Answer:
4/3
Step-by-step explanation:
2/3 TIMES 2 IS 4/3
In a class, there are 18 girls and 14 boys. If the teacher selects two students at random to attend a party with the principal, what is the probability that the two students are the same sex?
Answer:
0.492 is the answer
Step-by-step explanation:
The probability that the two students are the same sex is 0.49.
Since the class contain 32 (18+14) children out of which 18 girls and 14 boys.
First step
Using general multiplication rule
P(Two girls)=P(First girls)×P(Second girl; First girl)
P(Two girls)=18/32×17/31
P(Two girls)=18×17/32×31
P(Two girls)=306/992
P(Two boys)=P(First boys)×P(Second boys; First boys)
P(Two girls)=14/32×13/31
P(Two girls)=14×13/32×31
P(Two girls)=182/992
Second step
Use addition rule for mutually exclusive events
P(Same sex)=P(Two girls)×P(Two boys)
P(Same sex)=306/992×182/992
P(Same sex)=306+182/992
P(Same sex)=488/992
P(Same sex)=61/124
P(Same sex)=0.49
Inconclusion the probability that the two students are the same sex is 0.49.
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can you please help me
Three pounds of peaches cost $12.48. What is the cost of eight pounds?
Answer:
$33.28
Step-by-step explanation:
Find the cost of 1 pound of peach by divind by 3 then times that cost by 8.
PLEASE HELP 100 points ASAP!
Question & Answer choices attached!
Answer:
C. Graph B
Step-by-step explanation:
y ≥ 2x + 3
y ≤ -2x - 4
To find which side of the line the answer is, we can set y and x to 0 and see if the equation is true or false (this only works if the cordance of (0,0) does not lie on the line)
0 ≥ 2(0) + 3
0 ≥ 3 FALSE (the side of the line that should be shaded is the one that does not include the cordance of (0,0))
0 ≤ -2(0) - 4
0 ≤ - 4 FALSE (the side of the line that should be shaded is the one that does not include the cordance of (0,0))
how do you find the perpendicular distance between a line segment and a point? (photo attached) i’m stuck
Answer:
Exact Distance = [tex]\frac{4\sqrt{10}}{5}[/tex]
Approximate Distance = 2.529822
============================================
Explanation:
This process is quite involved if you don't know the shortcut formula. I'll go over the long method first, and then show the shortcut in the next section.
First we'll need the equation of the line through points O and M. Use of the slope formula will show line OM has slope -1/3, which you are correct in stating.
Then use point slope form to determine the equation of line OM is y = (-1/3)x+11/3. This converts to the standard form x+3y = 11.
For anything in the form Ax+By = C, the equation perpendicular to this is of the form Bx-Ay = D. The A,B coefficients swap, and one item is negated. This helps form the negative reciprocal slope needed for the perpendicular line.
Compare x+3y = 11 to Ax+By = C. We see that A = 1 and B = 3.
So Bx-Ay = D turns into 3x-y = D. Then plug in the coordinates of H(-3,2) and compute to get
3x-y = 3(-3)-2 = -9-2 = -11. So D = -11
The equation 3x-y = D turns into 3x-y = -11 which is the equation of the line through point H and this line is perpendicular to line OM.
At this point, we have this system of equations
x+3y = 11
3x-y = -11
Solve that system however you wish. Substitution may be the best choice. Doing so leads to the intersection point (-2.2, 4.4)
The last step is to apply the distance formula between the points H(-3,2) and the intersection point (-2.2, 4.4)
The distance you should get is [tex]\frac{4\sqrt{10}}{5} \approx 2.529822[/tex]
I'm skipping steps because listing everything out would take up way too much space in my opinion.
--------------------------------------------------------
The first section goes over a fairly lengthy process of finding the perpendicular distance. Luckily, there's a shortcut.
Consider an equation of the form Ax+By=C, aka standard form. Now consider a point P located at (m,n) that is not on the line Ax+By = C. We can find the distance from P to the line using this formula below
[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}[/tex]
In this case, A = 1, B = 3 and C = 11 found back in the previous section. So you'll still need to calculate the equation of line OM.
Also, we'll use (m,n) = (-3,2) which are the coordinates of point H
From here it's a fairly straightforward computation
[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}\\\\d = \frac{|1*(-3)+3*2-11|}{\sqrt{(1)^2+(3)^2}}\\\\d = \frac{|-8|}{\sqrt{1+9}}\\\\d = \frac{8}{\sqrt{10}}\\\\[/tex]
Optionally we can rationalize the denominator like so
[tex]d = \frac{8}{\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10}\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10*10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{100}}\\\\d = \frac{8\sqrt{10}}{10}\\\\d = \frac{2*4\sqrt{10}}{2*5}\\\\d = \frac{4\sqrt{10}}{5}\\\\d \approx 2.529822\\\\[/tex]
There are different ways to write down the answer, but they all represent the same number.
5. How many different singing quartets can be formed from a class of 30 singers?
Answer:
7
Step-by-step explanation:
since a quartet consists of 4 people, it's basically asking how many groups of 4 can you make out of 30.
You can do this in your head or divide: 30 / 4 =7 r2
PLS HELP I WILL GIVE U 30 POINTS !!!!!!!
What is the solution to the system of equations that is graphed below?
Answer:
(-4,-3)
Step-by-step explanation:
i'll give brainliest this is due soon so yeahmPLSSSSSSSSS
Answer:
He pays taxes on the amount after the discount. So 10% of $40.50 versus $45.
Step-by-step explanation:
10% on $40.50 = $4.05
10% on $45.00 = $4.50
when you take 10% of $45, you're left with $40.50 because you'd do 40*10/100. when you go to add the 10% tax, you are no longer taxing $45, you're taxing $40.50 which is $4.05. 40.50+4.05=44.55
Plainfield Community Center is buying new seating for their building. They want to purchase a combination of stools and chairs. Stools cost $50 and chairs cost $65. The center cannot spend more than $3000.
Which inequality represents all possible combinations of s stools and c chairs?
a) 50s + 65c ≤ 3000
b)50c + 65s ≤ 3000
c) 50c + 65s ≥ 3000
d) 50s + 65c < 3000
Answer:
A
Step-by-step explanation:
If you have s number of stools and c number of chairs, the price can be expressed as 50s + 65c. Since the question says you cannot spend more than 3000, you could spend less than or equal to 3000. So the inequality is 50s + 65c ≤ 3000.
Write the word sentence as an equation.
t less than 5 is 12
Answer:
t-5=12
Step-by-step explanation:
If f(x)= 3x-5 and g(x)= x+2, then what is f(x)+g(x) ?
Answer:
4x - 3
Step-by-step explanation:
Givens
f(x) + g(x)
f(x) = 3x - 5
g(x) = x + 2
Equation
f(x) + g(x) = 3x - 5 + x + 2
Solution
f(x) + g(x) = 4x - 3 Collected like terms from the equation.
Remark
If you think of f(x) and g(x) as equal to different y values, it might help you to solve questions like this.
Consider the figures shown below. Find the values of ∠1 and ∠2 for the given figures and complete the table accordingly.
Answer:
Figure 1: 98, 82
Figure 2: 64
Figure 3: 157, 23
Step-by-step explanation:
Figure 1: complementary angles theorem, coordinating angles theorem
Figure 2: vertical angles theorem
Figure 3: alternate interior angles theorem, complementary angles theorem
Let me know if this helped!
**please mark brainliest!!!
Mass = 10 g
Density = Mass/volume
Volume of a cube = (side length)3
Now that you have the side length, determine the volume. Then use the density formula to calculate the density of the material. Record your observations by selecting the data table icon.
You may use a calculator for this section.
Measurement1.7 cm
FIRST ANSWER GETS BRAINLIEST
Answer:Hello! Here we have a cube, with a mass of 10g and a side length of 2.5cm.
First we want to determine the volume.
The volume of a cube, is equal to his cubic side length, where L is the side length:
So
So the volume of the cube is 15.625 cubic centimeters.
Now we want to calculate te density of the material, as you know:
This means that the density is 0.64 grams per cubic centimeter.
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
1. Determine the value: V=L^3
so, (1.7)^3= 4.913
2. Calculate the density: mass divided by volume
10 divided by 4.913= 2.0
Answer: 2
using arc length formula find s when r=24 and θ=π/2
48π
24π
12π
Answer:
12π
Step-by-step explanation:
The formula for arc length is given as:
[tex] s = \frac{\theta}{360\degree} \times 2\pi r[/tex]
Plug r = 24 and θ=π/2 in the above formula, we fi d:
[tex] s = \frac{\frac{\pi}{2}}{360\degree} \times 2\pi \times 24\\\\
s = \frac{\frac{\pi}{2}}{2 \pi} \times 48\pi\\\\
s = \frac{\pi}{2\times 2 \pi} \times 48\pi \\\\
s = \frac{\pi}{4\pi} \times 48\pi \\\\
\huge \purple {\boxed{s = 12\pi}} \\
[/tex]
Step-by-step explanation:
ghjkkknn. bjkkmn. bhcddfkkkk answer in image
for most people, health club membership expenses are considered discretionary. alli lives in a big city and wants to join a health club. she researched monthly membership costs and found the following for health clubs within a 5-mile radius of her apartment. $65, $50, $44, $86, $90, $50, $35, $110, $70, $50, $35, $60, $56 a. what is the mean monthly membership fee? round your answer to the nearest cent. b. what is the median monthly membership fee? c. what is the mode monthly membership fee?
Order we can find the median is 56.
What is the mathematical mode?
The most common number, or the number that appears the most frequently. Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.A) 65 + 50+ 44+ 86 + 90 + 50+ 35 + 110 + 70 + 50 + 35 + 60+ 56/13
= 61.62
B) Arrange the number from small to large
35, 3,44,50,50,50,56,60,65,70,86,90,110
from this order we can find the median is 56.
c) we found that 50 was the most frequent acurrrence .
So, mode is 50.
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***!!!!URGENT!!!!**** PLEASE HELP
Answer:
y=1/2x-10
Step-by-step explanation:
X is the slope (1/2)
to find b=
-6=1/2(8)+b
-6=4+b. Subtract four from each side
-10=b
find the rise and run
(please point the points on the graph}
Answer:
rise = -3
run = 4
rise/run = -3/4
Step-by-step explanation:
See figure for visual
The rise/run ratio gives the slope of the line
Take any two points on the line. I chose A(x1 = 2, y1 = 3) and B(x2 = 6, y2 = 0) as shown in the graph
For these two points the rise is (y2 - y1) = 0 - 3 = -3
The corresponding run is (x2 - x1) = 6 - 2 = 4
rise/run = -3/4 which is the slope of the line. This line has a negative slope - as x increases, y decreases
Not sure if that's what they are looking for.
Hope that helps
Prove each of the following identities.
(e) (2 - sec^2 x)/(sec^2 x + 2tan x) = (cos x - sin x)/(cos x + sin x)
(f) cot^2 x - cot^2 y = (cos^2 x - cos^2 y)/(sin^2 x * sin^2 y)
The given trigonometry proof is given below
(a)[tex]\frac{1}{1+\sin (\theta)}+\frac{1}{1-\sin (\theta)}=2 \sec ^2(\theta)[/tex]
Manipulating left side
[tex]$$\begin{aligned}&\frac{1}{1+\sin (\theta)}+\frac{1}{1-\sin (\theta)} \\&\text { Simplify } \frac{1}{1+\sin (\theta)}+\frac{1}{1-\sin (\theta)}: \frac{2}{(\sin (\theta)+1)(-\sin (\theta)+1)} \\&=\frac{2}{(1+\sin (\theta))(1-\sin (\theta))}\end{aligned}$$[/tex]
Rewrite using trig identities
[tex]=\frac{2}{\cos ^2(\theta)}[/tex]
Use the basic trigonometric identity: [tex]\frac{1}{\cos (x)}=\sec (x)[/tex]
[tex]$$=2 \sec ^2(\theta)$$[/tex]
(b)[tex]\frac{\cos (x)}{1+\sin (x)}=\sec (x)-\tan (x)[/tex]
Manipulating right side
[tex]$$\sec (x)-\tan (x)$$[/tex]
Express with sin, cos
[tex]=\frac{1-\sin (x)}{\cos (x)}[/tex]
Rewrite using trig identities
[tex]=\frac{\cos (x)}{1+\sin (x)}[/tex]
(c)Manipulating right side[tex]$\tan (x)-\cot (x)$[/tex]
Express with sin, [tex]$\cos$[/tex]
[tex]$$\begin{aligned}&=\frac{-\cos ^2(x)+\sin ^2(x)}{\cos (x) \sin (x)} \\&\sin ^2(x)=1-\cos ^2(x) \\&=\frac{1-\cos ^2(x)-\cos ^2(x)}{\cos (x) \sin (x)} \\&=\frac{1-2 \cos ^2(x)}{\sin (x) \cos (x)}\end{aligned}$$[/tex]
(d) [tex]\frac{\sin (x)}{1-\cot (x)}+\frac{\cos (x)}{1-\tan (x)}=\sin (x)+\cos (x)[/tex]
Manipulating left side
[tex]\frac{\sin (x)}{1-\cot (x)}+\frac{\cos (x)}{1-\tan (x)}[/tex]
Express with sin, cos
[tex]=\cos (x)+\sin (x)[/tex]
(e)Manipulating left side
[tex]\frac{2-\sec ^2(x)}{\sec ^2(x)+2 \tan (x)}[/tex]
Express with sin, cos
[tex]=\frac{-1+2 \cos ^2(x)}{1+2 \cos (x) \sin (x)}$$[/tex]
Rewrite using trig identities
[tex]=\frac{\cos (x)-\sin (x)}{\cos (x)+\sin (x)}$$[/tex]
(f)Manipulating left side [tex]$\cot ^2(x)-\cot ^2(y)$[/tex]
Express with sin, cos
[tex]=\frac{\cos ^2(x) \sin ^2(y)-\cos ^2(y) \sin ^2(x)}{\sin ^2(x) \sin ^2(y)}$$[/tex]
Rewrite using trig identities
[tex]=\frac{\cos ^2(x)-\cos ^2(y)}{\sin ^2(x) \sin ^2(y)}$$[/tex]
Trigonometry is the field of mathematics that deals with certain angles' functions and how to use such functions in computations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.
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-3 + 4x = 41
What's x
Answer:
x=11 I hope it helps you
Step-by-step explanation:
Solve for 8:
-0.2 = 8 +(-0.8)
Convert the following equation
into slope-intercept form.
8x - 2y = -14
3x-8=3(x-4)+1 plz plz help me fast is it infinite or no or one solution
Answer:
no solution
Step-by-step explanation:
solve the equation
3x - 8 = 3(x-4) + 1
3x - 8 = 3x - 11
3x + 3 = 3x
x + 3 = x
A number x plus 3 cannot equal a number x.
the given equation has no solutions.
The equation 3x - 8 = 3(x - 4) + 1 is a linear equation. To determine the number of solutions, we can simplify and analyze the equation.
Expanding the right side of the equation, we have 3x - 8 = 3x - 12 + 1.
Simplifying further, we get 3x - 8 = 3x - 11.
By subtracting 3x from both sides, we have -8 = -11.
However, this leads to a contradiction. -8 is not equal to -11.
Since the equation leads to a contradiction, there is no solution to the equation.
In conclusion, the given equation has no solutions.
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James' 35 in. giant apple triples in size every week. Write an expression that would
represent how big the peach is after 4 weeks.
Answer:
35 times 3= 105 times 4
Step-by-step explanation:
The balance in Alex's bank account is $675. The account
earns 6% simple interest calculated twice per year. If Alex
makes no deposits or withdrawals for 2 full years, the
balance in his account (rounded to the nearest dollar) will
be -
Select one:
O
$852
$715
$837
$756
Answer:
$852
Step-by-step explanation:
From the given question, the following are given:
Present value, PV = $675
Rate, r = 6% = 0.06
Number of years, n = 2 years
Number of times per year, m = 2
The balance in his account is the future value (FV), so that;
Future value = PV[tex](1+r)^{nm}[/tex]
= 675[tex](1+0.06)^{(2*2)}[/tex]
= 675 x 1.26248
= 852.174
Future value = $852
Thus, the balance in Alex's account would be $852.
will give brainliest!! please help me!!
Answer:
D
Step-by-step explanation:
is 4.379 a whole number
No, 4.379 is not a whole number, it is a decimal number.
Whole numbers are those numbers which start from 0 and have 1 as common difference.. Such as, 0,1,2,3,4,5,...♾️Answer: No it is not a whole number.
Step-by-step explanation: Whole numbers are a set of numbers including all natural numbers and 0. They are a part of real numbers that do not include fractions, decimals, or negative numbers.
The volume of two identical cubes is related to the edge length of the cubes.
Which function represents the combined volume of these cubes?
Fy = 2x
G y = x3
Hy = 8x3
Jy = 2x2
The solution to the system is
( , )
Answer:
x = ½
y = 3
Step-by-step explanation:
—Math0,8 –4x = –0,4y ==> –4x + 0,4y = –0,8
6x + 0,4y = 4,2 ==> 6x + 0,4y = 4,2
______________–
–10x = –5,0
x = –5/–10
x = 1/2
–4x + 0,4y = –0,8
–4(½) + 0,4y = –0,8
–2 + 0,4y = –0,8
0,4y = –0,8 + 2
y = 1,2/0,4
y = 3
x = ½
y = 3
Follow my account^^
-42=-7+5x
Solve for x
Answer:
x = -7
Step-by-step explanation:
-42=-7+5x
-42 + 7 = 5x
5x = - 35
x = -35/5
x = - 7
Hope it helps!
Answer:
x = -7
Step-by-step explanation:
Given equation:
[tex]-42 = -7 + 5x[/tex]
Simplify the equation.[tex]-42 = 5x -7[/tex]
2. Flip the equation.
[tex]5x + 7 = -42[/tex]
3. Add 7 to each side.
[tex]5x - 7 + 7 = -42 + 7[/tex]
[tex]5x = -35[/tex]
4. Divide both sides by 5.
[tex]\frac{5x}{5}[/tex] = [tex]\frac{-35}{5}[/tex]
5. Divide the fraction.
[tex]-35[/tex] ÷ [tex]5[/tex] = [tex]-7[/tex]