b)² = a² + 2ab + b²a² - b² = (a + b)(a - b)What’s the answer to the picture I took?
Answer:
y = - x
Step-by-step explanation:
From the given table:-
( x_1,x_2): (5,-5)
( y_1,y_2): (6,-6)
1) Let's find the slope (m):-
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{ - 6( - 5)}{6 - 5} = \frac{ - 6 + 5}{1} = \frac{ - 1}{1} = - 1[/tex]
2) Substitute x_1= 5, y_1=-5 and m=-1 into y-y_1=m(x-x_1)
[tex]y - ( - 5) = - 1(x - 5)[/tex]
[tex]y + 5 = - x + 5[/tex]
[tex]y = - x + 5 - 5[/tex]
[tex]y = - x[/tex]
solve 8 = 2^x + 4.
A. x=-4
B. x=-1
C. x=0
D. x=7
Many of the amenities at a local ski hill are operated using gas generators. To transport gasoline to the top of the mountain, a special trailer has been designed. The trailer bed is in the shape of a square with a side length of 1.5 m. They wish to attach a cylindrical shaped gas tank to the trailer which is as large as possible, but cannot be taller than the trailer bed is. Determine the dimensions, volume and surface area of the gas tank.
The Dimension of the Cylinder: Height = 1.5 m and radius = 0.75 m
Volume of Cylinder = 2.649 m³
Surface Area = 10.59 m²
What is Cylinder?A cylinder is a three-dimensional solid figure which has two identical circular bases joined by a curved surface at a particular distance from the center which is the height of the cylinder.
Here, Trailer bed dimension = 1.5 m X 1.5 m
So, height of the cylindrical = 1.5 m
Radius = 1.5/2 = 0.75 m
Now, Volume of Cylinder = πr²h
= 3.14 X (0.75)²X1.5
= 2.649 m³
Surface area of cylinder = 2πrh + 2πr²
= 2πr (h + r)
= 2 X 3.14 X 0.75 ( 1.5 + 0.75)
= 10.59 m²
Thus, The Dimension of the Cylinder: Height = 1.5 m and radius = 0.75 m
Volume of Cylinder = 2.649 m³
Surface Area = 10.59 m²
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There is a circular pool in the backyard with an approximate area of 113 square inches. What was the diameter?
A.12 inches
B.36 inches
C.48 inches
D.144 inches
A circle is a curve sketched out by a point moving in a plane. The diameter of the circular poll is 12 inches. Thus, the correct option is A.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
The area of a circle is given as πR², where r is the radius of the circle. Since the area of the pool is 113 sq. inches, therefore, the radius of the circle will be,
Area of pool = πR²
113 sq. inches. = πR²
113/π = R²
R = √35.9690
R = 5.9974 ≈ 6 inches
Now, since the diameter of a circle is twice the radius of the circle, therefore, the diameter of the circle will be,
Diameter of the circle = 2 × 6 inches = 12 inches
Hence, the diameter of the circular poll is 12 inches. Thus, the correct option is A.
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Answer:
a. 12 inches
Step-by-step explanation:
113 ÷ 3.14 = 35.98726114649682
2√35.98726114649682 = 5.998938334947011
5.998938334947011 x 2 = 11.99787666989402
keyword approximate ;)
Find the Volume
I need correct answer
Answer:
70 cm^3; 1000 cm^3; 343 cm^3; 30 cm^3; 48 cm^3
Step-by-step explanation:
to find the volume to all of these shapes you can just multiply all the sides together
one looks like this
2 * 5 * 7 = 70
70 is the answer for the first one
you repeat this 4 more times
since a cube has all equal sides for 2 and 3 you can just cube your side length
10^3 = 1000
7^3 = 343
afterwards since they are all just rectangular prisms you can just multiply all the sides together
1 * 5 * 6 = 30
4 * 6 * 2 = 48
those are your answers
dont forget to add ^3 behind the cm
Step-by-step explanation:
70cm kr 5ko 12m y x W L H V
ksk
The measures of the angles of a triangle are in the extended ratio 4:5:6. Find the measure of the largest angle in the
triangle.
A 60°
B. 72°
C. 120°
D. 132°
A box shaped like a rectangular prism has a length of 8 inches and width of 8 inches. Its volume is 512 cubic inches. What is the height of the box?
What is 6 months to 5 years expressed as a ratio
Answer:
6:5
Step-by-step explanation:
What is the product?
StartFraction 2 y Over y minus 3 EndFraction divided by StartFraction 4 y minus 12 Over 2 y + 6 EndFraction
Two-thirds
Ten-ninths
StartFraction 4 y Over y minus 3 EndFraction
StartFraction 4 y Over y + 3 EndFraction
The value of the product [tex]\frac{2y}{y -3} \times \frac{4y - 12}{2y + 6}[/tex] is [tex]\frac{4y}{y + 3}[/tex]
How to determine the fraction?The product expression is given as:
[tex]\frac{2y}{y -3} \times \frac{4y - 12}{2y + 6}[/tex]
Factorize each factor of the expression
[tex]\frac{2y}{y -3} \times \frac{4(y - 3)}{2(y + 3)}[/tex]
Cancel the common factors
[tex]\frac{y}{1} \times \frac{4}{y + 3}[/tex]
Evaluate the product
[tex]\frac{4y}{y + 3}[/tex]
Hence, the value of the product [tex]\frac{2y}{y -3} \times \frac{4y - 12}{2y + 6}[/tex] is [tex]\frac{4y}{y + 3}[/tex]
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Answer:
4y/y+3
Step-by-step explanation:
edge 2022
Choose the best answer. The diagonals of a square:
A. bisect each other at different angles
B. are the same length and intersect at a right angle
C. do not bisect each other and intersect at right angles
D. are the same length and intersect at different angles
Answer:
D
Step-by-step explanation:
are the same length and intersect at different angles
Scientist want to estimate the population of a particular species of snake.
They collect a sample population of 20 snakes and mark them with tags.
After a few months they catch 120 snakes, 17 of which are marked with
tags. What is the best estimate of the total population of snakes?
Answer:
the answer is yuo 4utvnjj
Answer:
Step-by-step explanation
Answer= 224
x=224
190x20=3,800/17=223.529412 (make sure to round up)
224
a puppy weighs 1 pound. what does the puppy weigh after 4 weeks
Match the vocabulary words with their definitions. 1. an arrangement of data in logical order predict 2. to tell something in advance chart 3. a list of facts from which a conclusion can be drawn random sample 4. an opinion of the amount, value, or worth of something average 5. dividing the total number by the number being counted estimation 6. every member of a large group has an equal chance of being chosen data
Answer:
sorting, predict, data, access, divisor, sampling
Step-by-step explanation:
log_8(5x+4)=3x-4
Write the log equation as an exponential equation. You do not need to solve for X
The equivalent equation of the logarithmic equation is [tex]5x + 4 = 8^{3x - 4}[/tex]
How to rewrite the equation?The logarithmic equation is given as
Log_8(5x+4)=3x-4
Rewrite properly as:
[tex]\log_8(5x+4)=3x-4[/tex]
Apply the following law of logarithm
[tex]\log_a(b) = x \to a = b^x[/tex]
So, we have:
[tex]5x + 4 = 8^{3x - 4}[/tex]
Hence, the equivalent equation of the logarithmic equation is [tex]5x + 4 = 8^{3x - 4}[/tex]
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A stright road is 1.4 long and 0.04 km wide.what area does it cover?
Step-by-step explanation:
it is a rectangle !
a straight road and its width.
so, the area is (as for any other rectangle)
length×width
in our case
1.4 km × 0.04 km = 0.056 km²
Answer:
Area formula= length x width
length of road= 1.4 km
width of road= 0.04 km
Area= 1.4 x 0.04
= 0.056 km
Doug mcdougal is whipping up 72 different snacks for his 12th annual blooper bowl bash he invited 138 guess but only 16 are coming that doesn’t bother dog he still makes 100 bowls of nacho dip he makes twice as many bowls of chili how many guests are coming to the party
The number of guests coming to Doug McDougal party can be calculated to be 23 people.
What number of people are coming?Doug invited 138 guests and out of this, only 1/6 will be coming.
The number of people coming is therefore:
= Number invited x Proportion coming
Solving gives:
= 138 x 1/6
= 23 people
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