Final Answer:
The probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.
Explanation:
To find the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F, we can use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed if the sample size is sufficiently large. In this case, we can assume a sample size of 19 is large enough.
Given:
- Population mean (μ) = 98.20°F
- Population standard deviation (σ) = 0.62°F
- Sample size (n) = 19
- Target sample mean (X) = 98.50°F
We need to do the following steps:
1. Calculate the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the sample mean.
SEM = σ / √n
2. Calculate the Z-score for the sample mean of 98.50°F. The Z-score represents how many standard errors the value is away from the population mean.
Z = (X - μ) / SEM
3. Use the Z-score to find the area to the left of it on the standard normal distribution, which represents the probability that the sample mean is less than 98.50°F.
Let's calculate each step:
1. Calculate SEM:
SEM = σ / √n
= 0.62 / √19
≈ 0.62 / 4.3589
≈ 0.1422
2. Calculate Z-score:
Z = (X - μ) / SEM
= (98.50 - 98.20) / 0.1422
≈ 0.30 / 0.1422
≈ 2.1095
3. Lastly, to find the probability that the sample mean is less than 98.50°F, we look up the Z-score in the standard normal distribution table (Z-table), use statistical software, or a calculator that provides the cumulative distribution function (CDF) for the normal distribution.
A Z-score of 2.1095 corresponds to a probability of about 0.9826 (using Z-table or a calculator).
Therefore, the probability that the mean body temperature of a sample of 19 people will be less than 98.50°F is approximately 0.9826.
Among the options given, the closest to 0.9826 is 0.9826 itself. Hence, that is the correct answer.
$6000 is invested for 15 years with an APR of 3% and monthly compounding.
Answer:
$2700.00
Step-by-step explanation:
6000 x 3% =180.00
180.00 x 15= 2700.00
The pH of a solution is a measure of how acidic it is. The greater the acidity, the lower the pH. The function f(x) = −log x gives the pH of a solution, where x is the concentration of hydrogen ions, in moles per liter.
The graph of f(x) = −log x is________________of the graph of g(x)=log x
answer options:
a: vertical translation (not correct answer)
b: horizontal translation
c: reflection in the x-axis
d: reflection in the y-axis
Answer:
c. a reflection in the x-axis.
Step-by-step explanation:
All values of log x are made negative by the transformation so it is a reflection in the x axis.
The graph of [tex]f(x) =-log x[/tex] is the reflection in the x-axis of the graph of [tex]g(x)=log x[/tex].
What is a graph?" Graph is defined as a pictorial representation of the relation between the variables in the coordinate plane along x-axis and y-axis."
According to the question,
Given function on the graph,
[tex]f(x) =-log x[/tex]
[tex]g(x)=log x[/tex]
[tex]'x'[/tex] represents the concentration of hydrogen ions, in moles per liter.
value of [tex]'x'[/tex] remain the same in both cases.
[tex]f(x)[/tex] value is negative.
[tex]g(x)[/tex] value is positive.
The graph of [tex]f(x)[/tex] lying in the first quadrant and the graph of [tex]g(x)[/tex] lying in the fourth quadrant.
Therefore, the graph of [tex]f(x)[/tex] is the reflection in the x-axis of the graph of [tex]g(x)[/tex].
Hence, Option(C) is the correct answer.
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pleaseeeee helppppppp
Answer:
[tex]\large\boxed{A.\ \sqrt{-4}}[/tex]
Step-by-step explanation:
[tex]A.\ \sqrt{-4}=\sqrt{(4)(-1)}=\sqrt4\cdot\sqrt{-1}=2i\ -\ \text{complex number}\\\\i-\text{imaginary unit}[/tex]
[tex]B.\ \sqrt{13}\approx3.61\ -\ \text{real number}\\\\C.\ \sqrt{16}=4\ -\ \text{real number}\\\\D.\ \sqrt1=1\ -\ \text{real number}[/tex]
Luisa and Connor had $360 altogether . After Connor gave Luisa 2/5 of his money, she had the same amount of money has he did. How much money did Connor have in the beginning?
Answer:
$300
Step-by-step explanation:
Let's say that L is the amount of money Luisa had in the beginning, and C is the amount of money Connor had in the beginning.
C + L = 360
C - 2/5 C = L + 2/5 C
Simplifying the second equation:
3/5 C = L + 2/5 C
1/5 C = L
Substituting into the first equation:
C + 1/5 C = 360
6/5 C = 360
C = 300
Connor originally had $300, and Luisa $60. Connor gave Luisa $120, and they both had $180.
The sum of two numbers is 58. The first number is 8 less than half the second number. Let c represent the first number. Let d represent the second number. Which statements about solving for the two numbers are true? Check all that apply.
Answer : The true statements are:
The equation [tex]c+d=58[/tex] represents the sum of two numbers.
The equation [tex]c=\frac{d}{2}-8[/tex] represents the relationship between the two numbers.
The number c is, 14
The number d is, 44
Step-by-step explanation :
Given:
Let 'c' represent the first number. Let 'd' represent the second number.
The sum of two numbers is 58. The equation will be:
[tex]c+d=58[/tex] .........(1)
The first number is 8 less than half the second number. The equation will be:
[tex]c=\frac{d}{2}-8[/tex] .........(2)
Now by solving the two equations, we get the value of c and d.
As, [tex]c+d=58[/tex]
or, [tex]c=58-d[/tex] ..........(3)
Now put equation 3 in 2, we get the value of d.
[tex]58-d=\frac{d}{2}-8[/tex]
[tex]58-d=\frac{d-16}{2}[/tex]
[tex]2(58-d)=d-16[/tex]
[tex]116-2d=d-16[/tex]
[tex]3d=132[/tex]
[tex]d=44[/tex]
Now put the value of 'd' in equation 3, we get the value of 'c'.
[tex]c=58-d[/tex]
[tex]c=58-44[/tex]
[tex]c=14[/tex]
Thus, the value of c and d is, 14 and 44 respectively.
Answer:
ABGH
Step-by-step explanation:
The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new function? (x – 11)2 + 58 (x + 22)2 – 121 (x + 7)2 – 47 (x – 15)2 + 94
Answer:
Option C is correct.
Step-by-step explanation:
The given function f(x) is:
f(x) = x^2 + 22x + 58
To find the vertex find [tex](\frac{-b}{2a} )^2[/tex] and add and subtract it from both sides of the given function
b= 22, a= 1
Putting values:
[tex](\frac{-b}{2a} )^2 = (\frac{-22}{2(1)})^2\\=(\frac{-22}{2})^2\\= (-11)^2\\=11^2[/tex]
Adding (11)^2 on both sides
f(x) = x^2 + 22x + 58 +(11)^2 -(11)^2
f(x) = x^2+22x+(11)^2 +58-(11)^2
a^2 +2ab+b^2 = (a+b)^2 Using this formula:
f(x)=(x+11)^2+58-121
f(x)=(x+11)^2-63
The vertex of the given function is (-11,-63)
The function is translated 4 units to right and 16 units up
The vertex of new function will be:
(x+4,y+16) => (-11+4,-63+16)
=> (-7,-47)
So, the vertex of new function is (-7,-47)
The function will be
(x+7)^2 -47
So, Option C is correct.
Answer:
C
Step-by-step explanation:
In a conference room, the number of chairs,c, is equal to 6 times the number of tables,t. Which equation matches the information
Answer:
t x 6=c or c divided by 6= t
Step-by-step explanation:
Answer: [tex]c=6t[/tex]
Step-by-step explanation:
You need to analize the information provided in the exercise:
- "c" represents the number of chairs in the conference room.
- "t" represents the number of tables in the conference room.
- "6 times the number of tables" indicates a multiplication. This is:
[tex]6t[/tex]
Therefore if the number of chairs in the conference room is equal to 6 times the number of tables, you can write this equation that matches the information provided:
[tex]c=6t[/tex]
Of the 425 tickets sold, 275 were adult tickets. What percent of the tickets were adult tickets? Round to the nearest tenth of a percent.
Answer:
64.7%
Step-by-step explanation:
Write a proportion:
275 / 425 = x / 100
x = 64.7
64.7% of the tickets were adult tickets.
Which formula would be used to find the measure of
angle 1?
1/2 (aº + bº).
1/2(a-cº).
1/2 (b° +cº).
1/2(aº – bº).
Check the picture below.
The formula that would be used to find the measure of angle 1 will be
m<1 =12(a - b)
To get the measure of angle 1, the circle theorem below will be used as shown:
The angle at the vertex of the circle is equal to half of the difference of the intercepted arc.
Angle at the vertex = m<1 Angles at the intercepted arc ar m<a and m<bThe formula that would be used to find the measure of angle 1 will be
m<1 =12(a - b)
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Ryan is putting money into a savings account. He starts with
$450
in the savings account, and each week he adds
$30
Let S represent the total amount of money in the savings account (in dollars), and let
W represent the number of weeks Ryan has been adding money. Write an equation
relating S to W. Then use this equation to find the total amount of money in the savings account after 14 weeks.
equation=
total amount of money after 14 weeks= $?
the equation is S=30w+450
to find the answer just replace the w by 14
multiply 30 by 14 to get 420 and add 450 to it to get 870
The equation relating the total amount of money 'S' in the savings account to the number of weeks 'W' that Ryan has been saving is S = 450 + 30W. By substituting W with 14 in this equation, we find that Ryan will have $870 in his savings account after 14 weeks.
Explanation:In this case, Ryan had started with $450 in his savings account. His weekly contribution to the savings is $30. So the total amount of money 'S' in the savings account after 'W' weeks could be represented by the equation S = 450 + 30W.
Now, if you want to find out the total amount of money in the savings account after 14 weeks, just substitute W = 14 into the equation. Thus the equation becomes S = 450 + 30*14 = 450 + 420 = $870.
Therefore, Ryan will have $870 in his savings account after 14 weeks.
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what is the rise of ramp if slope is 2% and run is 4 feet
Answer:
.08 feet
Step-by-step explanation:
So slope=rise/run.
You are given slope is 2% or .02.
You are also given run is 4 ft.
Plug these into the formula
.02=rise/4
To solve this for rise multiply both sides by 4:
4(.02)=rise
.08=rise
The rise is .08 feet.
the area of a circle is 113.04in^2. what is the radius of the circle
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} A=113.04 \end{cases}\implies 113.04=\pi r^2\implies \cfrac{113.04}{\pi }=r^2 \\\\\\ \stackrel{using~\pi =3.14}{36}=r^2\implies \sqrt{36}=r\implies 6=r[/tex]
What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 2x + y - 1=0?
Answer:
y=-2x+4
Step-by-step explanation:
2x+y-1=0
2x+y=0+1
2x+y=1
y=1-2x
y=-2x+1
y=mx+b where m=slope and b=y-intercept
parallel means same slope,
so the slope would still be -2.
--------------
y-y1=m(x-x1)
y-2=-2(x-1)
y=-2x+2+2
y=-2x+4
In 2015,in buffalo,new York there were 8.625 arrest,2.678 robberies,865 assaults and 20 murders.The population of Buffalo is 258.959.What is the ratio of number of assaults to the number of robberies in simplest form
Answer:
[tex] \frac { 8 6 5 } { 2 6 7 8 } [/tex]
Step-by-step explanation:
We are given the following information for year 2015:
Number of arrests = 8625
Number of robberies = 2678
Number of assaults = 865
Number of murders = 20
Population of Buffalo = 258959
We are to find the ratio of number of assaults to the number of robberies in simplest form.
Ratio of number of assaults to number of robberies = [tex]\frac{865}{2678}[/tex]
What is the cube root of -729a^9b^6?
A. -9a^3b^2
B. -9a^2b^3
C. -8a^3b^2
D. -8a^2b^3
Answer:
[tex]\large\boxed{A.\ -9a^3b^2}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{-729a^9b^6}\qquad\text{use}\ \sqrt[n]{xy}=\sqrt[n]{x}\cdot\sqrt[n]{y}\\\\=\sqrt[3]{-729}\cdot\sqrt[3]{a^9}\cdot\sqrt[3]{b^6}\\\\=-9\cdot\sqrt[3]{a^{(3)(3)}}\cdot\sqrt[3]{b^{(2)(3)}}\qquad\text{use}\ (x^n)^m=x^{nm}\\\\=-9\cdot\sqrt[3]{(a^3)^3}\cdot\sqrt[3]{(b^2)^3}\qquad\text{use}\ \sqrt[3]{x^3}=x\\\\=-9a^3b^2[/tex]
Answer: A
Step-by-step explanation:
-9•9•9= -729a 9/3= 3
6/3=b^ 2
How do you solve the following equation:
[tex]\int_2^a (3x^2+x-1) dx=52[/tex] for [tex]a[/tex]?
[tex]\displaystyle\\\int \limits_2^a(3x^2+x-1)\, dx=52\\\left|x^3+\dfrac{x^2}{2}-x\right|_2^a=52\\a^3+\dfrac{a^2}{2}-a-(2^3+\dfrac{2^2}{2}-2)=52\\a^3+\dfrac{a^2}{2}-a-(8+2-2)=52\\a^3+\dfrac{a^2}{2}-a-8=52\\a^3+\dfrac{a^2}{2}-a=60\\2a^3+a^2-2a=120\\2a^3+a^2-2a-120=0[/tex]
Now you need to solve the resulting equation, but it's not easy. The approx. solution is [tex]a\approx 3.8[/tex]
The exact solution is
[tex]a=\dfrac{1}{6}\left(-1+\sqrt[3]{6461-78\sqrt{6861}}+\sqrt[3]{6461+78\sqrt{6861}}\right)[/tex]
Answer:
a = 3.84
Step-by-step explanation:
Let's integrate the function
3x^2 becomes 3x^3/3 =x^3
x becomes x^2/2
-1 becomes -x
The intergral is x^3 +x^2/2 -x
We take the upper limit minus the lower limit
a^3 +a^2/2 -a - (2^3 + 2^2/2 -2) and that is equal to 52
Simplify
a^3 + a^2/2 -a - (8+2-2) = 52
a^3 +a^2/2 -a -(8) = 52
Subtract 52 from each side
a^3 +a^2/2 -a -8-52 = 52-52
a^3 +a^2/2 -a -60 =0
Multiply by 2
2a^3 +a^2 -2a -120 = 0
Using a graphing system, we see it only has 1 real root
This is at approximately
3.84
Need help in number 9. Thanks for helping
Answer:
A 6/7
Step-by-step explanation:
3/4 ÷ 7/8
Copy dot flip
3/4 * 8/7
The numerator is 3*8 = 24
The denominator is 4*7 = 28
24/28
Divide the top and botto by 4
6/7
What is the sum of the angle measures of 24 - gon
[tex]\bf \textit{sum of all \underline{interior angles} in a polygon}\\\\ S=180(n-2)~~ \begin{cases} n=\textit{number of sides}\\ \cline{1-1} n=24 \end{cases}\implies \begin{array}{llll} S=180(24-2)\\\\ S=3960 \end{array}[/tex]
Hello,..... I will mark you as a brainliest
A frog is there in a 12m deep well. The frog wants to jump out of the well . Every time it jumps 3m & falls back by 1m. In how many jumps will he come out of the well ???
Remember, I will mark you as a brainliest...
Answer:
5 jumps
Step-by-step explanation:
Personally I would write it out, although there surely is a formula for it.
3 fall to 2 - 5 fall to 4 - 7 fall to 6 - 10 fall to 9 - 12.
This makes 5 jumps, since once he is out he won't fall back in.
How do I do rate of change???
Answer:
12
Step-by-step explanation:
For our problem since we only in 10 am:
I'm going to let x=4 represent the time 10:04 am
which means I'm going to let x=17 represent 10:17am.
So when x=4, y=23 miles and when x=17,y=179 miles.
You have two points.
You can use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
Or just line the points up vertically and subtract them vertically, then put 2nd difference over first difference. Like this:
( 17 , 179)
-( 4 , 23)
-----------------------
13 156
So the slope is 156/13=12 miles/hour.
ABCD is a rectangle. What is the value of x?
Explanation
We can use pythagorean theorem to solve for the value of x:
45^2 + x^2 = 53^2
2025 + x^2 = 2809
We now subtract 2025 from both sides:
2809 - 2025 = 784
x^2 = 784
Square both sides
[tex]\sqrt{784}[/tex] = 28
x = 28
Answer
The value of x is 28
Which best describes bias, if any, from the sample surveyed? survey: favorite sports sample: randomly selected fans at a baseball game A. Since the sample is randomly selected, there is unlikely to be any bias. B. Since baseball fans are also likely to be fans of other sports, there is unlikely to be any bias. C. Since baseball is played in the summer, there is likely to be bias against sports played in the winter. D. Since the sample is taken at a baseball game, it is likely to be biased in favor of baseball.
Answer: B
Step-by-step explanation:
This is because it is just a statement, and may be true for some people, but not others.
What is the solution to the system of equations below? y = -3X+5 and y=4x-2 (1, 2) (1, –18) (–1, 8) (–1, –6)
Answer:
(1, 2 )
Step-by-step explanation:
Given the 2 equations
y = - 3x + 5 → (1)
y = 4x - 2 → (2)
Substitute y = 4x - 2 into (1)
4x - 2 = - 3x + 5 ( add 3x to both sides )
7x - 2 = 5 ( add 2 to both sides )
7x = 7 ( divide both sides by 7 )
x = 1
Substitute x = 1 into (2) for corresponding value of y
y = (4 × 1) - 2 = 4 - 2 = 2
Solution is (1, 2 )
a landscaping company needs 160 gallons of 40% fertilize the shrubs in an office park. They have in stock 50% fertilizer and 30% fertilizer. how much of each type should they mix together?
Let
x--------> volume of 50% fertilizer
y--------> volume of 30% fertilizer
we know that
x+y=160-----> x=160-y-----> equation 1
x*0.5+y*0.3=160*0.4-----> equation 2
substitute equation 1 in equation 2
[160-y]*0.5+0.3*y=63.8----> 77-0.35*y+0.25*y=63.8
0.10*y=13.2------> y=13.2/0.10----> y=132 gal
x=220-y----> x=220-132----> x=88 gal
the answer is
88 gal of 50% fertilizer
132 gal 30% fertilizer
To obtain a 40% fertilizer mixture, the landscaping company should mix 80 gallons of 50% fertilizer with 80 gallons of 30% fertilizer.
Explanation:To solve this problem, we can set up an equation based on the amount of fertilizer needed and the percentage of fertilizer in each type. Let's call the amount of 50% fertilizer x and the amount of 30% fertilizer y. We know that the total amount of fertilizer needed is 160 gallons, so we can write the equation x + y = 160. We also know that the amount of fertilizer in the 50% type is 0.5x and the amount of fertilizer in the 30% type is 0.3y. Since we want a total of 40% fertilizer, we can write the equation 0.5x + 0.3y = 0.4 * 160. Solving this system of equations will give us the amounts of each type of fertilizer needed.
First, let's rearrange the first equation to solve for x: x = 160 - y. Substituting this into the second equation, we get 0.5(160 - y) + 0.3y = 0.4 * 160. Simplifying the equation, we get 80 - 0.5y + 0.3y = 64. Combining like terms, we have 80 - 0.2y = 64. Subtracting 80 from both sides, we get -0.2y = -16. Dividing both sides by -0.2, we get y = 80. Now we can substitute this value back into the first equation to solve for x: x = 160 - 80 = 80. Therefore, they should mix 80 gallons of the 50% fertilizer with 80 gallons of the 30% fertilizer to obtain the desired 40% mixture.
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choose the graph that represents the equation y=-|x+4|+1
The graph that represents y = -|x + 4| + 1 is graph (a)
The equation is given as:
y = -|x + 4| + 1
The above equation is a transformation from the parent function, which is represented as:
y = |x|
First the function is reflected across the x-axis, then translated 4 units left, and lastly 1 unit up.
The graph that represents this transformation is graph (a)
Hence, the graph that represents y = -|x + 4| + 1 is graph (a)
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What is the cube root of 512m12n15
Could anyone plz help me?
Answer:
[tex]8m^4n^5[/tex]
Step-by-step explanation:
cube root is basically taking to the power of [tex]\frac{1}{3}[/tex]
Also, there is a property that is [tex](x^m)^n=x^{mn}[/tex]
We can use these and find the cube root of the expression:
[tex](512m^{12}n^{15})^{\frac{1}{3}}\\=(512)^{\frac{1}{3}}*(m^{12})^{\frac{1}{3}}*(n^{15})^{\frac{1}{3}}\\=8*m^{\frac{12}{3}}*n^{\frac{15}{3}}\\=8*m^4 * n^5[/tex]
Thus, third answer chioce is right.
Answer:
C. 8m^4n^5[/tex]
Step-by-step explanation:
We are given [tex]\sqrt[3]{512m^{12}n^{15} }[/tex]
The cube root is nothing but the power of [tex]\frac{1}{3}[/tex]
Now we have to write 512 as the power 3.
512 = 8.8.8 = [tex]8^{3}[/tex]
So, [tex]\sqrt[3]{512m^{12}n^{15} }[/tex] = [tex](8^{3}.m^{12}.n^{15}) ^{\frac{1}{3}}[/tex]
We know that the exponent property: [tex](a^{m} )^n= a^{mn}[/tex]
Using this property, we can simplify the exponents.
= [tex]8.m^{4} .n^5 = 8m^4n^5[/tex]
Before any dinner service, the manager confirms when the number of reservations at a restaurant is subtracted from
Nice the number of loaves of bread on hand must be greater than 5. Which graph represents this scenario?
Final answer:
To graph the scenario where the number of loaves of bread on hand (L) minus the number of reservations (R) must be greater than 5, one would represent this inequality on a two-dimensional graph with L on the horizontal axis and R on the vertical axis, shading the region above the line L - R = 5.
Explanation:
The subject of the question is Mathematics, with a focus on inequalities and graphical representation of constraints. The scenario describes the requirement that the number of loaves of bread on hand minus the number of reservations must be greater than 5. To represent this mathematically, let's define the variable L as the number of loaves of bread on hand and R as the number of reservations. The inequality can, therefore, be expressed as L - R > 5.
This inequality needs to be represented on a graph. To do this, one typically uses a two-dimensional coordinate system where the horizontal axis, often labeled as x, could represent the number of loaves of bread (L), and the vertical axis, often labeled as y, could represent the number of reservations (R). The region that satisfies the inequality L - R > 5, would be shaded above the line L - R = 5 (since we are looking for L being greater than R by more than 5 units). This line will have a slope of 1 and a y-intercept at R = -5.
One angle of a right triangle measures 19∘. What is the measure of the other angle?
Answer:
71°
Step-by-step explanation:
The equation should be 19+90+x=180
Step 1: Add 19+90=109
Step 2: Subtract 180-109=71
So, you're answer is 71°
Final answer:
To find the measure of the other angle in a right triangle when one angle is given, subtract the given angle and the right angle from 180 degrees to get the third angle, which is the measure of the other angle.
Explanation:
One angle of a right triangle measures 19∘. In a right triangle, one angle is always 90 degrees. Therefore, to find the measure of the third angle, you need to subtract the sum of the given angle and the right angle from 180 degrees.
Third angle = 180° - 90° - 19° = 71°. So, the measure of the other angle in the right triangle is 71 degrees.
What is the vertex if angle XYZ
A Vertex is the point that 2 or more lines connect.
When an angle is written given the letters of the lines/ points, the point where the lines connect are always the middle letter.
For ∠XYZ, the vertex would be point Y, because it is the middle letter.
An angle is formed by two rays that have a common endpoint which is known as the vertex of the angle
The vertex of the angle ∠XYZ is point Y
The reason the above selection is correct is as follows;
There are three methods used in naming an angle, including;
Using three capital letters with the middle letter representing the vertexUsing only one capital letter, if the angle will not be confused with other anglesUsing a small letter or number in the middle of the angle. The given angle is ∠XYZ, therefore, the middle letter, Y, is the vertex
The vertex point is Y
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Calculate 1.7 x 106 times 5.3 x 10^9 by using scientific notation and the product rule.
Express your answer in scientific notation with the proper number of significant figures.