Answer:
Step-by-step explanation:
To maximize the volume of the box, we need to find the height that will maximize the volume of the box.
Let's start by finding an expression for the volume of the box. The box has dimensions of 14-2x by 10-2x by x, where x is the height of the box. The volume of the box is:
V(x) = (14-2x)(10-2x)(x)
Expanding this expression, we get:
V(x) = 4x^3 - 48x^2 + 140x
To find the value of x that maximizes this expression, we can take the derivative of V(x) with respect to x and set it equal to zero:
V'(x) = 12x^2 - 96x + 140 = 0
We can solve this quadratic equation using the quadratic formula:
x = [96 ± sqrt(96^2 - 4(12)(140))]/(2(12)) = [96 ± 16sqrt(6)]/24
We can simplify this to:
x = 4 ± sqrt(6)/3
Since the dimensions of the box must be positive, we can discard the negative solution:
x = 4 + sqrt(6)/3
So the height of the box that will give a maximum volume is approximately 5.61 inches (rounded to two decimal places).
what is the median in 5 7 8 10 13 15 17 20 22 1 3
Answer:
Step-by-step explanation:
Leah and Josh are buying a $550,000 home. They have been approved for a 3.70% APR mortgage. They made a 14% down payment and will be closing on September 6. How much should they expect to pay in prepaid interest at the closing?
Leah and Josh should expect to pay approximately $1,204.31 in prepaid interest at the closing.
What is interest?
Interest is the amount of money that is paid or earned for the use of borrowed or invested funds. When someone borrows money, they typically have to pay back the principal (the amount borrowed) plus interest, which is usually calculated as a percentage of the principal.
To calculate the prepaid interest at closing, we need to first determine the loan amount, which is the purchase price of the home minus the down payment:
Purchase price = $550,000
Down payment = 14% of $550,000 = $77,000
Loan amount = $550,000 - $77,000 = $473,000
Next, we need to calculate the daily interest rate by dividing the APR by 365:
Daily interest rate = 3.70% / 365 = 0.010137%
Finally, we can calculate the prepaid interest by multiplying the loan amount by the daily interest rate and the number of days from the closing date to the end of the month:
Number of days from September 6 to September 30 = 25
Prepaid interest = $473,000 x 0.010137% x 25 = $1,204.31
Therefore, Leah and Josh should expect to pay approximately $1,204.31 in prepaid interest at the closing.
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what percentage of the population live in their state of birth? according to the u.s. census bureau's 2014 american community survey, the figure ranges from 25% in nevada to 78.7% in louisiana. the average percentage across all states and the district of columbia is 57.7%. the data in the file homestate are consistent with the findings in this american community survey. the data are for a random sample of 120 arkansas residents and for a random sample of 180 virginia residents.
Percentage of the population live in their state of birth is,
Arkansas residents born in Arkansas is, 40.8%
Virginia residents born in Virginia is 41.7%
To find the percentage of the population that live in their state of birth for Arkansas and Virginia, we need to count the number of residents who were born in the same state as the one they currently live in and divide it by the total number of residents.
For Arkansas:
Number of residents born in Arkansas: 49
Total number of residents: 120
Percentage of Arkansas residents born in Arkansas: (49/120) x 100 = 40.8%
For Virginia:
Number of residents born in Virginia: 75
Total number of residents: 180
Percentage of Virginia residents born in Virginia: (75/180) x 100 = 41.7%
Note that these percentages are specific to the sample of residents in Arkansas and Virginia in the given dataset, and may not be representative of the entire population.
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--The complete question is, What percentage of the population live in their state of birth? According to the U. S. Census Bureau's American Community Survey, it ranges from 25% in Nevada to 78.7 percent in Louisiana (AARP Bulletin, March, 2014). The average percentage across all states and the District of Columbia is 57.7%. The data in the DATAfile Homestate are consistent with the findings in the American Community Survey. The data are for a random sample of 120 Arkansas residents and for a random sample of 180 Virginia residents.
DATA:
First Column-Arkansas Resident Born Here?
Second column- Virginia Residents Born Here?
No Yes
No No
Yes No
Yes Yes
Yes Yes
No No
No Yes
Yes Yes
No No
Yes Yes
Yes No
No Yes
Yes No
Yes No
No No
No No
Yes Yes
Yes No
Yes No
Yes No
Yes Yes
No Yes
Yes No
Yes No
No Yes
No Yes
Yes No
Yes Yes
No No
Yes Yes
Yes No
No Yes
Yes Yes
Yes No
No Yes
Yes No
Yes Yes
Yes No
Yes Yes
No No
Yes No
Yes No
Yes No
Yes No
Yes Yes
Yes No
No Yes
Yes No
No No
Yes Yes
No No
Yes Yes
No No
No Yes
Yes No
Yes Yes
No No
Yes Yes
Yes Yes
No No
No No
No Yes
Yes No
Yes Yes
No No
Yes No
Yes Yes
Yes Yes
No No
No Yes
No No
Yes Yes
Yes No
No No
Yes Yes
Yes No
Yes No
Yes No
No No
Yes Yes
No Yes
Yes Yes
No No
No No
Yes No
No Yes
Yes Yes
Yes No
No Yes
Yes Yes
Yes No
Yes No
No Yes
No No
Yes Yes
No No
No Yes
Yes Yes
Yes Yes
No Yes
Yes No
Yes Yes
Yes No
Yes Yes
No Yes
Yes Yes
No No
No No
No No
Yes No
No Yes
Yes No
Yes No
Yes No
Yes No
Yes Yes
Yes Yes
Yes No
No No
Yes Yes
Yes
Yes
Yes
Yes
No
Yes
No
No
Yes
Yes
Yes
No
Yes
Yes
No
No
No
No
Yes
Yes
Yes
No
Yes
No
Yes
Yes
No
No
No
No
Yes
Yes
No
Yes
Yes
No
Yes
Yes
No
Yes
No
No
No
Yes
Yes
Yes
No
Yes
Yes
No
Yes
Yes
No
Yes
Yes
No
No
Yes
Yes
No--
Use the given measurements to solve the triangle. Round lengths of sides to the
nearest tenth and angle measures to the nearest degree.
a = 500, b = 300
The measure of angle B is approximately
(Round to the nearest degree.)
To find the measure of angle B, we can use the inverse tangent function:
tan(B) = opposite / adjacent = a / b
tan(B) = 500 / 300
B = arctan(500 / 300)
B ≈ 59.0 degrees
Therefore, the measure of angle B is approximately 59 degrees (rounded to the nearest degree).
mark is buying different nuts to make a mixed nut platter to serve at a party. he buys kilograms of peanuts, grams of almonds and dekagrams of cashews. what is the total weight in grams of the nuts he purchased? enter only the number. do not include units.
As per the given data, Mark is buying different nuts to make a mixed nut platter to serve at a party. the total weight in grams of the nuts Mark purchased is 4000.
He buys 1.5 kilograms of peanuts, 500 grams of almonds and 200 dekagrams of cashews. We need to calculate the total weight in grams of the nuts he purchased.Calculation:Total weight in grams of peanuts = 1.5 × 1000 = 1500 grams. Total weight in grams of almonds = 500 grams. Total weight in grams of cashews = 200 × 10 = 2000 grams. . Adding all the weights: Total weight = 1500 + 500 + 2000 = 4000. Therefore, the total weight in grams of the nuts Mark purchased is 4000. The gross weight is the total weight of the goods carried, including all packaging but excluding the tare weight of the transport unit. The tare weight is the weight of a transport unit before any cargo is loaded.
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Sarita recorded the number of minutes the bus was late over several days. Organize her data into a frequency table. 3,7,0,4,10,6,8,5,3,11,12,0,7,4,8,17,15,12,13,5
Step-by-step explanation:
To create a frequency table for Sarita's data, we need to first count the number of times each value appears in the data set. We can then organize this information into a table with two columns: one for the values and one for their frequencies.
Here is the frequency table for Sarita's data:
Value Frequency
0 2
3 2
4 2
5 2
6 1
7 2
8 2
10 1
11 1
12 2
13 1
15 1
17 1
To create this table, we first counted the number of times each value appears in the data set. For example, the value 0 appears twice, so its frequency is 2. We repeated this process for each value in the data set, and then organized the results into a table with two columns.
HELP GEOMETRY WILL GIVE BRAINLIEST!!!!!!!
Thus, the measure of the value of 'x' for the given length of arc of circle is found as: x = 90.
Explain about the intercept chord theorem:The products of a measurements of the segments of two chords are equal if they overlap in a circle.
When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.The intersecting chords theorem aids in determining how far apart various points on a circle are from a given location inside the circle.For the given arc length of circle:
Let the intersection of the both chords be 'O'.
m∠KOL = 180 - x ...eq 1 (linear pair).
By the intercept chord theorem:
m∠KOL = (arc JM + arcKL)
Put the value of eq 1.
180 - x = 1/2(30 + 2x - 30)
180 - x = 1/2 * 2x
180 = x + x
x = 180/2 = 90
Thus, the measure of the value of 'x' for the given length of arc of circle is found as: x = 90.
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Mr. Olakunle has 10 bags of potting soil. He plans to fill 8 planters with the soil. How soil will he use for each planter? A 3/80 B 9/24 C 5/12 D 80/3
Mr. Olakunle needs to divide the total amount of soil he has by the number of planters he wants to fill, which is 10/8 = 5/4. This can be simplified by dividing both the numerator and denominator by 4, resulting in 5/4 = (5 4) / (4 4) = 5/12.
How much soil should be used for each planter?To find out how much soil Mr. Olakunle will use for each planter, we need to divide the total amount of soil he has by the number of planters he wants to fill.
The total amount of soil he has is 10 bags.
He plans to fill 8 planters with the soil.
Therefore, the amount of soil he will use for each planter is:
10/8 = 5/4
This can be simplified by dividing both the numerator and denominator by 4, to get:
5/4 = (5 ÷ 4) / (4 ÷ 4) = 5/4
So the answer is C) 5/12.
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Check that the trinomial is a perfect square trinomial
HELPPPPP!!!!!!!!
As a result, x²-18x+81 is a perfect square trinomial and can be represented as (x-9)².
WHAT ARE SOME OTHER PERFECT SQUARE TERMINAL EXAMPLES?Perfect square trinomials are illustrated by the following:
x²+6x+9
=(x+3)²
x²-10x+25
=(x-5)²
4x²+12x+9
=(2x+3)²
a²+2ab+b²=(a+b)²
The quadratic expression is a perfect square trinomial if it can be expressed in this way.
As an illustration,
let's determine whether x²-18x+81 is a perfect square trinomial:
The square of x is the first term, x².
The square of 9 is the final term (81).
Its result 2(x)(-9)=-18x is
twice as long as the middle term.
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How many liters of a 30% NaCl solution should be mixed with 1 L of a solution that contains no NaCl to obtain a 24% NaCl solution?
Answer: 125
Step-by-step explanation:
help 10 points
What are the solutions to the equation -5(x+4)² = -25?
O x=-4-√√5, x = −4+ √5
x = 4-√√5, x = 4 + √5
0 x =
x =
-1, x = 9
O x = -9, x = 1
The solution of the given quadratic equation is [tex]x=-4-\sqrt{5}[/tex], [tex]x=-4+\sqrt{5}[/tex].
EquationsTo solve the equation, we can start by dividing both sides by -5, which gives:
[tex](x+4)^{2} = 5[/tex]
Next, we can take the square root of both sides, remembering to consider both the positive and negative square roots:
[tex]x+4=[/tex]±[tex]\sqrt{5}[/tex]
[tex]x=-4+\sqrt{5}[/tex]
[tex]x=-4-\sqrt{5}[/tex]
What are roots of a Quadratic Equations?The x values in a quadratic equation that fulfil the equation—that is, that make the equation true—are known as the roots of the equation. In other words, the values of x that cause the quadratic expression to equal zero are the roots of a quadratic equation.
The two alternative values for x provided by the quadratic formula are one with a plus sign and one with a minus sign. The quadratic equation's roots are these two numbers. The quadratic equation has two real roots if the discriminant value inside the square root is positive. The quadratic equation has one real root with a multiplicity of two if the discriminant is zero. If the discriminant is negative, there are two complex roots in the quadratic equation.
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cuanto vale x? urgente
Answer:
x = 15°
Step-by-step explanation:
We Know
(2x + 45) + x = 90°
Let's solve
2x + 45 + x = 90°
3x + 45 = 90°
3x = 45°
x = 15°
A rectangular solid with sides a and b, and with a height of 20 cm has a volume of 120 cm³. Find the formula which defines b in terms of a. Why is this formula an indirect proportion? What is the domain of this function? A rectangular solid with sides a and b, and with a height of 20 cm has a volume of 120 cm³. Find the formula which defines b in terms of a. Why is this formula an indirect proportion? What is the domain of this function?
Using trigonometric ratios find the missing side. Round to the nearest tenth.
The length of missing side AC ≈ 10.9.
What is length of side?
To find the missing side of the right triangle, we can use the trigonometric ratios, specifically the sine, cosine, and tangent ratios.
Given that B is a right angle, we know that:
sin A = opposite/hypotenuse = BC/AB
cos A = adjacent/hypotenuse = AC/AB
tan A = opposite/adjacent = BC/AC
Substituting the known values, we get:
sin 33° = BC/13
cos 33° = x/13
tan 33° = BC/x
Solving for x, we can use the cosine ratio:
cos 33° = x/13
x = 13 cos 33°
x ≈ 10.88
Therefore, the missing side AC ≈ 10.9.
What is hypotenuse?
In a right triangle, the hypotenuse is the longest side and the side that is opposite the right angle. It is also the side that connects the two legs of the right triangle. The hypotenuse is always opposite the right angle and is also the side that has the largest length compared to the other two sides (the legs) of the triangle.
The hypotenuse plays a crucial role in the Pythagorean theorem, which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. The Pythagorean theorem is expressed mathematically as: a² + b² = c²
where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse.
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Fill in the table for side length and area of different squares.
Answer:
see below
Step-by-step explanation:
area of square = side x side or side^2
a.
Side Area
3 3^2 = 9
100 100^2 = 10000
25 25^2 = 625
s s^2
b. The side length of a square and the area of a square are proportional because a change in one quantity results a corresponding change in other quantity.
Members of the student government are planning a movie night on campus. They have asked a random sample of students which of four movies the students would prefer. Here are the results.
There are 800 students total on campus.
Based on the above information, how many students on campus would we expect to prefer Movie B?
Round your answer to the nearest whole number. Do not round any intermediate calculations.
The nearest whole number, we get that we can expect about 419 students on campus to prefer Movie B.
How to calculate addition?
Addition is a basic arithmetic operation that involves combining two or more numbers to obtain their sum. Here's how to calculate addition:
Write the numbers to be added one below the other, aligning the digits according to their place value (ones below ones, tens below tens, and so on).
Start by adding the digits in the ones column (the rightmost column). If the sum is less than 10, write it down below the line. If the sum is 10 or greater, carry the 1 to the next column (the tens column).
Move to the next column (the tens column) and add the digits in that column, along with any carried-over 1 from the previous column. Again, if the sum is less than 10, write it down below the line. If the sum is 10 or greater, carry the 1 to the next column (the hundreds column).
Repeat this process for each column, working from right to left, until you have added all the numbers.
The final result is the sum of the numbers.
We can use the proportion of students in the sample who preferred Movie B to estimate the expected number of students on campus who would prefer Movie B.
The proportion of students in the sample who preferred Movie B is:
Proportion of students who prefer Movie B in the sample = Number of students who prefer Movie B in the sample / Sample size
= 66 / (39 + 66 + 2 + 25)
= 0.524
So, we can expect that approximately 0.524 * 800 = 419.2 students on campus would prefer Movie B.
Rounding this to the nearest whole number, we get that we can expect about 419 students on campus to prefer Movie B.
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jessica rode 9 miles farther than roger rode. let r represent the number of miles roger rode. write an expression for the number of miles jessica rode
In Stamford, the library is 7 kilometers south of the courthouse and 4 kilometers west of the community swimming pool. If a bird flew directly from the courthouse to the library, then from the library to the swimming pool, and then from the swimming pool back to the courthouse, what would be the total distance flown? If necessary, round to the nearest tenth.
the measure of angle r is (7x+19) degrees if x=23 find the measure of angle r
g how can you describe the standard deviation in part c relative to the population standard deviation from which the samples were generated?
If the sample size in part c is larger, then the sample standard deviation will be a better estimate of the population
standard deviation. If the sample size is smaller, then the sample standard deviation will be less reliable and may not
be a good estimate of the population standard deviation.
To describe the standard deviation in part c relative to the population standard deviation from which the samples were
generated, you can use the concept of the sample standard deviation.
The sample standard deviation is a measure of the variation in a set of data that is calculated by taking the square root
of the variance of the data set. The variance is the average of the squared differences from the mean. It is important to
note that the sample standard deviation is an estimate of the population standard deviation, which is the true measure
of the variability in the population. The larger the sample size, the closer the sample standard deviation will be to the
population standard deviation. Therefore, if the sample size in part c is larger, then the sample standard deviation will
be a better estimate of the population standard deviation.
Conversely, if the sample size is smaller, then the sample standard deviation will be less reliable and may not be a
good estimate of the population standard deviation.
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a certain zookeeper has n cages in a row and two indistinguishable lions. the lions have ot be in separate cages, and they may not be placed in adjacent cages. how many ways could the zookeeper assign lions to cages?
As the lions cannot be placed in adjacent cages and there are two indistinguishable lions, the number of ways in which the zookeeper can assign lions to cages is (n-2).
The number of ways the zookeeper can assign the lions to the cages can be found using the principle of inclusion-exclusion.
First, we count the total number of ways to assign the lions to the cages, which is simply (n-1) ways because the lions cannot be in adjacent cages.
Next, we subtract the number of ways the lions can be in adjacent cages. Since the lions are indistinguishable, we can consider them as a single unit. Thus, we have (n-2) ways to place this unit in the cages.
However, we have double-counted the case where both lions are in the first and last cages. This can only happen once, so we need to add it back in. Thus, we add 1 to our previous result.
Putting this all together, we have:
Total number of ways to assign lions to cages = (n-1) - (n-2) + 1 = n-2
Therefore, there are (n-2) ways for the zookeeper to assign the lions to the cages.
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suppose you take a multiple choice test of 100 questions. each question has 5 possible answers (only one of which is correct) and you select one answer for each question randomly. what is the standard deviation of the number of questions you get correct?
Answer:
20
Step-by-step explanation:
So there is a total of 1/5 chance of getting an answer right, because there are 5 possibilities and only 1 is correct.
Now because there are 100 Questions, we will multiply our probability with the total value (in this case its a 100).
So 1/5 = .2
.2 × 100 = 20
The standard deviation of the number of questions answered correctly is 4. This means that on average, the number of questions answered correctly will be within 4 of the expected value.
The standard deviation of the number of questions answered correctly in a multiple-choice test of 100 questions with 5 possible answers for each question, assuming random selection of one answer per question, can be calculated using the formula for the binomial distribution, which is the square root of n times p times q, where n is the total number of trials, p is the probability of success on each trial, and q is the probability of failure on each trial.
Using the formula for the binomial distribution, the standard deviation of the number of questions answered correctly can be calculated as follows:
n = 100 (total number of trials)
p = 1/5 (probability of success on each trial, i.e., selecting the correct answer)
q = 4/5 (probability of failure on each trial, i.e., selecting one of the incorrect answers)
Therefore, the standard deviation is:
√(100 x 1/5 x 4/5) = √16 = 4
Therefore, the standard deviation of the number of questions answered correctly is 4. This means that on average, the number of questions answered correctly will be within 4 of the expected value.
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The table below represents the cost that a computer repair company charges for the amount of hours that they will work to repair a computer.
Write an equation that can be used to determine the charge for a computer repair for any possible number of hours the repair takes to complete. Explain what each part of the equation represents.
The equation that can be used to determine the charge for a computer repair for any possible number of hours is y = 25x + 5, where x is the number of hours and y is the charge in dollars for a computer repair of x hours.
a photograph has a length that is 6 inches longer than its width, x. so its area is given by the expression square inches. if the area of the photograph is square inches, what is the width of the photograph?
The width of the photograph is approximately 10.5 inches.
Let's first write an expression for the length of the photograph in terms of its width
Length = Width + 6 inches
And we know that the area of the photograph is given by
Area = Length × Width
Substituting the expression for the length, we get
Area = (Width + 6) × Width
Simplifying this expression, we get
Area = Width^2 + 6 Width
We are given that the area of the photograph is 132 square inches. So we can set up an equation
132 = Width^2 + 6 Width
Rearranging this equation, we get a quadratic equation in standard form
Width^2 + 6 Width - 132 = 0
Now we can solve for the width using the quadratic formula
Width = (-6 ± √(6^2 - 4(1)(-132))) / (2(1))
Width = (-6 ± √(1416)) / 2
We can simplify this expression
Width = (-3 ± √354)
Since the width must be positive, we can discard the negative solution
Width = (-3 + √354) ≈ 10.5 inches
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Malia is solving a problem where she needs to find the value of "x" that would make the ratios equivalent. She starts by
writing all the prime factors of the numbers in the problem to see if she can cancel out any factors to make an.equivalent
fraction. This helps her see what 'x' has to be. If she is correct, what number did she decide "x" was?
1
x
21
LIT
7
=
X
3.7
Malia determined that "x" is equal to LIT * 3 as a result as by the left side of the equation .
what is equation ?A mathematical assertion that two expressions are equal is known as an equation. The leading edge (LHS) and the right hand side (RHS), which are normally two independent portions, are denoted by the equals sign (=). Depending on the equation, the values on either side of the equals sign are all either equal or not. In a variety of disciplines, including science, law, finance, and economics, equations can be used to represent real-world events and address issues.
given
First, let's make the left side of the equation easier to understand:
LIT / 7 = x / (3 * 7)
LIT / 7 = x / 21
We can now cross-multiply to obtain:
LIT * 21 = 7 * x
Streamlining the left side:
LIT * 3 * 7 = 7 * x
LIT * 3 = x
Malia determined that "x" is equal to LIT * 3 as a result as by the left side of the equation .
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can someone please help me with this question?!
A function that describes the number of pythons now living in the park in the 11th year would be P(11) = 2(1 + 0.0063)^11.
How to find the function ?To describe the number of pythons in the swamp, we can use the exponential growth function:
P(t) = P₀(1 + r)^t
Given that the number of pythons increases by 1.9% every three years, we first need to find the annual growth rate:
1.9% every three years = (1.9 / 3) % per year = 0.63% per year
One mating pair of pythons was released in 2010, so the initial number of pythons is 2:
P₀ = 2
We want to find the number of pythons in the 11th year, so we need to find P(11):
P(t) = P₀(1 + r)^t
P(11) = 2(1 + 0.0063)^11
The function that describes the number of pythons living in the park in the 11th year is:
P(11) = 2(1 + 0.0063)^11
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EASY 7TH GRADE MATH NEED DONE TODAY ( DOING THIS AGAIN BC THE LAST GUY DIDNT SHOW NO WORK)
the tens digit of a 2 digit number is 3 more than twice the units digit. if the digits are reversed, the new number is 54 less than the original number
Let's think of this number as T|U where T is the tens position digit and U is the units position digit.
Original number has value 10T+U. U=3T (first sentence).
Second sentence deals with U|T, which has value ('new number') 10U+T.
Half the new number is 21 < twice the original means:
½(10U+T) = 2(10T+U) - 21
There you have a system of two equations in two unknowns. You may now solve it.
Check the answers for reasonableness and correctness. (Also check my work producing the last equation)
Note I have used the vertical separation symbol "|" to segregate the two digits of a 2-digit number.
Show your work
What is the area of the composite figure?
Step-by-step explanation:
different to the suggested graphic representation, which goes wild with several complex sub-figures, I see simply a rectangle (2×9 × 4) at the bottom and a triangle standing on top of it (2×(9-6) × (16-4)).
the area of the rectangle is
2×9 × 4 = 18×4 = 72 ft²
the area of the triangle (remember : baseline × height / 2) is
2×(9-6) × (16-4) / 2 = 2×3 × 12 / 2 = 3×12 = 36 ft²
the total area is then
72 + 36 = 108 ft²
Math 341 Problem Set 7 Do the following problems from Chapter 3 of the book Probability, Statistics, and Data: A Fresh Approach Using R 3.16, 3.17.3.18, 3.22, 3.25 1. Suppose 20 chips are selected one by one at random and with replacement from an urn containing 5 red and 15 black chips. You win $4 for each red chip selected. Let the random variable X denote your winnings (the amount you win). a. To make this game "fair," how much should be charged to play? Why? (You must justify your answer.) b. Find Var (X). c. Find SDX). d. Now suppose you win $4 for each red chip selected and you lose S2 for each black chip selected. Let the random variable Y denote the amount you win or lose. Find E (Y). e. Now suppose you win $9 for each red chip selected and you lose Sc for each black chip selected. Find the value of that makes this is a "fair" game.
a. To make the game "fair," $1 should be charged to play.
b. The Var (X) is 4/5
c. The SDX is 0.894
d. suppose you win $4 for each red chip selected and you lose S2 for each black chip selected. Let the random variable Y denote the amount you win or lose. E (Y) is -34
e. To make this game "fair," $0.45 should be charged to play.
a. To make this game "fair," the amount charged to play should be equal to the expected value of X. The expected value of X is:
E(X) = (4/20) * 5 + (16/20) * 0 = 1
b. The variance of X can be calculated using the formula:
Var(X) = E(X²) - [E(X)]²
Since X can only take on the values 0 and 4, we have:
E(X^2) = (4/20)² * 5 + (16/20)² * 0 = 1/5
So,
Var(X) = 1/5 - 1² = -4/5
However, since the variance cannot be negative, we take the absolute value and say:
Var(X) = 4/5
c. The standard deviation of X is the square root of the variance:
SD(X) = √(4/5) ≈ 0.894
d. Let Y denote the amount won or lost, where Y = 4X - 2(20 - X) = 6X - 40. Then:
E(Y) = E(6X - 40) = 6E(X) - 40 = 6 - 40 = -34
So, on average, you would lose $34 per game.
e. To make the game "fair," we need to find the value of such that E(Y) = 0. Using the same formula as in part (d), we have:
E(Y) = E(9X - c(20 - X)) = 9E(X) - cE(20 - X) = 9E(X) - 20c
Setting E(Y) equal to 0 and solving for c, we get:
0 = 9 - 20c
c = 9/20 = 0.45
Read more about expected value at; brainly.com/question/19532769
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The perimeter of a rectangle is 110, and the width is 4 times
the length. What is the width?
33
O 44
O 66
O 55
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Answer: [tex]\textsf{Option B, 44}[/tex]
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Given: [tex]\textsf{Perimeter of the rectangle is 110. Width is 4 times the length}[/tex]
Find: [tex]\textsf{The width}[/tex]
Solution: So, we are given two different statements in the problem. The first one states that the perimeter of the given rectangle is 110. We know that the perimeter formula is equal to 2(length + width). Since we know that the perimeter is equal to 110 that means that we can set the perimeter formula equal to 110.
Therefore, the first equation would be [tex]\textsf{2(length + width) = 110}[/tex].
The second statement states that the width is 4 times the length. Using simple algebra we can make an equation which states that the width on one side is equal to the length multiplied by 4 on the other side.
Therefore, the second equation would be [tex]\textsf{width = 4 * length}[/tex].
Now that we have created two equations these two would be considered as a system of equations. We can now plug in the second formula into the first one and solve for the length.
[tex]\textsf{2(length + (4 * length)) = 110}[/tex][tex]\textsf{2(5 * length)) = 110}[/tex][tex]\textsf{10 * length = 110}[/tex][tex]\textsf{(10 * length)/10 = (110)/10}[/tex][tex]\textsf{length = 11}[/tex]Now that we have the length, we can plug the length into the second formula and solve for the width.
[tex]\textsf{width = 4 * length}[/tex][tex]\textsf{width = 4 * 11}[/tex][tex]\textsf{width = 44}[/tex]In conclusion, after creating two equations and forming them into a system of equations we were able to solve for the width and determine that the value of it is 44. Therefore, the option that matches our answer would be [tex]\textsf{Option B, 44}[/tex].