A statistics professor plans classes so carefully that lengths of her classes are uniformly distributed between 46.0 and 56.0 minutes.The Probability that a given class period runs between 51.5 and 51.75 minutes is 0.025.
What is density?The density of a place refers to the quantity of things—which may include people, animals, plants, or objects—there are in it. Divide the number of objects by area's measurement to determine density. A country's population density is calculated by dividing its total population by its area, expressed in the square kilometers or miles.
A flat distribution with the same probability density for each number is called a uniform distribution. The area beneath the distribution's graph must be 1. This distribution has a range of 10.0 and runs from 46.0 to 56.0 minutes (56.0-46.0). Since the density must be 1/10, 10.0*0.1 Equals 1.0.
Multiply the range between the numbers by the probability density to get the likelihood of being between two numbers
range: 50.75-50.5 = 0.25
0.25*0.1 = 0.025
P(50.5 < x < 50.75) = 0.025
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What is the slope of the line through (-10, 1) and (0, -4)?
The slope of the line through (-10, 1) and (0, -4) is [tex]\frac{-1}{2}[/tex].
The slope of the line is m= [tex]\frac{y_{2}-y_{1} }{x_{2-x_{1} } }[/tex]
= [tex]\frac{ (-4)- (1)}{0- (-10)}[/tex]
= [tex]\frac{-5}{10}[/tex]
= [tex]\frac{-1}{2}[/tex]
What is slope?Slope is a measure of the steepness of a line or part of it connecting two points.
The slope of a line is the ratio of the amount by which y increases when x increases by some amount. The slope shows how steep the line is, or how much y increases as x increases.
Types of slopes
positive slope (if lines go up from left to right) negative slope (if lines go down from left to right) zero slope (if lines are horizontal) undefined slope (if lines go down) down from left to right) lines are vertical)
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Need help with Stats homework, Picture has been uploaded of the question
Solution:
Given that a livestock company reports that the mean weight of a group of young steers is 1123 pounds with a standard deviation of 84 pounds, this implies that
[tex]\begin{gathered} \mu=1123 \\ \sigma=84 \\ \end{gathered}[/tex]A) Percentage of steers that weigh over 1300 pounds.
Step 1: Evaluate the z score value.
The z score value is expressed as
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ where \\ x\Rightarrow sample\text{ value} \\ \mu\Rightarrow mean\text{ value} \\ \sigma\Rightarrow standard\text{ deviation of the sample} \end{gathered}[/tex]In this case, x equals 1300.
Thus, the z score value is evaluated as
[tex]\begin{gathered} z=\frac{1300-1123}{84} \\ \Rightarrow z=2.107142857 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would weigh over 1300 pounds.
Using the normal distribution table, we have
thus,
[tex]\begin{gathered} Pr(z>1300)=0.0175525991947 \\ \end{gathered}[/tex]The percentage of young steers that weigh over 1300 pounds is thus evaluated as
[tex]\begin{gathered} 0.0175525991947\times100 \\ =1.7552991947\% \\ \approx1.8\%\text{ \lparen1 decimal place\rparen} \end{gathered}[/tex]B) Percentage of steers that have weights under 1050 pounds.
Step 1: Evaluate the z score value.
Thus, we have
[tex]\begin{gathered} z=\frac{1050-1123}{84} \\ =-0.869047619 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would have weights under 1050 pounds.
Using the normal distribution table, we have
thus,
[tex]Pr(z<1050)=0.192410542709[/tex]Thus, the percentage of young steers that would have weight under 1050 pounds is evaluated as
[tex]\begin{gathered} 0.192410542709\times100 \\ =19.2410542709\% \\ \approx19.2\%(\text{ 1 decimal place\rparen} \end{gathered}[/tex]C) Percentage of young steers that weigh between 1000 and 1200 pounds.
Step 1: Evaluate the z score value.
[tex]\begin{gathered} z_1=\frac{1000-1123}{84} \\ =-1.464285714 \\ z_2=\frac{1200-1123}{84} \\ =0.9166666667 \end{gathered}[/tex]Step 2: Evaluate the probability that the steer would weigh between 1000 and 1200 pounds.
Using the normal distribution table, we have
thus, we have
[tex]Pr(1000Thus, the percentage of young steers that weigh between 1000 and 1200 pounds is evaluated as[tex]\begin{gathered} 0.748783381404\times100 \\ =74.8783381404\% \\ \approx74.9\% \end{gathered}[/tex]what is the length of a diagonal of an 18’ x 12’ rectangle
Step 1:
Draw the rectangle with the given dimensions
Step 2:
Next, apply the Pythagoras theorem
Opposite = 12
Adjacent = 18
Hypotenuse = L the side facing right angle
Step 3:
[tex]\begin{gathered} \text{Pythagoras theorem} \\ \text{Opposite}^2+Adjacent^2=Hypotenuse^2 \\ 12^2+18^2=L^2 \\ 144+324=L^2 \\ 468=L^2 \\ L\text{ = }\sqrt[]{468} \\ \text{L = 6}\sqrt[]{13} \\ L\text{ = 21.6'} \end{gathered}[/tex]Final answer
The length of the diagonal is 21.6
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4. Solve the quadratic equation x² = 16.
[tex]x^2=16\\\sqrt{x^2}=\sqrt{16}\\x=\lm+/-4[/tex]
x = 4, x = -4
Janet has $50 in a savings account that earns 10% annually the interest is not compounded how much interest will she earn in the next three years
When Janet has $50 in a savings account that earns 10% annually, the interest is $15.
How to calculate the interest?It should be noted that the interest is the extra amount that's given for keeping money for a specified period of time. Interest is the payment of a sum over and above the original amount owed by a lender or deposit-taking financial institution to a depositor or lender, at a set rate.
The formula for calculating interest is given as:
Interest = PRT / 100
where P = Principal. = $50
R = rate = 10%
T = Time = 3
Interest = PRT / 100
Interest = (50 × 10 × 3) / 100.
Interest = 1500 / 100
Interest = $15
The interest is $15.
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Please Help
this is math, PLEASE HELP
A statement of order that shows the relation of the in-town speed limit to the highway speed limit is that the in-town speed limit is less than or equal to 30 and the highway speed limit is less than or equal to 60.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
The rules for writing an inequality.In Mathematics, these four rules are generally used to write an inequality:
When the arrow points to the right on a number line, the inequality is either (≥ or >).When the arrow points to the left on a number line, the inequality is either (≤ or <).The circle/dot on a number line should be filled when the inequality symbol is (≥ or ≤).The circle/dot on a number line should not be filled when the inequality symbol is (> or <).Now, we would apply the aforementioned inequality rules to write the solution to the compound inequality shown in the graph above:
30 ≤ x ≤ 60.
In conclusion, x represent the speed limit for in-town and highway.
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Solve the simultaneous equations
y=x²-x-13
y=x+2
[tex] {x}^{2} - x - 1 = x + 2 \\ {x }^{2} - x - 1 - x - 2 = 0 \\ {x}^{2} - x - x - 1 - 2 = 0 \\ {x}^{2} - 2x - 3 = 0 \\ (x - 3)(x + 1) = 0 \\ x - 3 = 0 \\ \\ or \\ x + 1 = 0 \\ \\ x = 3 \\ \\ or \\ \\ x = - 1[/tex]
WHEN x=3
[tex]y = 3 + 2 \\ y = 5[/tex]
When x=-1
[tex]y = - 1 + 2 \\ y = 1[/tex]
NOW WE HAVE A PAIR OF SOLUTIONS AS
(3,5) and (-1,1)use the ruler to determine the quotients of 1 divided 1/10 and 4 divided 1/10
First:
1 divided 1/10:
1 divided 1/10= 10.
2. 4 divided 1/10:
Using the same procedure:
4 divided 1/10= 40.
Using the ruler:
this implies counting each millimeter contained in 1 centimeter, when it is 1 centimeter, there are ten centimeters, and when it is 4 cm there are 40 mm.
Answer:
1 divided 1/10= 10
4 divided 1/10= 40
my dad left me 2 weeks ago. My teacher said that I have to figure out how many bags of milk hes gotten in the last 2 weeks if he gets 1 bag of milk each day. I have no clue but I want my dad back
Answer:14 becuase
Step-by-step explanation:so your dad left you because he $H!T hates you and he want to divorces your mom and he told me to say $H!T you to you
Find the measure of <1, <2, and <3.
The measure of the angles for the given parallel lines are-
∠1 = 100°∠2 = 80°∠3 = 100°What is defined as the term linear pair?Once two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are referred to as linear. The sum of the angles of a linear pair always is 180°. These angles are also referred to as supplementary angles. The adjacent angles include those that share a vertex. As a result, the linear angles get a common vertex here as well.For the given question;
The set of parallel lines are given;
Thus,
∠1 + 80 = 180 (linear pair)
∠1 = 100°
Now, two set of parallel line form a parallelogram.
Thus, in parallelogram opposite angles are equal.
∠1 = °∠3 = 100°
So, ∠3 = 100°
And, ∠2 = 80° (opposite angle of 80)
Thus, the measure of the angles are calculated.
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please help me with this
The angle 4 is an alternate angle to 80° and this tells us that; ∠4 = 80°
How to find alternate angles?Alternate angles are defined as the angles that occur on opposite sides of the transversal line and have the same size. Thus, Alternate angles are always equal.
These interior alternate angles can be gotten by drawing a Z shape which produces two different types of alternate angles namely alternate interior angles and alternate exterior angles.
Now, we are given that only one known angle in the image which is 80°. However, we see that the angle we want to find which is angle 4 is an alternate angle to the known angle.
Thus, by definition of alternate angles, we can say that ∠4 = 80°
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A member of a book club wishesto purchase two books from aselection of eight booksrecommended for a certainmonth. In how many ways canshe choose them?Note: Crnn!r!(n-r)!
From a total of 8 books, she has a choice of 2 in 28 different ways.
What is permutation and combination ?When things are of diverse kinds, the term "permutation" is used to describe the various arrangements that could be made. Combination, meanwhile, is the quantity of smaller groups or sets that can be created from the components of a bigger set.
The member must select 2 books from a group of 8 books in the scenario that is provided. It is not important what sequence you select your books in. If a member chooses books A and B or books B and A, for instance, she is choosing the same books from the list of available titles (A,B,C,D,E,F,G, and H). By extension, this is a problem of combinations since the order of the selections is irrelevant in this situation.
Eight books, two at a time, must be combined to produce
The general formula of combination is :
[tex]nC_{r} = \frac{n!}{r!(n-r)!}[/tex]
Using the values of n=8 and r=2, we get:
[tex]8C_{2}[/tex] = [tex]\frac{8!}{2!(8-2)!}[/tex]
=28
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If a= -2, b= -4, and C=5,
evaluate c-(a+b)
Order -9, -8, 15, 0 from greatest to least
15, 0, -8, -9
Negatives go backwards
During an experiment, the temperature of a liquid, in degrees Celsius, is given by the function t(m)= -0.2m+6, where m is the number of minutes since the experiment began.
Which graph correctly shows this function?
The graph of the linear function t(m) = -0.2m + 6 is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the constant rate of change of the linear function.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis, and can also be interpreted as the initial value of the function.In this problem, the function is defined by:
t(m) = -0.2m + 6.
Hence:
The slope is of m = -0.2.The intercept is of b = 6.To graph the function, we have to consider the constraint that the time cannot be negative, hence the domain is:
t ≥ 0.
Thus, the graph is given by the image at the end of the answer.
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65 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows:
# of Pairs of Shoes 4 5 6 7 8 9 10 11 12 13
Frequency 8 5 4 4 7 14 6 7 6 4
The mean of the number of shoes according to the obtained results is; 8.49.
The median of the number of pairs of shoes obtained is; 9.
What is the mean and median of the frequency distribution?It follows from the complete task content that the mean and median of the data set are to be evaluated;
Since the mean is the average of all obtained data values, it follows from the mean formula;
Mean = Sum Total/Total Frequency
Mean = { ( 8 × 4 ) + ( 4 × 5 ) + .......+ (13 × 4) } / 65
Mean = 552/65
Mean = 8.49.
Also, the median of the set of 65 data values can be guessed to be the 33rd term.
On this note, the data value which corresponds to a cumulative frequency of 33 upon orderly arrangement is the median term.
Hence, since; 8 + 5 + 4 + 4 + 7 = 28; Hence, upon addition of 14, we have; 42.
Therefore, the median of the number of pairs of shoes is; 9 pairs of shoes.
Remark; The complete task requires that the mean and median be determined.
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Josie’s best friend is getting married and she wants to buy her something from her online wedding registry. She wants to buy some sets of dishes (d) that cost $35 each. Because she’s buying online, she must pay a shipping fee of $10. Josie wants to spend $150 or less. How many sets of dishes can Josie buy?
Answer:
Josie can by 4 dish sets.
Step-by-step explanation:
Josie’s best friend is getting married and she wants to buy her something from her online wedding registry. She wants to buy some sets of dishes (d) that cost $35 each. Because she’s buying online, she must pay a shipping fee of $10. Josie wants to spend $150 or less. How many sets of dishes can Josie buy?
can be represented by equation:
35d + 10 = 150
subtract 10 from both sides:
35d + 10 - 10 = 150 - 10
35d = 140
divide both sides by 35:
35d/35 = 140/35
d = 4
Josie can by 4 dish sets.
check:
35(4) + 10 = 150
(2.43u − 18) − (−7 + 6.8u)
Answer: The answer is -4.37u-11
Step-by-step explanation: Just do math.
Suppose that 15% of the time Danny goes swimming twice a week, 35% of the time he goes swimming once a week, and 50% of the time he doesn't go swimming at all in a given week. What is the expected value for the number of times Danny goes swimming during a week?
The expected value for the number of times Danny goes swimming during a week is 0.65.
Given that:-
Percentage of time Danny went swimming twice a week = 15 %
Percentage of time Danny went swimming once a week = 35 %
Percentage of time Danny doesn't go swimming at all in a given week = 50%
The expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values.
Hence, based on the data given in the question, we can write,
Expected value n how many times Danny will go to swimming in a week = 15 %*2 + 35 % * 1 + 50 % *0 = 0.3 + 0.35 + 0 = 0.65
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match the angle to its corresponding visual representation
1) Alternate interior angles
2) Corresponding angles
3) Alternate exterior angles
4) Same-side interior angles
5) Vertical angles (angles opposite of each other)
Describe the rate of change for the function f (x)=[tex]\sqrt{x}[/tex]
The rate of change is [tex]\frac{1}{2\sqrt{x} }[/tex]
What is rate of change ?The link between one quantity changing in respect to another is given by the rate of change formula.can be used to calculate the rate of change from y coordinates to x coordinates (x2 - x1 ). The rate of change m for a linear function is written as y=mx+b in the slope-intercept form for a line, whereas the rate of change for a function is written as (f(b)-f(a))/b-a. It is said that the rate at which one quantity changes in relation to another is known as the rate of change function. The amount of change in one item is simply divided by the comparable amount of change in another when calculating the rate of change.
Given that : The function f (x)=[tex]\sqrt{x}[/tex]
f (x)=[tex]\sqrt{x}[/tex]
[tex]f^{'} x = \frac{1}{2\sqrt{x} }[/tex]
The rate of change is [tex]\frac{1}{2\sqrt{x} }[/tex]
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Need help on homework
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
function G(x)
Step 02:
discrete finite function:
range:
we must analyze the function to find the solution.
range:
{ 3 , 5 , 8 }
The answer is:
range:
{ 3 , 5 , 8 }
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Una masa de 2,0 kg está unida al extremo de una cuerda de 5,0 m. La masa se mueve en una trayectoria circular sobre una superficie horizontal sin rozamiento. Si la resistencia a la rotura de la cuerda es 40 N, la máxima velocidad lineal con la que se puede hacer girar la masa sin que se rompa la cuerda es aproximadamente
La maxima velocidad lineal de la masa con la que se puede girar la masa es igual a 40 newtons.
¿Cuál es la velocidad lineal máxima permitida por la masa en movimiento circular uniforme?
En este problema tenemos el caso de una masa (m), en kilogramos, conectada a una cuerda y que experimenta un movimiento circular uniforme, en donde la partícula describe un movimiento a velocidad lineal constante (v), en metros por segundo, debido a una aceleración radial que está en la forma de tensión (T), en newtons, a través de la cuerda. En consecuencia, la velocidad máxima permitida es determinada a partir de las leyes de Newton:
T = m · (v² / R)
Donde:
m - Masa, en kilogramos.v - Velocidad lineal, en metros por segundo.R - Longitud de la cuerda, en metros.Si sabemos que m = 2 kg, R = 5 m y T = 40 N, entonces la maxima velocidad lineal permitida es:
40 N = (2 kg) · v² / (5 m)
v = 10 m / s
La maxima velocidad lineal permitida es igual a 10 metros por segundo.
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5. The weight of an empty box is 56.7 grams. If there are 940 feathers with unit
weight of 0.000567 kilogram in the box, find the total weight, in kilogram,
of the box with 940 feathers inside. Write your answer in scientific notation.
Round the coefficient to the nearest tenth.
the nearest tenth
The sum of the weight of the empty box and the 940 feathers is approximately [tex]5.90 \times {10}^{ - 1} [/tex] kg.
What is a scientific notation?A number is expressed using scientific notation when it contains a number larger than 1 but less than 10, that multiplies a power of 10
The empty weight of the box = 56.7 grams
The number of feathers added = 940 feathers
Mass of one feather (unit weight) = 0.000567 kilogram
The total weight of the box with the 940 feathers is found as follows;
56.7 grams = 0.0567 kilograms
Mass of the empty box in kilograms = 0.0567 kilograms
Total mass of the 940 feathers 0.000567 × 940 = 0.53298 kilograms
The total weight of the box with the 940 feathers inside is; 0.0567 kilograms + 0.53298 kilograms = 0.58968 kilograms
The total weight of the box and the feathers = 0.58968 kilograms =
[tex]5.8968 \times {10}^{ - 1} [/tex]
kilograms
Rounding the coefficient to the nearest tenth gives;
The total weight of the box and the feathers is approximately [tex]5.90 \times {10}^{ - 1} [/tex] kilograms
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pls help with geometry 9th-grade honors
The measures of the internal angles of the triangle are given as follows:
Angle A: 55º.Angle B: 90º.Angle C: 35º.What is the sum of the internal angles of a triangle?
A triangle is composed by three internal angles, and the sum of it's measures is of 180º.
In the context of this problem, the measures are given as follows:
Angle A: 3x + 10.Angle B: 6x.Angle C: 2x + 5.Considering that the sum is of 180º, we can build an equation to solve for x as follows:
3x + 10 + 6x + 2x + 5 = 180
11x + 15 = 180
11x = 165
x = 165/11
x = 15
Hence the measures of the angles are given as follows:
Angle A: 3(15) + 10 = 55º.Angle B: 6(15) = 90º.Angle C: 2(15) + 5 = 35º.More can be learned about the sum of the internal angles of a triangle at https://brainly.com/question/25215131
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The measure of the angles are;
m∠ A = 55 degreesm∠ B = 90 degreesm∠ C = 35 degreesHow to determine the value of each angleIt is important to note that the sum of angles in a triangle is supplementary.
Also, supplementary angles are defined as pair of angles that sum up to 180 degrees.
Two angles are termed supplementary when they add up to give 180 degrees.
Since, we have that the sum of the interior angles of a triangle are supplementary, then,
Angle A + Angle B + Angle C = 180 degrees
Given the values as;
m∠ A = 3x + 10m∠ B = 6xm∠ C = 2x + 5Now, put or substitute the values into the formula
3x + 10 + 6x + 2x + 5 = 180
collect like terms
3x + 6x + 2x = 180 - 15
Add or subtract like terms
11x = 165
Make 'x' the subject by dividing both sides by the coefficient of x, we have;
11x/11 = 165/11
Find the quotient
x = 15
But we have to find the angles by substituting the value of x
m∠ A = 3x + 10 = 3(15) + 10 = 55 degrees
m∠ B = 6x = 6(15) = 90 degrees
m∠ C = 2x + 5 = 2(15) + 5 = 35 degrees
Hence, the angles are 55 degrees, 90 degrees and 35 degrees respectively.
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6 plus 8 divided by 2
Using the PEMDAS ( In order to know the order of the operations)
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
Accordint to this, we need to divide first, and then we need to add the resultant number, so:
[tex]\begin{gathered} 6+8\div2=6+4=10 \\ \\ \end{gathered}[/tex]Answer:
10
Darius runs with an acceleration of 21 m/s2 and has a force of 400N. Calculate his mass.
we can use the formula
[tex]F=m\times a[/tex]where F is the force, m the mass and a the acceleration
now, replacing
[tex]400=m\times21[/tex]then solve for m
[tex]\begin{gathered} m=\frac{400}{21} \\ \\ m=19.05 \end{gathered}[/tex]the mass is 19.05Kg
What is the y-intercept? Select the correct choice below and fill in any answer boxes within your choice.
We have the relation:
y = 4x + 3
Since the slope (4) and the y-intercept (3) were already found, we need now to graph this line.
In order to do so, we can find two points belonging to this line and then draw a line that passes through those points.
The first point can be (0, 3), since we know that the y-intercept is 3, i.e., y = 3 for x = 0.
Now, to find a second point we can choose a value for x, let's say x = 1, and use it in the equation of the line to find the corresponding value of y:
y = 4x + 3 , x = 1
y = 4 * 1 + 3
y = 4 + 3
y = 7
So, (1, 7) is another point we can use.
Now, we can select the second button on the toolbox to draw a line through the points (0, 3) and (1, 7):