Answer:
34%
Step-by-step explanation:
The body temperatures of adults have a mean of 98.6° F and a standard deviation of 0.60° F.
We want to find the probability that the mean body temperature of 36 randomly selected adults is greater than 98.5° F.
The mean of the sampling distribution of the sample means is the same as the population mean,
[tex] \mu = 98.6 \degree[/tex]
The standard error of the mean becomes the standard deviation of the sampling distribution of the means.
[tex]SE= \frac{ \sigma}{ \sqrt{n} } [/tex]
[tex]SE= \frac{0.6}{ \sqrt{36} } = 0.1[/tex]
By the Central Limit Theorem, the distribution of mean of means is approximately normal
The z-score of 98.5° F
[tex] z= \frac{98.5 - 98.6}{0.1} = - 1[/tex]
By the empirical rule 68% of the distribution is within one standard deviation (-1 to 1).
Therefore from (-1 to 0), it will be approximately 34%
Final answer:
To calculate the probability that the mean body temperature of 36 randomly selected adults is greater than 98.5° F, you'd use the z-score formula after finding the standard error. The final probability is found by subtracting the z-score probability corresponding to a score of -1 from 1. The correct distribution for calculation is the z-distribution due to the known standard deviation.
Explanation:
The question pertains to calculating the probability that the mean body temperature of a randomly selected sample of 36 adults is greater than 98.5° F. Given that the mean is 98.6° F and the standard deviation is 0.60° F, one would first calculate the standard error of the mean (SE) using the formula SE = σ/√n, where σ is the standard deviation and n is the sample size. In this case, SE = 0.60/√36 = 0.10° F.
To find the probability, we can use the z-score formula, which is z = (X - μ) / SE, where X is the value we are finding the probability for, μ is the mean, and SE is the standard error. Plugging in the values, we get z = (98.5 - 98.6) / 0.10 = -1. When we look up the z-score of -1 in the z-tables or use a statistical software, we find the probability to the left of z=-1. However, since we want the probability that the mean temperature is greater than 98.5° F, we need to subtract this value from 1.
The final step will give us the probability that the mean of the selected sample is greater than 98.5° F. It's important to note that while the question hints at using the t-distribution due to not knowing the population standard deviation, since we're using the provided standard deviation of 0.60° F, we're actually using the z-distribution. If we were dealing with smaller sample sizes or truly didn't know the population standard deviation, we would use the t-distribution as suggested.
What is measure of angle P? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. ° P Q R is a right triangle. Q is a right angle. P Q is equal to eight centimeters, Q R is equal to fifteen centimeters and P R is equal to seventeen centimeters.
Given:
In ΔPQR, ∠Q = 90°
PQ = 8 cm
QR = 15 cm and
PR = 17 cm
To find the value of ∠P.
Formula
By Trigonometric ratio we get,
[tex]tan \theta=\frac{opp}{adj}[/tex]
Now let us take ∠P = θ
With respect to θ, QR be the opposite side and PQ be the adjacent side.
So,
tan θ = [tex]\frac{QR}{PQ}[/tex]
tan θ = [tex]\frac{15}{8}[/tex]
θ = [tex]tan^{-1} (\frac{15}{8} )[/tex]
θ = 61.93° (approx)
Hence, the value of ∠P is 61.93° (approx).
Answer:
61.93°
Step-by-step explanation:
Using cosine law:
15² = 8² + 17² - 2(8)(17)cosP
225 = 353 - 272cosP
cosP = 8/17
P = 61.92751306
6 x 1 x 5 x 1/10 as a decimal
Answer:
30.10
Step-by-step explanation:
Vicente has a prism-like water tank whose base area is 1.2 square meters. He bought 6 goldfish at the store, and the store owner told him to make sure their density in the tank isn’t more than 4 fish per cubic meter. Vicente needs to figure out how high to fill the water in the tank. What is the lowest possible height so the fish aren’t too crowded?
Answer:
1.25 m.
Step-by-step explanation:
Given,
Area of base = 1.2 m²
Number of gold fish = 6
Density of the tank should be = 4 fish/m³
Height of the tank= ?
4 fish = 1 m³
6 fish = 1.5 m³
Volume required for 6 fish is 1.5 m³
V = area of base x height
1.5 = 1.2 x h
h = 1.25 m
Hence, height of the tank is equal to 1.25 m.
Answer:
1.25
Step-by-step explanation:
Jared worked 10 hrs in one week and earned $87.50 how many dollars per hour did he earn
Answer:
8.75 per hour
you would put the overall money earned and divide it by how many hours he worked
example:
87.50 ÷ 10 = 8.75
Can anyone help me out with this?
Sarah lost her science book. Her school charges a lost book fee equal to 75% of the cost of the book. Sarah received a notice stating that she owed the school $60 for he lost book. How much did the school pay for the book.
Answer: the school paid $80 for the book.
Step-by-step explanation:
Let x represent the amount that the school paid for the book.
Her school charges a lost book fee equal to 75% of the cost of the book. It means that the amount that the school would charge on a book that cost $x is
75/100 × x = 0.75 × x = 0.75x
Sarah received a notice stating that she owed the school $60 for he lost book. It means that
0.75x = 60
x = 60/0.75
x = $80
If f(x) is discontinuous, determine the reason.[tex]f(x) = \left \{ {{x^2 + 4; x \leq 1} \atop {x+4; x \ \textgreater \ 1}} \right.[/tex]a. f(x) is continuous for all real numbersb. The limit as x approaches 1 does not exist c. f(1) does not equal the limit as x approaches 1 d. f(1) is not defined
Answer:
a. f(x) is continuous for all real numbers
Step-by-step explanation:
At x = 1
Piece 1:
f(x) = 1² + 4 = 5
Piece 2:
f(x) = 1 + 4 = 5
First piece ends at (1,5)
Second piece starts at (1,5)
So no discontinuity
Diana has a 32 ounce bag of mixed nuts: 1/2 of the mix is peanuts, 1/9 of the mix is Brazil nuts, and 1/12 of the mix is cashews. How many of the bag are cashews
Answer:
2.67 ounce of cashews are in the mix.
Step-by-step explanation:
Since we are dealing with a 32 ounce bag of mixed nuts and 1/12 of this bag is cashews (1/12 of the mix),
Then:
1/12 × 32 ounce = The actual quantity of cashew nuts in the mix.
= 1/12 × 32
= 32/12
= 2.67 ounce of cashews are in the bag.
Answer:
2.666ounce is contained in the bag
Step-by-step explanation:
Given that 32 ounce of bag has mixed nuts of which 1/12 of this bag contain cashews.
(1/12 of the entire mix),
Hence,
1/12 × 32 ounce
= 1/12 × 32
= 32/12
= 2.666ounce of cashews are in the bag.
Evaluate the numerical expression. (2/5)^2 • 100 ÷ 2/3 + [2^4 ÷ (13 - 5)]
Answer:
14 /3- fraction
(Decimal: 4.666667)
Step-by-step explanation:
The value of the numerical expression is 26
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the expression be A = (2/5)^2 • 100 ÷ 2/3 + [2^4 ÷ (13 - 5)]
Now , on simplifying the equation , we get
A = ( 2/5 )² x 100 / ( 2/3 ) + [ 2⁴ / 8 ]
A = ( 4/25 ) x ( 100 x 3 ) / 2 + 2
So , the equation will be
A = 4/25 x ( 300/2 ) + 2
A = 4/25 x 150 + 2
A = 4 x 6 + 2
A = 24 + 2
A = 26
Therefore , the value of A is 26
Hence , The value of the numerical expression is 26
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The triangle shown is rotated about line m. A triangle with side lengths of 6 centimeters, 8 centimeters, and 10 centimeters is shown. The triangle is rotated about line m at the side with length 8 centimeters. What is the approximate base area of the resulting three-dimensional figure? Area of a circle: A = πr2
From the information given, the area of the circle is: "113 sq. cm".
What is the formula for the area of a circle?The formula to find the area of a circle is πr².
Using the side as the radius of the circle, we can calculate the area of the base area.
Note;
r = 6
Thus,
A = π * 6²
A = (22/7) * 36
A = 3.14285714286 * 36
Hence, The area of the circle A = 113.142857143 or 113 sq. cm.
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18. At a store, a pack of six turkey burgers costs $5.00. A pack of six buns costs $3.00. One pack of turkey burgers and
one pack of buns serve one table of people at Tessa's barbecue. Iff) = 5x represents the total cost of x packs of
turkey burgers and if g(x) = 3x represents the total cost of x packs of buns, which function can Tessa use to determine
the total cost of servingx tables of people at her barbeque?
A. (x)=f(x) -9(x) B1(x) =F ch(x) = f(s) +g(x) D. (x) = f(x) - g(x)
Answer:
I would say add it up
Step-by-step explanation:
Answer:
Step-by-step explanation:
The correct answer would be C - h(x) = f(x) + g(x). The total cost for serving everyone at the barbecue would consist of adding the cost of both the buns and turkey burgers.
PLS PLS PLS PLS PLS PLS HELP!!!!! FIRST TO ANSWER CORRECTLY GETS MARKED THE BRAINLIEST!!!!!
Answer:
5 [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
A thirty minute TV program means that is the total.
If each commercial is 2 1/2 minutes long then we multiply that my three (for each of the times they show a commercial)
2 1/2 * 3 = 7 1/2 minutes (That's the commercials)
30 (Total) - 7 1/2 = 22 1/2 (That all the entertainment segments together)
Since there is 4 segments we divide 22 1/2 by 4
(22 1/2) / 4 = 5.625 or 5 and 5/8
Y = A system of equations. Y equals StartFraction 2 over 3 EndFraction x plus 1. Y equals negative StartFraction 2 over 3 EndFraction x minus 1x + 1 and y = x – 1
Final answer:
To solve the system of equations, you can substitute the value of y in terms of x from the third equation into the first two equations.
Explanation:
The system of equations given is:
Y = ½x + 1
Y = -½x - x + 1
y = x - 1
To solve these equations, we can substitute the value of y in terms of x from the third equation into the first two equations:
Substituting y = x - 1 into Y = ½x + 1:
Y = ½(x - 1) + 1
Simplifying, we get:
Y = ½x - ½ + 1
Substituting y = x - 1 into Y = -½x - x + 1:
Y = -½(x - 1) - (x - 1) + 1
Simplifying, we get:
Y = -½x + ½ + 1
Therefore, the system of equations can be simplified to:
Y = ½x - ½ + 1
Y = -½x + ½ + 1
What kind of slope does the following line have?
+
Answer:
horizontal and vertical
Step-by-step explanation:
if its the plus?
Hello Mr. White drove 15 miles in July. He drove 8 times as many miles in September as he did in July. He drove 3 times as many miles in August as he did in September. How many miles did Mr. White drive in August? And that is my question I don't get it
Answer:
360 miles
Step-by-step explanation:
15 times 8= 120 miles I. September
Times 3 in August=360 miles
pls help! i’m not sure if the answer i chose is the right 1.
Kevin and Ethan are employees for a company. Ethan is making a salary of $34,200. Ethan is earning a salary that is 28% lower than the salary of Kevin. What salary is Kevin earning?
Answer:
$45,000
Step-by-step explanation:
Let Kevin's Salary=x
Ethan's Salary=$34,200.
Since Ethan is earning a salary that is 28% lower than the salary of Kevin.
Ethan is earning (100-24)%=76% of Kevin's Salary.
76% of Kevin's Salary=$34,200.
0.76x=34200
Divide both sides by 0.76
x=45000
Kevin's Salary is $45,000.
Bethanine left at 3:00 in the afternoon and walked 3/10 of a mile to Bridget's house. Laney walked 36/100 of a mile to Bridget's house. How far did Bethanie and Laney walk altogether? Determine if there is extra or missing inform
Answer:
Bethanie and Laney walked a total of = 0.66 miles or ([tex]\frac{33}{50}[/tex]th of a mile)
Step-by-step explanation:
Bethanie walked 3/10th of a mile
Laney walked 36/100th of a mile
Lets divide and convert them to decimal:
3 divided by 10 gives us 0.30
36 divided by 100 gives 0.36
Total they walked:
0.30 + 0.36 = 0.66 miles
That would be (in fraction):
66/100 = 33/50 of a mile
Your college fund has $65,000. It is currently in an account which pays 2.3% compounded monthly. How much money will you have in 15 years
Answer:
$91,749.04
Step-by-step explanation:
Lets use the compound interest formula provided to solve this:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, change 2.3% into a decimal:
2.3% -> [tex]\frac{2.3}{100}[/tex] -> 0.023
Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:
[tex]A=65,000(1+\frac{0.023}{12})^{12(15)}[/tex]
[tex]A=91,749.04[/tex]
You will have $91,749.04 in 15 years.
The time it takes people to read a certain book is normally distributed with a mean of 147 minutes and a standard deviation of 12 minutes.
Approximately what percent of people take between 123 and 171 minutes to read the book?
Approximately 95.44% of people take between 123 and 171 minutes to read the book.
To find the percentage of people who take between 123 and 171 minutes to read the book, we'll use the properties of the normal distribution.
First, we need to find the z-scores for both 123 and 171 minutes using the formula:
[tex]\[ z = \frac{{X - \mu}}{{\sigma}} \][/tex]
Where:
-[tex]\( X \)[/tex] is the value (in minutes),
-[tex]\( \mu \)[/tex] is the mean (147 minutes),
- [tex]\( \sigma \)[/tex] is the standard deviation (12 minutes).
For 123 minutes:
[tex]\[ z_1 = \frac{{123 - 147}}{{12}} = -2 \][/tex]
For 171 minutes:
[tex]\[ z_2 = \frac{{171 - 147}}{{12}} = 2 \][/tex]
Now, we'll use a standard normal distribution table or calculator to find the percentage of values between these z-scores. For a standard normal distribution, approximately 95.44% of the data falls within ±2 standard deviations from the mean.
So, to find the percentage of people who take between 123 and 171 minutes, we subtract the percentage outside this range from 100%:
[tex]\[ \% = 100 - (100 - 95.44) = 95.44\% \][/tex]
Approximately 95.44% of people take between 123 and 171 minutes to read the book.
What are two numbers that equal to 28 in multiplication
Answer:
7*4
14*2
Step-by-step explanation:
Answer:
Answers will vary
Step-by-step explanation:
There are many possibilities, especially if you're going beyond whole numbers, meaning decimals work as well
Whole numbers
1 and 28
2 and 14
4 and 7
Decimals
3 and 9.33 or 9 1/3
5 and 5.6
6 and 4.67 or 4 2/3
8 and 3.5
9 and 3.11
10 and 2.8
These are just a few simple ones, it gets even more complicated if you have two numbers both with decimals
The following are the weights,in pounds, of some dogs at a kennel: 36,45,29,39,51,49.
find median:
suppose one of the weights were given in kilograms.Can you still find median.
Answer:
Median = 42 pounds
Step-by-step explanation:
It is given that the following are the weights,in pounds, of some dogs at a kennel: 36,45,29,39,51,49.
Arrange the data in ascending order.
29, 36, 39, 45, 49, 51
Total number of terms = 6 (even)
So, the formula for median is
[tex]Median=\dfrac{\frac{n}{2}\text{th term}+(\frac{n}{2}+1)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{\frac{6}{2}\text{th term}+(\frac{6}{2}+1)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{3\text{rd term}+4\text{th term}}{2}[/tex]
[tex]Median=\dfrac{39+45}{2}[/tex]
[tex]Median=42[/tex]
Hence, the median weight is 42 pounds.
To find the median, units of the data should be same. If one of the weights were given in kilograms, then we cannot find median.
John makes 35% of his free throw shots sue makes 40% of her free throw shot What is the possibility that John And sue both miss their shots
Answer:
The possibility that John And sue both miss their shots = 0.39
Step-by-step explanation:
John makes 35% of his free throw shots = 0.35
The probability of John missing his shot = 0.65
Sue makes 40% of her free throw shot = 0.4
The probability of Sue missing his shot = 0.6
The possibility that John And sue both miss their shots = 0.65 (0.6)
= 0.39
Jalen is trying to set a pole that is 10 feet long into the ground so that it is perpendicular with
the horizontal surface. Jalen locates a point 6 feet from the base of the pole, a C, and labels
it A He then measures the distance from point A to point What distance, to the nearest
tenth of a foot does Jalen need for the pole to be perpendicular? Justify,
10 font long board and an 18 foot long board. To make the ramp
isht triangle. How long should
Answer:
Step-by-step explanation:
The distance of point A from the top of the pole that will make the pole be perpendicular position to the ground
so, for the pole to be in perpendicular position it must obey Pythagorean theorem
Then, using Pythagoras theorem
c² = a² + b²
x² = 10² + 6²
x² = 100 + 36
x² = 136
x = √136
x = 11.662ft
To nearest tenth
x = 11.7 ft.
So, the pole must be at a distance of 11.7 ft from the top of the pole to point A.
To justify,
10 font long board and an 18 foot long board. To make the ramp right triangle. How long should ramp
So, to calculate the ramp, which is the hypotenuse we will still apply Pythagorean theorem
Then, using Pythagoras theorem
c² = a² + b²
x² = 10² + 18²
x² = 100 + 324
x² = 424
x = √424
x = 20.59 ft
To nearest tenth
x = 20.6 ft.
So, the ramp is 20.6 ft long
Jalen needs to measure 8 feet from point A to the base of the pole to set it perpendicularly to the ground.
To make the pole perpendicular to the ground, Jalen needs to measure the distance from point A to the base of the pole, which forms a right angle at point B.
Using the Pythagorean theorem: Distance AB = √((10)^2 - (6)^2) = √(100 - 36) = √64 = 8 feet.
Therefore, Jalen needs to measure 8 feet from point A to the base of the pole for it to be positioned perpendicularly.
Amelia is 3 years older than Caleb, and Caleb is 2 years more than half of Amelia's age. The system of equations represents this situation. A = 3 + C C = 2 + 0.5A How old is Amelia? How old is Caleb?
Step-by-step explanation:
Simple
If Amelia is 10 years old and so half of Amelia age = 5
Caleb is 2 years more so = 5 + 2 = 7
It means Caleb age = 7
And Amelia age = 10
its for geometry and i dont know it pls help
Hello.
The angle shown for 1 (and 3) is ∠40.
A straight line is shown, which is 180°. So the measure of ∠4 is 140°
0). Where is Point B on the number line?
Answer: point B should be the 2nd number on the number line.
Step-by-step explanation:
the answer is shove it up your whole
hAHA JK ITS B
The number part when a number and a variable are multiplied together in a term is called the _____.
Answer:
coefficient
Step by-step explanation:
Find the common ratio of the geometric sequence –1,-8, -64, ...
The common ratio of the geometric sequence –1,-8, -64, ... is 8. This is calculated by dividing a term in the sequence by its preceding term and is same across all consecutive terms.
Explanation:In a geometric sequence, the common ratio is found by dividing any term by its preceding term. Here, the sequence given is –1,-8, -64, ...
Let's calculate the ratio for this series: We divide the second term (-8) by the first term (-1), which is 8. Let's check it with the next terms, where we divide the third term (-64) by the second term (-8). We find the ratio to be 8 again.
Therefore, the common ratio of the given geometric sequence –1,-8, -64, ... is 8.
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The common ratio of the geometric sequence -1, -8, -64, ... is -8, which results from dividing any term of the sequence by its preceding term.
Geometric sequence: -1, -8, -64, ...
Common ratio:
To find the common ratio, we divide each term by its preceding term.
In this case, -8 ÷ (-1) = 8 and -64 ÷ (-8) = 8.
Therefore, the common ratio is 8.
PLEASE HELP!!!! Write the equation of a parabola with vertex (2,-1) and directrix y=-3.
Please show work and put your equation in graphing/vertex form.
Answer:
y = 1/8(x -2)^2 -1
Step-by-step explanation:
The vertex form of the equation of a parabola can be written as ...
y = (1/(4p))(x -h)^2 +k
for vertex (h, k) and vertex-to-directrix distance p. Here, the vertex has a y-value of -1, and the directrix has a y-value of -3, so the distance between them is -1 -(-3) = 2, and the desired equation with vertex (2, -1) is ...
y = 1/8(x -2)^2 -1
_____
Comment on the graph
One description of a parabola is that it is the locus of points equidistant from the focus and the directrix. I like to show that a point on the parabola (not the vertex) meets that requirement. That is what the dashed orange lines are for in the diagram. You can easily see that each has length 4.