The probability that the small bowl contains more cereal than the large one is 0.0228.
Given :
The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.
we know that,
z = x - μ / σ
here
x = 0
μ = 1
σ = 0.5
= 0 - 1 / 0.5
= -1/0.5
= -1 / 05 / 10
= -1 * 10 / 5
= -10 / 5
= -2
if z = -2 then p value = 0.0228
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Full question :
The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl.
If the difference follows the Normal model, what's the probability that the small bowl contains more cereal than the large one?
Find the equation of the line joining the points (2,-8) and (5,6)
The equation of the line joining the points (2,-8) and (5,6) is y = 14 / 3 x - 52 / 3
How to find the equation of a line?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line passes through the points (2,-8) and (5,6). Let's find the slope.
m = 6 + 8 / 5 - 2
m = 14 / 3
Let's find the y-intercept using (5, 6).
y = 14 / 3 x + b
6 = 14 / 3 (5) + b
6 = 70 / 3 + b
b = 6 - 70 / 3
b = 18 - 70/ 3
b = -52 / 3
Therefore, the equation is y = 14 / 3 x - 52 / 3
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The formula A=23.1 е⁰⁰¹⁵²⁺ models the pollution of US state, a, in millions ,t years after 2000.
A. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was million.
The population of the state in 2000 was 23.1 million and the population will be 28.3 million after 13.4 years.
What is an exponential function?The definition of an exponential function is given by the equation
y = aeᵇˣ, where bx is an exponent.
The given equation is [tex]A = 23.1e^{0.0152t}[/tex].
To find the population of the state in 2000, substitute t = 0 in the given equation:
[tex]A =23.1e^{0.0152(0)}\\\\A = 23.1[/tex]
Now, Substitute A = 28.3 into the given equation and solve for t:
[tex]28.3=23.1e^{0.0152t}\\\\e^{0.0152t}=1.2251\\\\0.0152t=\ln(1.2251)\\\\0.0152t=0.2030\\\\t=13.4[/tex]
Hence, the population of the state in 2000 was 23.1 million and the population will be 28.3 million after 13.4 years.
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Interest obtained on a sum of Rs. 5000 for 3 years is Rs. 1500. Find the rate percent
Rate percent is 10%
What is rate percent ?A coefficient that is a quotient of two values, where the denominator is written in percentage points and has the same units as the numerator when it is multiplied by a unit of time.
According to the given information
Sum of money ( principal ) P = 5000 rupees
Interest obtained in money = 1500 rupees
Time duration T = 3 years
According to the given information
I = P × T × [tex]\frac{R}{100}[/tex]
1500 = 500 × 3 × R/100
Rate percent is 10%
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Solve the system of equations by graphing.
1. y = x - 1
y = 2x - 2
2. y = 4x
y = x + 3
3. y - x = 1
y = x - 2 + 3
Answer:
Step-by-step explanation:
1) x - 1 = 2x - 2
-x = -1
x = 1
2) 4x = x + 3
3x = 3
x = 1
3) x + 1 = x + 1
infinite solutions (parallel lines)
For graphing, just look at the y-intercept, in the equation y = mx + b.
b is the y-intercept, so, for you plot the y-intercpet on the y-axis. You look at m, which is the slope. For positive, you go up how many ever it says in the numerator and then to the right how many ever it says in the denominator. For a negative you do the same thing except you go down and then to the right, or up and to the left. For positive there is only up and then to the right. I hope this answers your question.
Margo borrows $1000, agreeing to pay it back with 7% annual interest after 9 months. How much interest will she pay?
The interest over 18 months will be $105.00 if Margo borrows $1000, agreeing to pay it back with 7% annual interest.
What is simple interest?It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.
It is given that:
Margo borrows $1000, agreeing to pay it back with 7% annual interest after 9 months
I = Prt
= 1.5 x 7%
= 1.5 x .07
= 0.105
= $1000 x .105
= $105.00
Thus, the interest over 18 months will be $105.00 if Margo borrows $1000, agreeing to pay it back with 7% annual interest.
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A house was valued at $95,000 in the year 1991. The value appreciated to $165,000 by the year
2008.
Use the compound interest formula S = P(1 + r) to answer the following questions.
A) What was the annual growth rate between 1991 and 2008?
T =
Round the growth rate to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
T =
%.
C) Assume that the house value continues to grow by the same percentage. What will the value
equal in the year 2011?
value = $
Round to the nearest thousand dollars.
Hello,
I hope you and your family are doing well!
A) To find the annual growth rate between 1991 and 2008, we can use the compound interest formula:
S = P(1 + r)
Where S is the final value of the house, P is the initial value of the house, and r is the annual growth rate.
Plugging in the values from the problem, we get:
165,000 = 95,000(1 + r)
Dividing both sides of the equation by 95,000 gives:
1.737 = 1 + r
Subtracting 1 from both sides of the equation gives:
0.737 = r
The annual growth rate between 1991 and 2008 is 0.737.
B) To express the growth rate in percentage form, we can multiply it by 100%:
0.737 * 100% = 73.7%
So the annual growth rate between 1991 and 2008 was 73.7%.
C) To find the value of the house in the year 2011, we can use the compound interest formula again, with the initial value of the house set to the final value in 2008:
S = P(1 + r)
Plugging in the values from the problem, we get:
S = 165,000(1 + 0.737)
Solving for S gives:
S = 165,000 * 1.737 = 285,195
So the value of the house in the year 2011 will be approximately $285,195. Rounded to the nearest thousand dollars, this is $285,000
If you find this to be helpful, please consider giving it a heart, 5 stars, and brainliest to support my contribution.
Happy Holidays!
Ron and Annie have $1,571.13 in their checking account. During the week Annie goes to an ATM and withdraws
$80. The following week Ron deposits his paycheck of $456.82. Annie then pays bills online in the amounts of:
179.48, $74.73, $82.70, and $139.55. What is the current balance in their checking account?
Answer:
$1471.49
Step-by-step explanation:
1571.13-80=1491.13
1491.13+456.82=1947.95
179.48+74.73+82.70+139.55=476.46
1947.95-476.46=1471.49
someone please help i’ve been struggling for 20 minutes
The number of leaves on a tree which is 2 yards tall and receives 9 hours of sunlight is 324 leaves.
How many leaves are on the tree?The number of leaves on a tree = zHeight of the tree in yards = yHours of direct sunlight the tree receives = xz = k × y × x
Where,
k = constant of proportionalityIf y = 10 yards, x = 3 hours, z = 540 leaves
z = k × y × x
540 = k × 10 × 3
540 = 30k
k = 540/30
k = 18
Then, find z when y = 2 yards and x = 9 hours
z = k × y × x
= 18 × 2 × 9
z = 324 leaves.
In conclusion, given the constant of proportionality, the number of leaves on the tree is 324 leaves.
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Please help me on math very easy graphing! thank you!! due soon
Answer:
4x=4 or 4tims x =y
Step-by-step explanation:
1x4=4
3x4-=12
the manager of a theater wants to know whether the majority of its patrons are adults or children. One day, 5100 tickets were sold and the receipts totaled $29,484. The adult admission is $7.50, and the children's admission is $4.50. How many adult patrons were there
We can estimate the number of adult partons at 2187 by solving equations.
What do we mean by equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
A function is an equation that has only one answer for y for every possible value of x.
When utilizing a function, each input of a specific type receives exactly one output.
A function is commonly referred to as f(x) or g instead of y. (x).
Because f(2) instructs us to do so, we should figure out the value of our function when x is equal to 2.
So, the total number of adults present was thus:
Let a be an adult, and b and c be kids.
Ticket totals:
a + c = 5200
c = (5200-a)
Total amount:
7.50a + 4.50c = 29961
In the first equation, swap out c with (5200-a).
7.5a + 4.5(5200-a) = 29961
7.5a + 23400 - 4.5a = 29961
7.5a - 4.5a = 29961 - 23400
3a = 6561
a = 6561/3
a = 2187
Therefore, we can estimate the number of adult partons at 2187 by solving equations.
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-6.05+(-3.611) srrrrgggggggggggg
Answer:
-9.661
Step-by-step explanation:
Adding a negative is the same as subtracting a positive and you started with a negative number so:
-6.05
-3.611
------------
-9.661
Answer: -9.661
Step-by-step explanation:
A negative plus a negative will ALWAYS equal a negative. If you have an addition with two negatives, just add them normally and add the negative sign:
-6.05+(-3.611) = 6.05 + 3.611
6.05 + 3.611 = 9.661
Now add the negative sign:
9.661 = -9.661
Hope this helps!!
The owner of a factory wants to determine a confidence interval for the average wages at his factory. The population average wages is unknown. However, the owner was able to take a random sample of 64 workers. He found that the average salary for this sample of workers is $50,000. The population standard deviation is $3000. He calculated a 99% confidence interval for the population average wages at the factory. Which of the following choices is correct? Assume the distribution of wages is normally distributed.
4,034.06 ,5,965.94 are confidence interval for the population average wages at the factory.
What is confidence interval estimation?
Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.
If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty. Another term for probability in statistics is confidence.
The formula for confidence interval estimation is:
μ = M ± Z(sM)
where:
M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = √(s2/n)
M = 50000
Z = 2.58
sM = √(30002/64) = 375
μ = M ± Z(sM)
μ = 50000 ± 2.58*375
μ = 50000 ± 965.94
μ = 4,034.06 ,5,965.94
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The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle. Use words, numbers, or models to justify your answer.
The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle is 16.
Step-by-step explanation:We could use the distance formula to find the distance between the points in this problem, but when we look we see that the sides of the rectangle are parallel to the x and y-axis for each pair of sides. The first two points have a distance of 3 because 4-1=3. Since it is a rectangle, the opposite side will have the same length. For the sides perpendicular, we look at the points with the same x coordinate. Using (4,2) and (4,-3), we can calculate the length of the side by finding the distance by adding the absolute values of the y coordinate. 2+3=5. This means that the triangle has two sides with a length of 5 and two sides with a length of 3. Adding these together, 5+5+3+3 = 16.
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A local manufacturing firm produces four different metal products, each of
which must be machined, polished and assembled. The specific time
requirements (in hours) for each product are as follows:
Machining,
hours
Polishing, hours Assembling,
hours
Product I 3 1 2
Product II 2 1 1
Product III 2 2 2
Product IV 4 3 1
The firm has available to it on weekly basis, 480 hours of machining time, 400 hours
of polishing time and 400 hours of assembling time. The unit profits on the productare Birr 360, Birr 240, Birr 360 and Birr 480, respectively. The firm has a contract
with a distributor to provide 50 units of product I, and 100 units of any combination
of products II and III each week. Through other customers the firm can sell each
week as many units of products I, II and III as it can produce, but only a maximum
of 25 units of product IV. How many units of each product should the firm
manufacture each week to meet all contractual obligations and maximize its total
profit? Make a mathematical model for the given problem. Assume that any
unfinished pieces can be finished the following week.
Profit is the money you have left after paying for business expenses.
What is profit?Profit is the term used to describe the monetary gain experienced when the revenue from a business activity outpaces the costs, costs, and taxes incurred to maintain the activity in question.Any earnings go back to the company's owners, who can choose to keep the money for themselves, give it to shareholders as dividends, or put it to use again in the company.A business's profit is the money left over after all costs have been deducted. Any business, whether it be a lemonade stand or a publicly traded multinational corporation, has as its main objective making money. As a result, a business's success is measured by its profitability in all of its forms.Depending on the analyst, profitability before taxes and other expenses may be more important to them than top-line profitability. Others are only interested in profitability after expenses have been covered.
The production of the products are given below with the profit as well:
a. Production of Product 1 = 50 units per week
b. Production of Product 2 = 0 units per week
c. Production of Product 3 = 145 units per week
d. Production of Product 4 = 10 units per week
e. Total Profit = $1250 per week
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Answer:
Step-by-step explanation:
A local manufacturing firm produces four different metal products, each of
which must be machined, polished and assembled. The specific time
requirements (in hours) for each product are as follows:
Machining,
hours
Polishing, hours Assembling,
hours
Product I 3 1 2
Product II 2 1 1
Product III 2 2 2
Product IV 4 3 1
What is the remainder that the number 10^2023 leaves after division by 13?
Applying the property of exponents, the remainder that the number 10^2023 leaves after division by 13 is 9.
What is remainder?The remainder is the amount left over after a division operation.
What is exponent?An exponent is a number that indicates how many times a base number is used as a factor in a multiplication expression.
From the property of exponent:
We can rewrite 10^2023 as (10^13)^155 * 10^8:
10^2023 = (10^13)^155 * 10^8
We can then use the property of exponents to simplify:
10^2023 = (10^(13*155)) * 10^8
Since 10^13 is congruent to 1 mod 13, 10^(13*155) is congruent to 1 mod 13 as well. Therefore, 10^2023 is congruent to 10^8 mod 13.
We can find the remainder by calculating 10^8 mod 13:
10^8 = 100000000
After dividing 100000000 by 13, we get a remainder of 9.
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h
41. What is the solution of the system? (1 point)
y=9x-2
y=7x+3
5 41
2 29
5'5
1 13
22
29 need help quickly question is in unit eight lesson two semester final exam on Pecos
The solutions of the given system of Equations are (5/2, 41/2).
What are the Solutions of Equations:The set of values for each variable in a system of linear equations is referred to as the solution set.
The intersection or meeting points of the lines or planes used to illustrate the linear equations are also known as the solutions.
The elimination method is one way of resolving a system of linear equations. To obtain the equation in one variable using this technique, simply add or subtract the equations.
Here we have
y = 9x-2 --- (1)
y = 7x+3 --- (2)
From (1) and (2)
=> 9x - 2 = 7x + 3
=> 9x - 7x = 3 + 2
=> 2x = 5
=> x = 5/2
Substitute x = 5/2 in (1)
=> y = 9(5/2) - 2
=> y = (45/2) - 2
=> y = (45 - 4)/2
=> y = 41/2
Therefore,
The solutions of given system of Equations are (5/2, 41/2).
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In a certain rental shop, they have 63 vehicles. They allow you to rent bicycles and tricycles free for the first hour.If they had 149 tires in all, how many bicycles and tricycles do they have?
Answer:
There Are 40 Bicycles And 23 Tricycles
Step-by-step explanation:
Let, x be bicycles and y be tricycles
Condition 1;
: x + y= 63
: x =63-y
Condition 2;
Number Of Tires=149
:2x + 3y =149 [2x=Two Tires Of Bicycle And
3y=Three Tires Of Tricycle]
:x = 149-3y/2
Combination 1 & 2;
63-y = 149-3y/2
126-2y = 149-3y
y=23
x = 63-23
=40
If the ratio of hotels to office buildings with 4 to 9 find the ratio of office buildings to hotels
The ratio shows how many times one value is contained in another value.
The ratio of office buildings to hotels will be 9 : 4.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of hotels to office buildings = 4 : 9
Now,
The ratio of office buildings to hotels will be 9 : 4.
Thus,
The ratio of office buildings to hotels will be 9 : 4.
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Deandre has a large collection of movies on DVD. In the past month, he has bought 11 DVDs that cost $27.95 each, 7 that cost $17.95 each, and
one that cost $7.95. How much has he spent on DVDs in the past month?
Answer:$441.05
Step-by-step explanation:
For this question you would multiply the amount of each DVD by the price and add them all up
like this:
11(27.95) +7(17.95)+1(7.95)=$441.05
What is the area of the triangle?
7 cm
10 cm
Area = [?] cm²
Enter
Answer:
35cm^2
Step-by-step explanation:
Things To Keep In Mind:
Height: 7 cm
Length: 10 cm
(L*H)/2=area of triangle
7*10=70
70/2=35
If there are any problems with this answer please feel free to tell me, thanks :)
find the coordinaates of the turning point on the curve with equation y=9+18x-3x>2
The coordinates of the turning point on the curve with the quadratic equation y = 9 + 18x - 3x² is (3,36).
What is a quadratic equation?
Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
It is given that:
The quadratic equation is:
y = 9 + 18x - 3x²
To find the turning point:
Graph the above quadratic equation;
From the graph:
The maximum point from where the graph starts to decrease is (3,36)
Thus, the coordinates of the turning point on the curve with the Quadratic equation y = 9 + 18x - 3x² is (3,36).
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Mickey Here Hi justice as more point because you deserve it
Answer:
second
Step-by-step explanation:
2x+5>7
2x>2
x>1
therefore, second
A rectangle is 5 inches long and 2x inches wide. The value of the perimeter in inches) is equal to the value of the area (in square inches). Find x.
Answer:
the width of the rectangle is -5/3 inches.
Step-by-step explanation:
To find the perimeter of the rectangle, we add together the lengths of all four sides. Since the rectangle is 5 inches long and 2x inches wide, the perimeter is given by:
Perimeter = 5 + 2x + 5 + 2x = 10 + 4x
To find the area of the rectangle, we multiply the length by the width. The area is given by:
Area = 5 * 2x = 10x
Setting the perimeter equal to the area, we have:
10 + 4x = 10x
Subtracting 10 from both sides, we have:
4x = 10x - 10
Combining like terms, we have:
-6x = -10
Dividing both sides by -6, we have:
x = 10 / -6
Simplifying, we have:
x = -5/3
You volunteer to help drive children at a charity event to the zoo, but you
can fit only 6 of the 18 children present in your van. How many different
groups of 6 children can
you
drive?
18,564 different groups of 6 children can be driven.
Here we are given 18 Children in total and we can fit Only 6 Children out of them.
The number of different groups of 6 children that can fit into the van ca be calculated with a simple formula
The formula used will be -
n! = n(n-1)(n-2)(n-3).......1
n!= (18 x 17 x 16 x 15 x 14 x 13) / (6 x 5 x 4 x 3 x 2)
= 18,564
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WIL GIVE BRAINLIEST!!!!
What is the value of x in simplest radical form?
Look at the provided picture!!!
Answer: b
Step-by-step explanation:
3^2 + x^2 = 9^2
9 + x^2 = 81
x^2 = 72
x = sqrt(72)
which equation in point-slope from is equivalent to y=-3/4x + 9?
A. y-9=-3/4(x-0)
B. y-1=-3/4(x-9)
C. y-3/4=9(x-0)
D. y-1=9(x+3/4)
Answer:
Step-by-step explanation:
I know that in point-slope form, the equation is y - y1 = m(x - x1)
Fill in y1 and x1 with the points given in the multiple choices.
If you look at Letter A, it shows the point (0,9). If you fill that in the formula. You solve the equation:
y - 9 = -3/4(x - 0)
y - 9 = -3/4x
+9. =. +9
y = -3/4x + 9
Therefore your answer is letter A.
Jai and Keilantra are both driving along the same highway in two different cars to a
stadium in a distant city. At noon, Jai is 254 miles away from the stadium and
Keilantra is 293 miles away from the stadium. Jai is driving along the highway at a
speed of 41 miles per hour and Keilantra is driving at speed of 54 miles per hour. Let
J represent Jai's distance, in miles, away from the stadium & hours after noon. Let K
represent Keilantra's distance, in miles, away from the stadium t hours after noon.
Write an equation for each situation, in terms of t, and determine the number hours
after noon, t, when Jai and Keilantra are the same distance from the stadium.
The number of hours when Jai and Keilantra are the same distance from the stadium is 3 hours.
How to calculate the equation?Jai is 254 miles away from the stadium. Jai is driving along the highway at a speed of 41 miles per hour. This will be:
254 - 41h
Keilantra is 293 miles away from the stadium. Keilantra is driving at speed of 54 miles per hour. This will be:
293 - 54h
The equations will be:
254 - 41h = 293 - 54h
54h - 41h = 293 - 254
13h = 39
Divide
h = 39/13
h = 3
The number of hours is 3 hours.
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Find m in equation, W=1/2*m*v squared?
Answer: To find the value of m in the equation W = 1/2 * m * v^2, you need to know the values of W and v. The variable m represents the mass of the object, and W represents the kinetic energy of the object. The equation states that the kinetic energy of an object is equal to 1/2 of its mass multiplied by its velocity squared.
If you are given the values of W and v, you can solve for m by rearranging the equation as follows:
m = 2 * W / v^2
Plugging in the values of W and v will give you the value of m.
For example, if W = 100 joules and v = 10 meters per second, the equation would be:
m = 2 * 100 joules / 10 m/s^2 = 20 kilograms
This is the mass of the object.
[tex]m=\frac{2W}{v^{2} }[/tex].
Step-by-step explanation:1. Write the expression.[tex]W=\frac{1}{2} mv^{2}[/tex]
2. Divide both sides of the equation by [tex]\frac{1}{2}[/tex] and [tex]v^{2}[/tex].[tex]\frac{W}{\frac{1}{2} v^{2} }=m\\ \\[/tex]
3. Rewrite and simplify.[tex]m=\frac{W}{\frac{1}{2} v^{2} }\\ \\m=\frac{2W}{v^{2} }[/tex].
M < a = ?
M < d = ?
please help!!
Answer:
m∠A = 60
m∠D = 60
Step-by-step explanation:
∆ABC and ∆DEF are congruent triangles
So,
m∠A = m∠D
x + 30 = 2x
2x - x = 30
x = 30
So,
m∠A = x + 30 = 30 + 30 = 60
m∠D = 2x = 2(30) = 60
Thus, m∠A and m∠D are 60°
The average height of children who are 2 years old is 34 inches. A random sample of 35 children who are 2 years old in a large daycare franchise is collected, and they are found to average 29.50 inches with a standard deviation of 1.70 inches. The researchers are suspicious that the children at the daycare are not growing as quickly as they should be.
a. Write the hypotheses.
b. Calculate the test statistic.
c. Calculate the P-value
d. What is the conclusion for the hypothesis test?
There is sufficient evidence to support the claim.
What is sufficient evidence ?
Sufficient evidence is admitted evidence that has enough overall weight, in terms of relevance and credibility, to legally justify a particular conclusion.
This is left tailed test .
The null and alternative hypothesis is ,
H0 : mu= 34
Ha :mu < 34
Test statistic(t) = (x)
n= root (29.5 - 34) / 1.70
root 35
Test statistic = -15.66
P-value = 0
Alpha = 0.05
P-value <Alpha
Reject the null hypothesis .
There is sufficient evidence to support the claim.
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