The empirical rule tells us that approximately 99.7% of data in a normal distribution falls within three standard deviations of the mean. The lifespan of 32.2 years is three standard deviations from the mean lifespan of zebras in the zoo, so the probability of a zebra living less than 32.2 years is about 99.7%, which is very high.
To the lifespan of zebras being normally distributed, with a mean of 20.5 years and a standard deviation of 3.9 years.
To estimate the probability of a zebra living less than 32.2 years, we can use the empirical rule, also known as the 68-95-99.7 rule. This rule states that for a normal distribution:
Approximately 68% of the data falls within one standard deviation of the mean (both above and below).
About 95% fall within two standard deviations.
Almost all, or 99.7%, fall within three standard deviations.
To find the probability of a zebra living less than 32.2 years, we first calculate how many standard deviations away from the mean this is, which is called the z-score.
The difference between 32.2 and the mean is 32.2 - 20.5 = 11.7 years.
Dividing this by the standard deviation of 3.9 years, we get a z-score of approximately 3, indicating that 32.2 years is three standard deviations above the mean.
According to the empirical rule, the probability of a zebra living less than 32.2 years would include almost all of the distribution or approximately 99.7%.
Therefore, the probability of a zebra living less than 32.2 years is very high, close to 100%.
Work out the gradient of a line that is parallel to -2x+y-5=0
Answer:
gradient = 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
Given
- 2x + y - 5 = 0 ( add 2x and 5 to both sides )
y = 2x + 5 ← in slope- intercept form
with gradient m = 2
Parallel lines have equal gradients
Gradient of parallel line is m = 2
Show some graphing proportional and linear relationships
Write an equation to represent the following statement.
10 less than j is 35.
_______
Solve for j.
j =_____
Answer:
j - 10 = 35
j = 45
Step-by-step explanation:
When it says, "less than" it means subtracting. So 10 less than j is (j - 10)
The part where is says "is" means it is equal to.
So the equation would be = (j - 10) = 35
Answer:
Equation: (j - 10) = 35
j = 45
Step-by-step explanation: Lets translate 10 less than j:
Less than means 10 is being subtracted from j.
So we can write 10 less than j as j - 10.
The word is means equal.
So, we can write is 35 as = 35.
Now lets write the whole equation toghter.
j - 10 = 35
We can also write this as 35 = j - 10.
Now we can solve for j.
Add 10 to both sides of the equation to get j by itself.
j - 10 + 10 = 35 + 10
J=45
The following equation matches this situation:
j - 10 = 35
j = 45
Solve for x: −1 < x + 3 < 5
2 < x < 8
−4 < x < 2
2 > x > 8
−4 > x > 2
Answer:
-4<x<2
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask ÷)
the difference of a number x and 7 *
Answer:
C
Step-by-step explanation:
x-7 is the answer
Answer:
difference means subtract
x-7
C. is correct because it subtracts and the numbers are in order
Step-by-step explanation:
On Monday Julio ran 3,000 meters and on Wednesday he ran 4,500 meters how many meters did Julio run in all
Answer:
3000+4500= 7500
Consider the exponential function f(x) = 1 (154). What is the value of the growth factor of the function?
The value of the growth factor of the function is 15. To add to your answer, exponential growth happens when the rate of the number of the function corresponds with the present value of the function. This then lets its increase together with time be called an exponential function.
Answer:
15.
Step-by-step explanation:
f(x) = a b^x
The growth factor is b - in this case 15.
PLEASE HELP 30 POINTS PLEASE!!!!!
The function f(x)=−11sin(7/3x+1/6)−2 models the average rate of change in temperature of a substance monitored in an experiment. In the function, x represents the number of minutes since the commencement of the experiment and the temperature of the substance is measured in degrees Fahrenheit. Over what range of temperatures does the average rate of change in temperature fall?
The range in the average rate of change in temperature of the substance is from a low temperature of ____°F to a high of ____°F.
Answer:
-13ºF || 9ºF
Step-by-step explanation:
Answer:
-13ºF & 9ºF
Step-by-step explanation:
The range in the average rate of change in temperature of the substance is from a low temperature of -13º F to a high of 9º F.
PLZZZ HELP ME Sue travels by bus or walks when she visits the shops. The probability that she catches the bus to the shops is 0.4. The probability she catches the bus from the shops is 0.7. complete the tree diagram
last time i did this i got 1.4
Answer: 0.72
Step-by-step explanation:
0.7x0.4=0.28
1-0.28= 0.72
That is what I did in the box and got the correct answer. Hope you have a good day!
Helppp plzz!!! Julius is in charge of planting a peach orchard that covers 15 acres. He uses the same amount of ground space for each tree. Julius plants 25 trees in the section of the orchard called the South Hill region that measures 450 feet by 24 feet. Approximately how many trees does Julius plant in the orchard in all? (1 = 43,560 ).
A. 909
B. 1,151
C. 1,513
D. 1,746
Answer:
C
Step-by-step explanation:
Area of known planted trees: 450ft x 24ft = 10800 sq ft
total area of orchard: 43560 sq ft. x 15 acres = 653400 sq ft
653400 / 10800 = 60.5 "duplicated known areas"
25 trees in each "known area"
60.5 x 25 = 1512.5 trees
round to 1513 trees
C
I worked it out but not sure
Find the unknown side of the triangle when x =
12 in and y = 5 in.
Answer:
13
Step-by-step explanation:
As x and y are perpendicular - we can use pythagoras.
So, The length of side x squared + The length of side y squared = The missing length squared.
12^2=144
5^2=25
144+25=169
sqrt169=13
Answer:
Unknown side = 13 in
Step-by-step explanation:
If it is a right sided triangle, then you can use the Pythagoras theoreum.
unknown side = u
x² + y² = u²
12² + 5² = u²
u² = 144 + 25
u² = 169
u = + - SQRT(169)
{Only the positive value has a meaning}.
Unknown side = 13 in
Which pair(s) of expressions are equal in value? Check all that apply.
Answer:
Where is the expressions ?
Step-by-step explanation:
Answer:
a [4.9] and [3.1]
c [-6] and [-6]
Step-by-step explanation:
Edge 2020-2021
It's right I did it
Hope that helps
Ryan invests a sum of money in a savings account with a fixed annual interest rate of 4.31% compounded 12 times per year. After 10 years, the balance reaches $12,855.94. What was the amount of the initial investment?
Based on the information given the amount of the initial investment is $8,361.
Let P represent the amount of the initial investment
Hence,
12855.94 = P(1 + .0431/12) ^12(10)
12,855.94=P(1+0.0035917)^120
12,855.94=P(1.0035917)^120
12,855.94=P(1.53760782)
P=12,855.94/1.53760782
P=$8,360.8
P=$8,361 (Approximately)
Inconclusion the amount of the initial investment is $8,361.
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What's the answer will award brainiest
Answer:
D
Step-by-step explanation:
Answer:
D?
Step-by-step explanation:
Complete the work shown to find a possible
solution of the equation.
(x - 5) +5=2
(x - 5)2 = -3
A possible solution of the equation is
Answer:
It's 14.
Step-by-step explanation:
Took it on edg 2020
How do you do this anyone know how
Answer:
ok so........
Step-by-step explanation:
For example, the first one is -1/3. It's slope is going down to the right, so it's negative . It goes down 1 (y value) and over to the right 3 (x value). Since it goes down and to the right it is a slope of -1/3.
Solve the following system:
y=1
y=-6x-5
Answer:
x = -1
y = 1
Step-by-step explanation:
Since it gives you "y", plug in the number given into the equation:
y = -6x - 5
1 = -6x - 5
Then, add 5 to both sides:
1 = -6x - 5
+5 + 5
________
6 = -6x
Divide both sides by -6:
6 = -6x
-1 = x
So now you have, x = -1 and y = 1
plz help asap
I will mark you as BRAINLIEST
Answer:
-86 ≥ x
Step-by-step explanation:
Answer:
-87 ≥ x
Step-by-step explanation:
In this inequality, it states that -87 is greater than and equal to x.
So we know we have to use this sign.
≥
So, -87≥x
What is the relationship between segment RS and segment RU
Answer:
I would like to answer but where is the picture for the question. Download that to this page and i will answer it. Have a great day
Step-by-step explanation:
Nine bean plants were grown in varying amounts of light. Mark thinks that, if the light is too intense, a bean plant will not grow as
high.
Is Mark's prediction correct?
Yes; the tallest plants were the ones that got the weakest light.
No; some plants grew just as well while getting very strong light.
Yes, when the light was too strong the plants did not grow as well.
No: plants that got the strongest light were also the ones that grew best.
Answer: C) Yes, when the light was too strong the plants did not grow well
Step-by-step explanation:
You have boxes that will hold 1 cubic foot, 3 cubic feet,
9 cubic feet, and 27 cubic feet of paper. What is the fewest
number of boxes you need to hold 257 cubic feet of paper?
Answer:
13 boxes
Step-by-step explanation:
To calculate the minimum number of boxes that can be had with that amount of paper, they should be kept in the largest box, that is, the 27 cubic foot box, therefore, we divide:
257/27 = 9.51
Which means that we can save the paper in 9 boxes of 27 cubic feet, now we will save the rest in the next smaller box, the 9 cubic foot box.
First let's calculate how many leftover paper:
257 - 27 * 9 = 14
Therefore, we can only use 1 box of 9 cubic feet:
14 - 9 = 5
For the remaining 5 cubic feet use 1 box of 3 cubic feet and 2 boxes of 1 cubic foot.
Therefore, in total it would be:
9 of 27 ft ^ 3 + 1 of 9 ft ^ 3 + 1 of 3 ft ^ 3 + 2 of 1 ft ^ 3 = 13
a total of 13 boxes would be the minimum
Use the laws of logarithms and the values given below to evaluate the logarithmic expression.
log7=0.8451 log5=0.6990
log3=0.4771 log2=0.3010
The value of [tex]\(\log 12\)[/tex] is approximately 1.0792 based on the given logarithmic values. Option B [tex]$\approx 1.0791$[/tex]
Let's evaluate the logarithmic expression [tex]\(\log 12\)[/tex]. We'll use the given logarithmic values:
1. Recall that [tex]\(\log 12\)[/tex] represents the common logarithm (base 10 logarithm) of the number 12.
2. Apply the change of base formula:
[tex]\[ \log 12 = \frac{\log 12}{\log 10} \][/tex]
Given values:
[tex]- \(\log 12 \approx 2.4849\) (from \(\log 12\))[/tex]
[tex]- \(\log 10 \approx 2.3026\) (from \(\log 10\))[/tex]
Now calculate:
[tex]\[ \log 12 \approx \frac{2.4849}{2.3026} \][/tex]
[tex]\[ \log 12 \approx 1.0792 \][/tex]
Therefore, the value of [tex]\(\log 12\)[/tex] is approximately 1.0792.
The correct answer is b. [tex]\(\approx 1.0791\)[/tex].
The correct question is:
Use the laws of logarithms and the values given below to evaluate the logarithmic expression.
[tex]$$\begin{array}{ll}\log 7=0.8451 & \log 5=0.6990 \\\log 3=0.4771 & \log 2=0.3010\end{array}$$[/tex]
[tex]$\log 12$[/tex]
a. [tex]$\approx-1.0791$[/tex]
b. [tex]$\approx 1.0791$[/tex]
c. [tex]$\approx 3.0234$[/tex]
d. [tex]$\approx-3.0234$[/tex]
Girls in science class account for one-third of the total number of students in their 3rd period class. 3 girls are absent today. Find the total number of students in the class if four girls attended class today.
Answer:
See Explanation
Step-by-step explanation:
The question isn't clear enough. However, I'll solve for the total number of students in science class and I'll.also solve for the total number of students present in class.
Given
Proportion of girls = ⅓
Number of girls absent = 3
Number of girls present = 4
Required
Find the total number of students
If 3 girls were absent and 4 were present, then there are total of 7 girls in science class.
Let the number of students in the class be represented by y.
⅓ of the total number of students are girls;
This means
⅓ of y = 7
⅓ * y = 7
Multiply both sides by 3
3 * ⅓ * y = 3 * 7
y = 3 * 7
y = 21.
Hence, the total number of students in science class is 21
Recall that 3 girls are absent;
This means that 21 - 3 are presently in the class.
21 - 3 = 18.
Hence, 18 students are presently in class.
Orlando is making a design for a logo. He begins with a square measuring 22 inches on a side.
The second square has a side length of 17.6 inches, and the third square has a side length of
14.08 inches. Which square will be the first square with a side length of less than 10 inches?
A) fifth square
B) fourth square
C) sixth square
D) seventh square
Answer: A
Step-by-step explanation:
The first square is 22 inches on a side.
The second is 17.6 inches on a side
the third is 14.08 inches on a side.
We can suppose that we have a constant rate of decrease betwen the sides cubes, this means that:
22in*x = 17.6in
where x is the rate of scale.
x = 17.6/22 = 0.8
Now we test this with the second and third:
17.6in*0.8 = 14.08in
Ok, this works.
then the side of n-th cube can be found with the equation
L = 22*0.8^(n-1)
we can try the different options and see which one gives a value smaller than 10.
A) n = 5
L = 22*0.8^4 = 9.01
Then the correct option is A
Answer:
the answer is A i had a quiz
Step-by-step explanation:
Use one or more transformations to transform the pre-image (purple) onto the image (white).
Transformations in geometry include translation, rotation, reflection, and dilation, which are used to change a figure's position, orientation, or size. The appropriate transformation to use depends on the changes observed between the purple pre-image and the white image in the problem.
Explanation:In mathematics, specifically in geometry, we use transformations to move or change a figure in some way without altering its fundamental shape or size. The transformation of a pre-image onto an image can be achieved using transformations such as translation, rotation, reflection, or dilation.
To transform the purple pre-image onto the white image, firstly identify the type of transformation required. For instance, if the white image is the same size as the purple pre-image and only its position has changed, use translation. If the image is mirrored along a line, use reflection. If it's turned around a point, use rotation. If the image is an enlarged or reduced version of the original figure, use dilation.
Consequently, the precise steps depend on the type of transformation(s) required.
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Which expression is equivalent to 5y^-3
Answer:
Step-by-step explanation:
5
5y^-3 = ---------
y^3
Which expression is equivalent to
- 5/3?
Answer:
The first one! :)
Step-by-step explanation:
At the bottom of each question for example the first on it has 1 at the top then at the bottom it says 5/3 with a x.So if it does not say 5/3 it can be excluded.So it says only one 5/3.So one 5/3 is the exact same as 5/3!
And for the last one says -5/3.:)
And no im not saying 1 5/3 :(
(❁´◡`❁) (●'◡'●) ╰(*°▽°*)╯ (≧▽≦) (*/ω＼*) (^///^) ^_^ (┬┬﹏┬┬) ಥ_ಥ ಠ_ಠ
[tex]$\frac{1}{\sqrt[3]{x^{5}}}$[/tex] is equivalent to [tex]- 5/3[/tex].
The calculation of the given expression can be defined as
[tex]$\begin{aligned} \rightarrow x^{-\frac{5}{3}} &=\frac{1}{x^{\frac{5}{3}}} \\ &=\frac{1}{\sqrt[3]{x^{5}}} \end{aligned}$[/tex]
So, the final answer is "Option b".[tex]$\frac{1}{\sqrt[3]{x^{5}}}$[/tex]
What are Equivalent Fractions?Equivalent fractions are fractions that represent the same value, even though they look different. A fraction has two parts. The number on the top of the line is called the numerator which tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator and it shows the total number of equal parts the whole is divided into or the total number of equal parts which are there in a collection.To learn more about equivalent refer to:
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please help thanks will mark brainliest
Answer:
12 inches
Step-by-step explanation:
W = 9 + L
WL = 252
L = 12
Answer:
l = 12
Step-by-step explanation:
Let l = length
width = l+9
The area of rectangle is
A = lw
A = l * (l+9)
252 = l^2 +9l
Subtract 252 from each side
0 = l^2 +9l -252
Factor
What 2 numbers multiply to -252 and add to 9
21*-12 = 252
21-12 = 9
0 = (l+21) (l-12)
Using the zero product property
l+21=0 l-12=0
l = -21 l = 12
We cannot have a negative length
l = 12
*25 points* Hailey ran a few laps. D(n), models the duration (in seconds) of the time it took for Hailey to run her n^th lap. When did the lap duration increase faster?
A. Between the 3rd and 7th lap
B. Between the 7th and 9th lap
C. The lap duration increased at the same rate over both intervals
Answer:
B
Step-by-step explanation:
4 laps were ran between her 3rd and 7th lap (inclusive) and the duration increased by 14 seconds
But just 2 laps were ran between her 7th and 9th lap and the duration increased by 11 seconds
So obviously the lap duration increased faster between the 7th and 9th lap
Answer:
B
Step-by-step explanation:
I just did the quiz, so you all can trust me :)
A cone-shaped container has a height of 9 inches and diameter of 2.5 inches. It is filled with a
liquid that is worth $2 per cubic inch.
What is the total value of the liquid in the container?
Use 3.14 for .
Enter your answer in the box.
*pleaseee help i will mark brainliest if right*!!!!!
ps, thank you
Answer:
the total value of the liquid in the container is $29.4
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cone
The volume of a cone is expressed as
V=1/3(πr²h)
Given data
Height h= 9 inches
Radius r= diameter/2= 2.5/2= 1.25in
Substituting we have
V= 1/3(3.14)*(1.25)²*9
V= 1/3*(3.14)*14.06
V= 44.156/3
V= 14.7in³
The volume of the cone is 14.7in³
Hence If 1 in³ of liquid costs $2
14.7in³ will cost $x
x= 14.7*2
x= $29.4