Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 49 and 69 minutes is 0.8403 = 84.03%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 54, \sigma = 5[/tex]
The relative frequency of classical CDs with playing time X between 49 and 69 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 49, hence:
X = 69:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{69 - 54}{5}[/tex]
Z = 3
Z = 3 has a p-value of 0.9987.
X = 49:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 54}{5}[/tex]
Z = -1
Z = -1 has a p-value of 0.1584.
0.9987 - 0.1584 = 0.8403.
More can be learned about the normal distribution at https://brainly.com/question/4079902
#SPJ1
a
Find tan a.
r
√5,-√7)
✓[?
Enter
Answer:
[tex]tan(\alpha)=-\frac{\sqrt{35}}{5}[/tex]
Step-by-step explanation:
Tan can be defined as: [tex]\frac{sin(\theta)}{cos(\theta)}[/tex] as it simplifies to opposite/adjacent. If you know a bit about the unit circle, you'll know that the x-coordinate is going to be cos(theta) and the y-coordinate is going to be sin(theta). Since the sin(theta) is defined as opposite/hypotenuse, and the hypotenuse = 1, so sin(theta) is defined as the opposite side, which is the y-axis. Same thing goes for cos(theta), except the adjacent side is the x-axis.
Using this we can define tan
[tex]sin(\alpha)=-\sqrt{7}\\cos(\alpha)=\sqrt{5}\\\\tan(\alpha)=-\frac{\sqrt{7}}{\sqrt{5}} * \frac{\sqrt{5}}{\sqrt{5}}\\tan(\alpha)=-\frac{\sqrt{7*5}}{5}\\tan(\alpha)=-\frac{\sqrt{35}}{5}\\[/tex]
Answer:
tan α = -√35/5
Step-by-step explanation:
tan α = y/x
tan α = -√7/√5
tan α = -√7/√5 × √5/√5
tan α = -√35/5
Necesito ayuda en esto!!
1. f(x)= x²+3
2. f(x)= x²+1
3.f(x)= x²+4
4. f(x)= -x²-1
Por favor,ayúdenme
Answer:
they are no instructions so no answers either.
Step-by-step explanation:
am sorry I can't help you, the question might not have been complete. please do contact me when it's.
a cake shop sells cakes and cupcakes. a cake uses 5 cups of cake batter. a batch of cupcakes uses 4 cups of batter. the pastry chef has 40 cups of cake batter and wants to make at least 4 cakes. the profit on a cake is $35 and the profit for a batch of cupcakes is $30. How many cakes and batches of cupcakes should the pastry chef make in order to maximize profits? what is the maximum revenue?
Chef should prepare 4 cakes and 5 batches of pastry in order to achieve maximum profits and his maximum profit or revenue by solving through inequality is $260.
Given Chef uses 5 cups of cake batter for 1 cake and 4 cups of batter for 1 batch of cupcakes. Chef wants to make at least 4 cakes. Profit on 1 cake is $35 and $30 for 1 batch of cupcake.
let the number of cakes be x and the number of batches of cupcakes be y such that
5x+4y<=40--------1
x>=4---------------2
Maximize Profit=35x+30y
Inequalities contains different signs so we have to change one inequality.
5x+4y<=40
-x<=-4
Now assume them equalities
5x+4y=40-------3
-x=-4
multiply second equations by 5
-5x=-20-----------4
now add 3 and 4
5x+4y-5x=40-20
4y=20
y=5
now put the value of y in 5x+4y=40
5x+4*5=40
5x+20=40
5x=20
x=4.
Maximum Profit=35x+30y
=35*4+30*5
=$260
Hence chef should make 4 cakes and 5 batches of pastry and maximum profit of $260.
Learn more about inequality at https://brainly.com/question/11613554
#SPJ10
A bag contains marbles of 2 colors - green and blue. The theoretical probability of choosing a green marble is 0.55. The number of green marbles is 22. Find the number of blue marbles in the bag.
The number of blue marbles in the bag is 18.
What is the number of blue marbles?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability of choosing a green marble = total number of green marbles / total number of marbles
0.55 = 22/x
x = 22 / 0.55
x = 40
Total number of blue marbles = 40 - 22 = 18
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
Function g is defined as . What is the value of c?
The value of c is 3
How to solve for c?The complete question is in the attached image
The function definition is given as:
g(x) = f(x) - c
From the graph of functions f(x) and g(x), we can see that:
f(x) is shifted down by 3 units to get to g(x)
This means that:
g(x) = f(x) - 3
By comparing g(x) = f(x) - 3 and g(x) = f(x) - c,
We have:
c = 3
Hence, the value of c is 3
Read more about function transformation at:
https://brainly.com/question/13810353
#SPJ1
Find the contrapositive for the following statement if you are in college, then you graduated from high school
Answer:
If you didn't graduate from High school ,Then you are not in college
Step-by-step explanation:
statement :
if you are in college, then you graduated from high school
In the given statement we have :
The Hypothesis is : you are in college
The conclusion is : you graduated from high school
in order to get the contrapositive ,
• first we switch the hypothesis and the conclusion
( H ⇒ C becomes C ⇒ H )
• Second, we negate the hypothesis and the conclusion.
Then
• first ,if you graduated from high school , then you are in college
• second , If you didn't graduate from High school ,Then you are not in college
00
How many faces does the following shape have?
Answer:
this is a cube so it has 6 faces
Hope This Helps!!!
Write the equation of the line, in
standard form Ax+By=C, that has a
slope of -4 and passes through the point
(1, -3).
(Do NOT put any spaces between terms
when you type in your answer below.)
Answer:
4x + y = 1
Step-by-step explanation:
Start with the familiar format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).
With a slope of -4, we can write:
y = -4x + b
We need to find a value for b that forces the line through point (1,-3). This is done by entering this point in the equation and solving for b:
y = -4x + b
-3 = -4*(1) + b
b = 1
The equation is y = -4x + 1, This can be rewritten as:
4x + y = 1
Se attached graph.
Solve to find x and y in the diagram.
The figure shows two parallel lines and a transversal. The intersection of the first line and the transversal forms four angles, the bottom right angle measures 5 times x plus 4 times y degrees. The intersection of the second line and the transversal forms four angles, the top right angle is labeled as a right angle, the bottom right angle measures 12 times y degrees.
Considering the given information in the question, the value of x is [tex]12^{o}[/tex], and that of y is [tex]7.5^{o}[/tex].
A transversal is a line that cuts through two given parallel lines. Thus it intersects each parallel line at a point, forming four angles each.
From the given information in the question, it can be inferred that:
the given bottom right angle of the first intersection and the bottom right angle with the second intersection are congruent (corresponding angle property).
So that,
[tex](5x+4y)^{o}[/tex] = [tex](12y)^{o}[/tex]
[tex]5x^{o}[/tex] = [tex]12y^{o}[/tex] - [tex]4y^{o}[/tex]
[tex]5x^{o}[/tex] = [tex]8y^{o}[/tex]............ 1
Also given that the top right angle at the second intersection is a right angle, then;
[tex]12y^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex] (sum of angles on a straight line)
This implies that;
[tex]12y^{o}[/tex] = [tex]180^{o}[/tex] - [tex]90^{o}[/tex]
[tex]12y^{o}[/tex] = [tex]90^{o}[/tex]
So that,
y = [tex]\frac{90}{12}[/tex]
y = [tex]7.5^{o}[/tex]
Thus substituting the value of y in equation 1, we have;
[tex]5x^{o}[/tex] = [tex]8y^{o}[/tex]........ 1
= 8(7.5)
5x = 60
x = [tex]\frac{60}{5}[/tex]
x = [tex]12^{o}[/tex]
Therefore, x = [tex]12^{o}[/tex] and y = [tex]7.5^{o}[/tex]
For more clarification on a transversal of two parallel lines, check: https://brainly.com/question/1751268
#SPJ1
Kindly contact a 1-on-1 tutor if more explanations are needed.
An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic Step 1 of 2: Suppose a sample of 2676 new car buyers is drawn. Of those sampled, 642 preferred foreign over domestic cars. Using the data, estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places. AnswerHow to Enter 2 Points Tables Keypad Keyboard Shortcuts An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 2 of 2: Suppose a sample of 2676 new car buyers is drawn. Of those sampled, 642 preferred foreign over domestic cars. Using the data, construct the 98 % confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars. Round your answers to three decimal places, Answer low to Enter) 2 Points T Tables Keypad Keyboard Shortcuts Lower endpoint Upper endpoint:
The proportion of people who preferred foreign cars than domestic cars is 0.24 and the confidence interval for the population proportion of new cars over domestic cars of 98% confidence interval is (641.955,642.045).
Given sample size of 2676 and number of people preferred foreign cars than domestic cars is 642.
We have to calculate the proportion of people who preferred foreign cars than domestic cars and the confidence interval which shows the confidence interval of 98%.
Number of people prefer foreign cars than domestic cars=642
Sample size=2676
Proportion=642/2676
=0.2399
=0.24 (After rounding off)
Now we will find confidence interval.
X=642
n=2676
z value for the confidence interval 98% is 2.33
Confidence interval =X± z*s/[tex]\sqrt{n}[/tex]
Upper =642+2.33*1/[tex]\sqrt{2676}[/tex] (we have taken s=1)
=642+0.045
=642.045
Lower=642-2.33*1/[tex]\sqrt{2676}[/tex]
642-0.045 (putting values in formula given above)
=641.955
Hence the proportion of people preferred foreign cars than domestic cars is 0.24 and the confidence interval is (641.955,642.045).
Learn more about confidence interval at https://brainly.com/question/15712887
#SPJ4
Write an inequality that represents the set of all numbers shown on the number line.
Answer:
-8 ≤ x ≤ -1
Step-by-step explanation:
When working with inequalities, closed circles always represent greater than or equal to and less than or equal to signs.
The x is placed between the -8 and the -1, as it represents all numbers greater than -8 and less than -1
Answer: -8 ≤ x ≤ -1
Step-by-step explanation: :p
Find the x 44in 55in
Answer:
33in
Step-by-step explanation:
write the first step in an indirect proof of the given statement
Answer: C
Step-by-step explanation:
When doing an indirect proof, you begin by assuming the inverse of the statement you want to prove.
The mass of an electron is approximately 9 × 10-28 grams, while the mass of a neutron is approximately 2 × 10-24 grams. Which of the following is true?
A. The mass of a neutron is approximately 10,000 times the mass of an electron.
B. The mass of a neutron is approximately 1,000 times the mass of an electron.
C. The mass of a neutron is approximately 2,000 times the mass of an electron.
D. The mass of a neutron is approximately 20,000 times the mass of an electron.
Answer: the mass of a neutron is approximately 2,000 times the mass of an electron
Step-by-step explanation:
- the easiest way to solve this (in my opinion) is to simply divide the mass of a neutron by the mass of an electron
- [tex]2 x10^{-24} / (9 x10^{-28} )[/tex]
= [tex](2/9) x10^{-24--28}[/tex]
= [tex](2/9)x10^{-24+28}[/tex]
≈ [tex]0.2222x10^{28-24}[/tex]
≈ [tex]0.2222x10^{4}[/tex]
≈ which is approximately 2222
- so 2222 is approximately 2000 times
- therefore, the mass of a neutron is approximately 2,000 times the mass of an electron
hope this helps :)
Answer:
C. The mass of a neutron is approximately 2,000 times the mass of an electron.
Step-by-step explanation:
Divide the mass of the neutron by the mass of the electron:
[tex]\implies \sf \dfrac{mass\:of\:neutron}{mass \: of \: electron}=\dfrac{2 \times 10^{-24}}{9 \times 10^{-28}}[/tex]
Rewrite:
[tex]\implies \sf \dfrac{2}{9} \times \dfrac{10^{-24}}{10^{-28}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \sf \dfrac{2}{9} \times 10^{-24-(-28)}[/tex]
Simplify:
[tex]\implies \sf \dfrac{2}{9} \times 10^{4}[/tex]
[tex]\implies \sf 0.\.{2} \times 10^{4} \approx 2000[/tex]
Therefore, the mass of a neutron is approximately 2,000 times the mass of an electron.
Check
[tex]\begin{aligned}\textsf{mass of neutron} & = \sf \textsf{mass of electron} \times 2000\\\implies \textsf{mass of neutron} & =\sf 9 \times 10^{-28}\times 2000\\& =\sf 9 \times 10^{-28}\times 2 \times 10^3\\& =\sf 18 \times 10^{-28+3}\\& =\sf 18 \times 10^{-25}\\& = \sf 1.8 \times 10^{-24}\\& \approx \sf 2 \times 10^{-24}\end{aligned}[/tex]
A sample of neon gas at 50.°c and a volume of 2.5 l is cooled to 25°c. what is the new volume? use the formula: v1 t1 = v2 t2 2.3 l 2.7 l 5.0 l 32.3 l
The new amount of neon gas when the temperature drops is 2.30L.
Charles's law
Charles's law states, "The volume occupied by a particular amount of gas is directly proportional to its absolute temperature.
Initial temperature of gas T₁ = 50 ° C = 323.15K
Initial volume of gas V₁ = 2.5L
Final temperature T₂ = 25 ° C = 298.15K
Final capacity V₂ =? Neon gas, substitute the given value into the above equation:
V₁ / T₁ = V₂ / T₂
V₂ = V₁T₂ / T₁
V₂ = (2.5L × 298.15K) ) / 323.15K
V₂ = 2.30 l
Therefore, the new volume when the temperature of the neon gas drops is 2.30l.
Learn more about Charles's law here: brainly.com/question/12835309
#SPJ4
Answer:
A. 2.3
Step-by-step explanation:
How do you solve the expression 1x + 4 ≤ 8?
1x + 4 ≤ 8
x + 4 ≤ 8
x ≤ 8 - 4
=x ≤ 4
What is the sum of the first six terms of the geometric series? 2 – 6 18 – 54 ...
The sum of the first six terms of the geometric series is -364.
A geometric series is a sequence of terms in a fixed common ratio.
Apparently, the expression "geometric progression" comes from the "geometric mean" (Euclidean term) of segments of lengths a and b: it is the length of the side c of a square whose area is equal to the area of the rectangle. a and b. May
The series given is
2 – 6 + 18 – 54 + ...
The sum of n terms of a geometric series is given by
Sn=a1 * 1 - rn/1 - r
here the first term is 2
r = -6 /2 = -3
S = 2 (1-(-3)⁶)/(1-(-3))
S = -364
Therefore the sum of the First six terms of the geometric series is -364 .
Learn more about geometric series here:https://brainly.com/question/24643676
#SPJ4
Answer:
B
Step-by-step explanation:
Edge
Select the correct answer.
Which equation represents the measure of the unknown angles?
The equation which represents the measure of the unknown angles is x + x + 10 =130. Hence, option C is correct.
What is an equation?Equations are mathematical expressions that have two algebra on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the data given in the question,
As per the rules, the sum of the three sides of a triangle is 180°.
The angles are x, x+10, and 50.
Now,
x + x + 10 + 50 = 180
x + x + 10 = 180 - 50
x + x + 10 = 130°.
Therefore, the equation option above is the correct answer.
To know more about equation:
https://brainly.com/question/10413253
#SPJ2
332,519,000 in scientific notation
Answer:
332519000 in scientific notation is 3.32519 x 10^8
Step-by-step explanation:
Hope that helped
Answer:
The form is a * 10ᵇ where 0 < a < 10
Find the surface area. Round your answer to the nearest hundredths, if necessary. Leave your answer in terms of for answers that contain .
Answer:
Area of triangle = (base x height)/2
There are all together 4 triangles and 1 square.
Therefore, surface area = area of square + 4 x area of triangle
height = 5.8 in, base = 6 in. area of square = 6x6 = 36 in^2.
area of 1 triangle = (5.8x6)/2
area of 4 triangles = 2x5.8x6 = 69.6 in^2
surface area = 69.6 + 36 = 105.6 in^2
Step-by-step explanation:
The volume of the cube is 8 cubic inches. Find its side.
Answer:
a = 2
Step-by-step explanation:
Given:
Volume (V) = 8To find:
The side (edge)Steps:
a = V^1/3 = 8^1/3 = 2
Help me please for 50 points
I'll also give brainliest
Answer: B. 150°
Step-by-step explanation:
The angle is obviously obtuse and is therefore greater than 90°.
This rules out A. and C.
Also, this angle is not 180° because then it would be flat.
This rules out D.
Leaving the correct answer to be B. 150°
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What's
the solution set of this problem?
0 (-2,-21)
0 (-2,-21
O [-21,42)
(21,42)
Answer:
[tex]x \leqslant - 21[/tex]
Step-by-step explanation:
[tex]5(x + 27) \geqslant 6(x + 26)[/tex][tex]5x + 135 \geqslant 6x + 156[/tex]
[tex] - 21 \geqslant x[/tex]
[tex]x \leqslant - 21[/tex]
3. (a.) The 12th term of a linear sequence is 74 and the sum of the first three terms is 42, Find (i.) the first term and the common difference (ii.) the sum of the first 10th terms of the sequence. pls answer it is urgent pls
Select the correct answer from each drop-down menu.
Graph of transformation of functions on a coordinate plane. Curve A goes through (minus 1, minus 1) and (1, 1). Curve B goes through (minus 1, minus 4), (0, minus 2), and (1, minus 1). Curve C goes through (minus 1, minus 2), (0, 0), and (1, 2).
The parent function f(x) = x3 is represented by graph A. Graph A is transformed to get graph B and graph C. Write the functions represented by graph B and graph C.
Graph B represents the function g(x) =
.
Graph C represents the function h(x) =
.
The function g(x) = x³ - 2
The function h(x) = 2x³
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
parent function = x³
As, function is shifted vertically down by 2 units to obtain g(x).
So, g(x) = x³ - 2
function h(x) Horizontally by a factor of 2, to obtain, h(x).
So, h(x) = 2x³
Learn more about function here:
https://brainly.com/question/7747242
#SPJ1
2 dogs, 4 horses 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
Answer:
10
Step-by-step explanation:
2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.
Evaluate 8 + w / 4 when w =16
Answer:
12
Step-by-step explanation:
16/4=4
4+8=12
Which of the following best describes the graph of the following linear equation?
y − 9 = -9
Horizontal line with y-intercept at (0,0)
Vertical line with y-intercept at (0,0)
Vertical line with x-intercept at (18,0)
Horizontal line with x-intercept at (9,0)
Answer:
Horizontal line with y-intercept at (0,0)
Step-by-step explanation:
y - 9 = -9
Adding 9 to both sides:
y = 0
So it is the x axis.
Pls heeeelp!!!!!!!!!!!!!!!
The area of a parallelogram is simply its base (6.1 miles) multiplied by its height (2.6 miles).
Substitute the values into the formula for area.
[tex]A=6.1\cdot2.6[/tex]
Multiply.
[tex]A=\boxed{15.86}[/tex]
Note that the answer is given in square miles ([tex]\text{mi}^2[/tex]) since both of the measurements used are in miles.
A combination lock like the one shown has three dials. Each of the dials has numbers ranging from 0 to 4. How many different combinations are possible with the lock?
If combination requires 3 numbers ranging from 0 to 4 then number of combinations is 10.
Given A combination lock contains three numbers from 0 to 4.
Combinations refers to a technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Total numbers available to be selected are 5 from 0 to 4.
In this 0 is also included because it is also a number.
Numbers to be filled in the combination lock =3
So to calculate the combinations we need to use nCr formula in which n=5 and r=3.
Combinations=5C3
=5!/3!*(5-3)!
=5!/3!*2!
=5*4*3!/3!*2!
3! will be cancelled from numerator and denominator
=5*4/2
=10
Hence the number of possible combinations are 10.
Learn more about combinations at https://brainly.com/question/4658834
#SPJ10