The required original number that Peter was thinking about is 18.25.
Let us assume that the original number be x that Peter is thinking about.
Peter adds 6 to the number, therefore the number becomes = (6 + x )
Then doubles the new number therefore it becomes = 2(6 + x) = 12 + 2x
According to question by applying rule of forming equations ( from the information given ) we get,
12 + 2x = 48.5
⇒ 2x = 48.5 - 12
⇒ 2x = 36.5
⇒ x = 36.5/2
⇒ x = 18.25
Hence the original number is 18.25.
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The bearing of A from B is 129 and the bearing of C from B is 219. If B is equidistant from A and C, find the bearing of C from A
The bearing of C from A is 90 degrees when B is equidistant from A and C.
What is bearing?In navigation and geometry, bearing refers to the direction or angle between two points, measured clockwise from a fixed reference direction. Typically, bearings are measured in degrees, with 0 degrees indicating a direction due north, 90 degrees indicating a direction due east, 180 degrees indicating a direction due south, and 270 degrees indicating a direction due west. Bearings can be expressed as either magnetic bearings or true bearings, depending on the reference direction used.
According to the given informationLet's assume that the distance from B to A and from B to C is the same.
To find the bearing of C from A, we can use the fact that the interior angles of a triangle sum up to 180 degrees. Therefore, we can first find the bearing of A from C:
180 - 129 = 51
This means that the bearing of C from A is 51 degrees in the opposite direction of the bearing of A from C. Since the bearing of A from C is 219, the bearing of C from A is:
219 - 180 + 51 = 90 degrees
Therefore, the bearing of C from A is 90 degrees.
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Helpp (30,60,90) and (45,45,90) but in radical form
Answer:
In its simplest form, the ratios of the length of sides in a 45 45 90 special right angle triangles should be 1 : 1 : 2 1:1:\sqrt{2} 1:1:2on:
And because this is a 30-60-90 triangle, and we were told that the shortest side is 8, the hypotenuse must be 16 and the missing side must be 8 * 3 , or 8 3 . Our final answer is 8√3
Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $35 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $190, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.
After solving equation , the plumber put in 3.1 hours of work (or 3 hours, 6 minutes).
what is equation?A mathematical assertion that demonstrates the equality of two expressions is called an equation The equals symbol (=) is used to denote the separation of two phrases. Numerous mathematical ideas and relationships, including linear functions, quadratic functions, and trigonometric functions, can be represented by equations.
Let's use the letter 'h' to indicate how many hours the plumber put in.
The plumber costs $35 to come to Jerald's residence and $50 for every hour they work. If Jerald is charged a total of $190 by the plumber, the following equation can be written:
$50h + $35 = $190
To solve for 'h,' we obtain:
$50h = $190 - $35
$50h = $155
h = 155 / 50
h = 3.1
Consequently, the plumber put in 3.1 hours of work (or 3 hours, 6 minutes).
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Quadrilateral H'I'J'K' is a translation of quadrilateral HIJK. Write the translation rule. picture above
Since quadrilateral H'I'J'K' is a translation of quadrilateral HIJK, the translation rule include the following: (x, y) → (x - 8, y + 10).
What is a translation?In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.
By translating the pre-image of quadrilateral HIJK horizontally left by 8 units and vertically up by 10 units, the coordinate J of quadrilateral H'I'J'K' include the following:
(x, y) → (x - 8, y + 10)
J (8, -2) → (8 - 8, -2 + 10) = J' (0, 8).
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The line 2x+3y=-22 is tangent to a circle centered at (-1,2) What is the tangent point?
The point of tangency is (-3, -2).
How to find the intersection point?To find the point of tangency , we really want to find the convergence point between the line and the circle. We can begin by tracking down the situation of the circle with focus (- 1,2).
A circle's equation for its center (a,b) and radius (r) is as follows:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
Plugging in the values for the center and solving for r, we get:
[tex](x + 1)^2 + (y - 2)^2 = r^2[/tex]
Now we need to find the intersection point between this circle and the line 2x+3y=-22. We can do this by substituting y = (-2/3)x - (22/3) into the equation of the circle:
[tex](x + 1)^2 + ((-2/3)x - (16/3))^2 = r^2[/tex]
Expanding and simplifying, we get:
[tex]10x^2 + 24x + 44 = 9r^2[/tex]
Next, we can make use of the fact that the line intersects the circle at a tangent. This indicates that the distance between the intersection point and the center of the circle is the same as its radius. The distance between the center of the circle and the line can be determined using the distance formula:
distance = [tex]|2x + 3y - (-22)\sqrt{2^2 + 3^2}| = |2x + 3y + 22| \sqrt(13)[/tex]
Setting this equal to the radius r, we get:
[tex]|2x + 3y + 22| \sqrt{13} = \sqrt{10x^2 + 24x + 44} / 3[/tex]
Squaring both sides and simplifying, we get:
[tex]36(2x + 3y + 22)^2 = 13(10x^2 + 24x + 44)[/tex]
Expanding and simplifying, we get:
[tex]26x^2 + 36xy + 45y^2 + 52x + 132y + 240 = 0[/tex]
Now we can use the quadratic formula to solve for x:
x = (-18y - 13 ± [tex]\sqrt{169 - 720y^2[/tex])) / 13
Substituting this into the equation for the line, we get:
2(-18y - 13 ± [tex]\sqrt{169 - 720y^2))[/tex] / 13 + 3y = -22
Simplifying, we get:
y = -2
Substituting y = -2 into the equation for x, we get:
x = -3
Therefore, the point of tangency is (-3, -2).
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if a contingency table has nine rows and columns, how many degrees of freedom are there for the test for independence?
There are 64 degrees of freedom for the test for independence in this contingency table.
To find the degrees of freedom for a test for independence in a contingency table, you can use the following formula:
Degrees of freedom (df) = (number of rows - 1) * (number of columns - 1).
In your case, the contingency table has nine rows and nine columns. Using the formula:
df = (9 - 1) * (9 - 1)
df = 8 * 8
df = 64.
In a contingency table, the degrees of freedom (df) for the test of independence are calculated as:
df = (number of rows - 1) x (number of columns - 1)
In this case, the contingency table has nine rows and nine columns, so the degrees of freedom are:
df = (9-1) x (9-1) = 64
This means that there are 64 degrees of freedom for the test of independence.
Degrees of freedom are important because they determine the critical values for the test statistic, which in turn affects the decision to reject or fail to reject the null hypothesis.
In general, as the degrees of freedom increase, the critical values decrease, making it easier to reject the null hypothesis.
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There are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.
To determine the degrees of freedom for the test for independence in a contingency table with nine rows and columns, we use the formula df = (r-1)(c-1), where r is the number of rows and c is the number of columns.
Substituting in the values, we get:df = (9-1)(9-1)df = 8 x 8df = 64A contingency table is a table that shows the frequency distribution of two or more categorical variables.
A test for independence is a statistical test that checks whether the variables are related or not.
Therefore, there are 64 degrees of freedom for the test for independence in a contingency table with nine rows and columns.
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Find the exact value of cos a, given a=-3/7 and a is in quadrant 4
Answer:
9.955
Step-by-step explanation:
In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student who did not complete the homework passed the test?
The probability that a student who did not complete the homework passed the test is 0.25.
The recipe for one batch of
chocolate chip cookies calls
for 11/3 cups of chocolate
chips. Luca made 3½ batches
of cookies. How many cups of
chocolate chips did he use?
Answer:
Step-by-step explanation:
1 + 1 divided by 3 x 3.5 = 4.66 or 4 2/3
Use the functions f(x)=√x+1, g(x)=2x-5, and h(x) = 3x² - 3 to complete the table.
x
4
10
20
34
52
f(g(x))
Answer:
To find the values of f(g(x)) for the given values of x, we need to first evaluate g(x) for each value of x, and then plug the result into f(x).
Using the given functions:
g(x) = 2x - 5
f(x) = √(x+1)
Therefore, we have:
f(g(x)) = √(g(x) + 1) = √(2x - 5 + 1) = √(2x - 4) = 2√(x - 2)
So, we can complete the table as follows:
x f(g(x))
4 2
10 4
20 6
34 8
52 10
Therefore, the completed table is:
x f(g(x))
4 2
10 4
20 6
34 8
52 10
tom can type a report in 3 hours and nelson takes 5 hours. how long will it take the two of them typing together?
It will take Tom and Nelson 1.875 hours, or 1 hour and 52.5 minutes, to complete the report working together.
How to know work done together?To solve this problem, we can use the concept of work done. Let's assume that a report is a unit of work, and Tom and Nelson each do a fraction of the work in one hour.
Tom can do the entire report in 3 hours, which means he can do 1/3 of the report in one hour. Similarly, Nelson can do 1/5 of the report in one hour.
If they work together, the fraction of the report they can do in one hour is the sum of their individual fractions:
1/3 + 1/5 = 8/15
So, together they can do 8/15 of the report in one hour. To find out how long it will take them to do the entire report working together, we can use the formula:
time = work ÷ rate
where work is 1 (the whole report) and rate is 8/15 (the fraction of the report they can do in one hour).
time = 1 ÷ (8/15)
time = 1.875 hours
Therefore, it will take Tom and Nelson 1.875 hours, or 1 hour and 52.5 minutes, to complete the report working together.
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A class has 8 students who are to be assigned seating randomly. What is the
probability that the students will be arranged in order from shortest to tallest? Show
your work
The probability that the students will be arranged in order from shortest to tallest is 1/(8!) or 1/40320.
What is student?Student is an individual who is enrolled in an educational institution such as a university, college, or a trade school. A student typically takes courses in order to further their knowledge and skills, to prepare for further education or training, or to receive credentials necessary to pursue a job or career. Students can include both full-time and part-time learners. Depending on the institution, a student may also be referred to as a pupil, student-athlete, or scholar. Students can also take part in a variety of student-led activities and organizations, both on-campus and off-campus.
This is because there are 8! (8 factorial) ways in which the students can be arranged in order from shortest to tallest.
Therefore, the probability of any one arrangement is 1/8!
Thus, the probability of the students being arranged in order from shortest to tallest is 1/8! or 1/40320.
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a bank wishing to increase its customer base advertises that it has the fastest service and that virtually all of its customers are served in less than 11 minutes. a management scientist has studied the service times and concluded that service times are exponentially distributed with a mean of 4.5 minutes. determine what the bank means when it claims 'virtually all' its customers are served in under 11 minutes.
The bank's claim is exaggerated and not entirely accurate.
The bank's claim that virtually all of its customers are served in less than 11 minutes is misleading, as it implies that almost all customers are served in 11 minutes or less. However, based on the given information that service times follow an exponential distribution with a mean of 4.5 minutes, we can calculate the probability that a customer will be served in less than 11 minutes using the cumulative distribution function of the exponential distribution:
P(X < 11) = 1 - [tex]e^{(-11/4.5)[/tex] = 0.956
This means that approximately 95.6% of customers will be served in less than 11 minutes, not "virtually all." Therefore, the bank's claim is exaggerated and not entirely accurate.
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Here is a recipe for $$ cupcakes. • Terrance has $$ cup of flour and $$ eggs. • Duri has $$ cups of flour and $$ grams of butter. • Habib has $$ cups of milk and $$ cups of sugar. • Anika has $$ cup of sugar and $$ cups of milk. If each person has enough of all the other ingredients, how many cupcakes could they make on their own?
Duri can make 72 cupcakes on his own and Habib can make 36 cupcakes on her own, assuming they have enough of all the other ingredients.
To determine how many cupcakes each person can make on their own, we need to check if they have enough of all the other ingredients required to make 12 cupcakes.
Terrance has 1 cup of flour and 6 eggs, which is not enough to make 12 cupcakes.
Duri has 12 cups of flour and 1000 grams of butter, which is more than enough to make 12 cupcakes. However, the recipe requires 3/4 cup of sugar, 2 eggs, and 3/4 cup of milk, which we do not know if Duri has enough of.
Habib has 3 cups of milk and 6 cups of sugar, which is enough to make 12 cupcakes.
Anika has 1 cup of sugar and 4 cups of milk, which is not enough to make 12 cupcakes.
Therefore, only Duri and Habib have enough ingredients to make 12 cupcakes on their own.
To determine how many cupcakes they can make, we need to calculate how much of each ingredient is required for one cupcake and then divide the available ingredients by that amount.
For one cupcake, we need:
1/6 cups of flour
1/16 cup of sugar
1/6 eggs
1/16 cups of milk
125/12 grams of butter
Duri has 12 cups of flour and 1000 grams of butter, which is enough to make 72 cupcakes. Habib has 6 cups of sugar and 3 cups of milk, which is enough to make 36 cupcakes.
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What is the volume of a sphere with a diameter of 6. 3 cm, rounded to the nearest tenth of a cubic centimeter?
Step-by-step explanation:
Volume of a sphere is given by the formula
4/3 pi r^3 diameter = 6.3 cm so radius, r = 3.15 cm
4/3 * pi * (3.15)^3 = 130.9 cm^3
A new club sent out 200 coupons to boost sales for next year's memberships. They provided 3 times as many to potential members than to existing members. How many coupons did they send to existing members?
the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.
How to solve the question?
Let x be the number of coupons sent to existing members. Then the number of coupons sent to potential members is 3x, as they provided 3 times as many coupons to potential members than to existing members.
According to the problem, the total number of coupons sent is 200. Therefore, we can write the following equation:
x + 3x = 200
Simplifying this equation, we get:
4x = 200
Dividing both sides by 4, we get:
x = 50
Therefore, the number of coupons sent to existing members is 50, and the number of coupons sent to potential members is 3 times as many, or 150.
In conclusion, the new club sent out 50 coupons to existing members and 150 coupons to potential members to boost sales for next year's memberships.
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In artwork consists of the triangle shown with the shaded triangle is cut out of the larger triangle. What is the area of the remaining unshaded portion?
Thus, the area of unshaded portion for the given values of triangle is found as 48.6 sq. m.
Explain about the triangle:Three sides, three angles, plus three vertices make up a triangle.
A triangle's total internal angles have always been equal to 180 degrees. This is referred to as the triangle's angle sum property.The greatest side of a triangle is the side that faces the largest angle.The sum of the triangle's internal opposite angles is equal to any of its outer angles. This is referred to as the triangle's outside angle property.Area of triangle = 1/2*base *height
Area of unshaded portion = complete area - area of shaded triangle
Area of unshaded portion = 1/2*(20)*(8.1) - 1/2*8*(8.1)
Area of unshaded portion = 81 - 32.4
Area of unshaded portion = 48.6
Thus, the area of unshaded portion for the given values of triangle is found as 48.6 sq. m.
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The angle of elevation from point A to the top of a hill is 49°. If point A is 400 feet from the base of the hill, how high is the hill? Round to the nearest tenth.
1. 460.1 ft
2. 301.9 ft
3. 262.4 ft
4. 459.3 ft
The height of the hill for the given angle of elevation through which the given condition is satisfied is 460.1 ft
What about angle of elevation?
The angle of elevation is the angle between the horizontal plane and the line of sight or the direction of the observer's line of sight above the horizontal plane. It is measured upwards from the horizontal plane to the object being viewed. The angle of elevation is typically used in trigonometry and geometry to calculate the height, distance, or length of an object or location.
According to the given information:
Given, The given angle of elevation from point A to the top of a hill is [tex]49^{0}[/tex].
As, we know tan (x) = [tex]\frac{perpendicular}{base}[/tex]
tan [tex]49^{0}[/tex] = [tex]\frac{unknown}{400}[/tex]
1.15 x 400 = unknown
So, the unknown = 460.1 ft
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First person to help me on this will be rewarded plsss
The compound interest investment earns more interest than the simple interest investment, and the difference becomes more significant over time.
After 10 years, the difference is relatively small, but after 20 years, the compound interest investment has earned over $3,700 more than the simple interest investment.
What are the amounts after 10 and 20 years of the investment?To calculate the amount after 10 and 20 years, we can use the following formulas:
Simple Interest: A = P * (1 + r * t)
Compound Interest: A = P * (1 + r/n)^(n*t)
Where:
A is the amount after t yearsP is the principal amount (the initial investment)r is the annual interest rate (as a decimal)n is the number of times the interest is compounded per yeart is the time in yearsUsing these formulas and the information given in the table, we can calculate the amount after 10 years and 20 years for each type of investment.
For simple interest, the interest is not compounded, so we just add the interest to the principal:
Amount after 10 years: A = $50,000 * (1 + 0.0275 * 10) = $68,750
Amount after 20 years: A = $50,000 * (1 + 0.0275 * 20) = $87,500
For compound interest, we need to use the formula above with n=12 (since the interest is compounded monthly):
Amount after 10 years: A = $50,000 * (1 + 0.0275/12)^(12*10) = $68,704.23
Amount after 20 years: A = $50,000 * (1 + 0.0275/12)^(12*20) = $91,262.47
To compare the two investments, we can look at the difference between the amounts after 10 and 20 years:
Difference after 10 years: $68,750 - $68,704.23 = $45.77
Difference after 20 years: $87,500 - $91,262.47 = $3,762.47
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Jordan is looking for a new place to live. She saw an ad in the paper and went to
the apartment building to look at the available unit. There, she met Steve, the
person who manages the property. Steve's jobs include collecting rent, making
small repairs, and screening the people who answers the ads. The rent checks
are to be made to Dave, the owner of the building. Jordan loves the apartment
and is approved to sign the lease and move in.
In this scenario, Steve is the:
O Real estate agent
O Tenant
O Landlord
O Property manager
Based on the given scenario, Steve who manages the property is a real estate agent.
The correct answer choice is option A
Who is a real estate agent?A real estate agent is a person who serves as n intermediary between tenant and landlord, buyers and sellers of properties. They collect rent, make little repairs and screen interested people. The real estate agent receives their reward based on commission, that is, a particular percentage of the property.
Therefore, Jordan is the tenant, Dave is the landlord and Steve is the real estate agent.
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True or False. (a). X(x^2 + 4)/x^2 - 4 can be written as (A/x + 2)+ (B/x - 2)
(b). X^2 + 4/x(x^2 - 4) can be written as (A/x) + (B / x + 2) + (C/x - 2). (c). X^2 + 4/x^2(x - 4) can be written as (A/x^2) + (B/x - 4)
(d). X^2 - 4/x(x^2 + 4) can be written as (A/x) + (B / x^2 + 4)
(a) True. We can use partial fraction decomposition to write X(x² + 4)/(x² - 4) as (A/(x+2)) + (B/(x-2)).
(b) True. We can use partial fraction decomposition to write X² + 4/(x(x² - 4)) as (A/x) + (B/(x+2)) + (C/(x-2)).
(c) True. We can use partial fraction decomposition to write X² + 4/(x²(x - 4)) as (A/x²) + (B/x) + (C/(x-4)).
(d) False. We can use partial fraction decomposition to write X² - 4/(x(x² + 4)) as (A/x) + (Bx+C)/(x²+4).
(a) We want to write X(x² + 4)/(x² - 4) in the form (A/(x+2)) + (B/(x-2)). First, we find A and B by multiplying both sides by the common denominator (x+2)(x-2):
X(x² + 4) = A(x-2) + B(x+2)
Expanding both sides gives:
Xx² + 4X = Ax - 2A + Bx + 2B
Grouping terms by x gives:
Xx² + (A+B)x + (-2A+2B) = 4X
Now we have a system of two equations:
A + B = 0 (coefficients of x)
-2A + 2B = 4X (constant terms)
Solving for A and B gives:
A = -B
-2A + 2B = 4X
-2A + 2(-A) = 4X
-4A = 4X
A = -X
Therefore, B = X. Thus,
X(x² + 4)/(x² - 4) = (-X/(x+2)) + (X/(x-2))
(b) We want to write X² + 4/(x(x² - 4)) in the form (A/x) + (B/(x+2)) + (C/(x-2)). First, we find A, B, and C by multiplying both sides by the common denominator x(x+2)(x-2):
X² + 4 = A(x+2)(x-2) + Bx(x-2) + Cx(x+2)
Expanding both sides gives:
X² + 4 = Ax² - 4A + Bx² - 2Bx + Cx^2 + 2Cx
Grouping terms by powers of x gives:
(X² + 4) = (A+B+C)x² + (-2B+2C)x - 4A
Now we have a system of three equations:
A + B + C = 0 (coefficients of x²)
-2B + 2C = 0 (coefficients of x)
-4A = 4 (constant terms)
Solving for A, B, and C gives:
A = -1/4
B = 1/4
C = 1/4
Therefore,
X² + 4/(x(x² - 4)) = (-1/(4x)) + (1/(4(x+2))) + (1/(4(x-2)))
(c) We want to write X² + 4/(x²(x - 4)) in the form (A/x²) + (B/x) + (C/(x-4)). First, we find A, B, and C by multiplying both sides by the common denominator x²(x-4):
X²(x-4) + 4x² = Ax(x-4) + Bx²(x-4) + Cx²
Expanding both sides gives:
X²x - 4X² + 4x² = Ax² - 4Ax + Bx³ - 4Bx² + Cx²
Grouping terms by powers of x gives:
(X² + 4) = (B)x³ + (A-4B)x² + (-4A+C)x
Now that we have a common denominator of (x² - 4), we can combine the two fractions and simplify:
X(x² + 4) - 2(x² - 4) = A(x - 2) + B(x + 2)
Expanding and simplifying the left side:
x³ + 4x - 2x² + 8 = Ax - 2A + Bx + 2B
Grouping the like terms on each side:
x³ - 2x² + Ax + Bx + 4x - 2A + 2B + 8 = 0
Now we have a polynomial equation that we can use to solve for A and B. We can do this by equating the coefficients of like terms on both sides. Specifically, we can equate the coefficients of x² and x:
x³ - 2x² + Ax + Bx + 4x - 2A + 2B + 8 = 0
Coefficients of x²: -2 = A
Coefficients of x: 4 = B
Therefore, we have:
X(x² + 4)/(x² - 4) = (-2x)/(x² - 4) + (4)/(x² - 4)
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what is the probability that a simple random sample of 50 ten-gram portions results in a mean of at least 3.6 insect fragments? is this result unusual? what might we conclude?
a) The probability that a simple random sample of 50 ten-gram portions results in a mean of at least 3.6 insect fragments is approximately 0.027.
b) This result is somewhat unusual, as only about 2.7% of samples would be expected to have a mean of at least 3.6 insect fragments. However, it is not necessarily a cause for concern, as it is within the range of expected variation.
c) More information about the distribution of insect fragments in the population and the context in which the samples were collected would be needed to draw more definitive conclusions.
To answer this question, we would need to know the distribution of insect fragments in the population from which the samples are drawn. Let's assume that this distribution is approximately normal with a mean of 3.2 insect fragments and a standard deviation of 0.8 insect fragments, as suggested by FDA guidelines for chocolate.
The distribution of the sample means for samples of size n can be approximated by a normal distribution with mean µ and standard deviation σ/√n. In this case, µ = 3.2 and σ/√n = 0.8/√50 = 0.113.
To find the probability that a sample of 50 ten-gram portions has a mean of at least 3.6 insect fragments, we need to find the area under the normal curve to the right of 3.6. Using a standard normal distribution table or a calculator, we find that this probability is approximately 0.027.
This result is somewhat unusual, as only about 2.7% of samples would be expected to have a mean of at least 3.6 insect fragments. However, it is not necessarily a cause for concern, as it is within the range of expected variation. If the sample mean was much higher, say 4.0 or 4.5, it would be more concerning and warrant further investigation.
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tim wants his mean quiz score to be 90. his first 3 quiz scores were 86, 92, and 94. what score should he make on the 4th quiz in order to have a mean quiz score of exactly 90?
The score to be made on the 4th quiz in order to have a mean quiz score of exactly 90 is equal to 88.
Let us consider the score that Tim needs to get on his fourth quiz be x.
Score he needs to get in order to have a mean quiz score of 90,
Set up an equation using the formula for the mean ,
(mean score) = (sum of scores) / (number of scores)
If Tim wants his mean quiz score to be 90, then we have,
⇒ 90 = (86 + 92 + 94 + x) / 4
Multiplying both sides by 4, we get,
⇒360 = 86 + 92 + 94 + x
Simplifying this equation, we get,
⇒ x = 360 - 272
⇒ x = 88
Therefore, Tim needs to get a score of 88 on his fourth quiz in order to have a mean quiz score of exactly 90.
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what equation represent
Answer: I'll have to say it's C or D but I think it's D
Hope it helped :D
An item is regularly priced at 50 It is now priced at a discount of 70% off the regular price. What is the price now
Answer: $15
Step-by-step explanation:
If you have a 70% coupon for a $50 item, that means you are only paying 30% of the normal price.
0.3 x 50 = 15
The item will cost $15
A pre-image has coordinates N(3, -2), A(5, 0) and P(2, 4). The image has coordinates N’ (2, 0), A'(4, 2) and P'(1, 6). Write a transformation rule to describe the path the pre-image made to arrive at the image.
Answer:
f(x + 1) + 2
Step-by-step explanation:
All the points are translated 1 unit to the left and 2 units up.
To write a translation along the x-axis, movement to the right would be written as f(x - a), where a is the amount translated, and movement to the left would be written as f(x + a). In this case, we would need to write the translation as f(x + 1), since it is moving 1 unit to the left.
As for translations along the y-axis, movement upward would be written as f(x) + a, and movement downward would be written as f(x) - a. Thus, the transformation rule to describe the path the pre-image made to arrive at the image would be f(x + 1) + 2.
P.S. I'm a bit rusty with this stuff, so I apologize in advance if I messed something up.
Directions: Find the simplest ratio given a scenario.
1. A designated hitter made 10 hits in 15 games. Find the simplest ratio of hits to games.
The simplest ratio of hits to games is 2:3.
What are proportions?
In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:
a/b = c/d
The simplest ratio of hits to games can be found by dividing the number of hits by the number of games:
Hits/Games = 10/15
To simplify this ratio, we can divide both the numerator and denominator by their greatest common factor, which in this case is 5:
Hits/Games = (10/5) / (15/5) = 2/3
Therefore, the simplest ratio of hits to games is 2:3.
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6. Electronics Warehouse had a Super Bowl Sale on Televisions. They offered no interest no payments for 24 months on televisions larger than 50 inches. You have been dving to have a new 85" TV, so you pick out an amazing OLED on sale for $2299.99. You take advantage of the store offering no interest, no paymenus for 24 months, and go home smiling. The fine print on the credit card agreement states a 24.99% interest rate that accrues monthly. Additionallv. if the balance is not paid in full by the end of the 24 month promotion. the interest will be apolied to the remaining balance. If vou choose to not make a payment during the 24-month period, what will your balance be when you get your first bill?
If you choose not to make a payment during the 24-month period, your balance at the end of the promotion will be $3,637.16.
Explain month
A month is a unit of time equal to one-twelfth of a year, or approximately 30.44 days. It is often used to represent periodic phenomena, such as interest rates or seasonal trends, and to calculate the duration between two dates. The number of months between two dates is calculated by dividing the difference in days by 30.44.
According to the given information
If you do not make any payments during the 24-month period, your balance will increase each month due to the interest that accrues. After 24 months, your balance will be:
$2299.99 * (1 + 0.020825)²⁴ = $3,637.16
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Eight identical lights are connected in series across a 110-V line. What is the voltage across each bulb? If the current is 0.56A , what is the resistance of each bulb? If the current is 0.56A , what is the power dissipated in each?
The resistance of each bulb that is connected in series with a 110 V line is 24.55 Ω with a 13.75 V Voltage difference across each bulb. The power dissipated in each bulb is 7.7 W, if 0.56 A current flows through them.
The voltage across 8 identical bulbs is 110 V
Since they are connected in a series and identical, the Voltage difference across each bulb is [tex]\frac{110}{8}[/tex] V which is 13.75 V
According to the question,
The current flowing through the bulb = 0.56 A
So according to Ohm's Law,
V = IR
13.75 = 0.56 * R
R = 24.55 Ω
The power dissipated in each bulb can be calculated as
P = VI
P = 13.75 * 0.56 = 7.7 W
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In summary, the voltage across each bulb is 13.75V, the resistance of each bulb is 24.55Ω, and the power dissipated in each bulb is 7.7W.
When eight identical lights are connected in series across a 110-V line, the voltage across each bulb will be 110/8 = 13.75 V.
To find the resistance of each bulb, we can use Ohm's law, which states that resistance is equal to voltage divided by current (R = V/I). Therefore, the resistance of each bulb is 13.75/0.56 = 24.55 ohms.
To find the power dissipated in each bulb, we can use the formula P = VI, where P is power, V is voltage, and I is current. Therefore, the power dissipated in each bulb is 13.75 x 0.56 = 7.7 watts.
To find the voltage across each bulb, divide the total voltage by the number of bulbs:
Voltage across each bulb = Total Voltage / Number of Bulbs = 110V / 8 = 13.75V per bulb
Next, use Ohm's Law to find the resistance of each bulb:
Resistance (R) = Voltage (V) / Current (I) = 13.75V / 0.56A = 24.55Ω per bulb
Finally, find the power dissipated in each bulb using the formula:
Power (P) = Voltage (V) x Current (I) = 13.75V x 0.56A = 7.7W per bulb
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If you are trying to determine if an input variable may affect your key characteristic (output variable) by examining the correlation between variables, which tool should you use?
A. X-bar and R chart
B. p-chart
C. Pareto chart
D. Scatter plot diagram
E. Affinity diagram
If you are trying to determine if an input variable may affect your key characteristic (output variable) by examining the
correlation between variables, you should use the tool: D. Scatter plot diagram. therefore, option D.Scatter plot
diagram is correct.
A scatter plot diagram is a graphical representation of the relationship between two variables. It can help you visualize
the correlation between the input and output variables, making it easier to determine if there is a potential cause-and-
effect relationship.
The tool that you should use to examine the correlation between variables is D. Scatter plot diagram.
A scatter plot diagram is a graphical representation that displays the relationship between two variables.
The x-axis represents the input variable, while the y-axis represents the output variable.
By plotting the data points on the scatter plot diagram, you can visually analyze the correlation between the variables.
If there is a strong positive or negative correlation between the variables, it suggests that the input variable may affect
the key characteristic (output variable).
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D. Scatter plot diagram is the tool that should be used to examine the correlation between variables to determine if an input variable may affect your key characteristic (output variable).
The scatter plot diagram is a graphical representation that displays the relationship between two variables, and it is commonly used to identify patterns, trends, and correlations between variables. By examining the scatter plot diagram, you can determine whether there is a positive, negative, or no correlation between the variables, which can help you to identify potential cause-and-effect relationships.
To determine if an input variable may affect your key characteristic (output variable) by examining the correlation between variables, you should use:
A scatter plot diagram is a graphical tool that helps visualize the relationship between two variables, allowing you to identify any correlation between the input and output variables.
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