Answer:
a. 0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.
b. 0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.
c. 0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute
Step-by-step explanation:
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean:
[tex]\mu = 47[/tex]
(95% of data) range from 19 to 75 beats per minute.
This means that between 19 and 75, by the Empirical Rule, there are 4 standard deviations. So
[tex]4\sigma = 75 - 19[/tex]
[tex]4\sigma = 56[/tex]
[tex]\sigma = \frac{56}{4} = 14[/tex]
a. What is the probability that the heart rate is less than 25 beats per minute?
This is the p-value of Z when X = 25. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25 - 47}{14}[/tex]
[tex]Z = -1.57[/tex]
[tex]Z = -1.57[/tex] has a p-value of 0.0582.
0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.
b. What is the probability that the heart rate is greater than 60 beats per minute?
This is 1 subtracted by the p-value of Z when X = 60. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 47}{14}[/tex]
[tex]Z = 0.93[/tex]
[tex]Z = 0.93[/tex] has a p-value of 0.8238.
1 - 0.8238 = 0.1762
0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.
c. What is the probability that the heart rate is between 25 and 60 beats per minute?
This is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 25. From the previous two items, we have these two p-values. So
0.8238 - 0.0582 = 0.7656
0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute
Rewrite the following subtraction problem as an addition problem.
Answer:
x+129=592
Step-by-step explanation:
add 129 to each side
1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.
An inverse function is y = k/x
replace x and y with the given values:
6 = k/18
Solve for k by multiplying both sides by 18:
k = 108
1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.
Solution:-[tex]\sf{The \: relation \: y \: varies \: inversely \: as \: x \: translates \: to \: y = \frac{k}{x}.}[/tex]
Substitute the values to find k:
[tex]\sf\rightarrow{y= \frac{k}{x} }[/tex]
[tex]\sf\rightarrow{6= \frac{k}{18} }[/tex]
[tex]\sf\rightarrow{k=(6)(18)}[/tex]
[tex]\sf\rightarrow{K={\color{magenta}{108}}}[/tex]
Answer:-[tex]\sf{The \: equation \: of \: variations \: is \: y={ \color{red}{ \frac{108}{x} }}}[/tex]
[tex]{\huge{\color{blue}{━━━━━━━━━━━━}}}[/tex]
#CarryOnMath⸙
If AABC= A DEF, which congruences are true by CPCTC? Check all that
apply.
APEC correct answer is:
AB =DE
AC= DF
See photo.
Answer:
Options A, B and D
Step-by-step explanation:
If the two triangles are congruent, their corresponding parts will be congruent.
If ΔABC ≅ ΔDEF
By the property of CPCTC,
AB ≅ DE
AC ≅ DF
BC ≅ EF
∠A ≅ ∠D
∠C ≅ ∠F
∠B ≅ ∠E
Therefore, Options A, B and D are the correct options.
Which of these four sets of side lengths will form a right triangle? set 1 set 2 set 3 set 4
Answer:
hey um I cant see the picture
99 students at a college were asked whether they had completed their required English 101 course, and 71 students said "yes". Find the best point estimate for the proportion of students at the college who have completed their required English 101 course. Round to four decimal places.
Answer: 0.070
Step-by-step explanation:
The question is asking you to estimate how many students completed the English 101 course.
1. Round 99 and 71 to 100 and 70
2. I am not completely sure but I believe the answer is 0.070?
3. Hope it helps! :)
reduce 1/2 × 16/9 is to lowest form
Answer:
The correct answer will be "[tex]\frac{8}{9}[/tex]".
Step-by-step explanation:
The given expression is:
= [tex]\frac{1}{2}\times \frac{16}{9}[/tex]
By applying multiplication, we get
= [tex]\frac{16}{18}[/tex]
= [tex]\frac{8}{9}[/tex]
Thus, the above is the lowest form.
Determine which data are qualitative and which data are quantitative. Explain your reasoning
a. The yearly salaries of the employees at a school district. (9)
b. The employee numbers of the employees at an accounting firm.
c. The area codes of a sample of 350 residents of nursing homes. (2)
d. The ages of a sample of 350 residents of nursing home. (eta)
e. The answers to a survey of 5000 people about how likely is it that the US will enter a 1930s-like depression. The answers are: Very likely, somewhat likely, not very likely, not at all likely. (20)
f. The IQ index of the students in a statistics class.
What are the levels of measurement of data in question 4? Justify
a. Yearly salaries: (20)
b. Employee numbers: (ca)
c. Area codes: (eca)
d. The ages:
e. Survey answers: (ca)
f. IQ index: (en)
Answer:
1. A. Quantitative data
B. Quantitative data
C. Qualitative data
D. Quantitative data
E. Qualitative data
F. Quantitative data
2.a. Yearly salaries: interval or ratio data
b. Employee numbers: interval or ratio data
c. Area codes : nominal data
d. The ages: interval or ratio data
e. Survey answers: ordinal data
f. IQ index: interval or ratio data
Explanation:
Qualitative data is data in the form of a quality such as a characteristic. It is usually a noun, such as whether a person is fair or dark in complexion. Quantitative data is data in form of quantity such as the amount in dollars of one's salary.
There are four levels of data measurement. They are: nominal data, ordinal data, interval data, and ratio data. Nominal and ordinal data are qualitative data while interval and ratio data are quantitative data.
Parallelogram ABCD had coordinates A(0,7) and C(2, 1) Which statement will prove ABCD is a Rectangle?
The midpoint of AC is (1, 4).
The length of BD is √40.
The slope of BD is 1/3
The slope of AB is 1/3.
Answer:
Option (2)
Step-by-step explanation:
ABCD is a parallelogram having vertices A(0,7) and C(2, 1).
Therefore, length of diagonal AC = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(0-2)^2+(7-1)^2}[/tex]
= [tex]\sqrt{40}[/tex]
Since, diagonals of a rectangle measure the same and bisect each other,
Length of other diagonal BD will also measure [tex]\sqrt{40}[/tex].
Therefore, Option (2) will be the correct option.
a container has 16 1/2 cups of lemonade. Asher gives each of his classmates 3/4 of a cup if lemonade. if asher gives away all of the lemonade how many classmates does asher give lemonade to
Khusbu needs 650 gm flour and 30 gm sugar to bake a cake. How much
flour and sugar does he need to bake same size of 6 cakes?
Answer:
4080 gm
Step-by-step explanation:
To bake one cake, it will take us 650 gm flour and 30 gm sugar. When we add both of them together, it gives 680 gm (650+30). But this is only for one cake. To find the total amount of flour and sugar needed to bake 6 cakes, we will have to multiply 680 by 6. That will give you 4080 gm which is your final answer.
Prove the following statement by contradiction.
If a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational.
Proof by contradiction: Select an appropriate statement to start the proof.
A. Suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational.
B. Suppose not. That is, suppose there exist rational numbers a and b such that b ≠ 0, r is an irrational number, and a + br is irrational.
C. Suppose not. That is, suppose there exist rational numbers a and b such that b ≠ 0, r is an irrational number, and a + br is rational.
D. Suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is an irrational number, and a + br is rational.
E. Suppose not. That is, suppose there exist rational numbers a and b such that b ≠ 0, r is a rational number, and a + br is irrational.
Then by definition of rational,
a = c/d, b = i/j , and a + br = m/n
where c, d, i, j, m, and n are___and____. Since b ≠ 0, we also have that i ≠ 0. By substitution,
c/d + i/j r = m/n
Solving this equation for r and representing the result as a single quotient in terms of c, d, i, j, m, and n gives that
r = c - a/b
Answer:
spongebob at the bottom of the sea
Step-by-step explanation:
In a plain, robust, conversational style, the author known as “Elena Ferrante” has captivated readers worldwide with her chronicle of a complicated friendship between two women.
The step would be, "Suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational." Option A is correct.
Given that,
a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational. the first step of the proof with contradiction is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
For the statement,
a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational.
Contradiction will be "suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational."
Thus, the step would suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational.
Learn more about simplification here:
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18- 3 x 2/5 - 12
Could someone help me with this?
Answer:
I hope it helps u.......
NEED ASAP
What is the product?
а-3
11
5
15а а-3
о
о
Cul —
за
о за
O3
Answer:
1/3a
Step-by-step explanation:
[tex] \frac{(a - 3)}{15a} \times \frac{5}{(a - 3)} = \frac{5}{15a} = \frac{1}{3a} [/tex]
Which of the following is the general term for the sequence? -a, a^2, -a^3, a^4,...
-a(-a)^ n-1
(-a)^n + 1
(-1)a^n + 1
a(-1)^n - 1
Answer:
The answer would be [tex]-a(-a)^{n-1}[/tex].
Step-by-step explanation:
We can simply substitute the terms into this equation. Checking the 1st term, [tex]-a(-a)^{1-1} = -a(-a)^{0} = -a(1) = -a[/tex]. Moving on to the second term, we see [tex]-a(-a)^{2-1} = -a(-a)^{1} = -a(-a) = a^{2}[/tex]. And so on and so forth. We can see how the answer fluctuates between negative and positive, while gaining one more exponent every term, which fits with the sequence given. Therefore, the answer would be [tex]-a(-a)^{n-1}[/tex].
Hope this helped!
24×63_64
help me sll
Answer:
1448
Step-by-step explanation:
24 × 63-64
Multiply 24 and 63 to get 1512.
1512-64
Subtract 64 from 1512 to get 1448.
answer
1448
When wiring a house, an electrician knows that the time she will take is given by the formula Time= 2 hours + 12 minutes per lightswitch. She charges her customers a call out fee of £35, plus £20 per hour. How much should a customer be charged for wiring a house with 10 lightswitches?
Answer:
Step-by-step explanation:
Time = 2 hrs + 12 min (10) = 4 hrs.
Cost = 35 + 20*4
Cost = 35+80
Cost = 115
9514 1404 393
Answer:
£155
Step-by-step explanation:
We can write the function describing the charges as a composition.
t(s) = 2 + 12/60s = 2 +s/5 . . . . . hours for s switches
c(h) = 35 +30h . . . . . . . . . . . . . charge for h hours
Then the charge for s switches is ...
f(s) = c(t(s)) = 35 +30(2 +s/5) = 35 +60 +6s
f(s) = 95 +6s . . . . . . . charge for installing s switches
The charge for 10 switches is then ...
f(10) = 95 +6·10 = 95 +60
f(10) = 155 . . . . pounds
The electrician should charge her customer £155 for wiring a house with 10 switches.
10x-3(x-6)=x+30 please help me
Step-by-step explanation:
10x-3(x-6)=x+30
10x-3x+18=x+30
7x+18=x+30
6x=12
x=2
Answer:
x=2
Step-by-step explanation:
10x-3(x-6)=x+30
Distribute
10x -3x+18 = x+30
Combine like terms
7x +18 = x+30
Subtract x from each side
7x-x +18 = x+30-x
6x +18 = 30
Subtract 18
6x+18-18 = 30-18
6x = 12
Divide by 6
6x/6 = 12/6
x=2
In a math class, 9 pupils receive a grade of 90. If 18% of the class got 90, how many pupils are there in a class?
Answer:
Let the total number of pupil be x.
Given that,
Number of pupils that received a grade of 90=9
Percentage of pupil that receive a grade of 90=18%
So,
18% of x=9
18x/100=9
x=50
Hence, there are 50 pupils in the class.
The 11th term of an progression is 25 and the sum of the first 4 terms is 49. The nth term of the progression is 49
1. Find the first term of the progression and the common difference
2. Find the value of n
Answer:
For 1: The first term is 10 and the common difference is [tex]\frac{3}{2}[/tex]
For 2: The value of n is 27
Step-by-step explanation:
The n-th term of the progression is given as:
[tex]a_n=a_1+(n-1)d[/tex]
where,
[tex]a_1[/tex] is the first term, n is the number of terms and d is the common difference
The sum of n-th terms of the progression is given as:
[tex]S_n=\frac{n}{2}[2a_1+(n-1)d][/tex]
where,
[tex]S_n[/tex] is the sum of nth terms
For (1):The 11th term of the progression:
[tex]25=a_1+10d[/tex] .......(1)
Sum of first 4 numbers:
[tex]49=\frac{4}{2}[2a_1+3d[/tex] ......(2)
Forming equations:
[tex]98=8a_1+12d[/tex]
[tex]25=a_1+10d[/tex] ( × 8)
The equations become:
[tex]98=8a_1+12d[/tex]
[tex]200=8a_1+80d[/tex]
Solving above equations, we get:
[tex]102=68d\\\\d=\frac{102}{68}=\frac{3}{2}[/tex]
Putting value in equation (1):
[tex]25=a_1+10\frac{3}{2}\\\\a_1=[25-15]=10[/tex]
Hence, the first term is 10 and the common difference is [tex]\frac{3}{2}[/tex]
For 2:The nth term is given as:
[tex]49=10+(n-1)\frac{3}{2}[/tex]
Solving the above equation:
[tex]39=(n-1)\frac{3}{2}\\\\n-1=26\\\\n=27[/tex]
Hence, the value of n is 27
1. If f(x)=4*, then which of the following is the value of f(-2)?
Answer:
what is the following
Step-by-step explanation:
PLEASE HELP!!!
-Graphing Linear Inequalities
What is the difference between solid and dashed lines?
A gas pump measures volume of gas to the nearest 0.01 gallon. Which measurement shows an appropriate level of precision for the pump?
Answer:
12.3 Gallons
Step-by-step explanation:
Options of the question:-
Option A. 12.33 gallons
Option B. 10 gallons
Option C. 12 gallons
Option D. 12.3 gallons
Option D is the answer :-
As the least count or zero error is 0.1 so it can measure only upto one decimal place so answer will be 12.3
I’ll give u brainlest please
Answer:
315
Step-by-step explanation:
the formula is V = B * h
B is the area of the base
V = (1/2)(10)(7) * 9
odd number less than 5
Answer:
1 and 3 are the odd numbers that are less than 5. 0, 2 and 4 are the even numbers that are less than 5
Step-by-step explanation:
what is a line passing through the points (1, -1) and (9, 3) in equation form?
Answer:
[tex]x-2y=3[/tex]
Step-by-step explanation:
[tex]We\ are\ given,\\Line\ passes\ through\ the\ points\ (1,-1) and (9,3). Hence,\ this\ means\ that\ the\\ points\ are\ indeed\ solutions\ of\ the\ equation,\ which\ represents\ the\ line.\\Hence,\\We\ know\ that,\\The\ equation\ of\ a\ line\ (Point-Slope)\ is\ given\ by:\\y-y_1=m(x-x_1),\ where\ m\ is\ the\ slope\ of\ the\ graph.[/tex]
[tex]So\ first,\\Lets\ find\ the\ Slope\ of\ the\ Graph.\\Slope(m)=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}\\Hence,\\Here,\\Considering\ (1,-1)\ as\ the\ First\ Point\ and\ (9,3)\ as\ the\ Second\ Point,\ we\ have:x_1=1,x_2=9\ and\ y_1= -1, y_2=3\\Plugging\ the\ values\ in\ the\ Equation\ for\ the\ Slope,\ we\ have:\\[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-1)}{9-1}=\frac{3+1}{9-1}= \frac{4}{8}=\frac{1}{2}\\Hence,\\Coming\ back\ to\ our\ Point-Slope\ Formula\ for\ the\ equation:\\\ We\ already\ have:\\y-y_1=m(x-x_1)\\Substituting\ m=\frac{1}{2} , x_1=1,\ y_1=-1,\ we\ have: \\y+1=\frac{1}{2}(x-1)\\\therefore 2(y+1)=x-1\\\therefore 2y+2=x-1\\\therefore 2y-x=-3\\Multiplying\ with\ (-1)\ on\ both\ sides:\\\therefore x-2y=3\\Hence,\\x-2y=3,\ is\ our\ desired\ equation.[/tex]
Any help 13 points
If the price of tacos is $1.75, how many will consumers buy?
Answer:
B-100 If the price of tacos is $1.75, th consumers will buy 100 tacos
The dot plots below show the ages of students belonging to two groups of painting classes: Based on visual inspection, which group most likely has a lower mean age of painting students? Explain your answer using two or three sentences. Make sure to use facts to support your answer.
Answer:
it's group A because they have more reliable sources
4x^2 + 4y^2 - 24x - 32y + 72 = 0 is a circle. What is the radius of the cirlce?
Answer:
√7
Step-by-step explanation:
(4x²-24x)+(4y²-32y)= -72
(4x²-24x+36)+(4y²-32y+64)= -72+36+64
4(x-3)²+4(y-4)²= 28
(x-3)²+(y-4)²=7
The radius of the circle 4x² + 4y²- 24x - 32y + 72 = 0 is √7.
CircleWe know that the general equation for a circle is ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.
How to find the radius of the circle?The given equation is 4x² + 4y²- 24x - 32y + 72 = 0
Simplify the given equation in general equation for a circle.
(4x²-24x)+(4y²-32y)= -72
Add 100 on both side of equality
(4x²-24x)+(4y²-32y)+100= -72+100
(4x²-24x+36)+(4y²-32y+64)= 28
4(x-3)²+4(y-4)²= 28
(x-3)²+(y-4)²=7
(x-3)²+(y-4)²=(√7)²
Hence the radius of the circle is √7.
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I NEEED HELPPPPP PLEASEEEE UM BEGGING SOMEONE PLEASEEEEEEEEEEEE
Answer:
p = 28.56
Step-by-step explanation:
Circumference of circle
c = 2πr
Since this is a semicircle the perimeter is half the circumference
p = πr
p = 3.14 * 4
p = 12.56
---------------------------
Triangle
the outer perineter is just the two outer sides
p = 6 + 10
p = 16
-------------------------
total outer perimeter
p = 12.56 + 16
p = 28.56
a racer called the whirlwind. Its poster says that in 1/20 hour it covers 7/10 mile. What is the Whirlwind’s speed in miles per hour?
Answer:
Its speed is 14 mph.
Step-by-step explanation:
Given that regarding racer called The Whirlwind, its poster says that in 1/20 hour it covers 7/10 mile, to determine what is the Whirlwind’s speed in miles per hour the following calculation must be performed:
1/20 x 60 = 0.05 x 60 = 3 minutes
7/10 = 0.7
Therefore, every 3 minutes the Whirlwind travels 0.7 miles.
60/3 = 20
0.7 x 20 = 14
Thus, in an hour it travels 14 miles, with which its speed is 14 mph.
