Answer:
passed: 164
failed: 41
Step-by-step explanation:
Let the failed students be x, then the passed students will be 4x.
x + 4x = 205
x = 205/5 = 41
4x = 4*41 = 164
If cosθ=3/5, find tanθ
Answer and step-by-step explanation:
cos = adj/hyp (in a right triangle)
cos0 = 3/5
adj = 3
hyp = 5
opp = sqrt( 5^2 - 3^2) = sqrt( 25-9) = sqrt(16) = 4 (Pythogorean theorem)
tan0 = opp/adj = 4/3
Answer:
[tex]\boxed {\boxed {\sf tan( \theta)=4/3}}[/tex]
Step-by-step explanation:
Cosine is equal to adjacent over hypotenuse.
cos(x)=adjacent/hypotenuseWe are given: cosθ=3/5
Therefore, the adjacent is 3 and the hypotenuse is 5.We want to find tanθ. Tangent is equal to opposite over adjacent.
We need to find the other leg of the triangle, which is the "opposite". Use Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
The hypotenuse (c) is 5.
[tex]a^2+b^2=5^2[/tex]
One leg (a) is 3, the other (b) is unknown.
[tex]3^2+b^2=5^2[/tex]
Evaluate all the exponents.
[tex]9+b^2=25[/tex]
Subtract 9 from both sides of the equation.
[tex]9-9+b^2=25-9[/tex]
[tex]b^2=16[/tex]
Take the square root of both sides.
[tex]\sqrt{b^2} =\sqrt{16}[/tex]
[tex]b=4[/tex]
Now we know the "opposite" is 4. We can find the tangent now.
[tex]tan(x)=opposite/adjacent[/tex] (opposite=4, adjacent=3)
[tex]tan( \theta)=4/3[/tex]
The tangent of theta is 4/3
Clayton opens a savings account with 11 dollars he got from his grandmother
Answer:
The answer is "$3640.58"
Step-by-step explanation:
This question is incomplete, that's why we add another question in the attached file. Please find it.
P = [tex]\$ \ 1300[/tex] and effective per year is = interest rate per year = 7.2
Total [tex]\$ \ 1300[/tex] due after 8 years is P+PRT:
[tex]\to 1300(1+0.072 \times 8)\\\\\to 1300(1+ 0.576)\\\\\to 1300(1.576)\\\\\to \$ \ 2048.8[/tex]
[tex]\to Total \ X = \$ \ (7000-2048.8) \\\\[/tex]
[tex]= \$ \ 4951.2 \\\\= X(1 +0.072 \times 5)\\\\=1.36 X \\\\[/tex]
The number of dollars is X [tex]= \frac{4951.2}{1.36} = \$ \ 3640.58[/tex]
By visual inspection, determine the best-fitting regression model for the data plot below.
Answer:
Quadratic
Step-by-step explanation:
It looks like it’s forming a very wide arch so quadratic formulas are arches
The equation of the regression line model for the data plot determines a quadratic equation
What is linear regression line?The connection between the independent (x) and dependent (y) variables in the graph can be graphically represented using regression lines.
In a linear model, the terms are added rather than multiplied, divided, or provided as a non-algebraic function, as has been the case thus far in this section. Analysis of experimental, monetary, and biological data as well as complex system prediction are both possible using linear modelling.
A statistical technique used to build a linear model is called linear regression. The model explains how one or more independent variables Xi relate to a dependent variable y (also known as the response) (called the predictors). The distance between each data point and the regression line is called a residual.
Given data ,
Let the linear regression line be represented as A
Now , the value of A is
Let the first coordinate on the graph be P ( 1 , 5.5 )
Let the second coordinate on the graph be Q ( 2 , 6 )
And , the data plots on the graph represents a curve or parabolic equation
So , it is a quadratic equation
Hence , the data plot of the regression line is quadratic
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The sum of three consecutive odd integers is 153. Find the three odd integers.
First integer =
Second integer =
Third integer =
PLEASE HELPPPP!!
Answer:
49, 51, 53
Step-by-step explanation:
Let the first odd integer be n.
Then the consecutive odd integer will be (n+2).
This will be followed by (n+4).
We know that the sum of these three is 153. In other words:
[tex]n+(n+2)+(n+4)=153[/tex]
Solve for n. Combine like terms:
[tex]3n+6=153[/tex]
Subtract 6 from both sides:
[tex]3n=147[/tex]
Divide both sides by 3:
[tex]n=49[/tex]
Therefore, our first odd number is 49.
So, our consecutive numbers must be 51 and 53.
Hence, our sequence is:
49, 51, 53
Notes:
If we get an even number for n or a non-integer value, then there are no three consecutive odd integers that sum to 153.
Answer:
49, 51, 53
Step-by-step explanation:
All odd numbers:
49 + 51 = 100
100 + 53 = 153
A rock is thrown upward with a velocity of 17 meters per second from the top of a 31 meter high cliff and it missies the cliff on the way back down when will the rock ve 8 meters from the ground level
Answer:
[tex]4.5\ \text{s}[/tex]
Step-by-step explanation:
t = Time taken
u = Initial velocity =17 m/s
v = Final velocity
s = Displacement
a = Acceleration
g = Acceleration due to gravity = 9.81 m/s² = a
[tex]v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0^2-17^2}{2\times -9.81}\\\Rightarrow s=14.73\ \text{m}[/tex]
Total height the rock is to fall when it is 8 meters from the ground is [tex]14.73+(31-8)=37.73\ \text{m}[/tex]
[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-17}{-9.81}\\\Rightarrow t=1.73\ \text{s}[/tex]
Time taken to reach the maximum height is 1.73 s.
[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow 37.73=0+\dfrac{1}{2}\times 9.81t^2\\\Rightarrow t=\sqrt{\dfrac{37.76\times 2}{9.81}}\\\Rightarrow t=2.77\ \text{s}[/tex]
Time taken from the maximum height to the point which is 8 m from the ground is 2.77 s.
So, time taken from the moment of the throw to the point 8 m from the ground is [tex]1.73+2.77=4.5\ \text{s}[/tex].
what is the answer for 6.8×10²
Answer:
680
Step-by-step explanation:
Answer:
680
Step-by-step explanation:
10 to the 2nd power is 10 times 10 which is 100.
Now, 6.8 times 100 is 680.
Hope this helps you!!
The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of
Answer:
Answer and Explanation:
We have:
Population mean,
μ
=
3
,
000
hours
Population standard deviation,
σ
=
696
hours
Sample size,
n
=
36
1) The standard deviation of the sampling distribution:
σ
¯
x
=
σ
√
n
=
696
√
36
=
116
2) As per the central limit theorem, the expected value of the sampling distribution is equal to the population mean.
Therefore:
The expected value of the sampling distribution is equal to the population mean,
μ
¯
x
=
μ
=
3
,
000
The standard deviation of the sampling distribution,
σ
¯
x
=
116
The shape of the sampling distribution of
¯
x
is approximately normal. As the sample size is more than
30
.
3) The probability that the average life in the sample will be between
2670.56
and
2809.76
hours:
P
(
2670.56
<
x
<
2809.76
)
=
P
(
2670.56
−
3000
116
<
z
<
2809.76
−
3000
116
)
=
P
(
−
2.84
<
z
<
−
1.64
)
=
P
(
z
<
−
1.64
)
−
P
(
z
<
−
2.84
)
=
0.0482
Using Excel: =NORMSDIST(-1.64)-NORMSDIST(-2.84)
4) The probability that the average life in the sample will be greater than
3219.24
hours:
P
(
x
>
3219.24
)
=
P
(
z
>
3219.24
−
3000
116
)
=
P
(
z
>
1.89
)
=
0.0294
Using Excel: =NORMSDIST(-1.89)
5) The probability that the average life in the sample will be less than
3180.96
hours:
P
(
x
<
3180.96
)
=
P
(
z
<
3180.96
−
3000
116
)
=
P
(
z
<
1.56
)
=
0.9406
The expected value, standard deviation, and shape of the sampling distribution of will be 116.
What is Standard deviation?Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.
And, A simple random sample of 36 bulbs is taken.
Now,
Since, The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.
And, A simple random sample of 36 bulbs is taken.
Hence, The expected value, standard deviation, and shape of the sampling distribution of is,
⇒ Standard error = 696 / √ 36
= 696 / 6
= 116
Thus, The expected value, standard deviation, and shape of the sampling distribution of = 116.
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Brainliest to RIGHT answer
Answer:
It's C
Step-by-step explanation:
please help can yall solve this
Find the value of θ from the following equation.(θ≤90°)
Answer: 10°
__________________________________________________________
We are given:
Sin(6θ) = Cos(3θ)
Solving for θ:
Simplifying Cos(3θ):
We know that:
Cos(θ) = Sin(90-θ)
So, we can say that:
Cos(3θ) = Sin(90 - 3θ)
Finding the value of θ:
Sin(6θ) = Cos(3θ)
Sin(6θ) = Sin(90 - 3θ) [Since Cos(3θ) = Sin(90 - 3θ)]
6θ = 90 - 3θ [If Sin(θ) = Sin(A) ; θ = A]
9θ = 90 [adding 3θ on both sides]
θ = 10° [dividing both sides by 9]
A professional language translator gets paid an average of $320 per hour with a standard deviation of $41.75 per hour. What proportion of professional language translators get paid less than $250 per hour? Assume the population is normally distributed. Round your answer to four decimal places
Answer:
0.0475 or 4% professional language translators get paid less than $250 per hour
Step-by-step explanation:
Mean = 320
Standard Deviation = 41.75
We need to find proportion of professional language translators get paid less than $250 per hour i.e P(x<250)
First we will find value of z
Using formula: [tex]z=\frac{x-\mu}{\sigma}[/tex]
We have x=250, finding z
[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{250-320}{41.75}\\z=-1.67[/tex]
Now we will find P(z<-1.67) by looking into the normal distribution table
[tex]P(z<-1.67)=0.0475\\[/tex]
So,0.0475 or 4% professional language translators get paid less than $250 per hour
At the start of the month, the value of an investment was $53.92. By the end of the month, the value of the investment changed by a loss of $17.40. What was the value, in dollars, of the investment at the end of the month
Answer:
$36.52
you're welcome :)
Evaluate the expression.
1.2 exponent 2
answer choices =
1.44
14.4
1.728
1.5
Answer:
1.44
Step-by-step explanation:
Answer:
the answer is 1.44
Step-by-step explanation:
Because the exponent of a number says how many times to use the number in a multiplication. In 1.2 exponent 2 the "2" says to use 1.2 twice in a multiplication, so 1.2'2 = 1.2 × 1.2 = 1.44 In words: 1.2'2 could be called "1.2 to the power 2" or "1.2 to the second power.
Your welcome
Which equation represents a line that is parallel to the line whose equation is y=-3x?
A) 4x+2y=5
B) 2x+4y=1
C) y=3-4x
D) y=4x-2
Solve plz, this is due Tomorrow!!
.
Step-by-step explanation:
25) h=11
26). two sides are same = 12cm
27). time = 15 hours
28). veronica travelled = 6+1 = 7 days
29). number of tickets buyed by people each showing : 231
30) ©
Cara's new car holds 13.5 gallons of gas. If gas costs $2.98 per gallon, how much would it
cost her to fill the gas tank from empty?
Submit
O
Lenovo
Answer:
$40.23
Step-by-step explanation:
Answer:
40.23
Step-by-step explanation:
easy just do 13.5*2.98
What is 56/15 as a decimal rounded to the nearest tenth
Answer:
3.73
Step-by-step explanation:
56/15
3 11/15
3.73
A Fahrenheit thermometer shows that the temperature is 13 degrees below zero. Enter the integer that represents the temperature in degrees Fahrenheit
Answer:
-13??? weird question... do you mean celcius themometer?
Step-by-step explanation:
Answer:
The integer that represents 13 degrees below 0 is -13°F.
Step-by-step explanation:
This is because the phrase "13 degrees below 0" is obviously not an integer meaning that the corresponding integer to this phrase would be -13.
P.S.
This question was asked by somebody else and I answered already so I am not copying the answer!
Hope this helps! :)
what is the slope of the following line?
Answer:
-2
Hope this helps,
PumpkinSpice1
The slope of the line will be ( -1 / 2 ). The correct option is C.
Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The two points are (0,3) and ( 6,0). The slope of the line will be calculated by using the formula below;-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 0 - 3 ) / ( 6 - 0 )
Slope = -3 / 6 = -1 / 2
Therefore, the slope of the line will be ( -1 / 2 ). The correct option is C.
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100.6 + 296.5 using
mental math
Answer:397.1....i think
Step-by-step explanation:
Answer:
397.1
Step-by-step explanation:
I used mental math
swear no calculator or work done
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Use the distributive property to remove the parentheses (x+12)8
Answer:
Using distributive property to solve [tex](x+12)8[/tex] we get [tex]\mathbf{8x+96}[/tex]
Step-by-step explanation:
We need to used distributive property to solve (x+12)8
The distributive property of multiplication or addition states that: [tex]a(b+c)=ab+ac[/tex]
Using the property:
[tex](x+12)8\\=8x+8*12\\=8x+96[/tex]
So, using distributive property to solve [tex](x+12)8[/tex] we get [tex]\mathbf{8x+96}[/tex]
I NEED HELP WITH THIS PICTURE IS PROVIDED
Find the quotient:
7/8
Answer:
c.) 2 1/3
Step-by-step explanation:
i know
5+ x2 – 7х
What is the answer?
Answer:
[tex]-5x+5[/tex]
Step-by-step explanation:
[tex]5+2x-7x[/tex]
Combine like terms:
[tex]2x-7x+5\\[/tex]
which is
[tex]-5x+5[/tex]
Hope this helps :D
My Answers:
I think the equation you typed may have some typo error but:
If the problem is 5+2x-7x, then the answers would be:Factor the expression= 5(1-x)Simplify the expression= 5-5xBut if the expression you want to ask is 5+x⋅2-7x, the answer is:Simplify the expression= 5-5xHope this helps and if you could mark me as brainliest. Thanks!
12k-15=35+2k
answer pleasseeeeeeeee thank youu!!
Answer:
K=5
Step-by-step explanation:
12k-15=35+2k
12k=50+2k
10k=50
k=5
Answer:
[tex]k = 5[/tex]
Step-by-step explanation:
[tex]12k - 15 = 35 + 2k[/tex]
Our goal is to isolate k
[tex]12k - 15 = 35 + 2k\\\;\;\;\;+15 \;\;\;\;\;\;\; +15[/tex]
[tex]12k = 50 + 2k\\-2k \;\;\;\;\;\;\;\; -2k[/tex]
[tex]10k = 50[/tex]
Now we have k isolated to one side. Our final step is to have k be just k, no coefficient. We can do this by dividing each side by the coefficient.
[tex]\large\frac{10k}{10} = \frac{50}{10} \\\\10k\;\div\;10 = k\\50\;\div\;10 = 5\\[/tex]
[tex]\large\boxed {k \;=\;5}[/tex]
~[tex]InLoveWithPugs[/tex]
[tex]Moderator\\Math\ Enthusiast[/tex]
A box of 11 transistors has 4 defective ones.
A) If 2 transistors are drawn from the box together, what is the probability that both transistors are defective?
B) If 2 transistors are drawn from the box together, what is the probability that neither transistor is defective?
C) If 2 transistors are drawn from the box together, what is the probability that one transistor is defective?
Answer:
(a) 0.1325
(b) 0.4045
(c) 0.463
Step-by-step explanation:
Let X denote the number of defective transistors.
The proportion of defective transistors is, p = 4/11 = 0.364.
All the transistors are independent of the others.
The random variable X follows a binomial distribution.
(a)
Compute the probability that both transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=2)={2\choose 2}(0.364)^{2}(1-0.364)^{2-2}\\\\=1\times 0.132496\times 1\\\\=0.132496\\\\\approx 0.1325[/tex]
(b)
Compute the probability that neither transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=0)={2\choose 0}(0.364)^{0}(1-0.364)^{2-0}\\\\=1\times 1\times 0.404496\\\\=0.404496\\\\\approx 0.4045[/tex]
(c)
Compute the probability that one transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=1)={2\choose 1}(0.364)^{1}(1-0.364)^{2-1}\\\\=2\times 0.364\times 0.636\\\\=0.463008\\\\\approx 0.463[/tex]
A birdbath is filled to the top. On Day 1, the volume of water in the bowl decreases by 7/8 cup. On Day 2, the volume in the bowl decreases by 3/4 cup. What number represents the total change in the volume of water in the bowl after two days? Write your answer as a mixed number.
Answer:
-1 5/8
Step-by-step explanation:
Let the total amount in the bowl be x;
If on Day 1, the volume of water in the bowl decreases by 7/8 cup, the remaining water will be;
x - 7/8
If on day 2, the volume in the bowl decreases by 3/4 cup, the remaining volume of water after the second day will be;
= x - 7/8 - 3/4
= x - (7-2(3))/8
= x - (7+6)/8
= x - 13/8
This shows that the total change after the two days is -13/8
As a mixed fraction;
-13/8 = -1 5/8
in how many distinct ways can the letters in philosophy be arranged
Answer:
3 Letters Word: 6 Distinct Ways: 4 Letters Word: 24 Distinct Ways: 5 Letters Word: 120 Distinct Ways: 6 Letters Word: 720 Distinct Ways: 7 Letters Word: 5,040 Distinct Ways: 8 Letters Word: 40,320 Distinct Ways: 9 Letters Word: 362,880 Distinct Ways: 10 Letters Word: 3,628,800 Distinct Ways
Step-by-step explanation:
The number of ways in which the word 'PHILOSOPHY' can be arranged is 453,600.
What is a factorial?The product of a whole number 'n' with every whole number until 1 is called the factorial. The factorial of 4 is, for example, 43221, which equals 24.
As we can see that the word 'PHILOSOPHY' has 10 letters therefore, the letters of the word can be arranged in the 10! manner, but it contains the letter P, H and O twice therefore, there will be words that will look the same and are counted twice. Thus, the number of ways the word PHILOSOPHY can be arranged are,
[tex]\text{Number of ways} = \dfrac{10!}{2! \times 2! \times 2!} = 453,600[/tex]
Hence, the number of ways in which the word 'PHILOSOPHY' can be arranged is 453,600.
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Factorise fully 2x+8
Answer:
2(x+4)
Step-by-step explanation:
To factor you have to divide both terms by the greatest common factor, which in this case is 2. Using distribution you can check your answer.
Answer: 2(x + 4)
Explanation: If you're asked to factor a polynomial,
the first thing you want to look for is the greatest common factor
for the terms that are involved.
The greatest common factor of 2x and 8 is 2.
So a 2 can factor out.
Inside the parenthses, we have each term divided by
the 2 that factored out of the polynomial.
So we have 2(x + 4).
Help for mon pls I’ll make you famous
Answer:
1. x>-1
2. x<4
3. x<-1
4. x>-2
5. x<-3
6. x<7
Step-by-step explanation:
1. 2x>-2 Divide both sides by 2.
/2 /2
x>-1
2. 4x<16 Divide both sides by 4.
/4 /4
x<4
3. x+4<3 Subtract both sides by 4.
-4 -4
x<-1
4. 5x>-10 Divide both sides by 5.
/5 /5
x>-2
5. 3x<-9 Divide both sides by 3.
/3 /3
x<-3
6. x-4<3 Add 4 to both sides.
+4 +4
x<7
Hope this helps you out...next time, try to figure it out yourself without asking a lot of questions. By looking at one example, you can probably apply what to do for the other inequalities.