Rose's age should be a whole number, we can round 7.8 to the nearest whole number, which is 8.
Let's assume the number of primroses in the vase is p, and the number of celandines is c.
Each primrose has 5 petals, so the total number of primrose petals is 5p.
Each celandine has 8 petals, so the total number of celandine petals is 8c.
According to the given information, the total number of petals is 39. Therefore, we can set up the equation:
5p + 8c = 39 (Equation 1)
Aunt Lily mentions that the total number of flowers is exactly Rose's age. Since Rose's age is not provided, we'll represent it with the variable r.
The total number of flowers is p + c, which is also equal to Rose's age (r). Therefore, we have another equation:
p + c = r (Equation 2)
We need to find the value of r (Rose's age). To do that, we'll solve the system of equations by eliminating one variable.
Multiplying Equation 2 by 5, we get:
5p + 5c = 5r (Equation 3)
Now we can subtract Equation 1 from Equation 3 to eliminate the p term:
(5p + 5c) - (5p + 8c) = 5r - 39
This simplifies to:
-3c = 5r - 39
Now, let's rearrange Equation 2 to solve for p:
p = r - c (Equation 4)
Substituting Equation 4 into the simplified form of Equation 3, we have:
-3c = 5r - 39
Substituting r - c for p, we get:
-3c = 5(r - c) - 39
Expanding, we have:
-3c = 5r - 5c - 39
Rearranging the terms, we get:
2c = 5r - 39
Now we have a system of two equations:
-3c = 5r - 39 (Equation 5)
2c = 5r - 39 (Equation 6)
To solve this system, we can eliminate one variable by multiplying Equation 5 by 2 and Equation 6 by 3:
-6c = 10r - 78 (Equation 7)
6c = 15r - 117 (Equation 8)
Now, let's add Equation 7 and Equation 8 to eliminate c:
-6c + 6c = 10r + 15r - 78 - 117
This simplifies to:
25r = 195
Dividing both sides by 25, we get:
r = 7.8
Since Rose's age should be a whole number, we can round 7.8 to the nearest whole number, which is 8.
Therefore, Rose is 8 years old.
for such more question on whole number
https://brainly.com/question/2117233
#SPJ8
3
Which expression is equivalent to -x--xy?
2x-xy?
4
x(3-y)
4x(3-y)
x(3+y)
4x(3 + y)
The expression equivalent to -x--xy is 4x(3 + y).
To simplify the expression -x--xy, we can apply the rules of combining like terms and distribute the negative sign.
-x - (-xy)
Removing the double negative:
-x + xy
Factoring out the common factor of x:
x(-1 + y)
Now, let's compare the simplified expression with the given options:
Option 1: 2x - xy
This expression is not equivalent to -x - (-xy) as it includes an additional term of 2x.
Option 2: x(3 - y)
This expression is equivalent to the simplified expression x(-1 + y), as it represents the distribution of x over the terms inside the parentheses.
Option 3: 4x(3 - y)
This expression is not equivalent to -x - (-xy) as it includes the constant term 4.
Option 4: x(3 + y)
This expression is not equivalent to -x - (-xy) as it includes the positive sign before the y term.
Option 5: 4x(3 + y)
This expression is not equivalent to -x - (-xy) as it includes the constant term 4 and the positive sign before the y term.
From the given options, the expression that is equivalent to -x - (-xy) is:
Option 2: x(3 - y).
For similar question on expression.
https://brainly.com/question/723406
#SPJ8
PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS CORRECT (NO LINKS)
Identify the arc length of MA◠ in terms of a and rounded to the nearest hundredth.
The length of the arc in terms of π and the actual length is as follows;
8.17π m²
25.68 m²
How to find arc length?Let's find the length of the arc of the circle as follows:
Therefore,
length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleHence,
∅ = 180 - 88 = 92 degrees
r = 16 m
length of an arc MA = 92 / 360 × 2 × π × 16
length of an arc MA = 2944π / 360
length of an arc MA = 8.17π
Therefore,
length of an arc MA = 25.68 m²
learn more on arc length here: https://brainly.com/question/29273296
#SPJ1
A scatterplot includes data showing the relationship between the value of a painting and the age of the painting.
Which graph displays the line of best fit for the data?
A graph has age (years) on the x-axis and value (dollars) on the y-axis. A line with best fit is too steep.
A graph has age (years) on the x-axis and value (dollars) on the y-axis. A line with best fit is not steep enough.
A graph has age (years) on the x-axis and value (dollars) on the y-axis. A line with best fit is not steep enough.
A graph has age (years) on the x-axis and value (dollars) on the y-axis. A line with best fit goes through the points.
Mark this and return
The graph that displays the line of best fit for the data is the one where the line with the best fit goes through the points.
To determine which graph displays the line of best fit for the data, we need to analyze the provided options and identify the one that represents the relationship between the value of a painting and the age of the painting accurately.In a scatterplot, the line of best fit represents the trend or relationship between the two variables. It aims to summarize and capture the general pattern of the data points. The line of best fit should pass through the data points in a way that represents the overall trend.Analyzing the options, we see that three of them mention that the line with the best fit is either too steep or not steep enough. These options suggest that the line does not accurately capture the trend of the data.However, the remaining option states that the line with the best fit goes through the points. This implies that the line accurately represents the relationship between the value of a painting and the age of the painting by passing through the data points.Based on this analysis, we can conclude that the graph where the line of best fit goes through the points is the one that displays the most accurate representation of the relationship between the value of a painting and the age of the painting.For more such questions on graph, click on:
https://brainly.com/question/19040584
#SPJ8
(|7 − 3 x 5) | ÷ 4)³ + √64
Answer:
16
Step-by-step explanation:
(|7 − 3 x 5| ÷ 4)³ + √64
(|7 − 3 x 5| ÷ 4)³ + √64
(|7 − 15| ÷ 4)³ + √64
(|7 − 15| ÷ 4)³ + √64
(8 ÷ 4)³ + √64
(8 ÷ 4)³ + √64
2³ + √64
8 + 8
16
Answer:
16
Step-by-step explanation:
To solve, use PEMDAS as it applies to the expression.
First, you must carry out what is in the parenthesis.
Multiply (3*5 = 15), then subtract (7 - 15 = -8). The two little vertical lines surrounding (7 - 3 x 5) mean absolute value. This means that you will write -8 as +8.
Continuing on in the parenthesis, carry out (8 ÷ 4 = 2).
Next, we must do exponents.
We see that everything in the parenthesis is being raised to the power of three (cubed). Since we've solved what was in the parenthesis, we simply need to carry out ([tex]2^{3}[/tex] = 8).
Now, we need to quickly carry out [tex]\sqrt{64}[/tex]. Square roots are just whatever number can be multiplied by itself to get, in this case, 64.
[tex]\sqrt{64} = 8[/tex].
Finally, we must add what remains.
8 + 8 = 16.
So, (|7 - 3 x 5) | ÷ [tex]4)^{3}[/tex] + [tex]\sqrt{64}[/tex] = 16.
If the expenditure of a person is 75% of his income and his income tax which is 13% of his income is $585. What is his expenditure?
The person's expenditure is $1,755. (30 words)
To find the expenditure, we need to determine the person's income first. Since the income tax is 13% of the income and is given as $585, we can calculate the income. Dividing the income tax by the tax rate gives us the income. So, $585 divided by 0.13 equals $4,500, which is the person's income.
Now, we can calculate the expenditure. Given that the expenditure is 75% of the income, we can multiply the income by 0.75 to find the expenditure. So, $4,500 multiplied by 0.75 equals $3,375. Therefore, the person's expenditure is $3,375. (120 words)
In summary, the person's expenditure is $3,375. To find this, we first determined the person's income by dividing the given income tax of $585 by the tax rate of 13%, resulting in an income of $4,500.
Then, we calculated the expenditure by multiplying the income by 0.75 since the expenditure is stated to be 75% of the income. Thus, the person's expenditure is $3,375.
for such more questions on expenditure
https://brainly.com/question/2292799
#SPJ8
What is the radius of a circle that has a circumference of 68 cm
Step-by-step explanation:
The formula to calculate the circumference (C) of a circle is C = 2πr, where r represents the radius of the circle.
In this case, the given circumference is 68 cm. Plugging this value into the formula, we can solve for the radius (r):
68 = 2πr
To find the radius, we can divide both sides of the equation by 2π:
r = 68 / (2π)
Using an approximate value of π ≈ 3.14159, we can calculate the radius:
r ≈ 68 / (2 × 3.14159) ≈ 10.8419 cm
Therefore, the radius of the circle, which has a circumference of 68 cm, is approximately 10.8419 cm.
Therefore, The Radius of the Circle is 10.8 cm.
pls pls pls help
Based on the graph of F(x) below, which of the following statements is true
about F(x)?
The correct statement regarding the relative extremas of F(x) is given as follows:
F(x) has a relative maximum at x = -1 and a relative minimum at x = -0.8.
What are the relative minimums and the relative maximums of a function?The relative minimums of a function are given by the points in which the function's behavior changes from decreasing to increasing.The relative maximums of a function, meanwhile, are given by the points in which the function's behavior changes from increasing to decreasing.Hence the extremas for this problem are given as follows:
Maximum: x = -1.Minimum: x = 0.8.More can be learned about relative minimums of a function at https://brainly.com/question/9839310
#SPJ1
Solve b + 6 < 14.
Write your answer in set builder notation
There are 40 black marbles, 20 blue marbles, and 4 red marbles in a jar.
а. What is the probability of selecting one red marble?
b. What is the probability of selecting one black marble?
c. What is the probability of selecting one blue marble?
d. Which has the highest probability of being selected?
e. Which has the lowest probability of being selected?
Step-by-step explanation:
a. 4/64= 1/16 for red marble
b. 40/64= 5/8 black marbles
c. 20/64= 5/16 blue marble
d. highest: black marble
e. lowest: red marble
In 2010, the population of Houston, Texas, was 2,099,451. In 2017, Houston's population was estimated to be 2,312,717. What is the estimated annual growth rate of Houston's population?
Answer:
it 10:579
Step-by-step explanation:
it is the anser
B
C
W
A
E
Use the given diagram to answer the question,
Which line is the intersection of two of the planes
shown?
Which line intersects one of the planes shown?
Which line has points on three of the planes shown?
G
The line that intersects two of the planes is : Line X
The line that intersects one of the planes is : Line Z
The line that that has points on three of the planes shown is Line Y
How to find the intersection line on the plane?From this figure you can see that there are 3 different levels and 3 different lines. One line intersects two planes (line X), another line intersects only one plane (line Z). Line Y, on the other hand, has points in all three planes.
A line y has points A and B in all three planes.
A plane is simply a plane that can be intersected by a straight line connecting any two points on the plane.
Therefore, we can conclude from the figure
A line that intersects two planes is: line x
A line that intersects one of the planes is: line Z
A line with points on the three planes shown is Line Y.
Read more about Intersection Line at: https://brainly.com/question/1655368
#SPJ1
Please answer ASAP I will brainlist
Answer:
f(0) = 1
f(1) = 21.1
Step-by-step explanation:
Do as the problem says:
[tex]f(0)=4^{2.2(0)}=4^0=1\\f(1)=4^{2.2(1)}=4^{2.2}\approx21.1[/tex]
Find the surface area of the regular pyramid shown to the nearest whole number.
to scale.
13 m
6.5-√3 m
9m
NO LINKS!! URGENT HELP PLEASE!!
28. You are skiing on a mountain with an altitude of 1000 feet. The angle of depression is 19°. Find the distance you ski down the mountain. Draw a diagram to represent the situation. Round final answer to the nearest tenth.
Answer:
3071.6 ft
Step-by-step explanation:
In this situation,
We can use sine law,
in which Sin angle = opposite side/ hypotenuse
Similarly
In triangle ABC
SIn A=BC/AC
Sin 19°=1000/AC
Doing criss cross multiplication:
AC= 1000/(Sin 19°)
AC=3071.55 ft
Therefore, the distance I ski down the mountain is 3071.6 ft
The diagram is below.
==============================================
Work Shown:
sin(angle) = opposite/hypotenuse
sin(19) = 1000/x
xsin(19) = 1000
x = 1000/sin(19)
x = 3071.553487
x = 3071.6
Refer to the diagram below.
Note that the angle of depression ACD is equal to the angle of elevation BAC because of the alternate interior angles theorem.
which f(x) function is this?
Answer:
[tex]f(x) = - 3 {x}^{2} - 6x - 1[/tex]
Listed are 30 ages for Academy Award-winning best actors in order from smallest to largest.
12 14
22 23
35 37
15 20 21
26 28
38 39
47 52
53 55
58 60
61 66 70
72 73 75 78 79
784854
34
40
Find the percentile for age 40.
Answer:
Step-by-step explanation:
12 14 33 35========1,234,000,124,581.
Which model represents a percent error of 25%?
A- A model with 12 squares labeled exact value and 3 squares labeled error.
B- A model with 10 squares labeled exact value and 5 squares labeled error.
C- A model with 9 squares labeled exact value and 3 squares labeled error.
D- A model with 8 squares labeled exact value and 4 squares labeled error.
The correct answer is A- A model with 12 squares labeled exact value and 3 squares labeled error.
To determine which model represents a percent error of 25%, we need to compare the number of squares labeled "exact value" and "error" in each model and calculate the ratio between them.
Let's calculate the ratio for each model:
Model A: 3 squares labeled error / 12 squares labeled exact value = 0.25 or 25%.
Model B: 5 squares labeled error / 10 squares labeled exact value = 0.5 or 50%.
Model C: 3 squares labeled error / 9 squares labeled exact value ≈ 0.3333 or 33.33%.
Model D: 4 squares labeled error / 8 squares labeled exact value = 0.5 or 50%.
From the calculations, we can see that only Model A represents a percent error of 25%. The other models have ratios of 50% and 33.33%, which do not match the desired 25% error.
Consequently, the appropriate response is A- A model with 12 squares labeled exact value and 3 squares labeled error.
for such more question on exact value
https://brainly.com/question/27746495
#SPJ8
help please its due in 50 minutes ill mark brainliest answer too and no need to show work
The height, h, of the cylinder is approximately 1.27 centimeters when the volume is 100 cm^3 and the radius is 5 cm, rounded to the nearest tenth.
To find the height, h, of the cylinder, we can rearrange the formula for the volume of a cylinder:
V = πr^2h
Given that the volume, V, is 100 cm^3 and the radius, r, is 5 cm, we can substitute these values into the formula:
100 = π(5^2)h
Simplifying further:
100 = 25πh
To solve for h, divide both sides of the equation by 25π:
100 / (25π) = h
To calculate the value, we'll use an approximation for π as 3.14:
100 / (25 * 3.14) ≈ h
Simplifying:
100 / 78.5 ≈ h
h ≈ 1.27 cm
Therefore, when the volume is 100 cm3 and the radius is 5 cm, the cylinder's height, h, is about 1.27 centimetres, rounded to the closest tenth.
for such more question on height
https://brainly.com/question/6204273
#SPJ8
Geometric mean and Harmonic mean for the values 3, -11, 0, 63, -14, 100 are
Select one:
a. 0 and 0
b. 3 and -3
c. 3 and 0
d. Impossible
e. 0 and 3
Note: Answer C is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
The correct answer is an option (d): Impossible.
Both the geometric mean and harmonic mean require positive values. However, in the given set of values, we have negative values (-11 and -14), which makes it impossible to calculate the geometric mean and harmonic mean. Therefore, the correct answer is that it is impossible to calculate the geometric mean and harmonic mean for the given values.
Please answer ASAP I will brainlist
(a) The average cost in 2011 is $2247.64.
(b) A graph of the function g for the period 2006 to 2015 is: C. graph C.
(c) Assuming that the graph remains accurate, its shape suggest that: A. the average cost increases at a slower rate as time goes on.
How to estimate the average cost in 2011?Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:
g(x) = -1736.7 + 1661.6Inx
where:
x = 6 corresponds to the year 2006.
For the year 2011, the average cost (in dollars) is given by;
x = (2011 - 2006) + 6
x = 5 + 6
x = 11 years.
Next, we would substitute 11 for x in the function:
g(11) = -1736.7 + 1661.6In(11)
g(11) = $2247.64
Part b.
In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.
Part c.
Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.
Read more on exponential functions here: brainly.com/question/28246301
#SPJ1
Which inequality is equivalent to the given inequality? -4(x + 7) < 3(x - 2)
Answer:
Step-by-step explanation:
We must simplify and rearrange the variables to divide x in order to determine the comparable inequality to the supplied inequality, -4(x + 7) 3(x - 2).
Below are the steps to solve the problem:
-4(x + 7) < 3(x - 2)
Expanding the equation:
-4x-28<3x-6
Gather the variable term on one side and constants on the other:
Adding -4x and 28 on both sides:
-4x + 4x - 28 + 28 < 3x + 4x - 6 + 28
=>0 < 7x + 22
To make the coefficient of x positive, we divide the entire inequality by 7:
0/7 < (7x + 22)/7
=> 0 < x + 22/7
What is the answer 2x2+6
Answer:
2×2=44+6=10Step-by-step explanation:
First, we multiply 2×2 then the answer we obtain we add to it 6 which in total gives us 10
hmm this is tricky help
The diameter of the engine cylinder can be within the range of 4.995 cm to 5.005 cm (option e).
Given that the diameter of the engine cylinder needs to be 5 cm wide with a tolerance of ± 0.005 cm.
To determine the permissible range of the diameter, we need to consider both the upper and lower limits.
Upper limit: Add the tolerance to the desired diameter.
Upper limit = 5 cm + 0.005 cm = 5.005 cm.
Lower limit: Subtract the tolerance from the desired diameter.
Lower limit = 5 cm - 0.005 cm = 4.995 cm.
Therefore, the permissible range for the diameter of the engine cylinder is between 4.995 cm and 5.005 cm.
Hence, the final answer is that the diameter of the engine cylinder can be within the range of 4.995 cm to 5.005 cm.
For more such questions on diameter, click on:
https://brainly.com/question/28162977
#SPJ8
Please solve these:
[tex] \frac{7}{2} - (5x + 4) + 2[/tex]
[tex] - 2 = - \frac{1}{4} (x - 3)[/tex]
[tex] \frac{1}{2} (x - 3) + 6[/tex]
Step-by-step explanation:
1. Answer is 2
2. Answer is -3
3. Answer is 4
Answer:
i) -5x + 3/2
ii) x = 11
iii) x + 9/2
Hope this is helpful to u..
and please mark me as brainliest..
mark me as brainliest..Happy learning!
When five times a number is decreased by 8, the result is 37. What is the number?
Answer:
5n - 8 = 37
5n = 45
n = 9
The number is 9.
A 52-card deck contains 13 cards from each of the four suits: clubs ♣, diamonds ♦, hearts ♥, and spades ♠. You deal four cards without replacement from a well-shuffled deck so that you are equally likely to deal any four cards.
What is the probability that all four cards are clubs?
13/52 ⋅ 12/51 ⋅ 11/50 ⋅ 10/49 ≈0.0026
13/52 ⋅ 12/52 ⋅ 11/52 ⋅ 10/52 ≈0.0023
1/4 because 1/4 of the cards are clubs
The probability that all four cards are clubs is approximately 0.0026. Option A.
To understand why, let's break down the calculation. In a well-shuffled deck, there are 13 clubs out of 52 cards.
When dealing the first card, there are 13 clubs out of the total 52 cards, so the probability of getting a club on the first draw is 13/52.
For the second card, after the first club has been removed from the deck, there are now 12 clubs left out of the remaining 51 cards. Therefore, the probability of getting a club on the second draw is 12/51.
Similarly, for the third card, after two clubs have been removed, there are 11 clubs left out of the remaining 50 cards. The probability of drawing a club on the third draw is 11/50.
Finally, for the fourth card, after three clubs have been removed, there are 10 clubs left out of the remaining 49 cards. The probability of drawing a club on the fourth draw is 10/49.
To find the probability of all four cards being clubs, we multiply the probabilities of each individual draw:
(13/52) * (12/51) * (11/50) * (10/49) ≈ 0.0026.
This calculation takes into account the fact that the deck is being dealt without replacement, meaning that the number of available clubs decreases with each draw.
The third option, 1/4, is incorrect because it assumes that each card dealt is independent and has an equal probability of being a club. However, as cards are drawn without replacement, the probability changes with each draw. So Option A is correct.
For more question on probability visit:
https://brainly.com/question/7965468
#SPJ8
Note the complete question is
A 52-card deck contains 13 cards from each of the four suits: clubs ♣, diamonds ♦, hearts ♥, and spades ♠. You deal four cards without replacement from a well-shuffled deck so that you are equally likely to deal any four cards.
What is the probability that all four cards are clubs?
A.) 13/52 ⋅ 12/51 ⋅ 11/50 ⋅ 10/49 ≈0.0026
B.) 13/52 ⋅ 12/52 ⋅ 11/52 ⋅ 10/52 ≈0.0023
C.) 1/4 because 1/4 of the cards are clubs
Juan has some dimes and some quarters. He has no less than 20 coins worth a maximum of $2.75 combined. If Juan has 18 dimes, determine the maximum number of quarters that he could have. If there are no possible solutions, submit an empty answer.
Juan could have a maximum of 3 quarters.
1. Let's assume Juan has x quarters.
2. The value of x quarters in dollars would be 0.25x.
3. We are given that Juan has 18 dimes, which have a value of 0.10 * 18 = $1.80.
4. The combined value of Juan's dimes and quarters should be less than or equal to $2.75.
5. We can write the equation: 0.25x + 1.80 ≤ 2.75.
6. Subtracting 1.80 from both sides of the equation, we have: 0.25x ≤ 2.75 - 1.80.
7. Simplifying, we get: 0.25x ≤ 0.95.
8. Dividing both sides of the inequality by 0.25, we have: x ≤ 0.95 / 0.25.
9. Evaluating the expression, we find: x ≤ 3.8.
10. Since Juan cannot have a fraction of a quarter, the maximum number of quarters he could have is 3.
11. However, we need to check if the combined value of the dimes and quarters is at least $0.20.
12. If Juan has 3 quarters (0.25 * 3 = $0.75) and 18 dimes ($1.80), the combined value is $0.75 + $1.80 = $2.55.
13. Since $2.55 is less than $2.75, Juan can have 3 quarters.
14. Therefore, the maximum number of quarters Juan could have is 3.
Note: There are no possible solutions where Juan has more than 3 quarters and still satisfies the conditions.
For more such questions on quarters, click on:
https://brainly.com/question/26460978
#SPJ8
What is the solution to the equation below In X=3.1
Answer:
the solution would be X=3 as 3.1 represents 3×1.
Estimate the variation (strength) of the correlation of the scatter plot shown.
a.
moderate correlation
b.
no correlation
c.
strong correlation
d.
weak correlation
need now mamayang 11pm na pasahan
The strength of the correlation as shown in the scatter plot can be concluded to be: b) no correlation.
How to Estimate the variation (strength) of the correlation of a scatter plot shown?To estimate the strength of the correlation in a scatter plot, visually assess the clustering and linearity of the data points. If the points cluster tightly around a linear trend, it indicates a strong correlation, whereas dispersed and non-linear points suggest a weak correlation.
However, if the points on a scatter plot do not exhibit a discernible pattern (as shown in the image given above), it can be concluded that there is no correlation between the variables being plotted.
Therefore, the answer is: b. no correlation.
Learn more about correlation on:
https://brainly.com/question/13879362
#SPJ1
The mean height of an adult giraffe is 19 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X - N b. What is the median giraffe height? ft. c. What is the Z-score for a giraffe that is 22 foot tall?
d. What is the probability that a randomly selected giraffe will be shorter than 18.9 feet tal?
e. What is the probability that a randomly selected giraffe will be between 18.6 and 19.5 feet tall?
f. The 80th percentile for the height of giraffes is ft.
a. The distribution of X is a normal distribution.
b. The median giraffe height is also 19 feet.
c. The Z-score for a giraffe that is 22 foot tall is 3.
d. The probability that a randomly selected giraffe will be shorter than 18.9 feet tall is less than -0.1.
f. The 80th percentile represents the value below which 80% of the data falls.
a. The distribution of X is a normal distribution (or Gaussian distribution) with a mean of 19 feet and a standard deviation of 1 foot. This can be denoted as X ~ N(19, 1).
b. The median of a normal distribution is equal to its mean.
c. To find the Z-score for a giraffe that is 22 feet tall, we can use the formula: Z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get Z = (22 - 19) / 1 = 3.
d. To find the probability that a randomly selected giraffe will be shorter than 18.9 feet tall, we need to calculate the area under the normal curve to the left of 18.9. This can be done using the Z-score and a standard normal distribution table or a calculator.
Alternatively, we can use the Z-score formula from the previous question. The Z-score for 18.9 feet can be calculated as Z = (18.9 - 19) / 1 = -0.1. We can then look up the corresponding probability in the standard normal distribution table or use a calculator to find the probability that Z is less than -0.1.
e. To find the probability that a randomly selected giraffe will be between 18.6 and 19.5 feet tall, we need to calculate the area under the normal curve between these two values.
Again, we can use the Z-score formula to standardize the values and then find the corresponding probabilities using a standard normal distribution table or a calculator.
f. To find the height at the 80th percentile, we can use the standard normal distribution table or a calculator to find the Z-score that corresponds to the 80th percentile.
Once we have the Z-score, we can use the formula Z = (X - μ) / σ to solve for X. Rearranging the formula, we have X = Z * σ + μ. Plugging in the values for Z (obtained from the percentile) and μ (mean) and σ (standard deviation), we can calculate the height at the 80th percentile.
For more such questions on median
https://brainly.com/question/26177250
#SPJ8