Answer:
B) [tex]j=32m[/tex]
Step-by-step explanation:
Given:
Ayanna jumps at the rate of = 32 times/minute
To find the algebraic equation to express the function of the total number of time Ayanna jumped the rope.
Solution:
Let [tex]j[/tex] represent the total jumps made by Ayanna.
Let Ayanna jump for [tex]m[/tex] minutes.
Using unitary method to calculate total number of jumps made by Ayanna in [tex]m[/tex] minutes.
In 1 minute, Ayanna jumps = 32 times
Thus, in [tex]m[/tex] minutes Ayanna will jump = [tex]32\times m=32m[/tex] times
Thus, the function can be represented as;
[tex]j=32m[/tex] (Answer)
Answer: b
Step-by-step explanation:
David made a scale drawing of a mural he is going to paint. He used a scale of 1 cm=4ft. If the actual mural will be 16 feet long, how long is the mural in David's drawing
Answer:
4 cm
Step-by-step explanation:
we know that
The scale drawing is
[tex]\frac{1}{4}\ \frac{cm}{ft}[/tex]
That means ----> 1 cm in the drawing represent 4 ft in the mural
so
To find out the dimensions in the drawing, multiply the actual dimension by the scale drawing factor
so
[tex](16\ ft)(\frac{1}{4}\ \frac{cm}{ft})=4\ cm[/tex]
If AB is the diameter of the circle with center X and C is a point on the circle such that AC = AX = 3, what is the perimeter of triangle ABC ?
Answer:
Step-by-step explanation:
The perimeter of a shape or plane figure is the distance round the shape. The diagram of the circle and the triangle ABC formed is shown in the attached photo.
To determine the length of AC, we would apply the Pythagoras theorem which is expressed as follows
Hypotenuse^2 = opposite ^2 + adjacent ^2
AC = hypotenuse
Opposite = 3
Adjacent = 3
AC^2 = 3^2 + 3^2 = 9 + 9 = 18
AC = √18 = 4.24
BX = AX = 3(they are both radii)
BC = AC = 4.24
The perimeter of triangle ABC would be
3 + 3 + 4.24 + 4.24 = 14.48
Mr. Nordman gets a commission of $2.30 on each pair of women's shoes he sells, and a commission of $3 on each pair of men's shoes he sells. To meet his sales targets, he must sell at least 10 pairs of women's shoes and at least 5 pairs of men's shoes. He also wants to make at least a $60 a week in commissions. Define the variables, write a system of inequalities to represent this situation, and name one possible solution.
Answer:
x ≥ 5
y ≥ 10
3x + 2.3y ≥ 60
Step-by-step explanation:
Lets the number of men's shoes he sells be x and women's shoes be y.
For each men's shoes , he gets a commission of $3 and for each women's shoe, he gets a commission of $2.30 .
He needs to sell atleast 10 women's shoes and 5 men's shoes.
Also he needs to make atleast $60 per week.
x ≥ 5
y ≥ 10
3x + 2.3y ≥ 60
These are are the 3 required inequalities.
Now we will see an example.
If he sells 20 womens shoes and 10 mens shoes , he will meet the requirements.
He will make a total profit = [tex]2.3\times 20 + 3\times 10[/tex] =$76
The number 2^1993 + 3^1993 is a multiple of 5. What is the units digit of the quotient (2^1993 + 3^1993)/5?
The units digit of the quotient (2^1993 + 3^1993)/5 is 9.
Explanation:The units digit of the sum of two numbers is determined by the units digit of each number. To find the units digit of 2^1993, we can observe the pattern of its units digits: the units digit of 2 repeats every four powers. Therefore, 2^1993 has the same units digit as 2^1, which is 2. Similarly, the units digit of 3^1993 is the same as the units digit of 3^3, which is 7.
Now, we can calculate the units digit of the sum: 2 + 7 = 9. Since the sum is divisible by 5, and the units digit is 9, the quotient (2^1993 + 3^1993)/5 has a units digit of 9 as well.
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A rectangle has an area of 96cm2. The width is four less than the length. What is the perimeter?
Answer:
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The formula for determining the area of a rectangle is expressed
LW^2
The rectangle has an area of 96cm2. This means that
LW = 96 - - - - - - - - - - 1
The width is four less than the length. This means that
L = W + 4
Substituting L = W + 4 into equation 1, it becomes
W(W + 4)= 96
W^2 + 4W = 96
W^2 + 4W - 96 = 0
W^2 + 12W - 8W - 96 = 0
W(W + 12) - 8(W + 12) = 0
(W + 12)(W - 8) = 0
W = 8 or W = -12
Since the width cannot be negative, the W = 8cm
L = W + 4 = 8 + 4 = 12 cm
The formula for determining the perimeter of a rectangle is
Perimeter = 2(L + W)
Perimeter = 2(8 + 12) =2×20
Perimeter of rectangle = 40 cm
.
Final answer:
Perimeter is 40cm.
Explanation:
To find the perimeter of a rectangle with an area of 96 cm2 where the width is four less than the length, we first need to set up equations for the area and the relationship between the sides.
Let the length be represented by L and the width by W.
We know:
Area (A) = Length (L) × Width (W) = 96 cm2Width (W) = Length (L) - 4 cmWe can substitute the second equation into the first to find the length:
A = L × (L - 4 cm) = 96 cm2
L^2 - 4L - 96 = 0
(L - 12)(L + 8) = 0
L = 12
The perimeter (P) of a rectangle is given by 2 × Length + 2 × Width or P = 2L + 2W.
Substituting the values of L and W into this formula will yield the perimeter of the rectangle.
For example, if L = 12 cm (which is a possible solution to the above problem), then W = L - 4 cm = 8 cm.
Therefore, the perimeter would be:
P = 2L + 2W = 2(12 cm) + 2(8 cm) = 40 cm
Rewrite with only sin x and cos x.
sin 2x - cos x
2 sin x cos2x
sin x
cos x (2 sin x - 1)
2 sin x
Answer:
cos x (2 sin x − 1)
Step-by-step explanation:
sin(2x) − cos x
Use double angle formula.
2 sin x cos x − cos x
Factor.
cos x (2 sin x − 1)
Final answer:
The expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).
Explanation:
Given the expression sin 2x - cos x, we can rewrite it using only sin x and cos x. Using the trigonometric identity sin 2x = 2 sin x cos x, we can substitute it into the expression:
sin 2x - cos x = 2 sin x cos x - cos x
Factoring out the common factor cos x, we get:
sin 2x - cos x = cos x (2 sin x - 1)
So, the expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).
In June, Susie buys a dozen of cans of Dog's Dinner dog food at $1.89 per can. She also buys two bags of 'Dem Bones dental chews that each cost $12.69, and a new toy for $10.25. She pays sales tax at a rate of 7.25%. What is her total cost for the month of June?
Answer:
$62.54
Step-by-step explanation:
12 cans dog food = 12 × 1.89 = $22.68
2 bags dental chews = 2 × 12.69 = 25.38
1 toy = 10.25
Subtotal = 58.31
Sales tax = 0.0725 × 58.31 = 4.23
TOTAL = $62.54
Suzie's total cost for June was $62.54.
Two percent of the jazz records sold in April were from a new label. About how many records were from the new label?
Approximately, 2% of the jazz records sold in April were from the new label.To find this, multiply the percentage (2%) by the total jazz records sold, expressing the percentage as a decimal (0.02). The formula is[tex]\( N = 0.02 \times J \),[/tex] where [tex]\( N \)[/tex] is the number of records from the new label, and [tex]\( J \)[/tex]is the total number of jazz records sold.
Explanation:In order to determine the number of jazz records sold from the new label in April, you need to multiply the percentage by the total number of jazz records sold. Let's denote the total number of jazz records as J. The formula for calculating the number of records from the new label (N) is given by:
[tex]\[ N = (2/100) \times J \][/tex]
This is based on the fact that 2% is equivalent to 0.02 when expressed as a decimal. Therefore, the number of records from the new label is obtained by multiplying 0.02 by the total number of jazz records (J). This calculation provides the direct answer to the question.
Understanding percentages is essential in various fields, and in this scenario, it helps determine the specific quantity of records from the new label in relation to the total jazz records sold. This mathematical approach allows for a precise estimation, providing insights into the market share or performance of the new label within the jazz genre for the specified period, in this case, the month of April.
A boy thinks he has discovered a way to drink extra orange juice without alerting his parents. For every cup of orange juice he takes from a container of orange juice, he pours one cup of water back into the container. If he completes this process three times on the same container of juice, the resulting mixture will be exactly 50% water and 50% juice. How many cups of orange juice were originally in the container. (P.S ITS NOT 6)
Answer:
4.847 cups
Step-by-step explanation:
Let's say x is number of cups of orange juice originally in the container.
The boy takes 1 cup of orange juice out, so there is x−1 cups left out of a total volume of x cups. So the new concentration in the container is:
(x − 1) / x
Next, he takes another cup out, but this time, it isn't 100% orange juice any more. So the number of cups of orange juice left in the container is x − 1 − (x − 1) / x. The total volume is still x cups, so the new concentration is:
[x − 1 − (x − 1) / x] / x
Repeating this logic, after he replaces the third cup with water, the final concentration is:
{x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x
This final concentration is equal to 1/2.
1/2 = {x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x
1/2 x = x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x
1/2 x² = x (x − 1) − (x − 1) − [x − 1 − (x − 1) / x]
1/2 x² = x (x − 1) − (x − 1) − (x − 1) + (x − 1) / x
1/2 x² = x (x − 1) − 2 (x − 1) + (x − 1) / x
1/2 x³ = x² (x − 1) − 2x (x − 1) + (x − 1)
1/2 x³ = x³ − x² − 2x² + 2x + x − 1
0 = 1/2 x³ − 3x² + 3x − 1
0 = x³ − 6x² + 6x − 2
Using a calculator to solve this:
x = 4.847
There are originally 4.847 cups in the container.
A store buys a video game for the wholesale price of $39.99. The markup on the game is 70%. If sales tax is 8% then how much money would you need to buy the game?
Answer:The amount of money that you would need to buy the game is $73.324
Step-by-step explanation:
The store buys a video game for the wholesale price of $39.99. There was a markup of 70% on the price of the game. The value of the markup would be
70/100× 39.99 = 0.7×39.99 = $27.993
Cost of the game plus 70% markup would be
39.99 + 27.993 = $67.893
There is sales tax of 8% on the game. This means that the value of the tax would be
8/100 × 67.893 = 0.08 × 67.893 = $5.431
The amount of money that you would need to buy the game would be
67.893 + 5.431 = $73.324
A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:
the median from N
the right bisector of LP
the altitude from N
Answer:
Part A) [tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]
Part B) [tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]
Part C) [tex]y=\frac{2}{7}x+\frac{8}{7}[/tex]
see the attached figure to better understand the problem
Step-by-step explanation:
we have
points L(-3, 6), N(3, 2) and P(1, -8)
Part A) Find the equation of the median from N
we Know that
The median passes through point N to midpoint segment LP
step 1
Find the midpoint segment LP
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]
[tex]M(-1,-1)[/tex]
step 2
Find the slope of the segment NM
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
N(3, 2) and M(-1,-1)
substitute the values
[tex]m=\frac{-1-2}{-1-3}[/tex]
[tex]m=\frac{-3}{-4}[/tex]
[tex]m=\frac{3}{4}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{4}[/tex]
[tex]point\ N(3, 2)[/tex]
substitute
[tex]y-2=\frac{3}{4}(x-3)[/tex]
step 4
Convert to slope intercept form
Isolate the variable y
[tex]y-2=\frac{3}{4}x-\frac{9}{4}[/tex]
[tex]y=\frac{3}{4}x-\frac{9}{4}+2[/tex]
[tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]
Part B) Find the equation of the right bisector of LP
we Know that
The right bisector is perpendicular to LP and passes through midpoint segment LP
step 1
Find the midpoint segment LP
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]
[tex]M(-1,-1)[/tex]
step 2
Find the slope of the segment LP
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]m=\frac{-8-6}{1+3}[/tex]
[tex]m=\frac{-14}{4}[/tex]
[tex]m=-\frac{14}{4}[/tex]
[tex]m=-\frac{7}{2}[/tex]
step 3
Find the slope of the perpendicular line to segment LP
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=-\frac{7}{2}[/tex]
so
[tex]m_2=\frac{2}{7}[/tex]
step 4
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{7}[/tex]
[tex]point\ M(-1,-1)[/tex] ----> midpoint LP
substitute
[tex]y+1=\frac{2}{7}(x+1)[/tex]
step 5
Convert to slope intercept form
Isolate the variable y
[tex]y+1=\frac{2}{7}x+\frac{2}{7}[/tex]
[tex]y=\frac{2}{7}x+\frac{2}{7}-1[/tex]
[tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]
Part C) Find the equation of the altitude from N
we Know that
The altitude is perpendicular to LP and passes through point N
step 1
Find the slope of the segment LP
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]m=\frac{-8-6}{1+3}[/tex]
[tex]m=\frac{-14}{4}[/tex]
[tex]m=-\frac{14}{4}[/tex]
[tex]m=-\frac{7}{2}[/tex]
step 2
Find the slope of the perpendicular line to segment LP
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=-\frac{7}{2}[/tex]
so
[tex]m_2=\frac{2}{7}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{7}[/tex]
[tex]point\ N(3,2)[/tex]
substitute
[tex]y-2=\frac{2}{7}(x-3)[/tex]
step 4
Convert to slope intercept form
Isolate the variable y
[tex]y-2=\frac{2}{7}x-\frac{6}{7}[/tex]
[tex]y=\frac{2}{7}x-\frac{6}{7}+2[/tex]
[tex]y=\frac{2}{7}x+\frac{8}{7}[/tex]
give the equation of the circle whose center is (5 -3) and goes through (2 5)
Answer:
Step-by-step explanation:
The standard form for the equation of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
From the info given, we have the center, (h, k) as (5, -3) and the x and y coordinates of (2, 5). We will use these to solve for r-squared, then plug back in what we need to write the equation.
[tex](2-5)^2+(5-(-3))^2=r^2[/tex] which simplifies to
[tex](-3)^2+(8)^2=r^2[/tex] and
[tex]9+64=r^2[/tex] so
[tex]r^2=73[/tex]
Filling in the equation:
[tex](x-5)^2+(y+3)^2=73[/tex]
In order to raise revenue, the federal government planned a tax amnesty program that allows tax delinquents to pay all owed tax without added financial penalty. However, economists projected that the federal government would collect a far lower percentage of total tax owed by delinquents than did state governments implementing similar programs.
Answer:
The correct option is E: "Unlike most federal tax delinquents, most state tax delinquents fail to pay state tax because of an oversight rather than a decision not to pay."
Step-by-step explanation:
Option A is not the correct answer because it is out of context
Option B is also out of context because what we are looking for is a connection between defaulters at state and federal level
Option C is also wrong because it would lead to the direct opposite of the projection by economists.
Option D is also wrong because once again it is out of context.
Option E is correct
The nth harmonic number is defined non-recursively as: 1 1/2 1/3 1/4 ... 1/n. Come up with a recursive definition and use it to guide you to write a method definition for a double-valued method named harmonic that accepts an int parameters n and recursively calculates and returns the nth harmonic number.
Answer:
57
Step-by-step explanation:
In an obtuse isosceles triangle the angle measurements are, x∘, x∘, and (10x−2)=128∘. Find the measurement of one of the acute angles.
Answer:
26°
Step-by-step explanation:
An obtuse triangle is a triangle that has one obtuse angle. Obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees.
An isosceles triangle is a triangle that has two equal sides and angles.
Therefore, an obtuse isosceles triangle is a triangle with an obtuse angle and two equal sides that have two equal acute angles (angle less than 90° ).
Given:
The three angles of the triangle are given to be x°, x° and (10x−2) = 128°. The obtuse angle is 128°, the two x° are acute angles. We are not using equation 10x − 2 since the value of the obtuse angle has been given as 128°
The sum of angles in a triangle is 180°
∴ x° + x° + 128° = 180°
2x° = 180° - 128°
2x° = 52°
x° = 52° / 2
x° = 26°
The measurement of one of the acute angles is 26°
Suppose the newspaper states that the probability of rain today is 65%.
What is the complement of the event "rain today"?
rain yesterday
rain tomorrow
no rain today
no rain tomorrow
What is the probability of the complement?
The complement of 'rain today' is 'no rain today'. Its probability is 1 - the probability of 'rain today', which calculates to 35%.
Explanation:In probability theory, the complement of any event A represents 'not A'. In this context, the event is 'rain today', therefore the complement of the event would be 'no rain today'.
Probability of an event and its complement always add up to 1. Therefore, you can calculate the probability of the complement by subtracting the probability of the event from 1. So, the probability of the complement of the event 'rain today' is 1 - 0.65 which equals 0.35 or 35%.
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8. When starting your credit history, a low-credit-limit, high-interest-rate credit card should be paid ____.
in full, on time, every time
in even payments each time
at least the minimum due
as much as you can when due
9. APY means ____.
annual percentage yield
annual percentage yearly
apportioned percentage yield
applied percentage yield
Answer:
8. When starting your credit history, a low-credit-limit, high-interest-rate credit card should be paid in full, on time, every time.
9. APY means annual percentage yield.
Explanation:
8. A person's credit history tells about the ability of a person to pay and repay his debts. This is very important especially when you want to avail of a credit card from a company because it reflects on how responsible you are when it comes to repaying your debts. However, when you are just starting your credit history, it is important to give a good impression, so you'd have an easier approval in the future.
Usually, for starters with low salary, a low-credit-limit with a high-interest-rate credit card is common. It is very important to pay your debts in full, on time and every time in order to avoid incurring a balance that you will be carrying from one month to the other. If you do this, you will be ending up paying lots of interest charge.
Paying in full, on time and every time will also give you the chance to have an increased credit limit in the future.
9. APY is also known as "Annual Percentage Yield." This is the actual amount (rate of return) that a person could earn while his money is being deposited in the bank in one year. Other than the deposited money, investment that earns a rate of return could also refer to bonds and stock share. APY considers the compounding interest in its computation. This means that the higher your balance, the higher the APY. The value of the asset also increases.
On a farm A 4/5 of the number of sheep are equal to 1/2 of the number of sheep on farm B. The total number of sheep on farm A and farm B is 845. How many sheep are there on farm B
Answer:
There are 520 sheep on Farm B.
Step-by-step explanation:
Let the Number of sheep on farm B be x
Given:
On a farm A 4/5 of the number of sheep are equal to 1/2 of the number of sheep on farm B.
It means Number of sheep on farm A multiplied by 4/5 is equal to 1/2 multiplied by Number of sheep on farm B.
framing the equation we get;
[tex]\frac{4}{5}\times \textrm{Number of sheep on Farm A} = \frac{1}{2} \times x[/tex]
Number of sheep on Farm A = [tex]\frac{x}{2}\times\frac{5}{4} = \frac{5x}{8}[/tex]
Now Given:
Total Number of sheep =845.
We know that Total Number of sheep is equal to sum of sheep at farm A and sheep at farm B.
Framing equation we get;
[tex]\frac{5x}{8}+x=845[/tex]
Taking L.C.M we get;
[tex]\frac{5x\times 1}{8\times1}+\frac{x\times8}{8} =845\\\\\frac{5x}{8}+\frac{x}{8} =845\\\\\frac{5x+8x}{8}=845\\\\\frac{13x}{8}= 845\\\\13x=845\times8\\\\x=\frac{845\times8}{13} = 520[/tex]
Number of sheep on Farm B = 520 sheep
Number of sheep on Farm A = [tex]\frac{5}{8}\times 520 = 325\ sheep[/tex]
Hence There are 520 sheep on Farm B.
In a certain high school, the probability that a student drops out is 0.07 , and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.25 . What is the probability that a randomly selected student gets a GED?
Using probability concepts and the information given, it is found that there is a 0.0175 = 1.75% probability that a randomly selected student gets a GED.
The percentages given are:
7% of the students drop out, and of those, 25% get a GED.100 - 7 = 93% of the students do not drop hence, meaning of those, 0%, that is, none need to get a GED, as they will have the graduation diploma.Hence:
[tex]p = 0.07(0.25) + 0.93(0) = 0.0175[/tex]
There is a 0.0175 = 1.75% probability that a randomly selected student gets a GED.
A similar problem also involving probabilities. is given at https://brainly.com/question/14398287
The probability that a randomly selected student gets a GED is 0.0175, or 1.75%.
Explanation:To find the probability that a randomly selected student gets a GED, we need to multiply the probability of a student dropping out (0.07) by the probability of a dropout getting a GED (0.25). This can be calculated using the formula:
Probability of getting a GED = Probability of dropping out * Probability of getting a GED if dropped out = 0.07 * 0.25 = 0.0175
Therefore, the probability that a randomly selected student gets a GED is 0.0175, or 1.75%.
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Which of the equations below represents a line parallel to the y-axis? A. x = 4 B. x = -y C. x = y D. x = 4y
Answer:
b
Step-by-step explanation:
Hank has a board 1.75 meters long. He used 0.8 meter to build the walls of a birdhouse. He used 0.4 of what is left for the floor. He needs 0.6 meter for the roof. Dies he have enough wood for the roof? Explain
Answer:No, he doesn't have enough wood for the roof.
Step-by-step explanation:
Total length of Hank's board is 1.75 meters. He used 0.8 meter to build the walls of a birdhouse. This means that the length of the board left would be
1.75 - 0.8 = 0.95 meters
He used 0.4 of what is left for the floor. This means that the length of the board left would be
0.95 - 0.4 = 0.55 meters
He needs 0.6 meter for the roof. Since he has only 0.55 meters left, then, he doesn't have enough wood for the roof.
A student bought a juice pouch forn$2.50 and 3 bags of chips. The total cost was $5.05.Write and solve an equation to determine the cost of a bag of chips,c
Answer:
The cost of a bag of chips is [tex]c=\$0.85[/tex]
Step-by-step explanation:
Let
c ----> the cost of a bag of chips
we know that
The cost of a juice pouch ($2.50) plus the cost of 3 bags of chips must be equal to $5.05
The cost of 3 bags of chips is equal to multiply 3 by its cost c
so
The linear equation that represent this situation is
[tex]2.50+3c=5.05[/tex]
solve for c
Subtract 2.50 both sides
[tex]3c=5.05-2.50[/tex]
[tex]3c=2.55[/tex]
Divide by 3 both sides
[tex]c=2.55/3[/tex]
[tex]c=\$0.85[/tex]
Lisa is interested in how well people are able to detect whether another person is a "Cooperator", a "Competitor", or an "Individualist" simply by looking at a picture of the person’s face. She wants to know what kind of face can be identified most easily, and whether this varies by the race of the person in the picture. She designs a 2 x 3 within-group design where she has participants in her study look at faces from African-American and Caucasian people who are "Cooperators", "Competitors", or "Individualists." The participants identify the personality of the person in each picture and Lisa keeps track of the number of pictures accurately identified for each picture type. How many cells was each participant in?
Answer:
The answer is 6.
Step-by-step explanation:
In the question it is stated that Lisa has designed a "within-group" or "within-subject" experiment using three categories with 2 subject in each category.
Within-group / within-subject experiments mean that every participant is tested for each condition of the experiment, so everyone goes through the same process.
Considering these informations, we can calculate that each participant was in 6 cells because there are 3 categories and 2 subjects for each of the categories.
I hope this answer helps.
For her birthday, Kendra received a gift card in the mail from her grandparents. The gift card was worth $50. Kendra thought, since she had just received other gifts for her birthday, she would wait a while to spend the gift card. Unfortunately, Kendra forgot all about the gift card, and the card loses $5 every month after its date of purchase if it has not been used.
If Kendra forgot the card for three months, she lost $______.
a) 9 b) 10 c) 15 d) 12
Answer:
She lost $15 on her 50 dollar credit card.
Step-by-step explanation:
Kendra received a gift card in the mail from her grandparents. The gift card was worth $50.
Kendra forgot all about the gift card, and the card loses $5 every month after its date of purchase if it has not been used.
Kendra loses $5 each month,
She forget the card for 3 months.
So, Multiply the $5 by 3 months
$5×3=$15
Hence, she lost $15.
Suppose that x is normally distributed with a mean of 30 and a standard deviation of 3.What is P?
a) 0.469b) 0.956c) 0.493d) 0.490e) 0.466f) none of the above
Answer:
If we assume that the deviation is [tex]\sigma=3[/tex] then the solution is:
[tex]P(2.55<X<64.95)=P(-9.15<z<11.65)=P(z<11.65)-P(z<-9.15)[/tex]
f) None of the above
If we assume that the deviation is [tex]\sigma=15[/tex] then the solution is:
[tex]P(2.55<X<64.95)=P(-1.83<z<2.33)=0.956[/tex]
b) 0.956
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Solution to the problem
Let X the random variable that represent the variable of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(30,3)[/tex]
Where [tex]\mu=30[/tex] and [tex]\sigma=3[/tex]
We are interested on this probability
[tex]P(2.55<X<64.95)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(2.55<X<64.95)=P(\frac{2.55-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{64.95-\mu}{\sigma})=P(\frac{2.55-30}{3}<Z<\frac{64.95-30}{3})=P(-9.15<Z<11.65)[/tex]
And we can find this probability on this way:
[tex]P(-9.15<z<11.65)=P(z<11.65)-P(z<-9.15)[/tex]
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
[tex]P(-9.15<z<11.65)=0.99999[/tex]
If we assume that the deviation is [tex]\sigma=15[/tex] then the solution is:
[tex]P(2.55<X<64.95)=P(\frac{2.55-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{64.95-\mu}{\sigma})=P(\frac{2.55-30}{15}<Z<\frac{64.95-30}{15})=P(-1.83<Z<2.33)[/tex]
And we can find this probability on this way:
[tex]P(-1.83<z<2.33)=P(z<2.33)-P(z<-1.83)[/tex]
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
[tex]P(-1.83<z<2.33)=0.956[/tex]
Tyler ordered a pizza to eat while he watches a movie. Before the movie began, he ate 1/4 of the pizza. During the movie, he ate another 3/8 Before storing the remaining pizza, he ate a final 1/16 of the pizza. How much leftover pizza does Tyler have.
Answer:
Tyler has [tex]\frac{5}{16}[/tex] Left over Pizza.
Step-by-step explanation:
Given:
Total pizza = 1
Pizza ate at First time = [tex]\frac{1}{4}[/tex]
Pizza ate at Second time = [tex]\frac{3}{8}[/tex]
Pizza ate at Final time = [tex]\frac{1}{16}[/tex]
We need to find find the amount of pizza left.
Now to find the Amount of Pizza left is equal to Total Pizza minus Pizza ate at First time minus Pizza ate at second time minus Pizza ate at Final time.
Framing in the equation form we get;
Amount of Pizza left = [tex]1- \frac{1}{4} -\frac{3}{8} -\frac{1}{16}[/tex]
Now Taking the LCM we get;
Amount of Pizza left = [tex]\frac{1\times16}{16}- \frac{1\times4}{4\times 4} -\frac{3\times2}{8\times2} -\frac{1\times1}{16\times1}= \frac{16}{16}- \frac{4}{16} -\frac{6}{16} -\frac{1}{16}= \frac{16-4-6-1}{16}= \frac{5}{16}[/tex]
Hence Tyler has [tex]\frac{5}{16}[/tex] Left over Pizza.
A store sells hardcover books for $8 and paperback books for $5. You buy 7 books, represented by the equation x+y=7, where is the number of hardcover books and y is the number of paperback books. The equation 8x+5y=41 represents the total cost. How many of each type of book did you buy?
Answer:
Total number of Hardcover books is TWO while the number of Paperback books is FIVE
Step-by-step explanation:
No. of hardcover book = x
No. of paperback book = y
Cost of one hardcover book = $8
Cost of one paperback book = $5
We are given that:
x+y=7 (Equation 1)
8x+5y=41 (Equation 2)
We can find out value of x and y by solving both equations simultaneously.
[tex]Multiplying Equation 1 by 5:\\5x+5y=35\\8x+5y=41\\Subtracting both equations\\-3x=-6\\x=2\\\\According to Equation 1:\\x+y=7\\Putting value of x=2\\2+y=7\\y=5[/tex]
Hence, Total number of Hardcover books is TWO while the number of Paperback books is FIVE
You have 100 dollars, and there is a dollar bill behind each door. You roll a 100 sided die 100 times, and you take the dollar behind the door on the die roll if the bill has not been taken already (e.g. you roll 16, then you take the dollar behind door 16 if you haven’t already taken it). What is your expected payoff?
Answer:
63.21.
Step-by-step explanation:
You have 100 dollars, and there is a dollar bill behind each door. You roll a 100 sided die 100 times, and you take the dollar behind the door on the die roll if the bill has not been taken already (e.g. you roll 16, then you take the dollar behind door 16 if you haven’t already taken it). What is your expected payoff?
X=Σ100i=1 1Ai
where Ai is the event that door i is opened at least once, and 1Ai is the indicator function for event Ai.
Thus the expected payoff is:
E[X]=Σ100 as i=1 Pr[Ai].
to calculate Pr[Ai].
Ai∁ is the probability of the event that after 100 rolls, door i is not chosen, which is:
Pr[Ai∁]=(99/100)^100
Thus:
Pr[Ai]=1−Pr[Ai∁]=1−(99/100)^100.
E[X]=Σ100i=1Pr[Ai]=100×(1−(99/100)^100).
Also based on the following approximation for large n's:
(1−1n)n≈1e
we have:
(99/100)^100=(1−1/100)^100≈1/e.
The expected pay off is
E[X]=100×(1−(99/100)^100)≈100×(1−1/e)≈63.21.
In the scenario where you roll a 100-sided die 100 times to collect a dollar behind each numbered door, the expected payoff is $100, since each number has an equal likelihood of being rolled once.
Explanation:The question you're asking involves probability and expected value, a concept from mathematics specifically relevant in understanding outcomes in scenarios involving randomness and repetition, like the one described with 100-sided dice and dollars behind doors. When rolling a 100-sided die 100 times for dollars behind 100 doors, your expected payoff is relatively straightforward to calculate. Since each roll has an equal chance to land on any number between 1 and 100 and no number will be chosen more than once, the expected outcome is that you will roll each number once.
Thus, on average, you are expected to open each door exactly once, so the expected payoff would be neatly the sum of all the dollars behind every door. As there are 100 doors, each with a dollar behind it, your expected payoff is simply $100.
Kevin, Dustin, and Mike collect baseball cards. Together Dustin and Kevin have 81 cards. If Dustin and Mike combined their cards, they would total 96. The sum of Kevin's and Mike's cards is 93. How many baseball cards do they each have? Show all of your mathematical thinking below.
Answer: Kelvin has 39 cards
Dustin has 42 cards
Mike has 54 cards
Step-by-step explanation: please see attachment for explanation
A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm. A solid oblique pyramid has a square base with edges measuring x centimeters. The height is (x + 2) centimeters. Which expression represents the volume of the pyramid?
The expression to represent the volume of solid oblique pyramid is (x³+2x²)/3.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, a solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x+2) cm.
We know that, the volume of square base pyramid is a²h/3
Now, x²(x+2)/3
= (x³+2x²)/3
Therefore, the volume of solid oblique pyramid is (x³+2x²)/3.
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The volume of the given solid oblique pyramid with a square base of edge length x cm and height (x+2) cm can be calculated using the formula for the volume of a pyramid, 1/3 * (base area) * (height). The volume can thus be represented by the expression 1/3 * x^3 + 2/3 * x^2 cm^3.
Explanation:The question refers to a solid oblique pyramid with a square base, where the edge length of the base is x, and the height is (x+2) cm. To calculate the volume of the pyramid, you can use the formula for the volume of a pyramid: 1/3 * (base area) * (height). For the given pyramid, the base is a square with side length x, so the area of the base is x*x or x^2. Because the height of the pyramid is (x + 2), we substitute into the formula to get: 1/3 * x^2 * (x + 2). Multiplying it out, the expression representing the volume of the pyramid is: 1/3 * x^3 + 2/3 * x^2 cm^3.
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