Answer:
a
Step-by-step explanation:
A physics class has 40 students. of these, 15 students are physics majors and 16 students are female. of the physics majors, six are females. find the probability that a randomly selected student is female or a physics major
The probability that the randomly selected student is female or Physics major is 0.625.
Given Information
Total number of students = 40
Number of Physics major out of the total students, P = 15
Number of females in the class, F = 16
Number of females that are Physics major, (P∩F) = 6
We have to find the probability P(P∪F).
Calculating the Probability
Probability of Physics major students, P(P) = 15/40
= 0.375
Probability of female students, P(F) = 16/40
= 0.4
Probability of female students who are Physics major, P(P∩F) = 6/40
= 0.15
Since, we know that,
P(P∪F) = P(P) + P(F) - P(P∩F)
∴ P(P∪F) = 0.375 + 0.4 - 0.15
P(P∪F) = 0.625
Thus, the probability that the randomly selected student will be a Physics major or a female is 0.625
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Given that A varies directly as B and inversely as C and that; A=12 when B=3 and C=2. Find B when A=10 and C=1.5
1.9
Step-by-step explanation:
The above is direct and inverse variation.A = kB/C -----------(1)
A=12
B = 3
C= 2
substitute A, B and C into equation (1).
12 = K × 3/2
12 = 3k/2
12×2 = 3k
3K = 24
dividing bothsides by 3
3K/3 = 24/3
K = 8
substitute K = 8 into equation (1)
A = 8B /C --------------(2)
Equation (2) is the equation connecting
A,B and C.
Finding B when A = 10 and C = 1.5
10 = 8B / 1.5
10× 1.5 = 8B
15 = 8B
Dividing bothsides by 8 :
B = 15/8
B = 1.875
B = 1. 9 ( approximately)
Janelle makes fruit punch by mixing the ingredients listed below.
• 5 pints of orange juice
• 6 cups of grape juice
• 8 cups of apple juice
How many quarts of fruit punch does Janelle make?
Answer:
6 quarts
Step-by-step explanation:
2 pints = 1 quart
4 cups = 1 quart
• 5 pints of orange juice
5 pints = 5/2 =>2.5 quarts
• 6 cups of grape juice
6 cups = 6/4 => 1.5 quarts
• 8 cups of apple juice
8 cups = 2 quarts
2.5 + 1.5 + 2 = 6 quarts
Identify the graphic that depicts triangle ABC inscribed in sphere P.
The triangle ∆ABC inscribed in sphere P is given by the first graphic.
How can the inscribed triangle be found?One figure is said to be inscribed in another figure when the vertices of the inscribed figure rests on the perimeter of the circumscribing figure.
The relationship between the figures in the given diagram are;
1st graphic : All points of the triangle ∆ABC are located on the surface of the sphere, P
Therefore;
The first graphic depicts ∆ABC inscribed in sphere P2nd graphic: Point C of the triangle ∆ABC is located outside sphere P.
Therefore;
The 2nd graphic does not depicts ∆ABC inscribed in sphere P
3rd graphic: Point A of the triangle ∆ABC in the 3rd graphic is located outside sphere P.
Therefore;
The 3rd graphic does not depicts ∆ABC inscribed in sphere P
4th graphic: Point B of triangle ∆ABC in the 4th graphic is located outside sphere P.
Therefore;
The 4th graphic does not depicts ∆ABC inscribed in sphere P
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Quick algebra 1 questions for 50 points!
Only answer if you know the answer, shout-out to subtomex0, tysm for the help!
Answer:
no matter what he has to pay $52
Step-by-step explanation:
because it is annually.
Please help.. (This is meant to be infinite, so I can't use a calculator)
Answer:
5
Step-by-step explanation:
→ Let x = √20 + √20 .....
x
→ Square both sides
x² = 20 + √20 +√20 + √20
→ Replace √20 +√20 + √20 with x
x² = 20 + x
→ Move everything to the left hand side
x² - 20 - x = 0
→ Factorise
( x + 4 ) ( x - 5 )
→ Solve
x = -4 , 5
→ Discard negative result
x = 5
Note that
[tex]\left(\sqrt{x+a} + b\right)^2 = \left(\sqrt{x+a}\right)^2 + 2b \sqrt{x+a} + b^2 = x + 2b \sqrt{x+a} + a+b^2[/tex]
Taking square roots on both sides, we have
[tex]\sqrt{x+a} + b = \sqrt{x + 2b \sqrt{x+a} + a+b^2}[/tex]
Now suppose [tex]a+b^2=0[/tex] and [tex]2b=1[/tex]. Then [tex]b=\frac12[/tex] and [tex]a=-\frac14[/tex], so we can simply write
[tex]\sqrt{x-\dfrac14} + \dfrac12 = \sqrt{x + \sqrt{x - \dfrac14}}[/tex]
This means
[tex]\sqrt{x-\dfrac14} = -\dfrac12 + \sqrt{x + \sqrt{x - \dfrac14}}[/tex]
and substituting this into the root expression on the right gives
[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x + \sqrt{x - \dfrac14}}}[/tex]
and again,
[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac14}}}[/tex]
and again,
[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac14}}}}[/tex]
and so on. After infinitely many iterations, the right side will converge to an infinitely nested root,
[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{\cdots}}}}}[/tex]
We get the target expression when [tex]x=\frac{41}2[/tex], since [tex]\frac{41}2-\frac12=\frac{40}2=20[/tex], which indicates the infinitely nested root converges to
[tex]\sqrt{20+\sqrt{20+\sqrt{20+\sqrt{\cdots}}}} = \sqrt{\dfrac{41}2 - \dfrac14} + \dfrac12 \\\\ ~~~~~~~~ = \sqrt{\dfrac{81}4} + \dfrac12 \\\\ ~~~~~~~~ = \dfrac92 + \dfrac12 = \dfrac{10}2 = \boxed{5}[/tex]
If there are 300 cars and 80 of them are black, what percent of the cars are black
The percentage of cars that are black when 80 cars of 300 cars are black is 26.67 or 26 2/3 %.
The percentage is similar to the fractional representation of quantities, where the quantity is shown as a part of the whole, but here the whole is fixed to be 100.
To derive a percentage in fractional form, we divide it by 100.
To derive a fractional form in percentage, we multiply it by 100.
In the question, we are given that 80 cars of 300 cars are black.
We are asked the percentage of cars that are black.
The fraction representing black cars of whole cars can be shown as 80/300 = 4/15.
To convert this into a percentage, we multiply it by 100.
Thus, the percentage of cars that are black = 4/15 * 100% = 80/3% = 26 2/3% = 26.67%.
Thus, the percentage of cars that are black when 80 cars of 300 cars are black is 26.67 or 26 2/3 %.
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WILL MARK YOUR ANSWER AS BRAINLIEST how do I do this
By the definition of a rectangle, JML and KLM are right angles.
How to explain the information?From the information given, JKLM is a rectangle based on the definition as the opposite sides are equal.
Also, JML and KLM will be 90° since they're right angles. The opposite sides of a rectangle are congruent and equal.
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I can't seem to figure this out
Answer:
50
Step-by-step explanation:
→ Evaluate n as 1, 2, 3 and 4 in 5n
5, 10, 15 and 20
→ Find the sum of these numbers
5 + 10 + 15 + 20 = 50
22. For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?
22. Line 1: Passes through (0, 5) and (3, 3)
Line 2: Passes through (1, −5) and (3, −2)
Answer:
The given lines are perpendicular.
Step-by-step explanation:
In the question, two lines are given as line 1 passes through (0,5) and (3,3). Whereas, line 2 passes through (1,-5) and (3,-2).
It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.
To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.
Step 1 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{1}=\frac{3-5}{3-0} \\&m_{1}=\frac{-2}{3} \\&m_{1}=-\frac{2}{3}\end{aligned}$$[/tex]
Step 2 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{2}=\frac{-2-(-5)}{3-1} \\&m_{2}=\frac{3}{2} \\&m_{2}=\frac{3}{2}\end{aligned}$$[/tex]
And
[tex]$$\begin{aligned}&m_{1} m_{2}=-\frac{2}{3}\left(\frac{3}{2}\right) \\&m_{1} m_{2}=-1\end{aligned}$$[/tex]
Since, both slopes are reciprocals .
Therefore. the lines are perpendicular.
a wildlife photographer spent 5 minutes taking pictures of a bison at a park. when the bison then decided she didn't want her photograph published, the photographer spent the next 30 minutes convincing the bison that the publicity would be good for the park. by what percent was the time the photographer spent negotiating with the bison greater than the time he spent taking pictures?
The percent of time the photographer spent negotiating with the bison greater than the time he spent taking pictures is 500%
PercentageTime spent taking pictures = 5 minutesTime spent negotiating = 30 minutesPercentage of time negotiating greater than taking pictures = (difference in time) / time to take pictures × 100
= (30 - 5) / 5 × 100
= 25/5 × 100
= 5 × 100
= 500%
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What does the trigonometry angle range -[tex]\pi \leq \alpha \leq \pi[/tex] radians mean?
The trigonometry angle range -π ≤ α ≤ π in radians means angle α is
between -π radians and π radians or -180° and 180°.To answer the question, we need to know what a trigonometric angle range is
What is a trigonometric angle range?A trigonometric angle range is the range of values which the trigonometric angle can have
Since we need to find the meaning of the trigonometry angle range -π ≤ α ≤π.
We know that
-π radians = -π × 180°/π = -180° and π radians = π × 180°/π = 180°.Since α is in the range -π ≤ α ≤ π = -180° ≤ α ≤ 180°, this implies that the angle α is
between -π radians and π radians or between -180° and 180°.So, the trigonometry angle range -π ≤ α ≤ π in radians means that angle α is
between -π radians and π radians or between -180° and 180°.Learn more about trigonometric angle range here:
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Hurrry helpppp
Find the missing length for 2 of the pictures
Answer:
Step-by-step explanation:
So in this case you need to use the Pythagorean Theorem which states that: [tex]a^2+b^2=c^2[/tex] where c is the value of the hypotenuse, and a and b are the other two sides (the order in which you put them doesn't matter). So in this case I'll say a=8.4 (I could've also input it as b, doesn't matter) and c=10.5 (here it does matter, c is hypotenuse, it's not the other sides...)
So given this information we have the equation:
[tex](8.4 cm)^2 + b^2 = (10.5 cm)^2\\[/tex]
Square known values:
[tex]70.56 cm^2 + b^2 = 110.25 cm^2[/tex]
subtract 70.56 cm^2 from both sides
[tex]b^2 =39.69 cm^2[/tex]
Take the square root of both sides
[tex]b=6.3 cm[/tex]
x=6.3 cm
Problem 3: a = 9 cm, c=20 cm
Input known values
[tex](9 cm)^2 + b^2 = (20 cm)^2[/tex]
Square known values
[tex]81 cm^2 + b^2 = 400 cm^2[/tex]
Subtract 81 cm^2 from both sides
[tex]b^2 = 319cm^2[/tex]
take the square root of both sides
[tex]b\approx 17.86 cm[/tex]
so the side x is approximately 17.86 cm
Solve the inequality.
-1.5(4x+1) ≥ 45-25(x+1)
Answer:
x ≥ 21.5/19
Step-by-step explanation:
-1.5(4x + 1) ≥ 45 - 25(x + 1)
-6x - 1.5 ≥ 45 - 25x - 25
-6x + 25x ≥ 45 - 25 + 1.5
19x ≥ 21.5
x ≥ 21.5/19
The average adult in Bell Town makes $40,000
a year. The average female adult there makes
$50,000 a year. If Bell Town has a total of
6,000 adults, 4,000 of whom are female, how
much does an average male adult in Bell Town
make?
A. $20,000
B. $30,000
C. $40,000
D. $60,000
is y= -1/2x +25 linear???
What is the slope of a line that is parallel to the line y= 3/4 x + 2?
Answer:
Using the slope-intercept form, the slope is 34 . All lines that are parallel to y=3x4+2 y = 3 x 4 + 2 have the same slope of 34 .
Step-by-step explanation:
3/4
Step-by-step explanation:The slope of a line describes the steepness of a line, as well as the direction.
Slope-Intercept Form
To answer the question, we first need to find the slope of the original line. This line is represented in the slope-intercept form, which is y=mx+b.
In this formula, m is the slope.So, using this information we can say that the slope is 3/4.
Parallel Lines
Parallel lines are 2 lines that will never intersect. You can tell if 2 lines are parallel by their slopes. All parallel lines have equal slopes.
This means that the slope of a line parallel to y = 3/4x + 2 must be 3/4 as well.
-0.2 2 is repeating as a fraction
-0.22 as a repeating fraction is -22/99
How to rewrite as a fraction?The decimal is given as:
-0.22
Express as fraction
-22/100
Subtract 1 from the denominator to rewrite it as a repeating number
-22/99
Hence, -0.22 as a repeating fraction is -22/99
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How many tonnes of wheat are there is in 1000 bushels if there are 39.368 bushels/tonne
Answer:
25.40134119
Step-by-step explanation:
1000/39.368
Name each angle pair
The angle pairs that we can observe from the figure are
1 and 5 3 and 4Straight angle pairs, often referred to as linear pairs, are formed when two lines cross, creating two side-by-side angles that sum to 180 degrees. The requirement that the two angles in a straight angle or linear pair be adjacent is crucial. The two angles cannot form a linear pair if they are not side-by-side (share the same side) (even if they add to 180 degrees). Check out the depiction of straight angle/linear pairings in the picture below.
The angle pairs that we can observe from the figure are
1 and 5 3 and 4As we can see in the following figure that supplementary angles are called angle pairs.
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Where would the line go??? Please help asap!!
Answer: Draw a line through (0,5) and (1,2)
The graph is shown below.
=====================================================
Reason:
The equation y = -3x+5 is in the form y = mx+b
m = -3 = slope
b = 5 = y intercept
The y intercept is where the graph crosses the y axis. In this case, it's at (0,5). This is one point needed.
Another point can be found by going down 3 and to the right 1 to arrive at (1,2). The motion "down 3, right 1" is from the slope of -3/1.
Therefore, this line goes through (0,5) and (1,2)
-------------
Another approach:
Plug in x = 0 to get...
y = -3x+5
y = -3(0) + 5
y = 5
The input x = 0 leads to the output y = 5
This tells us the point (x,y) = (0,5) is on the line.
Repeat for x = 1
y = -3x+5
y = -3(1)+5
y = 2
So (1,2) is another point on the line.
-------------
Check out the graph below.
Step-by-step explanation:
[tex]y=-3x+5.\\[/tex]
x | 0 | 1 |
y | 5 | 2 |
Find the lateral area and total surface area of each of the following. GEOMETRY!!! HELP PLS
(a) The lateral surface area of the prism is 720 sq units and the total surface area is 752 sq units.
(b) The lateral surface area of the cone is 136π sq units and the total surface area is 200π sq units.
(c) The lateral surface area of the cylinder is 242π sq units and the total surface area is 484π sq units.
Lateral surface area of the prism
L.S.A = Ph
where;
P is perimeter of the baseh is height of the prismh² = 17² - 8²
h² = 225
h = 15
L.S.A = (3 x 16) x 15 = 720 sq units
Total surface area of the prismT.S.A = PH + 2B
T.S.A = 720 + 2(16) = 752 sq units
Lateral surface area of the coneL.S.A = πrt
where;
t is the slant height = 17r² = 17² - 15²
r² = 64
r = 8
L.S.A = π(8)(17) = 136π sq units
Total surface area of the coneT.S.A = πrt + πr²
T.S.A = 136π sq units + π(8)²
T.S.A = 200π sq units
Lateral surface area of the cylinderL.S.A = 2πrh
where;
r is the radius of the cylinder = 11h is height of the cylinder = 11L.S.A = 2π(11 x 11) = 242π sq units
Total surface area of the cylinderT.S.A = 2πrh + 2πr² = 2πr(r + h)
T.S.A = 2π(11)(11 + 11)
T.S.A = 484π sq units.
Thus, the lateral surface area of the prism is 720 sq units and the total surface area is 752 sq units.
the lateral surface area of the cone is 136π sq units and the total surface area is 200π sq units.the lateral surface area of the cylinder is 242π sq units and the total surface area is 484π sq units.Learn more about surface area here: https://brainly.com/question/76387
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Volume=
What is the volume?
Help please
Answer: 360
Step-by-step explanation:
The area of the bottom square is 100.
The area of each of the four triangular faces is 65.
Adding these together, we get 65(4) + 100 = 360.
2. Find the value of root4 (81)-2
Step-by-step explanation:
[tex]\sqrt[4]{81} -2\\=3-2 \\=1[/tex]
What is the inverse of this function?
Step-by-step explanation:
f(x) = y = -1/2 × sqrt(x + 3), x >= -3
-2y = sqrt(x + 3)
4y² = x + 3
x = 4y² - 3
and now we need to rename x to y and y to x to make it a "normal" function :
y = 4x² - 3
since in the original function x >= -3, this gave us y <=0.
and therefore (remember the x of the inverse function actually stands for the y of the original function) the limit for the inverse function is x <= 0.
so, again, the full answer is
f^-1(x) = 4x² - 3, x <= 0
90 more points to go!
Answer:
[tex](x+8)^2=y;\ x\ge -8[/tex]
Step-by-step explanation:
So the inverse is when the x and y are swapped
Original equation:
[tex]y=\sqrt{x}-8[/tex]
Swap x and y:
[tex]x=\sqrt{y}-8[/tex]
add 8 to both equations:
[tex]x+8=\sqrt{y}[/tex]
Square both sides
[tex](x+8)^2=y[/tex]
Now while this looks like a normal quadratic, it has to have the range restriction the original function had, but as it's domain restriction. So the range of the original function was y >= -8, because the smallest value you could input is 0, and the square root of that is 0, then subtract 8 and you get -8. So the domain is x >= -8
In the figure, PQ || SR, PS 1 PQ and SR, and QR 1 PQ and SR.
SR¸
P
R
Which statement describes a relationship between angles in the figure?
Om XPQR = m XPSR ÷ 2
m XPQR = m }TQR : 2
m XSRU = m PQT x 2
O
S
O
O
m XSRU = m XQPS × 2
Ug
The statement that best describes a relationship between angles in the figure is option d: m SRU = m QPS x 2.
What is the angle about?In Geometry, an angle is known to be any figure is is created by two rays or lines that is said to have a common endpoint known as an angle.
Note that:
An angle on a straight line is 180 degrees.A right angle is 90 degrees.From the diagram, angle QPS is right angle and angle SRU is an angle on a straight line.
Therefore:
= QPS x 2
= 90 x 2
= 180 degrees
Angle SRU = 180 degrees
Therefore, The statement that best describes a relationship between angles in the figure is option d: m SRU = m QPS x 2.
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Answer:
Step-by-step explanation:
The table shows coffee preferences from a survey.
Coffe Type Plain Sugar Creamer
Regular 0.27 0.19 0.32
Decaf 0.05 0.08 0.09
If a person is chosen at random in this survey, what is the P(decaf or sugar)?
0.54
0.41
0.22
0.08
Using it's concept, the desired probability is given as follows:
P(decaf or sugar) = 0.41.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. A probability can also be represented as a proportion.
From the table, we have that:
P(decaf) = 0.05 + 0.08 + 0.09 = 0.22.P(sugar - decaf) = 0.19.Hence:
P(decaf or sugar) = 0.22 + 0.19 = 0.41.
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What is the probability of getting an even number on the spinner? A. 5/6 B. 4/6 C. 3/6 D. 1/3
What is the √81 x √144….?
(square root of 81 X square root of 144)
Answer:
108
Step-by-step explanation:
First evaluate both the squares separately, because combining the two within the sqrt symbol would result in a large number(harder to deal with).
sqrt81 = 9 (because 9*9=81)
sqrt144 = 12 (because 12*12=144)
Then multiply.
9*12 = 108