Using traditional methods it takes 8.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 21 students and observed that they had a mean of 8.8 hours with a variance of 1.21 . Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Assume the population distribution is approximately normal. Step 1 of 5 : State the null and alternative hypotheses
Answers
As the p-value of the test is of 0.215 > 0.05, there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
What are the null and the alternative hypothesis?At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:
[tex]H_0: \mu = 8.5[/tex]
At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:
[tex]H_1: \mu \neq 8.5[/tex]
What is the test statistic?The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.
The equation is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]
Hence the test statistic is calculated as follows:
[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}}[/tex]
z = (8.8 - 8.5)/(1.11/square root of 21)
z = 1.24.
What is the p-value and conclusion?The p-value is obtained using a z-distribution calculator.
We have a two-tailed test, as we are testing if the mean is different of a value, with a test statistic of z = 1.24, hence the p-value is of:
0.215.
(2 multiplied by the subtraction of one and the p-value of z = 1.24).
The p-value is greater than the significance level of 0.05, meaning that there is not enough evidence to reject the null hypothesis and conclude that there is a difference between the two methods.
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Related Questions
29. Jamie spent $56 for blue blouse. A red blouse cost two-thirds of this price. What was the cost of the red blouse? PLEASE HELP ME WITH THIS QUESTION MY MATH TEACHER WILL BE VERY UPSET PLEASEEE!!!
Answers
2. Noah said the equation 1. 20(d+5)=42 also represents the situation. Do you agree with Noah? Explain your reasoning ✓ Share with Class
Answers
No, I'm not agree with Noah. Because the equation 1. 20(d+5)=42 is a mathematical equation and can be false depending on the value of the variable d.
THE EQUATION REPRESENT SITUATION BY VARIABLEThe equation 1. 20(d+5)=42 is a mathematical equation that contains a variable d. The equation states that when you multiply 20 with (d+5) the result should be 42.
The equation is true if there is a value of d that makes the equation true. For example, if d=1, then 20(1+5)=20(6)=120 which is not equal to 42, so this value of d does not make the equation true.
On the other hand, if d=-7, then 20(-7+5)=20(-2)= -40 which is equal to 42, so this value of d makes the equation true.
Therefore, the equation can be true or false depending on the value of the variable d. In general, without knowing the specific context or situation in which the equation is being used, it is impossible to determine if the equation accurately represents a situation or not.
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In an amphitheater, eat are aranged in 50 emi-circular rowfacing a dome tate. The firt row contain 23 eat, and each row contain4more eat than the previou row. How many eat are in the amphitheater?
Answers
In an amphitheater, seat are arranged in 50 semi-circular row-facing a dome Tate. The first row contain 23 seat, and each row contain 4 more eat than the previous row. Therefore, there are 6050 seat are in the amphitheater.
Given that:
There are total 50 semi circular row.
In the first row there are 23 seats.
The given problem is AP series:
Arithmetic Series:
An arithmetic sequence is defined as an algebraic sequence in which each successive term has an equal difference. It is obtained by adding a constant to any preceding term. For the first term 'a' and the tolerance 'd' of the AP, here is a list of commonly used arithmetic progressions to solve various AP related problems:
Common Difference of AP: d = a2 - a1 = a3 - a2 = a4 - a3 = an - a(n-1) nth term of AP.AP: an = a + (n - 1)d of AP Sum of n terms: Sn = n/ 2( 2a+(n-1)d) = n/2(a + l),where l is the last term in the arithmetic progression.
Now,
Sum of n terms = n/2 [ 2a + (n-1)d]
= 50/2 [ 2× 23 + (50 -1)4]
= 25 [46 + 49×4]
= 25 × 242
= 6050
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three cards are chosen from a pack of 52 cards. what is the probability that they are not all the same color
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Three cards are chosen from a pack of 52 cards. what is the probability that they are not all the same color is 0.8824 or 88.24%
What is the definition of probability?The likelihood or chance that a specific event will occur is represented by a probability.
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportion with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Given that three cards are chosen from a pack of 52 cards.
There are 26 cards of each color (i.e. 26 cards are red color and 26 cards are of black color)
The probability of drawn first card of any one color is
P(1)= 26/52 = 1/2
The probability of drawn second card of same color is
P(2)= 25/51
The probability of drawn third card of same color is
P(3)= 24/50 = 12/25
The probability of having three cards are same color is
P = P(1)*P(2)*P(3)
P = 1/2 * 25/51 * 12/ 25
P = 6/51
So the probability that three cards are not all the same color is
P' = 1 - P
P' = 1 - 6/51
P' = (51-6)/51
P' = 45/51 = 15/17
P' = 0.8824
The likelihood that the three cards are not all red is roughly 0.8824, or 88.24%,
.
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Albert is a marine biologist studying the bluefin tuna population in Caro Bay. When he first started monitoring the population, there were about 1,550 bluefin tuna in the bay. One year later, he estimated that the population of bluefin tuna had decreased to about 1,488. Albert expects the population of bluefin tuna to continue decreasing each year.
Write an exponential equation in the form y=a(b)x that can model the population of bluefin tuna in Caro Bay, y, x years after Albert began monitoring it.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
Answers
The exponential function that models the population of bluefin tuna after x years is given as follows:
y = 1550(0.96)^x.
The parameters of the exponential function are given as follows:
a = 1550.b = 0.96.How to define the exponential function?An exponential function is defined as follows:
y = a(b)^x.
For which the parameters are given as follows:
a is the initial value.b is the rate of change.When he first started monitoring the population, there were about 1,550 bluefin tuna in the bay, meaning that the parameter a is given as follows:
a = 1550.
One year later, he estimated that the population of bluefin tuna had decreased to about 1,488, hence the parameter b is obtained as follows:
b = 1488/1550 = 0.96.
Hence the function is defined as follows:
y = 1550(0.96)^x.
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HELP PLEASE IVE BEEN STUCK ON THIS PROBLEM ALL DAY
Answers
The table that is a justification for the given solution to the system of equations is table 1
How to determine the table that bears the correct values?The two linear equations are
y=4x-9 and
y=2x-5
We that the following points for x : -1, 0, 1, 2, 3
When we substitute the values in the two equations we will have
x y₁ y₂
-1 -13 -9
0 -9 -5
1 -5 -3
2 -1 - 1
3 3 1
Conclusively the values of y₁, and y₂ are shown in the table above
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Match the partition type to its description.
1 . Logical partition A partition with an extended partition 2 . System partition The partition where you place the boot loader 3 . Primary partition The section of the hard drive that will become the bootable drive
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Logical partition - A partition within an extended partition
System partition - The partition where you place the boot loader
Primary partition - The section of the hard drive that will become the bootable drive
IBM and Microsoft initially kept internal lists of designated partition types to be used in the MBR partition table. As the market for PC operating systems and disc tools expanded and became more open, other suppliers also needed to give their products specialised partition kinds. Third parties began to merely allocate partition types on their own behalf in a largely uncoordinated trial-and-error fashion because Microsoft neither documented all of the partition types already given by them nor wished to retain foreign assignments. This resulted in several conflicting assignments, which occasionally caused serious compatibility issues between certain products. [1]
In the 1990s, a number of industry professionals including Hale Landis, Ralf D. Brown, Matthias R. Paul, and Andries E. Brouwer began investigating partition kinds.
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For the function Y= X +4 what is the output value if three is the input value
Answers
Answer: 7
Step-by-step explanation:
1. You need to know that the input value means the x-value, which means x = 3.
2. Input 3 in the function
3. Solve 3+4
4. 3+4 = 7
Answer:
put y=4 then four comes with- and 4-3=2
If you have 20 balls (10 black, 10 white) and two urns, how could you place the balls into the urns so as to maximize your chance of drawing a black ball
Answers
To fill one urn with one white ball and the second urn with the remaining nine white and ten black balls.
Explain about the probability?Probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. A coin flip is the most basic illustration. There are only two outcomes that can occur when you flip a coin: either heads or tails.
The basic probability formula is: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or P(A) = f/N
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Robin tosses a pair of 6-sided dice. The odds in favor of the sum of the 2 dice rolls being greater than 8 are 5:13.
What is the probability that the sum of the 2 dice rolls will not be greater than 8?
Answers
The probability that the sum of the 2 dice rolls will not be greater than 8 are 8 : 13.
How to evaluate for the probabilityWhen the probability of an event occurring is know, it is easy to calculate the probability that the event does not occur. Hence, If P(A) is the probability of event A, then 1 - P(A) is the probability that the event does not occur.
the probability that the sum of the 2 dice rolls being greater than 8 are expressed in the ratio 5:13 and expressed in fraction as 5/13
then;
probability that the sum of the 2 dice rolls will not be greater than 8 = 1 - 5/13
probability that the sum of the 2 dice rolls will not be greater than 8 = (13 - 5)/13
probability that the sum of the 2 dice rolls will not be greater than 8 = 8/13
Therefore probability that the sum of the 2 dice rolls will not be greater than 8 can be expression as the ratio 8 : 13
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A single-engine plane can travel up to 140 miles per hour. The total number of miles m is represented by the function m = 140h, where h is the number of hours traveled. Determine appropriate input values for this situation.
Answers
Answer: The input values for this function are the number of hours traveled, represented by the variable h. Therefore, appropriate input values for this function would be any positive number representing a number of hours traveled.
For example, some appropriate input values could be:
h = 1: This represents 1 hour of travel, or a total distance of 140 miles.
h = 2: This represents 2 hours of travel, or a total distance of 280 miles.
h = 3.5: This represents 3.5 hours of travel, or a total distance of 490 miles.
Note that the input values do not have to be whole numbers, they can be any positive number representing a number of hours traveled.
Step-by-step explanation:
How many five ounce glasses of wine have the same alcohol content as one 12-ounce beer? responses one one two two three three four
Answers
A total of 3 five ounces glass are needed so have the same alcohol as that of a 12 ounce glass.
In order to find the number of glass of capacity five ounces that will have the same capacity as that of the twelve ounce glass can be calculated as followed,
Let us say that n number of five ounces glasses are required to equate 12 ounce glass.
Now, we can write the relation,
using simple algebra,
n(Five ounces glasses) = 1 Ounce alcohol content
n = 12/5
n = 2.4
But, we have to answer an integral value, so, we will say that the required number of the glasses is 3.
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Mr. Brust can eat 3/4 of a bucket of wings in 3/4 hour. How many wings does Mr. Brust eat in one hour?
Answers
Answer:
1 bucket
Step-by-step explanation:
3/4 buckets = 3/4 hours
multiply both sides by 4/3 to get one hour
(4/3) * (3/4) buckets = (4/3) * (3/4) hours
1 bucket = 1 hour
40% of Damien‘s marbles are blue. Damien has three marbles how many of the marbles are not blue
Answers
40% of Damien’s marbles are 6/5 or 1.2.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Damien has three marbles.
40% of Damien’s marbles are blue.
That means,
40% of 3 blue marbles.
So, using the percentage formula,
40% of 3,
= 40 x 3/100
= 120/100
= 12/10
= 6/5
= 1.2
Therefore, 1.2 marbles are blue.
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Mrs. Campos is making cupcakes for a bake sale. She uses the equation c = 0. 55x to determine the cost, c, for x cupcakes. Which best represents the constant rate at which cupcakes are sold at the bake sale?
55 cupcakes per dollar
$0. 55 per cupcake
$4 per cupcake
4 cupcakes per dollar
Answers
Best represents the constant rate at which cupcakes are sold at the bake sale $0. 55 per cupcake
Mrs. Campos is making cupcakes for a bake sale. She uses the equation c = 0. 55x to determine the cost, c, for x cupcakes. Which best represents the constant rate at which cupcakes are sold at the bake sale?
55 cupcakes per dollar
$0. 55 per cupcake
$4 per cupcake
c = 0. 55x
to determine the cost, c,
for x cupcakes.
CASE 1
55 cupcakes per dollar
therefor x = 55
c = 0. 55x
c = 0. 55 × 55
= 30.25
case2
$0. 55 per cupcake
x = 1
c = 0. 55x
c = 0. 55 × 1
= 0. 55
case 3
$4 per cupcake
x = 1
c = 0. 55x
c = 0. 55 × 1
= 0. 55
therefor conclusion is best represents the constant rate at which cupcakes are sold at the bake sale $0. 55 per cupcake
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(2x + 5) (4x − 3) (5x - 4) can be expanded and fully simplified to give an expression of the form ax³ + bx² + cx + d.
Work out the values of a, b, c and d.
Answers
Answer:
To expand (2x + 5) (4x − 3) (5x - 4), you can use the distributive property and the FOIL method.
The distributive property states that for any two algebraic expressions a and b, and for any two numbers x and y, (a+b)(x+y) = ax + ay + bx + by.
The FOIL method is a way to multiply two binomials. It stands for First, Outside, Inside, Last, and it involves multiplying the first term of the first binomial by the first term of the second binomial, the first term of the first binomial by the second term of the second binomial, the second term of the first binomial by the first term of the second binomial, and the second term of the first binomial by the second term of the second binomial.
Using these methods, you can expand (2x + 5) (4x − 3) (5x - 4) as follows:
(2x + 5) (4x − 3) (5x - 4) = (2x)(4x)(5x) + (2x)(4x)(-4) + (2x)(-3)(5x) + (2x)(-3)(-4) + (5)(4x)(5x) + (5)(4x)(-4) + (5)(-3)(5x) + (5)(-3)(-4)
This can be simplified to:
= 40x³ - 32x² - 60x³ + 48x² - 20x³ + 15x² + 60x - 20x + 100x² - 20x + 12
Combining like terms, we get:
= -12x³ + 143x² + 100x + 12
So, the values of a, b, c, and d are a = -12, b = 143, c = 100, and d = 12.
Step-by-step explanation:
Your mortgage payment is $954. 32/month. Using proportions, what is the minimum yearly amount you must have in realized income to keep your housing expenses in the acceptable range? $Fill in the blank text field 1
Answers
The mortgage payment exists $954. 32/month then the annual realized income exists 42,414.22.
What is meant by mortgage payment?Principal, interest, taxes, and insurance make up the majority of mortgage payments. Your outstanding loan balance is reduced by the amount in the principal part. Borrowing money has a cost, which is interest. Both the interest rate and the loan balance affect how much interest you pay.
You repay your mortgage loan through monthly payments. This will often be a monthly payment that aids in your gradual mortgage repayment. There will also be taxes, insurance premiums, and loan interest due.
Assume a mortgage repayment schedule that is reasonable, using 27% of gross monthly income.
The product of the monthly mortgage payment by 12 months, divided by the acceptable rate, yields the annual realized income.
[tex]$& \frac{\text { Mortgage }}{\text { Acceptable Rate\% }} * 12 \\[/tex]
substitute the values in the above equation, we get
[tex]$& =\frac{954.32}{0.27} * 12[/tex]
= 42,414.22
Therefore, the annual realized income exists 42,414.22.
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The mortgage payment exists $954. 32/month then the annual realized income exists 42,414.22.
What do you mean by mortgage payment?Generally speaking, mortgage payments are made up of principal, interest, taxes, and insurance. The sum in the principle component is deducted from your outstanding loan balance. Interest is a cost associated with borrowing money. The amount of interest you pay depends on both the interest rate and the loan balance.
Monthly payments are made to pay down your home loan. This will frequently be a monthly payment to help you slowly pay down your mortgage. Taxes, insurance premiums, and loan interest will all need to be paid.
Assume a mortgage repayment schedule that is reasonable, using 27% of gross monthly income.
The product of the monthly mortgage payment by 12 months, divided by the acceptable rate, yields the annual realized income.
[tex]\frac{Mortage}{Acceptable rate } *12[/tex]
substitute the values in the above equation, we get
[tex]\frac{954.32}{0.27} *12[/tex]
= 42,414.22
Therefore, the annual realized income exists 42,414.22.
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A barrel shaped like a cylinder is laid on its side and rolled up a ramp. The barrel has a circular base that is 1.1 inches in diameter. If the barrel turns 47 times in being rolled up the ramp, how long is the ramp?
Answers
The length of the ramp is 161.62 inches when the barrel turns 47 times in being rolled up the ramp.
What is the Circumference of a circle?The Circumference of a circle is defined as the product of the diameter of the circle and pi.
C = πd
where 'd' is the diameter of the circle
The circumference of the circular base of the barrel is given by the formula C = πd, where C is the circumference and d is the diameter of the base.
In this case, d = 1.1 inches, so C = π1.1 inches = 3.46 inches.
Since the barrel turns 47 times, the distance it travels is 47 times the circumference of the base,
47 × 3.46 inches = 161.62 inches
Therefore, the length of the ramp is 161.62 inches.
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The table below shows the times taken for
a group of athletes to finish a 200 m race.
Work out the percentage of the athletes
who took more than 28 s to finish the race.
Time, t(s)
24
26
28
30
Frequency
3
6
9
7
Answers
Therefore , the solution of the given problem of percentage comes out to be athletes who took move 285 to finish the race is 64%.
Define percentage.A percentage is what is used to describe a fraction of a whole when it is stated as a number range between 0 and 100. 100% of something, 50% of something, and 0% of something are all equal. After dividing the portion of the whole by the entire, multiply the result by 100 to arrive at a percentage.
Here,
For the table to get the total frequency is:
=> 3+6+9+7
=>9+9+7
=>25
The frequency greater than 285 is
9+7 = 16
So,
the percentage of the athletes who took move 285 to finish the race is:
=> 16/25 * 100
=> 0.64 * 100
=> 64%
Therefore , the solution of the given problem of percentage comes out to be athletes who took move 285 to finish the race is 64%.
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test form 1a answers 6th grade three times Geoff's age plus 3 is myrkas age. myrka is 48. what is Geoff's age
Answers
Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.
What does a math reshuffle mean?Rearranging terms in an equation to get the solution is known as "solving by rearranging." Keep these guidelines in mind when solving by rearranging: To shift terms from one side to the other, do the reverse operation.Rearranging terms in an equation to get the solution is known as "solving by rearranging." Keep these guidelines in mind when solving by rearranging: To shift terms from one side to the other, do the reverse operation.Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.Age of Myrka = 3x + Age of Geoff
3x + 3 = 48
3x = 48 - 3
3x = 45 x = 15
Geoff is therefore 15 years old.
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Complete the equation describing how x and y are related -2
Answers
The equation of the line found is:
y = 3x + 1.
Since the rate of change is always the same, that is, when x changes by 1, y always changed by the same value, this is a linear equation.
Linear equation:
A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. where x is a variable, A is a coefficient, and B is a constant. The standard form of linear equations in two variables is of the form Ax + By = C. where x and y are variables, A and B are coefficients, and C is a constant.
The equation of a line is given by:
y = mx + b
In which:
m is the slope, that is, by how much y changes when x changes by 1.
b is the y-intercept, which is the value of y when x = 0.
From the table, when x =0 and y =1 , thus b = 1.
When x = and y = 1 . When x =1 and y = 4 , when x = 2 and y =7 , and so on. That is, when x changes by 1, y changes by 3, and the slope is m = 3.
The equation of the line is:
y = 3x + 1.
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The length of one diagonal of a rhombus is 4 times the length of the other diagonal. Write an expression that represents the perimeter of the rhombus. Let d be the length of the shorter diagonal.
Answers
The expression that represents the perimeter of the rhombus is 2d√17
How to determine the expression that represents the perimeter of the rhombus?
From the question, we have the following parameters that can be used in our computation:
The length of one diagonal of a rhombus is 4 times the length of the other diagonal.
This means that
Length 1 = 4 * Length 2
From the question, we have
Let d be the length of the shorter diagonal.
This means that
Length 1 = 4d
Length 2 = d
The perimeter of the rhombus from the diagonals is calculated as
P = 2√(Length 1² + Length 2²)
Substitute the known values in the above equation, so, we have the following representation
P = 2√((4d)² + d²)
Evaluate the exponents
P = 2√(16d² + d²)
So, we have
P = 2√(17d²)
Evaluate the exponents
P = 2d√17
Hence, the perimeter is 2d√17
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Jenny babysits for $6)per hour plus $10 for taxi fare. Mary charges ($3 every ?half ?hour plus $15 in taxi fare.
Answers
Answer:
Step-by-step explanation:
122121
The perimeter Of rectangle is 106 cm its length is 2X -1 cm and breath is X +9 cm find its length and breadth
Answers
[tex] \longmapsto \: 2(2x - 1 + x + 9) = 103 \\ \\ \longmapsto \: 2(3x + 8) = 106 \\ \\ \longmapsto \: 6x +16 = 106 \\ \\ \longmapsto \: x = \frac{90}{6} \\ \\ \longmapsto \: x = 15 [/tex]
So,
[tex]l = 2 \times 15 - 1 = 29 \\ \\ b = 2 + 15 = 17[/tex]
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the breadth (or width) of the rectangle.
In this case, we know that the perimeter is 106 cm, so we can set up the equation:
106 = 2(l + (X + 9))
106 = 2l + 2X + 18
We also know that the length of the rectangle is 2X - 1, so we can set this equal to l:
2X - 1 = l
Now we have a system of two equations with two unknowns (l and X). We can substitute the value of l from the second equation into the first equation and solve for X:
106 = 2(2X - 1 + (X + 9))
106 = 2(3X + 8)
106 = 6X + 16
90 = 6X
X = 15
Now that we know the value of X, we can substitute it back into the equation for the length of the rectangle to find the length:
l = 2X - 1 = 2(15) - 1 = 29 cm
And then we can use the value of X again to find the breadth:
w = X + 9 = 15 + 9 = 24 cm
So the length of the rectangle is 29 cm and the breadth is 24 cm.
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Find the coordinates of the intersection of the diagonals of the parallelogram with the vertices $Q\left(-1,\ 3\right),\ R\left(5,\ 2\right),\ S\left(1,-2\right),$ and $T\left(-5,-1\right)$
Answers
The coordinates of the intersection of the diagonals of the parallelogram QRST is (0, 1/2)
The coordinates of the parallelogram QRST are:
Q = (-1, 3)
R = (5, 2)
S = (1, -2)
T = (-5, -1)
The diagonals of parallelogram QRST are QS and RT.
Let M be the point of the intersection of the diagonals of the parallelogram QRST
The diagonals of a parallelogram bisect each other.
This means, M is midpoint of diagonals QS and RT.
Consider diagonal QS.
Let (x1, y1) = (-1, 3) and (x2, y2) = (1, -2)
Using midpoint formula the coordinates of M would be,
M = ((x1 + x2)/2, (y1 + y2)/2)
M = ((-1 + 1)/2, (3 - 2)/2)
M = (0/2 , 1/2)
M = (0, 1/2)
Therefore, the point of intersecton of QS and RT is (0, 1/2)
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A quadrilateral with vertices at A(4, -4), B(4, -16), C(12, -16), and D(12,-4) has been dilated with a center at the
origin. The image of D, point D', has coordinates (36, -12). What is the scale factor of the dilation? 1/9. 1/3
3
9
Answers
Answer:
scale factor = 3
Step-by-step explanation:
since the origin is the centre of dilatation then the scale factor is the ratio of corresponding coordinates, image to original.
given D (12, - 4 ) and D' (36, - 12 ) , then
scale factor = [tex]\frac{36}{12}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3
Wanda has 5 different fish in a small, crowded tank. She decides to randomly scoop up individual fish and transfer them to a new tank until a total of 4 fish have been moved. How many sequences of 4 fish are possible?
Answers
Answer:
64 sequences of 4 fish are possible.
There are 12 girls and 16 boys in Mr jonsons 3rd period class of these students 3 girls and 4 boys wear glasses what percentage of the Stu in Mr jonsons class wear glasses
Answers
Answer:
25%
Step-by-step explanation:
Of the 12 girls and 16 boys in Mr. Johnson's class, 3 girls and 4 boys wear glasses. You want to know the percentage of students in the class who wear glasses.
PercentageThe percentage is the fraction multiplied by 100%. The fraction is the ratio of glasses-wearers to total students.
percentage = (girls w/ glasses + boys w/ glasses)/(girls + boys)×100%
percentage = (3 +4)/(12+16) × 100% = 7/28 × 100% = 25%
25% of the students in Mr. Johnson's class wear glasses.
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The population of HaleyValley, Alabama was 4,403 in 2010. Haleyville has been experiencing a population decline of 0. 6% per year since 2000. What will be the projected population of HaleyValley in 2020?
Answers
The projected Population in 2020 is given by 4146.
What is compounding ?Compounding is the method through which interest is added to both the principle balance already in place and the interest that has previously been paid. Thus, compounding may be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."
Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The main (initial) sum and the interest that has previously accrued over the course of prior periods are used to compute compound interest.
Number of years to compound is 10 years from 2010 to 2020.
The population deplition is 0.6 % = next year population is 99.4% of present.
So population after 10 years = 4403 * [tex].994\x^{10}[/tex] = 4145.84 =4146
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3. The difference between the digits in a two-digit numeral is 3. The units’ digit is twice the tens’ digit. Find the numeral.
Answers
Answer:
36
Step-by-step explanation:
let the number be 10x+y
x - y = 3 (eq 1)
given: y = 2x (eq 2)
putting 2 in 1
x - 2x = 3
-x = 3 (we can ignore the negative sign for now because we only need to find the absolute value)
y = 6
number is 36