I believe the parts are:
A. What is the probability that Upper X greater than 95X>95?
B. What is the probability that Upper X less than 75X<75?
C.What is the probability that Upper X less than 85X<85 and Upper X greater than 125X>125?
D. 95% of the values are between what two X-values (symmetrically distributed around the mean)?
Solution:
We use the equation for z score:
z = (X – μ) / σ
Then use the standard normal probability tables to locate for the value of P at indicated z score value.
A. Z = (95 – 100) / 10 = - 0.5
Using the tables, the probability at z = -0.5 using right tailed test is:
P = 0.6915
B. Z = (75 – 100) / 10 = - 2.5
Using the tables, the probability at z = -2.5 using left tailed test is:
P = 0.0062
C. Z = (85 – 100) / 10 = - 1.5
Using the tables, the probability at z = -2.5 using left tailed test is:
P = 0.0668
Z = (125 – 100) / 10 = 2.5
Using the tables, the probability at z = 2.5 using right tailed test is:
P = 0.0062
So the probability that 85<X and X>125 is:
P(total) = 0.0668 + 0.0062
P(total) = 0.073
D. P(left) = 0.025, Z = -1.96
P(right) = 0.975, Z = 1.96
The X’s are calculated using the formula:
X = σz + μ
At Z = -1.96
X = 10 (-1.96) + 100 = 80.4
At Z = 1.96
X = 10 (1.96) + 100 = 119.6
So 95% of the values are between 80.4 and 119.6 (80.4< X <119.6).
Something greater tha 1/2 yard but less than 5/8 yard??
The base of the building is an equilateral triangle 180 meters on each side. The height of the prism is 25m. Find the height, of the triangular base.
The height of the triangular base is 155.46 m.
To find the height of the equilateral triangle base of the prism, we'll first determine the height of one of its constituent triangles.
The height ( h ) of an equilateral triangle is given by [tex]\( h = \sqrt{3}/2 \times \text{side length} \).[/tex]
Calculate the height of one triangle:
[tex]\[ h = \frac{\sqrt{3}}{2} \times 180 \, \text{m} = \frac{\sqrt{3} \times 180}{2} = \frac{180\sqrt{3}}{2} = 90\sqrt{3} \, \text{m} \][/tex]
Calculate the total height of the prism:
The height of the prism is given as 25 m.
Calculate the total height:
Total height = height of one triangle + height of the prism
[tex]\[ \text{Total height} = 90\sqrt{3} \, \text{m} + 25 \, \text{m} = 90\sqrt{3} + 25 \, \text{m} = 155.46 \, \text{m} \][/tex]
So, the height of the triangular base is 155.46 m
find the product. List the units. 8 h $9/h
The product is equivalent to $72.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a rate of $9 per hour for 8 hours.
Now, for 1 hour, the cost is $9. Therefore, for 8 hours, we can write -
x = 9 x 8
x = $72
Therefore, the product is equivalent to $72.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/14441381
#SPJ2
if a population of scores is normally distributed, has a mean of 45 and a standard deviation of 6, the most extreme 5% of the scores lie beyond the score(s) of _________.
a. 35.13
c. 56.76 and 33.24
b. 45.99
d. 45.99 and 35.13
Final answer:
To find the most extreme 5% of normally distributed scores with a mean of 45 and a standard deviation of 6, we look for scores beyond the z-score cut-offs corresponding to 2.5% and 97.5%. The z-score around 1.96 gives us two scores: 56.76 on the high end and 33.24 on the low end, indicating that answer 'c' is correct.
Explanation:
To determine the most extreme 5% of the scores in a normally distributed population with a mean of 45 and a standard deviation of 6, we need to find the z-score that corresponds to the tails of the distribution where the cumulative area is either less than 2.5% or greater than 97.5% (since 5% is split into two tails of the distribution).
Using a standard normal distribution table or a calculator, the z-score that corresponds to the upper 97.5% is typically about 1.96 (or sometimes 1.645 for a one-tailed test). To find the actual scores corresponding to these z-scores, we use the formula for transforming a z-score into an actual value which is:
X = μ + (z • σ)
For the upper extreme:
X = 45 + (1.96 • 6) = 56.76
For the lower extreme:
X = 45 - (1.96 • 6) = 33.24
Thus, the most extreme 5% of the scores lie beyond scores of 56.76 and 33.24. Therefore, the correct answer is c. 56.76 and 33.24.
A flag in the shape of a right triangle is hung over the side of a building as shown below. The total weight of the flag is 250 pounds and it has uniform density. a = 15 and b = 39.
Answer:
(a) The density of flag is [tex]\dfrac{25}{27}[/tex] Pounds per square foot
(b) The weight of strip is [tex]\dfrac{20}{9}(15-h)\Delta h[/tex] Pounds
(c) The work is [tex]\dfrac{20}{9}(15-h)h\Delta h[/tex] foot-pounds
(d) The exact work by roof is 1250 foot-pounds
Step-by-step explanation:
(a) We are given a flag in the shape of a right triangle.
The total weight of flag is 250 pounds and Uniform density.
Base of the flag [tex]=\sqrt{b^2-a^2}[/tex]
[tex]=\sqrt{39^2-15^2}=36[/tex]
Area of the flag [tex]=\dfrac{1}{2}\times 36\times 15 = 270[/tex]
Weight of flag = 250 pounds
[tex]Density =\dfrac{Weight}{Area}=\dfrac{250}{270}=\dfrac{25}{27}[/tex]
Hence, The density of flag is [tex]\dfrac{25}{27}[/tex]
(b) Weight of strip which is h feet below the roof.
Length of strip [tex]=\dfrac{36}{15}(15-h)[/tex]
Width of strip [tex]\Delta h[/tex]
Weight = Density x area
[tex]=\dfrac{25}{27}\times \dfrac{36}{15}(15-h)[/tex]
[tex]=\dfrac{20}{9}(15-h)\Delta h[/tex]
Hence, The weight of strip is [tex]\dfrac{20}{9}(15-h)\Delta h[/tex]
(c) Work slice to move h feet above to the roof
work[tex]=Weight\times displacement[/tex]
[tex]=\dfrac{20}{9}(15-h)\Delta h\times h[/tex]
[tex]=\dfrac{20}{9}(15-h)h\Delta h[/tex]
Hence, The work is [tex]\dfrac{20}{9}(15-h)h\Delta h[/tex] foot-pounds
(d) Exact work on the roof by hanging flag
[tex]W=\int_0^{15}\dfrac{20}{9}(15-h)hd h[/tex]
[tex]W=\dfrac{20}{9}(\dfrac{15h^2}{2}-\dfrac{h^3}{3})|_0^{15}[/tex]
[tex]W=1250-0[/tex]
[tex]W=1250[/tex]
Hence, The exact work by roof is 1250 foot-pounds
Final answer:
The weight of the flag is distributed uniformly across its area, with the entire 250 pounds concentrated at the centroid point.
Explanation:
To find the centroid of a right triangle, we can use the following formulas:
[tex]\[ x_c = \frac{b}{3} \][/tex]
[tex]\[ y_c = \frac{a}{3} \][/tex]
Where:
[tex]- \( x_c \)[/tex] is the x-coordinate of the centroid.
[tex]- \( y_c \)[/tex] is the y-coordinate of the centroid.
[tex]- \( a \)[/tex] is the length of the side perpendicular to the base (height).
[tex]- \( b \)[/tex] is the length of the base.
Given \( a = 15 \) and \( b = 39 \), we can calculate the centroid as follows:
[tex]\[ x_c = \frac{39}{3} = 13 \][/tex]
[tex]\[ y_c = \frac{15}{3} = 5 \][/tex]
So, the centroid of the triangle is located at the point (13, 5).
Now, regarding the weight distribution, if the flag has uniform density, the center of mass (or centroid) would be the point where the total weight is concentrated. Since the total weight of the flag is 250 pounds, and the centroid is the point of concentration of mass, the entire weight of the flag, 250 pounds, can be considered to act at the centroid.
Therefore, the weight of the flag is distributed uniformly across its area, with the entire 250 pounds concentrated at the centroid point.
List any restrictions on the domain for the equation [tex] \frac{x+9}{x+2} [/tex]
What is the approximate length of the diameter,d?
Answer:
The diameter of the circle is 14in
Step-by-step explanation:
There is an equation that says: If you have the circumference (C) of a circle you can get the Diameter (d):
d=C/π(constant number)
In the problem you have C=44 in
Then:
π=3,1416
d=44in/3,1416
d=14in
Lenny uses two pieces of yarn for a craft project. The first piece is 5.89 meters long. The second piece is 2.147 meters long. What is the total length of the two pieces of yarn? Enter your answer in the box. M__
Answer: 8.04 meters
Step-by-step explanation:
length of first piece of yarn = 5.89 meters
length of second piece of yarn = 2.147 meters
Total length of of the two pieces of yarn = length of first piece of yarn + length of second piece of yarn = 5.89 meters + 2.147 meters = 8.037 meters
The rule apply for the addition and subtraction is :
The least precise number present after the decimal point determines the number of significant figures in the answer.
Thus the answer will be 8.04 meters as least precise number 5.89 contains two decimal places.
True or false, the decimal form of 3 3/8 is 3.38
David has $425 worth of items in his shopping cart. He receives a discount of 30% for the items at the checkout. If he then has to pay an 8% sales tax, what is the final amount that David paid?
Find the 75th derivative of y = cos(2x).
The 75th derivative of y = cos(2x) can be found by dividing 75 by 4 to find the cycle it falls into due to the repeating pattern of cos and sin. Due to remainder 3 after division, the 75th derivative is equivalent to the 3rd derivative from the cycle, which is 8sin(2x), but scaled by 2 to the power of the number of completed cycles (18). This gives the final answer 2^18 * 8sin(2x).
Explanation:The process of finding the 75th derivative of a function can seem daunting or time-consuming, but with functions like cosines and sines, we can rely on the cycling pattern of these functions to simplify the task. This will significantly decrease the amount of computational effort needed.
When you find the derivative of y = cos(2x), the function cycles in a pattern every four times. The first derivative of y = cos(2x) is -2sin(2x), the second derivative is -4cos(2x), the third derivative is 8sin(2x), and the fourth derivative is 16cos(2x). As you can see, we've returned to the original function (scaled by a factor of 16).
So to find the 75th derivative, divide 75 by 4 to get remainder of 3. This means the 75th derivative is the same as the 3rd derivative, but scaled by 2 to the power of the number of full cycles (which is 18). Hence, the 75th derivative of y = cos(2x) is 2^18 * 8sin(2x).
Learn more about Derivatives of functions here:https://brainly.com/question/25752367
#SPJ11
How many ways are there to select 6 students from a class of 25 to hold six different executive positions on a committee?
Selected from this population. find the probability that the sample mean is greater than 2.1 but less than 2.6.
Sarah washes cars at the car wash. She makes $8.25 per hour and earns $30 in tips per day. Give an expression that Sarah could use to calculate her daily earnings.
A) $8.25x + $30
B) $8.25 + $30
C) $8.25 - $30
D) $8.25 + $30x
you would need to multiply 8.25 by the number of hours worked (x) and then add the tips
so it would be A. 8.25x+30
Adam makes $632 gross income per week and has claimed four allowances. According to the table below, what is Adam’s net income after tax withholding? 2007-05-03-00-00_files/i0140000.jpg a. $99 b. $533 c. $731 d. $502
Answer:
The net income of the tax withholding $533 dollars.
Confirmed on R09.
19³ x 19³ =
1. 19 *exponent* 3
2. 19 *exponent* 4
3. 19 *exponent* 5
4. 19 *exponent* 6
--
Please help!!
124,248-55,679 show me how you get this answer
Which pair of measurements is not equivalent?
24 feet, 8 yards
24 inches, 2 feet
10 feet, 120 inches
3 miles, 15,480 feet
The pair of measurements that is not equivalent is 3 miles and 15,480 feet. All other pairs are equivalent when converted to the same units. This determines which measurements do not match in the same units.
To determine which pair of measurements is not equivalent, we need to convert them into the same units and compare them:
24 feet, 8 yards: 1 yard = 3 feet, so 8 yards = 8 * 3 = 24 feet. Therefore, 24 feet is equivalent to 8 yards.24 inches, 2 feet: 1 foot = 12 inches, so 2 feet = 2 * 12 = 24 inches. Therefore, 24 inches is equivalent to 2 feet.10 feet, 120 inches: 1 foot = 12 inches, so 120 inches = 120 / 12 = 10 feet. Therefore, 10 feet is equivalent to 120 inches.3 miles, 15,480 feet: 1 mile = 5280 feet, so 3 miles = 3 * 5280 = 15,840 feet. Therefore, 3 miles is not equivalent to 15,480 feet.Thus, the pair of measurements that is not equivalent is 3 miles, 15,480 feet.
A correlation coefficient of .89 indicates that _____.
The correlation coefficient indicates the strength of the relationship between variables. The closer it is to 1, the stronger the relationship. If it is 0, there is no relationship.
Explanation:The number portion of the correlation coefficient indicates the strength of the relationship. The closer the number is to 1 (be it negative or positive), the more strongly related the variables are, and the more predictable changes in one variable will be as the other variable changes. The closer the number is to zero, the weaker the relationship, and the less predictable the relationships between the variables becomes. For instance, a correlation coefficient of 0.9 indicates a far stronger relationship than a correlation coefficient of 0.3. If the variables are not related to one another at all, the correlation coefficient is 0.
5x-3 (2x-4)=7x+16. solve for x
Nancy withdrew $19 from her bank account to pay for markers write in integer to represent this situation
After eating a 100 calorie snack mark exercised to burn 100 calories show answer in number line
Four friends have decided to visit the art museum. Admission costs $5.75 per person. If x represents the total cost for the four friends to go to the museum, which equation is true?
A. $5.75 • x = 4
B. 4 • $5.75 = x
C. 4 + x = $5.75
D. 4 • x = $5.75
Answer:
B
Step-by-step explanation:
I just did a test
Mr. Potts, the college Pastry Chef, baked three apple pies, two blueberry pies, five cherry pies, and six key lime pies for the student fundraiser. What percent of the pies were apple?
Answer:
18.75%
Step-by-step explanation:
Mr. Potts, the college Pastry Chef baked pies for the student fundraiser.
He baked apple pies = 3
Blueberry pies = 2
Cherry pies = 5
Key lime pies = 6
We have to calculate the percentage of the apple pies.
Total number of pies that he baked = 3 + 2 + 5 + 6 = 16 pies
Percentage of Apple pies = [tex]\frac{3}{16}[/tex] × 100
= 0.1875 × 100
= 18.75%
18.75% was apple pie.
Find the total cost of 3.4 pounds of caramel nut clusters at $8.25 per pound and 5.2 pounds of chocolate covered cashews at $9.35 per pound.
When you use the distance formula, you are building a(n) _____ whose hypotenuse connects two given points.
Simplify 9 - 10
A:-19
B: -1
C: 1
D: 19
I need help with this ....!!!!!
If the population decreases with a constant rate of change and the decrease is 7% in the first year, what will the town's population be in 6 years? (round to the nearest person)
Suppose in a market for iTune cards demand is Qd = 1500 - 250P, and supply is Qs = 850P. Find the equilibrium P* and Q*.