Assume that females have pulse rates that are normally distributed with a mean of 76.0 beats per minute and a standard deviation of 12.5 beats per minute. A) If 4 adult female is randomly selected, find the probability that her pulse rate is less than 80 beats per minute.
The probability that their mean pulse rate is less than 80 beats per minute is of:
0.7389 = 73.89%.
How to obtain a probability using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 76, \sigma = 12.5, n = 4, s = \frac{12.5}{\sqrt{4}} = 6.25[/tex]
The probability that their mean pulse rate is less than 80 beats per minute is the p-value of Z when X = 80, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (80 - 76)/6.25
Z = 0.64
Z = 0.64 has a p-value of 0.7389.
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If the figure above is rotated 90° counterclockwise, in which quadrant will it appear?
A. I
B. II
C. III
D. IV
Answer: Depends on what quadrant it starts in/on.
Step-by-step explanation:
Quadrant 1 is the top-right corner.
Quadrant 2 is the top-left corner.
Quadrant 3 is the bottom-left corner.
Quadrant 4 is the bottom-right corner.
Depending on what quadrant you started on will determine what quadrant you're on after rotating 90 degrees counter-clockwise.
If a sum of $500 were shared among a group of people in the following ratios, how much would each person receive?
If a sum of $500 were shared among a group of people in the following ratios,
a) 6:4 then, 6x = 300 and 4x = 200.
b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.
c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50
d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.
What is ratio?
Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.a) 6:4
Let it be 6x , 4x
6x + 4x = 500
10x = 500
x = 50
Then, 6x = 300 and 4x = 200.
b) 1:4:5
Let be x, 4x, 5x
x + 4x + 5x = 500
10x = 500
x = 50.
Then x = 50 , 4x = 200 and 5x = 250.
c) 1 : 8 : 1
x + 8x + x =500
10x = 500
x = 50
Then, x =50 , 8x = 400 and x = 50
d) 10 : 5: 4: 1
10x + 5x + 4x + x = 500
20x = 500
x = 25
Then, 10x = 250 , 5x = 125, 4x = 100, x = 25.
Hence, If a sum of $500 were shared among a group of people in the following ratios,
a) 6:4 then, 6x = 300 and 4x = 200.
b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.
c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50
d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.
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2/5*6/7 multiple and write fraction or mixed number in simplest form
Answer:
[tex]\frac{12}{35}[/tex]
Step-by-step explanation:
multiple the numerators together 2 x 6 = 12 and multiply the denominators togethers 5 7 = 35
what is the solution to -3x-3<6
Answer:
x>-3
Step-by-step explanation:
1
Add
3
to both sides
-3x-3<6
-3x-3+
2
Simplify
Add the numbers
Add the numbers
-3x<9
3
Divide both sides by the same factor, and flip the relation because the factor is negative
-3x<9
4
Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
x>-3
The administrative assistant at a software company often provides breakfast when there is a morning meeting. For last week's sales meeting, she purchased 4 dozen doughnuts and 1 dozen croissants, spending a total of $34. In preparation for yesterday's safety meeting, she spent $52 on 7 dozen doughnuts and 1 dozen croissants. Write a system of equations that could be used in this situation.
Hint: I JUST WANT THE EQUATIONS NOT THE FINAL SOLUTION.
A dozen of doughnuts cost $6 and a dozen of croissants cost $10.
What is meant by a linear equation?A linear polynomial over a field, from which the coefficients are taken, can be reduced to a linear equation by equating it to zero.
Such an equation's solutions are the values that, when used as placeholders for the unknowns, result in the equality being true.
When there are just two variables, it is possible to interpret each solution as the Cartesian coordinates of a particular point on the Euclidean plane. In the Euclidean plane, a linear equation's solutions are represented by lines, and each line can be thought of as the collection of all the solutions to a linear equation with two variables.
Let,
The cost of dozen doughnuts be x
And the cost of dozen croissants be y
Given,
4x+y=34
7x+y=52
By solving both the equations, we get
-3x=-18
x=6
4x+y=34
4(6)+y=34
24+y=34
y=10
Therefore, a dozen of doughnuts cost $6 and a dozen of croissants cost $10.
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The volume of a cube is 64 cubic inches. Which expression represents s, the length of a side of the cube?
Recall the formula Cube volume = s cubed.
Answer:
S=64 x S = length
A production line estimates that 1.50% of the items it produces is defective. In a package containing 200 items, find the probability that no item is defective
The probability of the defective items is given as 0.015.
Given that,
A production line estimates that 1.50% of the items it produces is defective. In a package containing 200 items,
Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
Number of the item = 200
1.5% of the item is defective, = 0.015 [200]
Probability of the defective item = 0.015[200] / 200 = 0.015
Thus, the probability of the defective items is given as 0.015.
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Which property is shown in the matrix addition below?
-6
9
15 -2
0
-3
+
6
-9
-15 2
0
3
commutative property
associative property
Oinverse property
Oidentity property
0 0 0
0 0 0
For the given matrix the additive inverse property is shown.
What is additive inverse of matrix?
The matrix that is created by changing the sign of each matrix element is known as the additive inverse. -(-A)=A is the notation for the additive inverse of the matrix A.
Rows and columns serve as a measure of a matrix's dimensions. Given that it has three rows and three columns, for instance, the matrix below has a dimension of 3 x 3. Three by three can be read off as the matrix's dimension. We consequently obtain the additive inverse of the matrix
M = - M.
Consider the given matrix,
[tex]\left[\begin{array}{ccc}-6&15&-2\\9&0&-3\end{array}\right] + \left[\begin{array}{ccc}6&-15&2\\-9&0&3\end{array}\right] = \left[\begin{array}{ccc}0&0&0\\0&0&0\end{array}\right][/tex]
Here each element in first matrix is negative of the element of second matrix.
That is each element is inverse of the element in second matrix.
And the addition of elements is 0.
Hence, for the given matrix the additive inverse property is shown.
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John's bank account was overdrawn. The status of his account was $-141. He did not realize the problem and wrote another check for $29. The bank charged him a $15 fee for being overdrawn. What was the new status of John's account at this point ?
Answer:
$-185
Step-by-step explanation:
If Johns bank account is at $-141, and he continues to use money, then the equation would look something like this:
-141 + -29 + -15 =?
It's simple! Just add the numbers together!
141 + 29 = 170
170 + 15 = 185
Johns bank account status is now $-185.
Use the following table to find the rate of change. Remember the below equation rise/ run
X 2 4 6 8 10
Y 4 8 12 16 20
pls help :)
The rate of change of the function that is defined by the table:
X: 2 4 6 8 10
Y: 4 8 12 16 20
is r = 2
How to find the rate of change?For a function with two known points (x₁, y₁) and (x₂, y₂), the rate of change between these two points is written as:
r = ( y₂ - y₁)/(x₂ - x₁)
Here we have the table that defines a function:
X: 2 4 6 8 10
Y: 4 8 12 16 20
Here we can use any pair of two points on the table, for example, if we use the first pair and last pair:
(2, 4) and (10, 20)
The rate is:
r = (20 - 4)/(10 - 2) = 16/8 = 2
If we use the first two pairs (2, 4) and (4, 8) we get:
r = (8 - 4)/(4 - 2) = 4/2 = 2
So the rate of change of the function is r = 2.
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A restaurant prepares 250 side salads per day and estimates that 15% of the salads will spoil. What s the spoilage amount for the side salads? (Round up to nearest whole number.) A. 38 salads B. 15 salads C. 40 salads D. 6 salads
Answer:
A
Step-by-step explanation:
15 : 100 = x : 250
x = 250 * 15 / 100
x = 2.5 * 15
x = 37.5
x = 38
A fruit-packing company produced peaches last summer whose weights were normally distributed with mean 14 ounces and standard
deviation 0.8 ounce. Among a sample of 1000 of those peaches, about how many could be expected to have weights of more than
11.2 ounces?
About 999 plants have weights more than 11.2 ounce.
What is z- score?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a given data point deviates from the mean. In essence, standard deviation represents the degree
Given:
Mean= 14
Standard deviation = 0.8
So, P( x > 11.2) = P( (x- [tex]\mu[/tex])/ [tex]\sigma[/tex] > (11.2- 14/ 0.8)
= P( (x- [tex]\mu[/tex])/ [tex]\sigma[/tex] > -3.5)
= 0.999767
Hence, about 999 plants have weights more than 11.2 ounce.
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(need help asap please this is urgent)
Use the systems of inequalities graphed below to answer the questions.
what is the inequality symbol of the green line?
-y is greater than ax+b -y is greater than or equal to ax+b
-y is less tham ax+b
-y is less than or equal to ax+b
what is the inequality symbol of the green line?
-y is greater than ax+b
-y is greater than or equal to ax+b
-y is less tham ax+b
-y is less than or equal to ax+b
is the point (-3, -5) a solution to the system of inequalities?
-yes -no
is the point (1,6) a solution to the system of inequalities?
-yes -no
Answer:
Green line: y is greater than or equal to ax+b
Purple line: y is less than ax+b
(-3, -5) : Yes
(1, 6) : No
Step-by-step explanation:
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Green line
From inspection of the given graph, the green line is a solid line and the shading is above the line.
Therefore, the inequality symbol of the green line is ≥.
"y is greater than or equal to ax+b"
Purple line
From inspection of the given graph, the purple line is a dashed line and the shading is below the line.
Therefore, the inequality symbol of the purple line is <.
"y is less than ax+b"
The solutions to a graphed system of inequalities are found in the overlapping shaded region.
Yes, point (-3, -5) is a solution to the system of inequalities as this point is in the overlapping shaded region.
No, point (1, 6) is not a solution to the system of inequalities as this point is not in the overlapping shaded region.
Select the correct answer.
Consider the graph and the equation of function f.
f(x)=2 sin (1/2x) + 1
Answer:
y = 1
Step-by-step explanation:
The middle of the equation on the graph is y = 1.
URGENT!!!!!!!!!!
identify the conic section represented by the equation x+2=-2(y-3)^2
circle
ellipse
hyperbola
parabola
Step-by-step explanation:
[tex] - \frac{x}{2} - 1 = (y - 3) {}^{2} [/tex]
[tex] - 0.5(x + 2) = (y - 3) {}^{2} [/tex]
A parabola with a vertex (-2,3)
Choose ALL correct answers
(1, -3)
(4, 1)
(6, 3)
(2, -2)
Answer:
(a) (1, -3)
(b) (2, -2)
Step-by-step explanation:
You want to identify two points on the line through (3, -1) that has a y-intercept of -4.
GraphGraphing the line and points is suggested. The attached shows that graph, and identifies the two points on the line as ...
(1, -3) and (2, -2)
__
Additional comment
The equation of the line is x-y=4, so you can tell if the points fall on the line by seeing if they have that difference.
Which of the functions is represented by the graph
Answer:
a
Step-by-step explanation:
just becsue
Put the following values in order from greatest to least.
Justify your answer.
0.388
3/8
38.38%
0.39
Answer:
0.39, 0.388, 38.38%, 3/8
Step-by-step explanation:
Simplify by combining like terms.
3a +15-2a²+5a²-7+5a
Answer:
8a + 3a^2 + 8
The following figure is made of 1 triangle and 1 rectangle.
7,2,11 find the area for each part of the figure and the whole figure
The area of the figures is shown:
Rectangle A: 54 units²
Rectangle C: 21 units²
Triangle B: 3 units²
What is the area?The measurement that expresses the size of a region on a plane or curved surface is called an area.
Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
The area of rectangle A:
Area = l*b
Area = 9*6
Area = 54 units²
Area of rectangle C:
Area = l*b
Area = 3*7
Area = 21 units²
Area of triangle B:
Area = 1/2 * b * h
Area = 1/2 * 3 * 2
Area = 1 * 3
Area = 3 units²
Therefore, the area of the figures is shown:
Rectangle A: 54 units²
Rectangle C: 21 units²
Triangle B: 3 units²
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The Mosley family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt. How much baking powder would they need if they used 1 teaspoon of salt? Simplify your answer and write it as a proper fraction, mixed number, or whole number.
The amount of baking powder would they need to used 1 teaspoon of salt will be 6 teaspoons.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The Mosley family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt.
Now,
Since, The Mosley family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt.
Hence, The amount of baking powder would they need to used 1 teaspoon of salt = 2 × 3
= 6
Thus, The amount of baking powder would they need to used 1 teaspoon of salt will be 6 teaspoons.
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Tim answered all the questions on the math test but got 10 wrong answers. He got 4 points for each correct answer, there were no penalty points for incorrect answers. His score was 76 points. Write an equation to find the total number of questions (q) on Tim’s math test
The equation to find the total number of questions (q) on Tim's math test is 76 = 4x + 0
How to write and solve equation?
Number of wrong questions = 10
Points received for right question = 4 points
Points received for wrong question = 0 points
Total of Tim's score = 76%
According to the given question:
Let the number of questions right answered by Tim be x.
Total points gained by Tim for the right answer = number of questions right answered x Points received for a right answer
= x × 4
= 4x
Points gained by Tim for the wrong answer = number of questions wrong answered x Points received for a wrong answer
= 10 × 0
= 0
Total points scored by Tim = Points gained for the right answer + Points gained for the wrong answer
76 = 4x + 0
76 = 4x
divide both sides by 4
x = 76/4
x = 19
Hence, the number of question answered right by Tim are 19.
Total number of questions attempted by Tim
Total number of questions attempted by Tim
= number of questions answered right +number of questions answered Wrong
= 19 + 10
= 29
Hence, the total number of questions attempted by Tim is 29.
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write the equation of the trigonometric graph.
A trigonometric equation is an equation containing one or more trigonometric ratios of unknown angles. It is expressed as the ratio of the sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) angles. For example, cos2 x + 5 sin x = 0 is a trigonometric equation.
What are examples of trigonometric equations?
Trigonometric equations are equations containing trigonometric functions with one variable. For example, sin x + 2 = 1 is an example of a trigonometric equation. The equation can be as simple as this, or as complex as sin2 x – 2 cos x – 2 = 0.
What are the 4 types of trigonometry?
Side length ratios can be found with six trigonometric functions. The six functions are sine (sin), cosine (cos), tangent (tan), cosecant(cosec), secant (sec), and cotangent (cot).
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Answer(s):
[tex]\displaystyle y = 3sin\:(\frac{2}{3}x + \frac{\pi}{2}) + 2 \\ y = -3cos\:(\frac{2}{3}x \pm \pi) + 2 \\ y = 3cos\:\frac{2}{3}x + 2[/tex]
Step-by-step explanation:
[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{3}{4}\pi} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{2}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\pi} \hookrightarrow \frac{2}{\frac{2}{3}}\pi \\ Amplitude \hookrightarrow 3[/tex]
OR
[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\pi} \hookrightarrow \frac{2}{\frac{2}{3}}\pi \\ Amplitude \hookrightarrow 3[/tex]
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 3sin\:\frac{2}{3}x + 2,[/tex]in which you need to replase “cosine” with “sine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{3}{4}\pi\:units[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{3}{4}\pi\:units,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{3}{4}\pi} = \frac{-\frac{\pi}{2}}{\frac{2}{3}}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3sin\:(\frac{2}{3}x + \frac{\pi}{2}) + 2.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-4\frac{1}{2}\pi, -1],[/tex]from there to [tex]\displaystyle [-1\frac{1}{2}\pi, -1],[/tex]they are obviously [tex]\displaystyle 3\pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 3\pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 2,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Find the equation of the line joining the points (2,-8) and (5,6)
Answer:
y=3/2x-11
x,=2 and x2=5y1= -8 and y2= 6change in y over change in x get x use the formulae[tex]y = mx + c[/tex]thats the formular u got mfind c using one pairYou can play a game for $1. In the game, you roll an 8-sided die. If you roll an 8, you get $9. If
roll an odd number, you get $1. Otherwise, you gain nothing.
(a) What is the expected value of this game?
The expected value of the game, given the amounts to be made when a number is rolled, is $ 1.25
How to find the expected value ?First, find the probability of rolling an 8 :
= Number of eights / Number of sides
= 1 / 8
= 0.125
The the probability of rolling an odd number :
= Odd numbers from 1 to 8 / Number of sides
= 4 / 8
= 0.5
The expected value of the game is:
= ( Probability of getting an 8 x Amount if you get 8 ) + ( Probability of getting an odd x Amount if you get an odd ) + ( Probability of not getting an 8 or odd x Loss )
= ( 0.125 x 9 ) + ( 0.5 x 1 ) + ((1 - 0.125 - 0.5) x -1)
= $ 1.25
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Find the value of each trigonometric ratio.
Answer:
sinA = 7/25
tanX = 35/12
Step-by-step explanation:
Trigonometric ratio for:
sinA = perpendicular/hypotenuse = 14/50 = 7/25
tanX = perpendicular/base = 35/12
A car starts out at a speed of 50mph. A second car starts out 3 hours later at 65mph to overtake the first one. How many hours will the first car be on the road at the point where it is overtaken?
50 PTS! Please answer quick. you will get brainliest
Answer:
13 hours----------------------------------
Both cars will make same distance but the first one will be on road for 3 more hours.
Let the number of hours the first car in travel be x.
Then set an equation:
50x = 65(x - 3)50x = 65x - 19565x - 50x = 19515x = 195x = 13Need help with math question
A vertex with degree 2 in a graph has an edge that loops around itself. The graph is therefore a cycle graph.
What is Euler circuit?Every edge of a graph is used precisely once in an Euler circuit. An Euler path has two distinct vertices where it begins and finishes. A vertex serves as the beginning and conclusion of an Euler circuit.In an Eulerian path, we pass over two unvisited edges with one end point, v, each time we visit a vertex. As a result, the degree of each middle vertex in the Eulerian Path must be even. Since any vertex can be the central vertex in an Eulerian cycle, all vertices must have an even degree.All of a graph G's vertices must be even if it has an Euler circuit. Or, to put it another way, G cannot have an Euler circuit if the number of odd vertices is more than 0.To learn more about Euler circuit refer :
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LaShonda is buying tickets for a group of families going to a ballet. She wants to have at least 25 tickets. Each adult ticket costs $22.50 and each child ticket costs $17.50. LaShonda wants to spend no more than $400. Which system of inequalities can LaShonda use to find the number of tickets she can buy?
Answer: You Like Big Black Men and You love them dancing on you
Step-by-step explanation:
I have your search history ;)
The system of inequalities can LaShonda use to find the number of tickets she can buy will be;
⇒ x + y ≤ 25
⇒ 22.50x + 17.50y < 400
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
She wants to have at least 25 tickets. Each adult ticket costs $22.50 and each child ticket costs $17.50.
LaShonda wants to spend no more than $400.
Now,
Let the number of adult tickets = x
And, The number of child tickets = y
Here, She wants to have at least 25 tickets.
So, We get;
⇒ x + y ≤ 25
And, Each adult ticket costs $22.50 and each child ticket costs $17.50.
LaShonda wants to spend no more than $400.
So, We get;
⇒ 22.50x + 17.50y < 400
Thus, The system of inequalities can LaShonda use to find the number of tickets she can buy are;
⇒ x + y ≤ 25
⇒ 22.50x + 17.50y < 400
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