The weights of bushels of corn produced by a large farm are approximately normally distributed with a mean of 89.46 pounds and a standard deviation of 2.31 pounds. A store is buys 5 bushels of corn from the farm. Assume the 5 bushels the store receives is a random sample of all bushels of corn the farm produces. What is the approximate probability that the 5 bushels will have a mean weight of more than 90 pounds
The approximate probability that the 5 bushels will have a mean weight of more than 90 pounds is 0.41
How to determine the probability?The given parameters are:
Mean, μ = 89.46
Standard deviation, σ = 2.31
The z-score at x = 90 is calculated using
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{90 - 89.46}{2.31}\\[/tex]
Evaluate
z = 0.234
The probability is then calculated as:
P(x >90) = P(z > 0.234)
From z table of probabilities, we have:
P(x >90) = 0.41
Hence, the approximate probability that the 5 bushels will have a mean weight of more than 90 pounds is 0.41
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Use the change of base formula to compute logo 4.
Round your answer to the nearest thousandth. Yea
Answer:
[tex]\log_{9}4\approx 0.631[/tex]
Step-by-step explanation:
The change of base formula we can use is
[tex]\log_{b}a=\frac{\log{a}}{\log{b}}[/tex]
Not all calculators will allow the user to directly enter the logarithms with a given base, so the change of base can be used for all calculators, which use the common log.
Common logs have a base of 10.
Let's convert your expression:
[tex]\log_{9}4=\frac{\log4}{\log9}[/tex]
Using our calculator, we will compute log 4 divided by log 9:
[tex]\frac{\log4}{\log9}\approx0.631[/tex].
Kate is the captain of a large cruise ship. As she
drives the ship, she sits 50 meters above the sea.
Paul is the captain of a boat. He sits 15 meters
above the sea. If the radius of the earth is
6,371,000 meters, how much further can Kate see
across the horizon than Paul?
Kate can see across the horizon by 3.33 times further than Paul.
What is the shape of the horizon?The volume of the cone can be used to determine how far they can see across the horizon from the cone shape.
Using the volume of the cone
[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
For Kate:
Height (h) = 50 mRadius (r) = 6,371,000 m[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{50 }{3}}[/tex]
V = 2.12526863 × 10¹⁵ m³
For Paul
Height (h) = 15 mRadius (r) = 6,371,000 m[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]
[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{15 }{3}}[/tex]
V = 6.3758059 × 10¹⁴ m³
To determine how much further can kate see across the horizon than Paul, we have:
= 2.12526863 × 10¹⁵ m³/6.3758059 × 10¹⁴ m³
= 3.33 times further.
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Labor supply and demand are market forces that, ignoring all other factors, determine the equilibrium wage. In the real world, other factors, including government regulations, can play a part in setting wage levels for a given occupation. Describe a government regulation that may affect wage levels. Explain your thinking.
50! POINTS
Federal agencies have the power to enforce those laws through regulation. State lawmakers, in turn, make laws that typically supplement federal legislation. State government regulation examples include setting a higher minimum wage than the federal requirement
Adding extra tax for Imported goods rather than Built in country goods
Look at a situation
In south east Asia ,Tesla is tryiny to import cars from foreign and trying to sell thereBut the tax is about 90% .So it's unfair and not possible for occupationThe figure shown is a rectangle. If you draw a new rectangle in which the dimensions are doubled, what is the relationship between the AREAS of the two rectangles? A) The area of the new rectangle is twice that of the original rectangle. B) The area of the new rectangle is one-half that of the original rectangle. C) The area of the new rectangle is four times that of the original rectangle. D) The area of the new rectangle is eight times that of the original rectangle.
Answer:
Step-by-step explanation:
Givens
L = 5
w = 3
Formula
Area = L*w
Solution
Area = 3 * 5
Area = 15
Now double both the width and the Length.
New Length = 2*5 = 10
New Width = 2 * 3 = 6
Area = New Length * New Width
Area = 10 * 6
Area = 60
Answer (look at the choices)
The old rectangle has an area of 15. The new Rectangle has an area of 60. If you double 15, do you get 60. No, so the answer is not A
The new rectangle is 60. If you halve it, do you get 15. No so the answer is Not B
C is the answer
D is you multiply 8 * 15, do you get 60? No so the answer is not D
I really don't understand Adding and Subtracting Fractions with unlike Denominators?
5/8 - 2/32 =
Answer:
answer is 9/16 (9 over 16) Decimal form 0.5625
Step-by-step explanation:
Alice and malice are twins. they have a brother bob who is 8 years older. if the sum of their ages is 23, find the ages
Answer:
Alice's age = 5 years
Malice's age = 5 years
Bob's age = 5+8 =13 years
Step-by-step explanation:
Let x be the age (in years of Alice and Malice (They have the same age because they are twins).
Age of Bob: x+8 (because he is 8 years older than the twins).
Then the sum of their three ages is 23:
x (Alice's age) + x (Malice's age) +(x+8 ) (Bob's age)= 23
2x + ( x+8) = 23
3x+8 = 23
3x = 15
(3x)/3 = 15/3
x = 5
So ...
Alice's age = 5 years
Malice's age = 5 years
Bob's age = 5+8 =13 years
Solve the equation on the
interval [0, 2π).
5 cos x - √3 = 3 cos x
Answer:
[tex]\displaystyle x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex]
Step-by-step explanation:
[tex]\displaystyle 5\cos x-\sqrt{3}=3\cos x;\:0\leq x < 2\pi\\\\5-\frac{\sqrt{3}}{\cos x}=3\\ \\-\sqrt{3}\sec x=-2\\\\\sec x=\frac{2}{\sqrt{3}}\\\\\sec x=\frac{2\sqrt{3}}{3}\\ \\\cos x=\frac{3}{2\sqrt{3}}\\ \\\cos x=\frac{3\sqrt{3}}{6}\\ \\\cos x=\frac{\sqrt{3}}{2}\\\\x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex]
Classify the shapes shown below. Write the letter of each shape in the category that describes it. Shapes may fall into more than one category, and not all shapes will be used. At Least 1 Right Angle At Least 2 Sides of Equal Length At Least 1 Pair of Parallel Sides (sorry i can´t show the shapes it wont let me)
The classification of the shapes into the categories described is as follows;
At Least 1 Right Angle; Right triangle, Square and Rectangle.At Least 2 Sides of Equal Length; Rectangle, Square, isosceles triangle, Parallelogram. At Least 1 Pair of Parallel Sides; Square, Rectangle, Parallelogram.What are the characteristics of place shapes?Plane shapes have peculiar characterization in each case. A triangle can either be isosceles (2 sides of equal length) or right (90⁰ angle measure).
Rectangles, squares and Parallelograms all have parallel sides.
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!
Answer:
multiply the number with 4
Step-by-step explanation:
2 8 32 128
2x4 =8
8×4=32
32×4=128
128×4=512
[tex]\text{First term,}~ a =2\\\\\text{Common ratio,}~ r = \dfrac{8}2 = 4\\\\\text{Nth term} = ar^{n-1}\\\\\text{7th term} = 2 \cdot 4^{7-1} = 2 \cdot 4^6=8192\\ \\\text{Hence, the 7th term in the geometric series is 8192.}[/tex]
write an equation in point-slope form for the given point and slope: point: (-7, 5) slope: 3
Answer:
y - 5 = 3(x + 7)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = 3 and (a, b ) = (- 7, 5 ) , then
y - 5 = 3(x - (- 7) ) , that is
y - 5 = 3(x + 7)
Sherry is a waitress at a country club restaurant. She receives an automatic 15% tip which is added to the member's check for the
meal.
If she earns $3.25 an hour, works 25 hours this week, and has served meals costing $415, what is Sherry's gross pay?
O $108.90
O $122.75
O $127.25
O 143.50
Answer:
143 50
Step-by-step explanation:
I hope it helps pa brainlest po
3.2 Tshego also intends tiling the dining room and lounge floors. The dimensions of the lounge floor are 4 m by 5 m and of the dining room floor 3 m by 4 m. Information and cost: Tshego intends using tiles that are 35 cm by 35 cm. One box of 4 tiles costs RI43,84. Tile cement costs R99,90 per 20 kg bag, which covers 3 m². She needs 4 bags of tile grout at R89,90 per 5 kg bag. The cost of labour is R2 500. Tshego's total budget for the tiling project is R15 000. Use the information above to answer the questions that follow. 3.2.1 Show that the total floor area to be tiled is 32 m². You may use this formula: Area of a rectangle = length x width (2)
Using the area of a rectangle, the total floor area to be tiled = area of the dinning room + area of the lounge floor = 32 m²
What is the Area of a Rectangle?The area of rectangle = (length)(width).
Total floor area to be tiled = area of the dinning room + area of the lounge floor
Total floor area to be tiled = (4)(5) + (3)(4)
Total floor area to be tiled = 20 + 12
Total floor area to be tiled = 32 m²
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8. (06.04 MC)
Calculate the area of triangle ABC with altitude BD, given A (-6,0), B (0,0), C (0,6), and D (-3,3). (5 points)
18 square units
21 square units
9 square units
18.5 square units
Check the picture below.
the area of the triangle whose base is AC and height is BD, is the same area of the triangle whose base is AB and altitude is BC, namely
[tex]A=\cfrac{1}{2}(\stackrel{b}{6})(\stackrel{h}{6})\implies 18[/tex]
7. Graph the equation using the slope and the y-intercept.
Please help
Answer:
See below ~
Step-by-step explanation:
Select the correct answer.
Consider the piecewise function shown on the graph.
Over which interval of the domain does the graph represent an exponential function?
A. x ≥ 6
B. -3 ≤ x ≤6
C. x ≥ 1
D. -4 < x ≤ 1
Answer:
The answer is D I hope this helps
The required domain for the function given on the graph represents the exponential function is x ≥ 1. Option C is correct.
Given that,
A graph of a function is shown that has 3 distinct functions for its domain, we have to determine which of these 3 functions shows an exponential function.
The function which is in format f(x) = where, a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Since, as we can see throughout the graph the graph constantly decreases to -4 and then shows a parabolic function from -4 to 0.9 afterward it starts increasing exponentially.
Thus, the required domain for the function given on the graph represents the exponential function is x ≥ 1. Option C is correct.
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What is the length of BD?
Round to one decimal place.
Answer:
4.0
Step-by-step explanation:
Here is one way
By pythag theorem AD = sqrt (5,5^2 - 4.3^2) =3.42928564
Then pythag theorem again for the lower triangle
BD = sqrt (5.3^2 - 3.42928564^2) = 4.041
I need help understanding this, please explain it with the answer.
Suppose y varies inversely with x, and y = −3 when x = 14.
What is the value of y when x = −7?
This is the last question on my HW, and I'm tired, so help would be greatly appreciated :)
Using a proportional relationship, it is found that when x = -7, the value of y will be of y = 6.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
When y varies inversely with x, the rule is given by:
[tex]y = \frac{k}{x}[/tex]
y = −3 when x = 14, hence we use this to find k.
[tex]-3 = \frac{k}{14} \rightarrow k = -42[/tex]
Then:
[tex]y = -\frac{42}{x}[/tex]
Then when x = -7, y = -42/-7 = 6.
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DIFFICULT EXACT TRIGONOMETRY, NON-CALCULATOR, PLEASE HELP
Step-by-step explanation:
area of quadrilateral = sum of area of triangles
area of triangle ADC = .5 * b * h
= .5 * 12 * 5 = 30 km^2
area of ∆ABC = .5 * sinx* ab* ac
= .5 * sin 30 * 3* 13 = 39/4 = 9.75 km^2
area of quadrilateral = 39.75 km^2
total cost =$ 397.5 million
evaluate the expression when m=5 and n=29 n-4m
Answer:
9
Step-by-step explanation:
substitute m = 5 and n = 29 into the expression
n - 4m
= 29 - 4(5)
= 29 - 20
= 9
HELP ASAP PLSSSS!!!!
If you need an image im putting it down below
Which line best represents the line of best fit for this scatter plot?
Graph shows numbers from 0 to 10 at increments of 1 on the x axis and numbers from 0 to 18 at increments of 2. Scatter plot shows ordered pairs 1, 1 and 2, 4 and 3, 12 and 4, 6 and 5, 8 and 6, 8 and 7, 12 and 8, 10 and 9, 14 and 10, 18. A line labeled P joins ordered pair 0, 1 and 9, 18. A line labeled Q joins ordered pairs 0, 1 and 10, 16. A line labeled R joins ordered pairs 0, 1 and 10, 10. A line labeled S joins ordered pairs 0, 1 and 10, 6.
Line P
Line Q
Line R
Line S
This line is fairly close to the majority of the points shown. Unfortunately there's an outlier left out, but it isn't too far from the main cluster. The further the outlier is, the more pull it will drag the line away from the main cluster.
Line Q
The suitable line should contain most dots near itQ contains atleast 4 around it.No other has soQ is correct
Is the point (2,-11) on the circle with radius 5 and center (2,13)?
Answer:
No
Step-by-step explanation:
Identify the equation for the circle
[tex](x-h)^2+(y-k)^2=r^2\\(x-2)^2+(y-13)^2=5^2\\(x-2)^2+(y-13)^2=25[/tex]
Check if (2,-11) is a point on the circle
[tex](x-2)^2+(y-13)^2=25\\(2-2)^2+(-11-13)^2=25\\0^2+(-24)^2=25\\576\neq25[/tex]
Since both sides of the equation are not equal to each other, then (2,-11) is not a point on the circle.
James, John and Jane decided to buy a piece of land. James paid 3/5 of the total cost while John paid 3/8 of the reminder. if Jane paid 30000.what was the total cost of the piece of land?
The total cost of the piece of land for which James, John and Jane decided to buy a piece of land is 1,200,000.
What is the total cost?Total cost or the final cost is the summation of all the cost spend while buying any good or taking any service.
James, John and Jane decided to buy a piece of land. James paid 3/5 of the total cost while John paid 3/8 of the reminder. Thus, the fraction of amount paid by Jane is,
[tex]x=1-\dfrac{3}{5}-\dfrac{3}{8}\\x=\dfrac{40-24-15}{40}\\x=\dfrac{1}{40}[/tex]
The Jane paid, 30000 of total cost which is 1/40 part of it. Thus, the total cost of the piece of land is,
[tex]\dfrac{1}{40}x=30000\\x=30000\times40\\x=1200000[/tex]
Thus, the total cost of the piece of land for which James, John and Jane decided to buy a piece of land is 1,200,000.
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PLEASE HELP ILL GIVE BRAINLIST OR WHATEVER
Answer:
1) $181.40
2) $100
3) $81.40
Step-by-step explanation:
Interest rate is 1.5% which mans that the decimal multiplier is 1.015.
1) To find for 40 yrs we do:
40 yrs = 100 x [tex]1.015^{40}[/tex]
= $181.40
2) He contributed $100
3) He gained $181.40 - $100
= $81.40
Using the image above, what is the measure of Side AC? Round to the nearest hundredth
To solve this problem, we just have to use trigonometric ratios and apply which of the ratios is needed here and proceed to solve. The value of side AC is 2.85 units
Trigonometric RatioIn the given diagram, we have the value of angle and hypothenuse and we are required to find the adjacent side of the triangle.
Data;
Angle = 32.9 degreesHypothenuse = 3.4Let's use cosine rule for this.
[tex]cos\theta = \frac{adjacent}{hypothenuse}[/tex]
Proceed to substitute the values into the equation and solve.
[tex]cos 32.9 = \frac{AC}{3.4} \\AC=3.4cos32.9\\AC = 2.85[/tex]
From the calculations above, the value of side AC is 2.85 units
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6 times 10^5 is how many times as as large as 3 times 10^3?
Answer:
200
Step-by-step explanation:
(6 × 10^5) / (3 × 10^3) = 6/6 × 10^5/10^3 = 2 × 10^2 = 200
Answer:
200
Step-by-step explanation:
(6 × 10^5) / (3 × 10^3) = 6/6 × 10^5/10^3 = 2 × 10^2 = 200
In a certain family, the probability of having twins in 0.08 and the probability of having a single baby is 0.92. What is the probability of a family having two sets of twins?
Answer:
0.0064
Step-by-step explanation:
Probability (2 sets of twins) :
When a probability of an event is asked multiple, apply the number of times as an exponent to the probability of the eventP = (0.08)²P = (8 x 10⁻²)²P = 64 x 10⁻⁴P = 0.0064In 1990, the population of Math Valley was 15,000. If the population is increasing at an annual rate of 2.4%, what was the population in 1965?
if this helped you say meow
i may be wrong but i think you should divide 2.4% by the 15000 wicth is
0.00000016 or just 0.16 or maybe muptication 2.4% x15000 whicth is 360 hope this helps :D
Find m.
30°
m
Write your answer in simplest radical form.
feet
60°
6 ft
Answer:
M=3ft
Step-by-step explanation:
Use trigonometric ratio Sin to get M which is the opposite side of the given angle of 30°
[tex]sin = \frac{opp}{hyp} [/tex]
[tex]sin30 = \frac{m}{6} [/tex]
Multiply 6 on both sides:
[tex]6sin30 = m[/tex]
Use a calculator:
3=M
or..
use special angles:
Sin30=0.5
6×0.5=3
Therefore M is 3 ft
Need help quick please! Find the surface area. Hint you will need to use Pythagorean theorem
Answer:
80
Step-by-step explanation: