Answer:
After solving [tex](45x-7)4x=57[/tex] we get [tex]\mathbf{x=0.645 \ or \ x = -0.490}[/tex]
Step-by-step explanation:
We need to solve the equation: [tex](45x-7)4x=57[/tex]
Solving:
[tex](45x-7)4x=57[/tex]
Multiply 4x with terms inside the bracket
[tex]180x^2-28x=57[/tex]
[tex]180x^2-28x-57=0[/tex]
We need to solve above equation to find value of x
Using quadratic formula for finding value of x: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a=180, b=-28 and c=-57
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-28)\pm\sqrt{(-28)^2-4(180)(-57)}}{2(180)}\\x=\frac{28\pm\sqrt{784+41040}}{360}\\x=\frac{28\pm\sqrt{41824}}{360}\\x=\frac{28\pm204.51}{360}\\x=\frac{28+204.51}{360} \ or \ x=\frac{28-204.51}{360}\\x=0.645 \ or \ x = -0.490[/tex]
Values of x are [tex]\mathbf{x=0.645 \ or \ x = -0.490}[/tex]
So, After solving [tex](45x-7)4x=57[/tex] we get [tex]\mathbf{x=0.645 \ or \ x = -0.490}[/tex]
which expression is equivalent to mn+z
PLEASE HELP ME QUICK!!A train moves at a constant speed of 8 miles every 6 minutes. Fill in the table below to show how far the train travels according to different
amounts of time.
Answer:
1. 4
2. 20
3. 80
Step-by-step explanation:
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]
Select all that apply.
Which of the following are proportions?
25/10 = 5/2
3/4 = 8/10
2/8 = 3/12
3/4 = 15/20
Answer:
Step-by-step explanation:
3/4=15/20 are proportions
For every 3 you get a 4
So 5*3= 15 and 5*4=20
25/10 = 5//2 is another one.
Answer:
25/10 = 5/2
3/4 =15/20
Step-by-step explanation:
there are 18 people at the party. some are boys and some are girls. the number of boys is the same as the number of girls
Answer:
9 boys 9 girls
Step-by-step explanation:
18 = 2x
9
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]
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
there is a ratio of 7 boys to every 4 girls. If there are 64
s, how many boys are in the school?
Answer:
112
the answer is 112 :)))))
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]
Find tan θ if sec θ = root 37/6 and sin θ < 0
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
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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what is the slope of the graph in the picture
pls help it's closing in 40 minutes
pls explain how you got the answer
Answer:
-2
or
-2/1
Explanation:
**Slope = rise/run**
By counting the distance between the points, from (0,3) to (1,1) , it went down 2 units and right by 1 unit
Answer:
m= -2
Step-by-step explanation:
Pick two points and subtract the y coordinates, then subtract the x coordinates, (0,3) and (1,1) or (1,1) and (2,-1)
[tex]m = \frac{y_{2_ } - y_{1} }{x_{2} -x_{1} } = \frac{1-3}{1-0} = \frac{-2}{1} = -2[/tex] [tex]\frac{-1-1}{2-1} = \frac{-2}{1} = -2[/tex]
4x - 2y = -20
7x + 2y = -2
Answer:
(-2, 6)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationSolving systems of equations by graphingStep-by-step explanation:
Step 1: Define systems
4x - 2y = -20
7x + 2y = -2
Step 2: Rewrite systems
4x - 2y = -20
Add 2y to both sides: 4x = 2y - 20Divide 4 on both sides: x = 1/2y - 5Step 3: Redefine systems
x = 1/2y - 5
7x + 2y = -2
Step 4: Solve for y
Substitution
Substitute in x: 7(1/2y - 5) + 2y = =-2Distribute 7: 7/2y - 35 + 2y = -2Combine like terms: 11/2y - 35 = -2Add 35 to both sides: 11/2y = 33Isolate y: y = 6Step 5: Solve for x
Define original equation: 7x + 2y = -2Substitute in y: 7x + 2(6) = -2Multiply: 7x + 12 = -2Subtract 12 on both sides: 7x = -14Divide 7 on both sides: x = -2Step 6: Graph systems
Check the system.
1/3 exponent 4??? pls help immediately
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!!
Factorise fully the following 2x+8
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 :)
Use the method of lagrange multipliers to find
a. The minimum value of x+y, subject to the constraints xy=196, x>0, y>0
b. The maximum value of xy, subject to the constaint of x+y=196
Answer:
a) The function is: f(x, y) = x + y.
The constraint is: x*y = 196.
Remember that we must write the constraint as:
g(x, y) = x*y - 196 = 0
Then we have:
L(x, y, λ) = f(x, y) + λ*g(x, y)
L(x, y, λ) = x + y + λ*(x*y - 196)
Now, let's compute the partial derivations, those must be zero.
dL/dx = λ*y + 1
dL/dy = λ*x + 1
dL/dλ = (x*y - 196)
Those must be equal to zero, then we have a system of equations:
λ*y + 1 = 0
λ*x + 1 = 0
(x*y - 196) = 0
Let's solve this, in the first equation we can isolate λ to get:
λ = -1/y
Now we can replace this in the second equation and get;
-x/y + 1 = 0
Now let's isolate x.
x = y
Now we can replace this in the last equation, and we will get:
(x*x - 196) = 0
x^2 = 196
x = √196 = 14
then the minimum will be:
x + y = x + x = 14 + 14 = 28.
b) Now we have:
f(x) = x*y
g(x) = x + y - 196
Let's do the same as before:
L(x, y, λ) = f(x, y) + λ*g(x, y)
L(x, y, λ) = x*y + λ*(x + y - 196)
Now let's do the derivations:
dL/dx = y + λ
dL/dy = x + λ
dL/dλ = x + y - 196
Now we have the system of equations:
y + λ = 0
x + λ = 0
x + y - 196 = 0
To solve it, we can isolate lambda in the first equation to get:
λ = -y
Now we can replace this in the second equation:
x - y = 0
Now we can isolate x:
x = y
now we can replace that in the last equation
y + y - 196 = 0
2*y - 196 = 0
2*y = 196
y = 196/2 = 98
The maximum will be:
x*y = y*y = 98*98 = 9,604
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
6 friends all use $2 off coupons to buy themselves movie tickets. They spend a total of $42 Write the equation
Answer:
(C / n) + 2
Step-by-step explanation:
Amount spent (C) = 42
Number of friends (n) = 6
Coupon on ticket = $2
Original price of ticket will be :
Cost per coupon ticket = (Total amount spent / number of friends)
(Total amount spent / number of friends) + coupon on ticket
= (C / n) + 2
= (42 /6) + 2
= 7 + 2
= 9
X^3 = 1000 for math please help
Answer:
x=10
Step-by-step explanation:
since there are 3 zeroes in 1,000
x is 10
because 10^3=1000
Answer:
10
Step-by-step explanation:
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
I NEED HELP WITH THIS PICTURE IS PROVIDED
2.5 divided by 1.5 round to nearest tenth
Answer:
1.7
Step-by-step explanation:
2.5÷1.5
5/3
1.66666
1.7
The divisions of 2.5 divided by 1.5 gives to 5/3 or 1.6667.
What is Division?One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.
Given:
2.5 divided by 1.5
So, 2.5 / 1.5
= 25 x 10 / 15 x 10
= 25/15
= 5 x 5 / 5 x 3
= 5/3
Hence, the divisions results to 5/3 or 1.6667
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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! :)
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
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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What is the square root of 153 divided by 13
plz help me fast
Answer:
About 0.95
Step-by-step explanation:
Answer:
0.9514859136
Step-by-step explanation: I use calculator lol
A fair die is tossed 6 times. Find the probability that
(a) 1 “one”, 2 “twos” and 3 “threes” will turn up,
(b) each side will turn up once.
Answer:
Step-by-step explanation:
hi
Answer:
B
Step-by-step explanation: