which of the following conditions must be met to conduct a two-proportion significance test? the populations are independent. the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population. the sample sizes are greater than 30.
The following conditions must be met to conduct a two-proportion significance test:
the populations are independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.
The two-proportion significance test is a hypothesis test that compares the proportions of two independent populations.
To conduct the two-proportion significance test, the following conditions must be met:
Populations must be independent.
Sample sizes are greater than 30.
The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.
The sample size should be large enough so that the sampling distribution of the sample proportion is nearly normal. The sample sizes should be large enough so that the central limit theorem can be applied.
In short, to conduct a two-proportion significance test, the populations must be independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.
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if the matrix product a1b is known, how could you calculate b1a without necessarily knowing what a and b are?
We can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.
The matrix product of two matrices, A and B, is defined as the matrix C, where C = AB. To calculate the product of two matrices, we must take the dot product of each row of A and each column of B. If we are given a matrix product A1B, then we can calculate B1A without necessarily knowing what A and B are.
To do so, we must first invert the matrix A1B. We can do this by solving a system of equations. We can set up this system of equations by treating the entries of A1B as the coefficients in a system of equations, and solving for the entries of B1A. Once we have found the inverse, we can calculate the matrix B1A.
Finally, once we have the matrix B1A, we can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.
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9 km
7 km
3 km
3 km
3 km
2 km
8 km
9 km
3 km
7 km
Answer: what do you mean? I need more info-
Step-by-step explanation:
I can answer it with more info :)
you roll a dice with 6 sides what is the probability of....... write your answer as a fraction....roll a 5,roll a 6,roll a c or 4,roll an odd number,roll an even nuber,roll a number greater than 3?,roll an even number less that 5?,roll a multiple of 2(2,4,6),roll a factor of 6(6,4,2,1).
Roll a 5: There is only one way to roll a 5 out of six possible outcomes, so the probability of rolling a 5 is 1/6.
Roll a 6: Similarly, there is only one way to roll a 6 out of six possible outcomes, so the probability of rolling a 6 is 1/6.
Roll a c or 4: There are two ways to roll a 4 (rolling a 4 or rolling a 3) and one way to roll a 3, so there are three ways to roll a 4 or c out of six possible outcomes. Therefore, the probability of rolling a 4 or c is 3/6, simplifying it to 1/2.
Roll an odd number: There are three odd numbers (1, 3, 5) out of six possible outcomes, so the probability of rolling an odd number is 3/6, simplifying to 1/2.
Roll an even number: There are three even numbers (2, 4, 6) out of six possible outcomes, so the probability of rolling an exact number is 3/6 or 1/2.
Roll a number greater than 3: There are three numbers greater than 3 (4, 5, 6) out of six possible outcomes, so the probability of rolling a number greater than 3 is 3/6, which simplifies to 1/2.
Roll an even number less than 5: There is only one number less than 5 (2) out of six possible outcomes, so the probability of rolling an actual number less than 5 is 1/6.
Roll a multiple of 2 (2, 4, 6): There are three multiples of 2 out of six possible outcomes, so the probability of rolling a multiple of 2 is 3/6, simplifying to 1/2.
Roll a factor of 6 (1, 2, 3, 6): There are four factors of 6 out of six possible outcomes, so the probability of rolling a factor of 6 is 4/6, which simplifies to 2/3.
So the probabilities for each event expressed as fractions are:
Roll a 5: 1/6
Roll a 6: 1/6
Roll a 4 or c: 1/2
Roll an odd number: 1/2
Roll an even number: 1/2
Roll a number greater than 3: 1/2
Roll an even number less than 5: 1/6
Roll a multiple of 2: 1/2
Roll a factor of 6: 2/3
Angle PQR is isosocles with PQ=PR= 7. 5cm and QR = 9cm. The height PS from P to QR,is 6cm. Find the area of Angle PQR. What will be the height from R to PQ that is RT
The height RT from R to PQ is approximately 3.16 cm.
To find the area of triangle PQR, we can use the formula:
Area = 1/2 * base * height
Since PQR is isosceles with PQ = PR, the base is PQ or PR. We can choose PQ as the base. Then the height is PS.
Area of PQR = 1/2 * PQ * PS
Since PQ = PR = 7.5 cm and PS = 6 cm, we can substitute these values into the formula and simplify:
[tex]Area of PQR = 1/2 * 7.5 cm * 6 cm[/tex]
[tex]Area of PQR = 22.5 cm^2[/tex]
Therefore, the area of triangle PQR is [tex]22.5 cm^2[/tex].
To find the height RT from R to PQ, we can use the Pythagorean theorem.
Let's draw a perpendicular line from R to PQ, intersecting at T. Then we have a right triangle PRT with hypotenuse PR and legs PT and RT.
Since PQR is isosceles, we can also see that angle PQR is equal to angle PRQ. Therefore, angles PQR and PRQ are equal and each is approximately 69.3 degrees (using inverse cosine function).
Using the sine function, we can find the length of PT:
sin(69.3) = PT / 7.5
PT = 7.5 * sin(69.3)
PT ≈ 6.93 cm
Using the Pythagorean theorem, we can find the length of RT:
[tex]RT^2 + PT^2 = PR^2[/tex]
[tex]RT^2 = PR^2 - PT^2[/tex]
[tex]RT^2 = 7.5^2 - 6.93^2[/tex]
RT ≈ 3.16 cm
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To make cleaning easier, a rectangular horse trough will be lined with plastic. The trough is 40 inches long, 14 inches wide, and 24 inches deep. How many square inches of plastic are needed to line the trough? Count only the trough's five faces. A net containing 5 rectangles. Two rectangles have length of 40 inches and width of 14 inches. Two rectangles have length of 14 inches and width of 24 inches. One rectangle has length of 40 inches and width of 24 inches.
Using the area formula for the rectangle, we can find that 2752 in² of plastic is needed to line the trough.
Define area?To determine the area a rectangle occupies within its perimeter, apply the formula for calculating a rectangle's area. Multiplying the length by the width yields the area of a rectangle (breadth).
As a result, the area of a rectangle with the length and breadth l and w, respectively, is calculated as follows. L × W = the rectangle's area. Hence, the area of a rectangle is equal to (length width).
Now in the given question,
We have 5 faces of the cuboid.
Now to find the total area of the required space we have to find the area of all the rectangles.
Area of rectangle with dimensions, l = 40inches and b = 14 inches.
Area = l × b
= 40 × 14
= 560in²
Now there are 2 rectangles with the same dimensions, so the total area = 560 + 560 = 1120in².
Now area of rectangles with dimensions, l = 14 inches and b = 24 inches.
Area = l × b
= 14 × 24
= 336in².
There are 2 rectangles with the same dimensions, so area = 336 + 336 = 672in².
Area of the final rectangle = l × b
= 40 × 24
= 960in².
So, the total required area = 1120 + 672 + 960 = 2752in².
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8x 2 + [ 3x3-8] = with explanation pls and its due in six minutes
Answer: 16x+3x^3−8
Please mark me brainliest :)
Covert 1/4 to seconds
Answer:
a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds
Answer:
90 seconds
Step-by-step explanation: We know that,
A quarter of an hour= 60×1/4 =15 mins
15 minutes is equal to 15 minutes × 60 = 90 seconds.
what is the probability that the first question she gets right is question number 4? group of answer choices
The probability that the first question she gets right is question number 4, is 0.1054.
Number of options there are for a single query = 4
P(guessing correct answer for a single question) = 1/4
P(guessing correct answer for a single question) = 0.25
Probability of getting correct answer P(correct) = 0.25
Probability of getting wrong answer P(wrong) = 1 - Probability of getting correct answer
Probability of getting wrong answer P(wrong) = 1 - 0.25
Probability of getting wrong answer P(wrong) = 0.75
So, the probability that the first question she gets right is question number 4 = Probability of getting 1st question wrong × Probability of getting 2nd question wrong × Probability of getting 3rd question wrong × Probability of getting 4th question right
The probability that the first question she gets right is question number 4 = 0.75 × 0.75 × 0.75 × 0.25
The probability that the first question she gets right is question number 4 = 0.1055
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The complete question is:
In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. (Round your answers to four decimal places.)
What is the probability that the first question she gets right is question number 4?
five girls and five boys randomly sit in ten seats that are equally spaced around a circle. the probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is , where and are relatively prime positive integers. find .
The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is [tex]\frac{7}{12}[/tex] , where 7 and 12 are relatively prime positive integers. The answer is 7+12=19.
The probability that there is at least one diameter of the circle with two girls sitting on opposite ends of the diameter is 1 minus the probability that no diameter of the circle has two girls sitting on opposite ends of the diameter.
There are
[tex]{10\choose5}[/tex] =252
ways to seat the five girls and five boys.
There are 5 ways to choose a diameter of the circle.
Once this diameter is fixed, there are [tex]{5\choose2}[/tex] = 10 ways to choose a pair of seats on the diameter to place two girls (in the order in which they appear counterclockwise).
There are 5!=120 ways to seat the remaining 3 girls and 5 boys such that no two girls sit on the same diameter.
Hence, there are [tex]5\cdot10\cdot120[/tex] =6000 valid seatings that satisfy the condition in the question.
Thus, the desired probability is 1 - [tex]\frac{6000}{252}[/tex] = [tex]\frac{7}{12}[/tex], as stated above.
Thus, the answer is 7+12 = [tex]\boxed{19}[/tex]
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The point on the graph represents Ann's location. She is using a metal detector on the beach to see what she can find. Each unit on the graph represents 2 feet. A pile of bottle caps is located at (4, -10). Find the length of the most direct path between Ann and the pile of bottle caps. Round to the nearest whole number.
Answer:
30 feet
Step-by-step explanation:
Coordinates of Ann: (-4,3)
Coordinates of bottle caps: (4,-10)
Distance from Ann to bottle caps can be found out using the distance formula:
[tex]x_2=4, x_1=-4\\y_2=-3,y_1=-10\\Distance=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2 } \\=\sqrt{(4-(-4))^2 + ((-10)-3)^2} \\=15.26\\15\text{ is the answer}[/tex]
Six flags Great America sells adult tickets for $68 each and children tickets for $47 each. A middle school wants to take students and teachers on a field trip to Six Flags for spring break. The school has a budget of spending at most $12000. They can also only take no more than 225 teachers and students.
The school can purchase 91 adult tickets and 41 children tickets, allowing for a total of 132 teachers and students to go on the trip within the budget of $12000.
Let's start by defining some variables to represent the quantities we're interested in: Let A be the number of adult tickets purchased. Let C be the number of children tickets purchased. Let T be the total number of teachers and students who go on the trip. To maximize the number of teachers and students while staying within budget, we can use linear programming. The objective function is N = T - A - C, where N is the number of teachers and students. The inequalities are 68A + 47C ≤ 12000 and T ≤ 225. Solving this linear program, we find that the school can purchase 91 adult tickets and 41 children tickets, allowing for a total of 132 teachers and students to go on the trip within the budget of $12000.
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the complete question :
A middle school wants to take students and teachers on a field trip to Six Flags Great America for spring break. The school has a budget of spending at most $12,000. They can also only take no more than 225 teachers and students. The adult tickets cost $68 each, and children tickets cost $47 each. How many adults and children can the school take to Six Flags within the given budget and attendance limit?
How to turn 0. 1212121212 into a simplified fraction
Answer:
4/33
Step-by-step explanation:
You want to write 0.1212...(repeating) as a simplified fraction.
Repeating decimalA repeating decimal beginning at the decimal point can be made into a fraction by expressing the repeating digits over an equal number of 9s.
Here, there are 2 repeating digits, so the basic fraction is ...
12/99
This can be reduced by removing a factor of 3 from numerator and denominator:
[tex]0.\overline{12}=\dfrac{12}{99}=\boxed{\dfrac{4}{33}}[/tex]
__
Additional comment
Formally, you can multiply any repeating decimal by 10 to the power of the number of repeating digits, then subtract the original number. This gives the numerator of the fraction. The denominator is that power of 10 less 1.
0.1212... = (12.1212... - 0.1212...)/(10^2 -1) = 12/99
Doing this multiplication and subtraction also works for numbers where the repeating digits don't start at the decimal point. Finding a common factor with 99...9 may not be easy.
You can also approach this by writing the number as a continued fraction. The basic form is ...
[tex]x=a+\cfrac{1}{b+\cfrac{1}{c+\cdots}}[/tex]
where 'a' is the integer part of the original number, and b, c, and so on are the integer parts of the inverse of the remaining fractional part. The attachment shows how this works for the fraction in the problem statement.
A calculator cannot actually represent a repeating decimal exactly, so error creeps in and may eventually become significant.
Jason has a block of clay that is made up of two rectangular pieces of
different colors. Find the volume of the block of clay.
The measurements of the two clay blocks are:
6 cm
4 cm
3 cm
5 cm
Answer: 132 cubic centimeters
Step-by-step explanation:
To find the volume of the block of clay, we need to add the volumes of the two rectangular pieces.
The volume of a rectangular solid can be found by multiplying its length, width, and height. Let's call the first rectangular piece A and the second rectangular piece B. Then the dimensions of A are 6 cm (length), 4 cm (width), and 3 cm (height), and the dimensions of B are 5 cm (length), 4 cm (width), and 3 cm (height).
The volume of A is:
Volume of A = length x width x height = 6 cm x 4 cm x 3 cm = 72 cubic centimeters
The volume of B is:
Volume of B = length x width x height = 5 cm x 4 cm x 3 cm = 60 cubic centimeters
So the total volume of the block of clay is:
Volume of block = Volume of A + Volume of B = 72 cubic centimeters + 60 cubic centimeters = 132 cubic centimeters
Therefore, the volume of the block of clay is 132 cubic centimeters.
Noah was at home. He got on his bike and rode to his friends
Answer:
what's your exact question
Answer:
can u pls type the full question
The supplement of an angle is 30 more than twice its complement. What is the measure of the
angle?
Answer: 30
180 - x = 180 - 2x + 30
x = 30
Answer:
The measure of the unknown angle is 30°.
Step-by-step explanation:
Let the measure of the unknown angle be x°.
Supplementary angles are two angles whose measures sum to 180°.
Complementary angles are two angles whose measures sum to 90°.
Therefore, the supplement of x° is (180 - x)°, and its complement is (90 - x)°.
Given that the supplement is 30° more than twice its complement:
(180 - x)° = 2(90 - x)° + 30°
To find the measure of the angle, solve the equation:
⇒ (180 - x)° = (180 - 2x)° + 30°
⇒ 180° - x° = 180° - 2x° + 30°
⇒ 180° - x° = 210° - 2x°
⇒ 180° - x° + 2x° = 210° - 2x° + 2x°
⇒ 180° + x° = 210°
⇒ 180° + x° - 180° = 210° - 180°
⇒ x° = 30°
Therefore, the measure of the unknown angle is 30°.
GIVING BRAINLIEST FOR THE CORRECT ANSWER (i need a proof that what you’re saying is right bc ppl are giving me the wrong answers)
Answer:
x [tex]\geq[/tex]2
Step-by-step explanation:
Since the arrow is pointing to the right, we know that it is greater than two. We also know that it could be equal to 2 because the dot is filled in on the number line. So, the answer is x is greater than or equal to 2.
Determine whether segment lengths form a triangle. If so, classify the triangle as acute, right or obtuse.
1. 10, 7, sqrt(658)
Answer:
it is a triangle bc it has angles of points
Step-by-step explanation:
a children's liquid medicine contains 100 mg of the active ingredient in 5 ml . if a child should receive 300 mg of the active ingredient, how many milliliters of the medicine should the child be given? for the purposes of this question, assume that these numbers are exact.
The child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.
The given problem requires us to determine the number of milliliters of a liquid medicine that a child should receive in order to obtain a specific dosage of the active ingredient. We are given that the medicine contains 100 mg of the active ingredient in 5 ml.
The child needs to receive 300 mg of the active ingredient, and there are 100 mg of the active ingredient in 5 ml of the medicine. Therefore, the child should be given:
[tex]\frac{300 mg}{100mg/5ml} = \frac{300\text{ mg} \times 5\text{ ml}}{100\text{ mg}} = 15\text{ ml}$$[/tex]
So the child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.
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Philippe knows there is a $20\%$ chance that it will rain tomorrow and an $80\%$ chance that it will not rain tomorrow. Part A Philippe considers making a spinner to simulate the probability of it raining tomorrow. Describe what the spinner could lPhilippe knows there is a $20\%$ chance that it will rain tomorrow and an $80\%$ chance that it will not rain tomorrow. Part A Philippe considers making a spinner to simulate the probability of it raining tomorrow. Describe what the spinner could look like and the steps he should take to perform the simulation. Ook like and the steps he should take to perform the simulation
Philippe can perform a simulation of rain or no rain for tomorrow by spinning a spinner with two sections labeled "Rain" and "No rain."
The spinner could be divided into two sections, one labeled "Rain" and the other labeled "No rain." To perform the simulation, Philippe would need to give the spinner a spin and observe which section it lands on. If it lands on the "Rain" section, he would consider that as an outcome of rain for tomorrow, and if it lands on the "No rain" section, he would consider that as an outcome of no rain for tomorrow. To make the simulation more accurate, he could repeat the process multiple times and record the number of times the spinner lands on each section.
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Proportions
Two plus x divided by twelve equals one dived by three. Solve for x.
Two plus x divided by twelve equals one divided by three
Case 1 :
Rewrite into numbers : 2 + x /12 = 1/3
-> x/12 = 1/3 - 2 = -5/3
-> x = -5/3 x 12 = -20
Case 2 :
Rewrite into numbers : (2 + x)/12 = 1/3
-> 2 + x = 1/3 x 12 = 4
-> x = 4 - 2 = 2
i dont know if you meant it the right way or the wrong way but ill just put them both
x=2
Step-by-step explanation:
(2+x)/12=1/3
3(2+x)=12
2+x=4
x=4-2
x=2
help me, please I will give 30 points
We can solve the system by elimination without multiplying first only when, [tex]$a = 8$[/tex].
How to solve the system by elimination?To solve the system by elimination, we want to eliminate one of the variables, either x or y, from one of the equations. To do this, we need to find a multiple of one equation that cancels out one of the variables in the other equation.
We can eliminate x by multiplying the first equation by -4 and adding it to the second equation:
[tex]-4(ax+3y) + (4x+5y) &=\\ -4(7) + 15\(-4a+4)x + (5-12)y &=\\ -13\ (4-4a)x - 7y &= -13[/tex]
By adding the first equation to the second equation and multiplying it by -4, we can get rid of x:
[tex](4-4a)x-7y=13\\4x+5y=15[/tex]
We can eliminate y by multiplying the second equation by 7 and subtracting it from the first equation:
[tex](4-4a)x - 7y &=\\ -13-28x - 35y &=\\ -105[/tex]
Simplifying this last equation, we get:
[tex](4a-4)x &= 28x\\4a &= 32\\a &= 8[/tex]
Therefore, we can solve the system by elimination without multiplying first only when, [tex]$a = 8$[/tex].
For any other value of a, we need to multiply one or both equations by a constant before we can eliminate a variable.
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the number of hours needed to complete a trip, h, varies inversely with the driving speed, s. a trip can be completed in 5 hours at a speed of 60 miles per hour. find the equation that represents this relationship.
The equation that represents the relationship between the number of hours needed to complete a trip, h, and the driving speed, s, is h = 5/s. This means that the number of hours needed to complete the trip is inversely proportional to the driving speed.
When the driving speed is 60 miles per hour, the number of hours needed to complete the trip is 5 (h = 5/60). If the driving speed is increased to 90 miles per hour, the number of hours needed to complete the trip is 5/90 (h = 5/90).
In general, as the driving speed increases, the number of hours needed to complete the trip decreases.
To summarize, the equation that represents the inverse relationship between the number of hours needed to complete a trip and the driving speed is h = 5/s. This equation can be used to determine the number of hours needed to complete a trip at any given speed.
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pizzas are sized by diameter. what percent increase in area results if chantel's pizza increases from a 10-inch pizza to a 12-inch pizza?
Step-by-step explanation:
Area of circle = pi r^2
10 inch = pi (5)^2 = 25 pi
12 inch = pi (6)^2 = 36 pi
12 inch is 11pi bigger
percentage: 11 pi is what percentage of 25 pi ?
11 pi / 25 pi x 100% = 44 % bigger
The area of a pizza increases with the square of the diameter. Therefore, a 10-inch pizza has an area of [tex]π*(10/2)^2= 78.54[/tex] square inches, and a 12-inch pizza has an area of [tex]π*(12/2)^2 = 113.10[/tex] square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%.
To explain further, the diameter of a pizza is measured from one side to the other through the center of the pizza. As the diameter of the pizza increases, the area of the pizza increases. This is because the area of a pizza is calculated as [tex]π*(d/2)^2[/tex], where d is the diameter. So, if the diameter increases, the area increases as well.
For example, if a 10-inch pizza has an area of 78.54 square inches, a 12-inch pizza would have an area of 113.10 square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%. This is because the diameter of the pizza has increased by 2 inches (10 inches to 12 inches), and the area has increased by 44.2%.
It is important to note that increasing the diameter of the pizza does not just increase the circumference of the pizza, but also the area. The increase in area is directly related to the increase in diameter, and can be calculated by taking the difference between the areas of the two pizzas.
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suppose there is $600 in the account with an annual interest rate of 4%. after how many years will the amount triple?
it will take approximately 22.56 years for the amount to triple.
The given information for this problem is that there is an initial investment of $600 in an account with an annual interest rate of 4%. The task is to determine after how many years the amount will triple.Using the compound interest formula, we can find the amount in the account after t years:A = P(1 + r/n)nt Where,A = final amount in the account, P = initial amount in the account r = annual interest rate ,n = number of times the interest is compounded per year ,t = time in years.
From the problem statement, we know that the initial amount, P, is $600 and the annual interest rate, r, is 4%. Let's assume that the interest is compounded annually, i.e., n = 1.Substituting these values in the formula, we get:A = $600(1 + 0.04/1)1t Simplifying this expression,A = $600(1.04)t.
Taking the ratio of the final amount to the initial amount, we get: 3P = $600 × 3 = $1800. Therefore,A/P = 3 = (1.04)t.Dividing both sides by P, we get:3 = (1.04)t ln(3) = ln(1.04)t. Using the logarithmic property, we can bring down the exponent to the front:ln(3) / ln(1.04) = t Using a calculator, we get ≈ 22.56. Therefore, it will take approximately 22.56 years for the amount to triple.
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Assume that Item is some class available to the code below and that n and m are two integer variables correctly initialized. Consider the following array declaration and initialization. Item[][] list= new Item[n][m]; What expression would give the total number of elements in the array list? O n*m O (n-1) * (m - 1) O n+m On + m - 1 1 O n.length * m.length
Therefore, the expression that would give the total number of elements in the array list is n*m.
The Student question is given below :Assume that Item is some class available to the code below and that n and m are two integer variables correctly initialized. Consider the following array declaration and initialization.
[tex]Item[][] list= new Item[n][m];[/tex]
What expression would give the total number of elements in the array list?
The expression that would give the total number of elements in the array list is n*m. The given array declaration and initialization is Item[][] list= new Item[n][m]; This declaration and initialization signify that the array list is a 2D array with n rows and m columns. The total number of elements in this array can be determined by computing the product of the total number of rows (n) and the total number of columns (m).
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The triangles are similar. Find the value of x.
Since the triangles are similar, the value of x is equal to: C. 18 units.
What are the properties of similar triangles?In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
By applying the properties of similar triangles, we have the following ratio of corresponding side lengths;
AC/RS = AB/RT
By substituting the given side lengths into the above equation, we have the following:
x/24 = 24/32
By cross-multiplying, we have the following;
32x = 24(24)
32x = 576
x = 576/32
x = 18 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Out of 80 customers at an ice cream van, 48 had syrup, 28 had sprinkles and 16 had both
toppings on their ice cream. Use a Venn diagram to find the probability that a randomly
selected customer doesn't have either topping, given that they don't have sprinkles.
I know the answer is 20/52, I just can’t work out how to get to that answer…
Answer:
20/52 or simplified to 5/13
Step-by-step explanation:
The Venn Diagram is provided
Let
n(A) = number of customers who had syrup
n(B) = number of customers who had sprinkles
n(A and B) = number of customers who had both syrup and sprinkles = 16
This would be the number in the overlapping region
n(A or B) = number of customers who had either syrup or sprinkles or both
= n(A) + n(B) - n(A and B)
= 48 + 28 - 16
= 60
Therefore number of customers who had neither topping = 80 - 60 = 20
This number is indicated outside both circles but within the rectangle
The number of customers who had only syrup is given by set difference
= No. of customers who had syrup - No. of customers who had both
= n(A) - n(A and B)
= 48 - 16
= 32
This is the figure inside the left circle
Let's consider the statement: Customers who didn't have sprinkles
This would be customers who had only syrup(32) + customers who had neither topping(20)
= 32 + 20 = 52
Number of customers who did not have either topping = 20
P(selected customer doesn't have either topping, given that they don't have sprinkles)
= 20/52
= 5/13
the stopping distance s of a car varies directly as the square of its speed v. if a car traveling at 40 mph requires 80 ft to stop, find the stopping
If a car traveling at 40 mph requires 80 feet to stop, the stopping distance S of a car varies directly as the square of its speed v and is equal to 180 feet.
Given, the stopping distance S of a car varies directly as the square of its speed v. So the relation can be represented as,
S ∝ v2
Here, the constant of proportionality is k.
S = kv2 ——— (1)
Given, when the speed v = 40 mph, stopping distance s = 80 feet.
Therefore, from equation (1), we have
80 = k × 402
k = 80/1600
k = 0.05
Hence, the relation between the stopping distance S and the speed v of the car can be given as
S = 0.05v2
To find the stopping distance S of the car at speed v = 60 mph, substitute v = 60 in the above equation.
S = 0.05 × 602
S = 0.05 × 3600
S = 180 feet
Therefore, the stopping distance of a car traveling at 60 mph would be 180 feet.
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if the odds on a bet are 16:1 against, what is the probability of winning? express your answer as a fraction.
The probability of winning is 1/17, which can also be expressed as a decimal (approximately 0.059) or as a percentage (approximately 5.9%).
The odds on a bet represent the ratio of the probability of winning to the probability of losing. In this case, the odds are 16:1 against winning, which means that the probability of winning is 1 out of 16.
To express this probability as a fraction, we can use the formula:
Probability of winning = 1 / (odds + 1)
Plugging in the given odds, we get:
Probability of winning = 1 / (16 + 1)
Probability of winning = 1/17
In this case, the odds of 16:1 against winning correspond to a probability of 1/17, which represents the chance of winning the bet.
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