We reject the null hypothesis and conclude that the true average temperature of COVID patients exceeds 100, with a type I error rate of 10% and a p-value of 0.0068 indicating a low probability of obtaining the observed sample mean if the null hypothesis were true.
To test if the true average temperature of COVID patients exceeds 100, we can use a one-sample z-test.
The null and alternative hypotheses are
Null hypothesis: The true average temperature of COVID patients is less than or equal to 100.
Alternative hypothesis: The true average temperature of COVID patients exceeds 100.
We can calculate the test statistic as
z = (x - μ) / (σ / sqrt(n))
where x is the sample mean, μ is the hypothesized population mean (100 in this case), σ is the population standard deviation, and n is the sample size.
Substituting the given values, we get
z = (101.2 - 100) / (6 / sqrt(56))
z = 2.47
We can find that the p-value is 0.0068. This means that if the true average temperature of COVID patients is actually 100, there is only a 0.68% chance of getting a sample mean of 101.2 or higher.
Since the alpha level is 10%, and the p-value is less than 10%, we reject the null hypothesis and conclude that the true average temperature of COVID patients exceeds 100.
The type of error that could have occurred is a type I error, which is rejecting the null hypothesis when it is actually true. The probability of a type I error is equal to the chosen alpha level, which is 10% in this case.
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There is a spinner with 14 equal areas, numbered 1 through 14. If the spinner is spun one time, what is the probability that the result is a multiple of 3 or a multiple of 4?
Answer:
Okay, let's solve this step-by-step:
There is a spinner with 14 equal areas, numbered 1 through 14
We want to find the probability that the result is a multiple of 3 or a multiple of 4
There are 14 possible outcomes (numbers 1 through 14) when the spinner is spun.
Of these 14 numbers:
4 are multiples of 3: 3, 6, 9, 12
4 are multiples of 4: 4, 8, 12, 16
However, 12 is also a multiple of both 3 and 4, so we have counted it twice.
We need to subtract 1 from each to account for this:
Multiples of 3: 3
Multiples of 4: 4
So there are 3 possible multiples of 3 and 3 possible multiples of 4.
In total, there are 3 + 3 = 6 possible multiples of 3 or 4.
To calculate probability:
Probability = (Number of favorable outcomes) / (Total possible outcomes)
= 6 / 14
= 3/7
Converting to a percent: 3/7 = 42.9%
Rounded to the nearest whole percent: 43%
Therefore, the probability that the result is a multiple of 3 or a multiple of 4 is 43%.
Step-by-step explanation:
Jayla's math certificate is 19 centimeters tall and 29 centimeters wide. Jayla wants to put the certificate in a fancy frame that costs $0.03 per centimeter. How much will it cost to frame Jayla's math certificate?
Answer: It will cost $2.88 to frame Jayla's math certificate with the fancy frame.
Step-by-step explanation: To calculate the cost of framing Jayla's math certificate, we need to determine the perimeter of the certificate, which is the sum of the lengths of all four sides.
Perimeter = 2 × (height + width)
Perimeter = 2 × (19 + 29)
Perimeter = 2 × 48
Perimeter = 96 centimeters
So the perimeter of the certificate is 96 centimeters.
To find the cost of framing, we need to multiply the perimeter by the cost per centimeter of the fancy frame:
Cost = perimeter × cost per centimeter
Cost = 96 × $0.03
Cost = $2.88
Therefore, it will cost $2.88 to frame Jayla's math certificate with the fancy frame.
Paul considers investing $8,000 in three different accounts for 6 years.
Option A: 5% simple interest
Option B: 4.5% interest compounded continuously
Option C: 4.75% interest compounded yearly
After 6 years, Option B, to the nearest dollar, will be worth
$
more than Option A and
$
less than Option C.
linearexponentialquadraticconstant
Option A is a
function while Options B and C are
functions. While the
function gains
value the fastest initially, over time the
functions will gain value faster.
Answer:
Step-by-step explanation:
Option A: 8,000(1+6(0.05))
is equal to 10,400
Option B is 10,479.72
Option C: 8,000(1+0.0475)^6
is equal to 10,568.52
making B about $80 more than A and $89 less than C
Mrs. Brown records the rainfall in Seattle, Washington during each month of 2021. (8.75, 4.68, 2.61, 1.03, 1.12, 1.91, 0.00, 0.11, 3.02, 5.76, 10.62, 4.38} Mrs. Brown wants to use a graphical representation that will allow her students to see the overall shape of the data and provide enough information to determine the 5-number summary Which representations should Mrs. Brown consider? Select all that apply.
Mrs. Brown should consider the box and whisker plot as well as the stem and leaf plot to represent the data and determine the 5-number summary.
Mrs. Brown should consider using a box plot (also called a box and whisker plot) and/or a modified box plot.
A box plot is a useful graphical representation because it shows the overall shape of the data and displays the 5-number summary, which includes the minimum value, first quartile (Q1), median (second quartile, Q2), third quartile (Q3), and the maximum value. A modified box plot also provides this information and additionally identifies any potential outliers in the data.
Therefore, Mrs. Brown should consider the box and whisker plot as well as the stem and leaf plot to represent the data and determine the 5-number summary.
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Correct question is "Mrs. Brown records the rainfall in Seattle, Washington during each month of 2021. (8.75, 4.68, 2.61, 1.03, 1.12, 1.91, 0.00, 0.11, 3.02, 5.76, 10.62, 4.38} Mrs. Brown wants to use a graphical representation that will allow her students to see the overall shape of the data and provide enough information to determine the 5-number summary then find which representations should Mrs. Brown consider? "
If one zero of the polynomial (3
2 + 8 + ) is the reciprocal of the
other, then find the value of k
If one zero of the polynomial 3x^2 + 8x + k is the reciprocal of the
other, then k = 3 by applying product of roots formula.
The quadratic polynomial is 3x^2 + 8x + k.
Let the roots of 3x^2 + 8x + k be m and n where m and n are reciprocal of each other. Therefore, n = 1/m
Thus, the product of roots is = m*n = m*(1/m) = 1 ____(1)
The general equation of a quadratic equation can be written as,
ax^2 + bx + c = 0
where a and b are coefficients of x^2 and x respectively and c is a constant term.
From product of roots formula we know that,
Product of roots =constant term/ coefficient of x^2 = c/a
Therefore, for polynomial is 3x^2 + 8x + k we get,
Product of roots = k/3 ____(2)
From equating equation (1) and (2) we get,
k/3 = 1
⇒ k = 3
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The given question is incomplete, the complete question is
"If one zero of the polynomial 3x^2+8x+k is the reciprocal of the other, then find the value of k."
The number of turns of a pencil sharpener needed to sharpen a brand W pencil is approximately Normally distributed with a mean of 4.6 and a standard deviation of 0.67. The number of turns needed to sharpen a brand H pencil is approximately Normally distributed with a mean of 5.2 and a standard deviation of 0.33. If 30 pencils of each brand are randomly selected and sharpened, what is the probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H? approximately 0 0.0005 0.9995 approximately 1
The probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H is approximately 0.0005.
How to find the the probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand HLet X be the number of turns needed to sharpen a brand W pencil and Y be the number of turns needed to sharpen a brand H pencil. Then, we are interested in finding P(X > Y), the probability that the mean number of turns needed to sharpen a brand W pencil is higher than the mean number of turns needed to sharpen a brand H pencil.
The difference between the means of X and Y is 4.6 - 5.2 = -0.6. The standard error of the difference between the means can be calculated as:
SE = sqrt[(0.67^2/30) + (0.33^2/30)] = 0.178
The test statistic is:
Z = (-0.6 - 0) / 0.178 = -3.37
Using a standard normal distribution table, the probability of getting a Z-score less than -3.37 is approximately 0.0005.
Therefore, the probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H is approximately 0.0005.
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3 At a restaurant, small tables have a chairs, and large tables have b chairs.
Donna notices that there are 12 small tables and 8 large tables.
How can the expression 12a + 8b help her find the total number of chairs in the dining
room? Explain your reasoning.
Answer:
20 tables
Step-by-step explanation:
12a is the small tables and 8b is the 8 large tables so they are adding it together and getting 20 tables.
what is the answer to the following questions 32 − 14
Answer:
Step-by-step explanation:
18
Eric is building a storage box for his nephews. The box will be 42 inches long, 24 inches deep, and 20 inches tall. He plans to cover the entire outside of the box with three coats of a clear coat protective finish. If each can of finish covers about 27. 5 square feet, what is the minimum number of cans of finish needed for the job? Explain how you found your answer
Eric will need at least 6 cans of finish to cover the entire outside of the box with three coats.
To find the minimum number of cans of finish needed for the job, we first need to calculate the total surface area of the box that will be covered with the finish.
The box has a length of 42 inches, a depth of 24 inches, and a height of 20 inches. To find the total surface area, we can use the formula for the surface area of a rectangular prism:
Surface area = 2(length x width + width x height + height x length)
Surface area = 2(42 x 24 + 24 x 20 + 20 x 42)
Surface area = 2(1008 + 480 + 840)
Surface area = 6656 square inches
Since the finish will be applied in three coats, we need to multiply the total surface area by three to get the total area of finish needed:
Total area of finish = 3 x 6656 square inches
Total area of finish = 19968 square inches
Now we can convert the total area of finish from square inches to square feet by dividing by 144:
Total area of finish = 19968 square inches / 144 = 138.67 square feet
Since each can of finish covers about 27.5 square feet, we can calculate the minimum number of cans needed by dividing the total area of finish by the coverage of each can:
Minimum number of cans = 138.67 square feet / 27.5 square feet per can
Minimum number of cans = 5.04 cans
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More than 96 percent of the very largest colleges and universities (morethan15,000 total enrollments) have some online offerings. Suppose you randomly pick 13 such institutions. We are interested in the number that offer distance learning course
Using the binomial probability formula, we get a probability of approximately 1 or 100%.
This problem involves a binomial probability distribution, where we are interested in the number of successes (colleges with distance learning courses) in a fixed number of trials (picking 13 institutions), where each trial has a constant probability of success (the probability that a college offers distance learning courses).
We can use the binomial probability formula
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
where X is the number of successes, k is the number of successes we are interested in, n is the total number of trials, p is the probability of success, and C(n, k) is the binomial coefficient.
Substituting the given values, we get
P(X = k) = C(13, k) * 0.96^k * 0.04^(13-k)
To find the probability that at least one college offers distance learning courses, we can find the probability that none of the 13 colleges offer distance learning courses and subtract it from 1
P(X ≥ 1) = 1 - P(X = 0)
P(X = 0) = C(13, 0) * 0.96^0 * 0.04^13 = 0.000000005096
P(X ≥ 1) = 1 - 0.000000005096 ≈ 1
Therefore, the probability that at least one college out of 13 offers distance learning courses is approximately 1 or 100%.
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What is 1/2% to decimal
Answer: 0.5
Step-by-step explanation:
1/2% is equal to 50 out of 100, or 50/100.
So you turn that into a decimal (fifty one hundredths).
0.50
You can get rid of the 0 at the end.
0.5
Hope this helps!!! :)
6. age of his son by A two-digit number is such that the sum of the digits is 13 and the product of the digits is 40. Find the number.
7 A two-digit number is less than 6 times the sum of its digits by 1. The difference between the digit is 1. Find the number.
Answer:
6.
solution:
8+5=13
8×5=40
what is 100000^3? my caculater wont tell me!
Answer:
1e+15 or 1.000.000.000.000.000
Step-by-step explanation:
what is 100000^3? my caculater wont tell me!
100000³ = 100000 × 100000 × 100000
100000 × 100000 × 100000 =
10000000000 × 100000 =
1e+15 or 1.000.000.000.000.000
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 6 grams and the amount of gold in each necklace is 24 grams. The jeweler made a total of 16 bracelets and necklaces using 258 grams of gold. Determine the number of bracelets made and the number of necklaces made.
Using a system of equations, the number of bracelets made and the number of necklaces made are:
Bracelets = 7Necklaces = 9.What is a system of equations?A system of equations is two or more equations that can be solved simultaneously or at the same time.
Simultaneous equations can be solved concurrently.
Quantity of gold in each bracelet = 6 grams
Quantity of gold in each necklace = 24 grams
The total number of bracelets and necklaces made = 16
The total quantity of gold used in making the 16 pieces = 258 grams
Let the number of bracelets made = x
Let the number of necklaces made = y
Equations:x + y = 16 ...Equation 1
6x + 24y = 258 ...Equation 2
Multiply Equation 1 by 6:
6x + 6y = 96 ...Equation 3
Subtract Equation 3 from Equation 2:
6x + 24y = 258
-
6x + 6y = 96
18y = 162
y = 9
x = 7 (16 - 9)
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study of ancient pottery. refer to the chance (fall 2000) study of ancient pottery found at the greek settlement of phylakopi, presented in exercise 2.14 (p. 36). of the 837 pottery pieces uncovered at the excavation site, 183 were painted. these painted pieces included 14 painted in a curvilinear decoration, 165 painted in a geometric decoration, and 4 painted in a naturalistic decoration. suppose 1 of the 837 pottery pieces is selected and examined. a. what is the probability that the pottery piece is painted? b. given that the pottery piece is painted, what is the probability that it is painted in a curvilinear decoration?
To discover the probability that the ceramics piece is painted, we basically separate the number of painted pieces by the whole number of pieces: P(painted) = 183/837 ≈ 0.2185
b. To discover the likelihood that the painted ceramics piece is painted in a curvilinear enhancement, we utilize Bayes' hypothesis:
P(curvilinear | painted) = P(painted | curvilinear) * P(curvilinear) / P(painted)
We are given that there are 183 painted pieces, of which 14 are painted in a curvilinear enrichment. In this manner,
P(painted | curvilinear) = 14/183 ≈ 0.0765
We are moreover given that there are 837 pieces in add up, of which 183 are painted.
P(painted) = 183/837 ≈ 0.2185, we ought to discover the likelihood that a painted piece is painted in a curvilinear enrichment, which is given as 14 out of 183 painted pieces. P(curvilinear) = 14/183 ≈ 0.0765
P(curvilinear | painted) = (0.0765) * (0.0765) / (0.2185) ≈ 0.0266
thus, given that the pottery piece is painted, the likelihood that it is painted in a curvilinear enhancement is roughly 0.0266, or 2.66%.
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1. Ignoring commission, 512 shares of Targa Resources (TRGP) were purchased for $2,790.40 at the close
for the week. Find the close price for the week. Then, find the quarterly dividend payment per share if
the annual dividend amount paid was $40.96.
The quarterly dividend payment per share based on the question above will be: $0.02.
The close price for the week will be: $5.45.
What is the dividend?For one to find the closing price for the week, we have to divide the total cost of the shares by using the number of shares that was bought so it will be:
Close price = Total cost / Number of shares
= $2,790.40 / 512
= $5.45
To know the quarterly dividend payment per share, we have to calculate the annual dividend payment per share before we can get it so it will be:
Annual dividend per share = Total annual dividend / Number of shares
= $40.96 / 512
= $0.08
From the question, the dividend was paid quarterly, we then divide the annual dividend per share by 4 so as to get the quarterly dividend per share:
Quarterly dividend per share = Annual dividend per share / 4
= $0.08 / 4
= $0.02
Hence the quarterly dividend payment per share will be: $0.02.
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See text below
Ignoring commission, 512 shares of Targa Resources (TRGP) were purchased for $2,790.40 at the clos for the week. Find the close price for the week. Then, find the quarterly dividend payment per share if the annual dividend amount paid was $40.96. (7pts)
EARNINGS
52-WEEK
TICK
VOL.
WEEK'S
LATEST
THIS NEXT DIV
High Low
Name
Sym.
100s
Yld.
P/E Last Chg.
Year
Year
Year
Amt
8.50
3.20
Targa Resources
TRGP
412574 1.8
PO
dd
+0.41
0.25
0.18
0.12
Can someone show me step by step correctly for a better grade
There are approximately 7.48 liquid gallons in a cubic foot. If a cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet, what is the approximate height of the water tank? Approximate using π = 3.14 and round to the nearest tenth.
4.6 feet
14.4 feet
46.0 feet
147.1 feet
The height of the cylindrical water tank is 4.6 feet. Therefore, the answer is A.
How to find the height of the water tank?The cylindrical water tank holds 1,100 liquid gallons and has a radius of 3.2 feet.
Therefore, the height of the tank can be calculated as follows:
7.48 liquid gallons = 1 ft³
1100 liquid gallons = ?
cross multiply
volume of the tank = 1100 / 7.48 = 147.058823529 ft³
Therefore, let's find the volume of the cylindrical tank.
volume of the cylindrical tank = πr²h
where
r = radiush = heightTherefore,
r = 3.2 feet
h = ?
The volume of the cylindrical tank in feet cube is 147.058823529 ft³
Let's find the height, h
volume of the cylindrical tank = 3.14 × 3.2² × h
147.058823529 = 3.14 × 10.24 × h
32.1536h = 147.058823529
divide both sides by 32.1536
h = 147.058823529 / 32.1536
h = 4.57363405653
Therefore,
height of the water tank = 4.6 feet
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Sam decides to build a square garden. If the area of the garden is 9x^2 - 24x + 16 square feet, what is the length of the garden?
The length of the square garden is s = ( 3x - 4 ) feet
Given data ,
Let the length of the square garden be s
Now , The area of a square is given by the formula A = s², where s is the length of one side of the square.
We are given that the area of the garden is:
A = 9x² - 24x + 16
To find the length of the garden, we need to take the square root of the area:
s = √(A)
Substituting the given expression for A, we get:
s = √(9x² - 24x + 16)
We can simplify this expression by factoring the quadratic under the square root sign:
s = √[(3x - 4)(3x - 4)]
Using the property that the square root of a product is equal to the product of the square roots, we can simplify further:
s = (3x - 4)
Hence , the length of the garden is 3x - 4 feet
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Question 4(Multiple Choice Worth 2 points) (Reflections MC) Use the graph to answer the question. Graph of polygon ABCDE with vertices at negative 3 comma 5, negative 3 comma 8, 1 comma 8, 1 comma 5, negative 1 comma 3. A second polygon A prime B prime C prime D prime E prime with vertices at 13 comma 5, 13 comma 8, 9 comma 8, 9 comma 5, 11 comma 3. Determine the line of reflection. Reflection across the x-axis Reflection across the y-axis Reflection across x = 5 Reflection across y = 6
The line of reflection must be the line halfway between the x-coordinates of the corresponding vertices of each polygon. This line is x=4.
So, the line of reflection is x=4.
What is line of reflection?A line of reflection is a line used in mathematics that functions like a mirror, reflecting all points on one side of the line onto the other side so that each point is equally distant from the line as its reflected point on the other side. It is also known as the mirror line or the axis of reflection.
To determine the line of reflection that maps polygon ABCDE to polygon A' B' C' D' E', we need to look for a line that is equidistant from each corresponding pair of points.
Reflection across the x-axis or y-axis will not work because the corresponding vertices of the two polygons have different y-coordinates or x-coordinates, respectively.
Reflection across x=5 or y=6 will also not work because the line is not equidistant from each corresponding pair of points.
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In a math class with 25 students, a test was given the same day that an assignment
was due. There were 15 students who passed the test and 16 students who completed
the assignment. There were 6 students who failed the test and also did not complete
the assignment. What is the probability that a student who completed the homework
passed the test?
Answer:
Let's first calculate the number of students who passed the test and completed the assignment. We know that 15 students passed the test and 6 students who failed the test and did not complete the assignment. Therefore, there are 25 - 15 - 6 = 4 students who failed the test but completed the assignment.
Now we can calculate the probability that a student who completed the homework passed the test by dividing the number of students who passed the test and completed the assignment by the total number of students who completed the assignment.
The number of students who passed the test and completed the assignment is 15 - 6 = 9. The total number of students who completed the assignment is 16 - 6 = 10. Therefore, the probability that a student who completed the homework passed the test is 9/10 or 0.9.
Step-by-step explanation:
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the inequality is
- 6x + 15 < 10 - 5x and An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
We have the inequality -3(2x - 5) < 5(2 - x)
Now, simplifying each side of inequality
-3(2x - 5) = -3(2x) + -3(-5)
-3(2x - 5) = - 6x + 15
and, 5(2 - x) = 5(2) + 5(-x)
5(2 - x) = 10 - 5x
So, - 6x + 15 < 10 - 5x
Now, Subtract 15 from both sides
- 6x < -5 - 5x
- x < - 5
x > 5
The correct statements are:
- 6x + 15 < 10 - 5x and An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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18. 12 cm 14 cm 12 cm 14 cm 8 cm Find the area of the rectangle and the triangle independently. What is the ratio comparing the area of the triangle to the area of the trapezoid (the entire figure put together)? (Must be in Reduced Form)
The ratio of the area of the triangle to the area of the trapezoid is 3:8.
How to calculate the ratioArea of the rectangle will be:
= 14 cm x 12 cm
= 168 cm²
Height of the triangle
= 14 cm - 8 cm
= 6 cm
Area of the triangle will be:
= 1/2 x 12 cm x 6 cm
= 36 cm²
Area of the trapezoid will be:
= 1/2 x (base1 + base2) x height
= 1/2 x (12 cm + 12 cm) x 8 cm
= 96 cm²
Ratio will be:
Area of the triangle / Area of the trapezoid
= 36 cm² / 96 cm²
= 3/8
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dominik used 7/8 cup of sugar for a bread recipe. he used 3/4 cup of sugar for a muffin recipe. how much sugar, in cups, did dominik use for both recipes?
Dominik used 7/8 cup of sugar for a bread recipe. he used 3/4 cup of sugar for a muffin recipe.
To find out how much sugar Dominik used in total for both recipes, we need to add the amounts of sugar he used in each recipe.
7/8 cup + 3/4 cup
To add these two fractions, we need to find a common denominator. In this case, the smallest common denominator is 8, which is the same as the denominator of the first fraction.
7/8 cup + 3/4 cup = (7/8) cup + (6/8) cup
Now we can add the two numerators
(7/8) cup + (6/8) cup = 13/8 cup
Hence, Dominik used 13/8 cups of sugar for both recipes combined.
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There are 31 students in a class. Each student was asked how many pets he has at home. The table below summarizes the data.
Based on the data, estimate the probability that a randomly selected student from this class has four or more pets at home. Round your answer to the nearest two decimal places.
Please help :DDD
The estimated probability that a randomly selected student from this class has four or more pets at home is approximately 0.13.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. Usually, it is stated as a number between 0 and 1, where 0 denotes that an event is impossible and 1 denotes that it is certain to happen.
According to question:Out of the 31 students surveyed, 6 reported having no pets, 8 reported having one pet, 10 reported having two pets, 3 reported having three pets, and a total of 4 (1+2+1) reported having four or more pets.
Thus, the probability that a randomly selected student from this class has four or more pets at home is:
P(four or more pets) = 4/31 ≈ 0.13 (rounded to two decimal places)
Therefore, the estimated probability that a randomly selected student from this class has four or more pets at home is approximately 0.13.
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When children roll a die for a game, their probability of rolling a 5 is 17%. This is an example of which type of probability?
The probability of rolling a 5 when playing a game with a die is an example of empirical probability.
Empirical probability is determined through observation and experimentation, by counting the number of times an event occurs and dividing it by the total number of trials. In this case, the children have likely rolled the die multiple times and recorded the number of times a 5 was rolled.
They then calculated the probability of rolling a 5 by dividing the number of times a 5 was rolled by the total number of rolls. Empirical probability is commonly used in fields such as science and statistics, where data is gathered through experimentation and observation.
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Kiera had 1 1/3 cups of coffee in the morning and 1 1/4 cups of coffee in the afternoon. She wants to add the fractions 1 1/3+ 1 1/4 to find how much coffee she drank in all.
She can add the whole numbers, but before she can add the fractions she must find the common denominator. Drag and drop the numbers into the boxes to make the statement true.
Picture attached to
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
To add and Kiera found the common denominator is Response area. Before adding the fractions together she wrote the numerator of the first fraction as Response area and the numerator of the second fraction as Response area.
For given problem, The common denominator is 12 and Before adding the fractions the numerator of first fraction was 16 and numerator of second fraction was 15.
What are fractions?The representation of sections or portions of a whole using fractions is common. It consists of Numerator and the denominator reflects the total number of equally sized pieces that make up the whole, whereas the numerator represents the number of components we have.
For example, in the fraction 5/4, 4 is the denominator and 5 is the numerator.
Now for given problem,
Kiera had [tex]1\frac{1}{3}[/tex] cups of coffee in the morning, equivalent to [tex](4/3)[/tex] cups of coffee.
Kiera also had[tex]1 \frac{1}{4}[/tex] cups of coffee in the afternoon, equivalent to [tex](5/4)[/tex] cups of coffee.
Now we can add the two fractions together:
[tex](4/3) + (5/4)[/tex]
To find common Denominator;
(LCM) of 3 and 4 is 12
Making denominator of both fraction 12;
[tex](4/3) * (4/4) + (5/4) * (3/3)[/tex]
[tex](16/12) + (15/12)[/tex]
[tex]16/12 + 15/12 = (16 + 15)/12 = 31/12[/tex]
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a fair coin is tossed three times, and the events a and b are defined as follows: a: 5at least one head is observed.6 b: 5the number of heads observed is odd.6 a. identify the sample points in the events a, b, a b, ac , and a b. b. find p1a2, p1b2, p1a b2, p1ac 2, and p1a b2 by summing the probabilities of the appropriate sample points. c. use the additive rule to find p1a b2 . compare your answer with the one you obtained in part b. d. are the events a and b mutually exclusive? why?
The evaluated solution for the given question comprises of sample point of a that are {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH} , the event probability is 0.875 and the probability of implementing a, b is 3/4 below under the condition of a fair coin is tossed three times, and the events a and b are defined.
a) Points sample for event a: {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH}
Points sample for event b: {HTT, THT, TTH, HHH}
Points sample for event a b: {HTT, THT, TTH, HHH, HHT, HTH, THH}
Points sample for event ac: {TTT}
Points sample for event a c: {TTT, HHHH}
b) Event a probability= 7/8 = 0.875
Event b probability= 1/2 = 0.5
Event ab probability = 3/8 = 0.375
Event ac probability = 1/8 = 0.125
Event a c probability = 1/16 + 1/8 = 0.1875
c) Probability of a b implementing additive rule
P(a b) = P(a) + P(b) - P(a ∩ b)
P(a ∩ b) = P(a) + P(b) - P(a b)
P(a ∩ b) = (7/8) + (1/2) - (3/8)
P(a ∩ b) = 9/8 - 3/8
P(a ∩ b) = 6/8
P(a ∩ b) = 3/4
d) Hence, events a and b are not mutually exclusive due to the lack of chances of having common sample points {HHH}.
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A rock dropped into a pond and creates a circular area of ripples whose radius increases at a constant rate of 2 feet per second. At what rate is the circular area increasing with respect to time when the radius os exactly 3 feet
The rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the radius is exactly 3 feet.
To solve this problem, we need to use the formula for the area of a circle:
[tex]A = πr^2[/tex],
where A is the area and r is the radius.
We also need to use the chain rule of differentiation because we are dealing with a changing radius over time.
First, we can find the rate of change of the area with respect to time (dA/dt) by differentiating the formula for the area:
dA/dt = 2πr(dr/dt)
where dr/dt is the rate of change of the radius with respect to time, which is given as 2 feet per second in the problem.
Therefore, we can substitute these values into the formula to get:
dA/dt = 2π(3)(2)
dA/dt = 12π
So, the rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the
radius is exactly 3 feet.
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Help 44 PONITS
Graph the inverse for each relation below ‐ show answers right over the existing graph on the same
plane. 3 points each
The inverse of the graphs are added as an attachment
Plotting the inverse of the graphTo plot the inverse of a graph, you can follow these steps:
Start with a function f(x).Replace f(x) with y.Swap the x and y variables so that the equation is in terms of x and y.Solve for y to get y = f^(-1)(x), which represents the inverse function.Plot the original function f(x) on a coordinate plane.Reflect the graph of f(x) across the line y = x to get the graph of fSee attachment for the graphs
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A 35 foot ladder is set against the side of a house so that it reaches up 21 feet. If Elijah grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 17 ft.) Round to the nearest tenth of a foot.
Answer:
[tex] {21}^{2} + {x}^{2} = {35}^{2} [/tex]
[tex] {x}^{2} =784[/tex]
[tex]x = 28[/tex]
[tex] {y}^{2} + {32}^{2} = {35}^{2} [/tex]
[tex] {y}^{2} = 201[/tex]
[tex]y = \sqrt{201} = 14.18[/tex]
The ladder will reach about 14.2 feet up the side of the house.