Answer: 63
Step-by-step explanation:
PEMDAS, so parentheses come first,
9+9=18
And the next in your problem would be Addition.
So,
18+45=63
Answer:
60
Step-by-step explanation:
Randi went to Lowe’s to buy wall-to-wall carpeting. She needs 109.41 square yards for downstairs, 30.41 square yards for the halls, and 160.51 square yards for the bedrooms upstairs. Randi chose a shag carpet that costs $13.60 per square yard. She ordered foam padding at $3.10 per square yard. The carpet installers quoted Randi a labor charge of $3.75 per square yard.
What will the total job cost Randi? (Round your answer to the nearest cent.)
Rounded to the nearest cent, the total job cost for Randi is $6,138.99.
To calculate the total cost for Randi's carpeting job, we need to consider the cost of the carpet, foam padding, and labor.
1. Carpet cost:
The total square yards of carpet needed is:
Downstairs: 109.41 square yards
Halls: 30.41 square yards
Upstairs bedrooms: 160.51 square yards
The total square yards of carpet required is the sum of these areas:
109.41 + 30.41 + 160.51 = 300.33 square yards
The cost of the carpet per square yard is $13.60.
Therefore, the cost of the carpet is:
300.33 * $13.60 = $4,080.19
2. Foam padding cost:
The total square yards of foam padding needed is the same as the carpet area: 300.33 square yards.
The cost of the foam padding per square yard is $3.10.
Therefore, the cost of the foam padding is:
300.33 * $3.10 = $930.81
3. Labor cost:
The labor cost is quoted at $3.75 per square yard.
Therefore, the labor cost is:
300.33 * $3.75 = $1,126.99
4. Total job cost:
The total cost is the sum of the carpet cost, foam padding cost, and labor cost:
$4,080.19 + $930.81 + $1,126.99 = $6,138.99
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how many different positive integers divisible by $4$ can be formed using each of the digits $1,$ $2,$ $3,$ and $4$ at most once, and no other digits? for example, $12$ counts, but $512$ does not.
There are six different positive integers divisible by 4 that can be formed using each of the digits 1, 2, 3, and 4 at most once and no other digits: 12, 24, 32, 42, 43, and 124.
1. 12: 1 and 2
2. 24: 2 and 4
3. 32: 3 and 2
4. 42: 4 and 2
5. 43: 4 and 3
6. 124: 1, 2 and 4
The six different positive integers divisible by 4 that can be formed using each of the digits 1, 2, 3, and 4 at most once and no other digits are 12, 24, 32, 42, 43, and 124. To find these numbers, we begin by examining all the possibilities that can be formed using the digits 1, 2, 3, and 4. We can form 12, 24, 32, 42, 43 and 124 by combining different combinations of the digits. For example, 12 is made up of the digits 1 and 2. 24 is made up of 2 and 4. 32 is made up of 3 and 2. 42 is made up of 4 and 2.
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the quotient of a number and 3 is 8
Answer:
The number is 24
Step-by-step explanation:
The quotient is the answer of a division problem. If a number is divided by 3 and the answer is 8, then the number would be 24. You could set it up into an equation.
x/3=8
then you multiply both sides by 3 and you will get
x=24
The quotient is indeed the number generated by dividing one integer by the other. Whenever a fraction is simplified, the division is the whole amount that results.
The quotient is the solution to a division issue. Whenever a number is divided by three and the answer is eight, the amount is twenty-four.Calculation of the equation:
\(\to \bold{\frac{x}{3}=8}\\\\\to \bold{x=8\times 3} \\\\\to \bold{x=24}\)
Therefore, the final answer is "24".
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andre notices that he is a little taller than lin but is shorter than their math teacher, who is 164 centimeters tall. write two inequalities to describe andre's height.
Answer: a>l and a<164
Step-by-step explanation:
The first one is that because Andre’s height is greater than Lin’s (the letters represent their names, but if the paper says to use other variables, do that)
The second one is because Andre’s height is less than his teacher’s, which is 164. For that one, you could also do 164> a, but I’d go with the first one.
Hope this helps :D
price of two games in ratio a:b. If both prices decreased by £10, ratio = 3:5. If both prices increase by £5, ratio = 3:4. Work out ratio a:b.
The ratio of a: b is = 5:7
The price of the two games are in the ratio a:bWhen the prices are both decreased by £10, the ratio becomes 3:5When the prices are both increased by £5, the ratio becomes 3:4
Here the ratio is a:b
When the prices are both decreased by £10, the new ratio
= a-10 : b-10
When the prices are both increased by £5, the new ratio
= a+5 : b+5
By the given conditions,
a-10 : b-10 = 3:5
or, \(\frac{a-10}{b-10\\}\) =\(\frac{3}{5}\)
or, 5(a-10) = 3(b-10)
or, 5a -50 = 3b-30
or, 5a -3b = 20 .... ...(1)
and a+5 : b+5 =3 : 4
or,\(\frac{a+5}{b+5}\) = \(\frac{3}{4}\)
or, 4(a+5) = 3(b+5)
or, 4a +20 = 3b+15
or, 4a-3b= -5 .... ...(2)
subtract the equation(2) from equation(1)
5a -3b - (4a -3b) =20 - (-5)
or, 5a-3b-4a+3b = 20+5
or, 5a-4a = 25
Therefore, a =25
Putting a=25 in equation (1), we get
125-3b=20
or, 3b= 105
therefore, b=35
a :b =25:35
= 5:7
Hence, the ratio of a: b = 5:7
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How many gallons are in 4 pints simplify a right or answer as an improper fraction 
Answer:
The answer is 1/2 gallon.
Step-by-step explanation:
1 gallon is equal to 8 pints, so 4 pints is equal to 4/8 = 1/2 gallon. The answer is 1/2 gallon.
Explain briefly the six main criteria that can be used to define normality and abnormality, by illustrating them with one psychological "abnormality" (other than homosexuality).
What may be the values and limitations of using the medical model and classification systems (which are originated from diagnosing and treating physical illnesses) to the understanding and treating of psychological disorders?
The six criteria are:
1. Abnormality as statistical infrequency (Involves comparison with other people)
2. Abnormality as personal distress (Involves consequences of the behavior for self)
3. Abnormality as others’ distress (Involves the consequences of the behavior for others)
4. Abnormality as unexpected behavior (Involves another kind of comparison with others’ behavior)
5. Abnormality as highly consistent/inconsistent behavior (Involving making comparisons between both the actor and others, and between the actor and him/herself in different situations)
6. Abnormality as maladaptiveness or disability (Concerns about the (disabling) consequences for the actor)
The six main criteria to define normality and abnormality include statistical infrequency, personal distress, others' distress, unexpected behavior, highly consistent/inconsistent behavior, and maladaptiveness/disability.
1. Abnormality as statistical infrequency: This criterion defines abnormality based on behaviors or characteristics that deviate significantly from the statistical norm.
2. Abnormality as personal distress: This criterion focuses on the individual's subjective experience of distress or discomfort. It considers behaviors or experiences that cause significant emotional or psychological distress to the person as abnormal.
For instance, someone experiencing intense anxiety or depression may be considered abnormal based on personal distress.
3. Abnormality as others' distress: This criterion takes into account the impact of behavior on others. It considers behaviors that cause distress, harm, or disruption to others as abnormal.
For example, someone engaging in violent or aggressive behavior that harms others may be considered abnormal based on the distress caused to others.
4. Abnormality as unexpected behavior: This criterion defines abnormality based on behaviors that are considered atypical or unexpected in a given context or situation.
For instance, if someone starts laughing uncontrollably during a sad event, their behavior may be considered abnormal due to its unexpected nature.
5. Abnormality as highly consistent/inconsistent behavior: This criterion involves comparing an individual's behavior to both their own typical behavior and the behavior of others. Consistent or inconsistent patterns of behavior may be considered abnormal.
For example, if a person consistently engages in risky and impulsive behavior, it may be seen as abnormal compared to their own usually cautious behavior or the behavior of others in similar situations.
6. It considers behaviors that are maladaptive, causing difficulties in personal, social, or occupational areas. For instance, someone experiencing severe social anxiety that prevents them from forming relationships or attending school or work may be considered abnormal due to the disability it causes.
The medical model and classification systems used in physical illnesses have both value and limitations when applied to psychological disorders. They provide a structured framework for understanding and diagnosing psychological disorders, allowing for standardized assessment and treatment. However, they can oversimplify the complexity of psychological experiences and may lead to overpathologization or stigmatization.
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A student makes a three-day visit to a hacienda. On the first day walk 5 km south-east from the barn of the hacienda. The second day walks 12 km in a 30 "north-east direction and the third day 12 km west: to. How far and in the direction you are from the barn. b. The distance and direction you must travel to return to the starting point
After a three-day visit to a hacienda, the student finds themselves approximately 14.2 km away from the barn, in a direction of 43 degrees south of east.
Let's break down the three days of travel. On the first day, the student walks 5 km southeast from the barn. This creates a right-angled triangle with one leg of length 5 km. On the second day, they walk 12 km in a 30-degree north-east direction. This adds another leg to the triangle, forming a parallelogram. Using trigonometry, we can determine that the second leg has a length of approximately 10.4 km. On the third day, the student walks 12 km west, which completes the triangle.
To find the total distance and direction from the barn, we can combine the lengths and directions of the three sides. By adding the horizontal components and vertical components separately, we get approximately 12 km east and 12 km south. Applying Pythagoras' theorem, the total distance from the barn is approximately 16.97 km. To find the direction, we use inverse trigonometry, which yields approximately 43 degrees south of east.
To return to the starting point, the student needs to retrace their steps. Since the third day's walk was in the opposite direction, they need to travel a distance of approximately 12 km west. Combining this with the 10.4 km north-east component from the second day, we get a total distance of approximately 20.4 km. To find the direction, we again use inverse trigonometry, which gives us approximately 57 degrees north of west.
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Find a function f such that F = Vf. F(x, y, z) = 6y2z3i + 12xyz?j + 18xy?z?k Step 1 Since all the component functions of F have continuous partials, then F will be conservative if curl(F) = 0 Step 2 For F(x, y, z) = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k = 6y2z3i + 12xyzºj + 18xy2z2k, we have the following. op - OR = Submit Skip (you cannot come back)
Given,
F(x, y, z) = 6y2z3i + 12xyzj + 18xyzk
We know that, if `F(x, y, z)` is a conservative vector field, then there exist a scalar potential function `f` such that `F=∇f`.
There is no function `f` which satisfies the given condition `F = Vf`.
We have to find the potential function `f` for `F(x, y, z)`In other words, we have to evaluate`∫CF.dr` along a curve C from any arbitrary point `P (x1, y1, z1)` to `Q (x2, y2, z2)` in the domain of `F(x, y, z)`.
If `F(x, y, z)` is a conservative vector field, then the value of the line integral `∫CF.dr` depends only on the end points `P (x1, y1, z1)` and `Q (x2, y2, z2)` and not on the path joining `P` and `Q`.i.e., `∫CF.dr` only depends on the values of `f` at the points `P (x1, y1, z1)` and `Q (x2, y2, z2)`.
Now, let's calculate the partial derivative of the each component function with respect to variables `y` , `z` and `x`, respectively.
∂P/∂y = 12yz
∂Q/∂x = 12yz
∂Q/∂y = 12xz
∂R/∂x = 18yz
∂R/∂y = 18xz
∂P/∂z = 18y2z2
Hence, `curl(F) = ∇×F`
=` ( ∂R/∂y - ∂Q/∂z) i - ( ∂R/∂x - ∂P/∂z ) j + ( ∂Q/∂x - ∂P/∂y ) k`
=` `( 18xz - 12yz ) i - ( 18yz - 6y2z2 ) j + ( 12xy - 18xy ) k`
`=` `( 6y2z2 - 18yz ) j + ( 12xy - 6y2z2 + 18yz - 12xy ) k`
=` `(- 12yz + 18yz ) j + ( 6y2z2 + 18yz - 6y2z2 - 12xy ) k`
=` `0 j + (-12xy) k`
=` `-12x y k`
As curl(F) is not zero, so `F` is not a conservative field .
Hence, `F` doesn't have a potential function. Thus, the function `f` does not exist.
Therefore, there is no function `f` which satisfies the given condition `F = Vf`.
Conclusion: Therefore, there is no function `f` which satisfies the given condition `F = Vf`.
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the tampa bay skeptics performed an experiment to see whether an acclaimed psychic has extrasensory perception (esp). a crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table. the experiment was repeated seven times, and x, the number of decisions, was recorded. (assume that the seven trials are independent.) a. if the psychic is guessing (i.e., if the psychic does not possess esp), what is the value of p, the probability of a correct decision on each trial? b. if the psychic is guessing, what is the expected number of correct decisions in seven trials? c. if the psychic is guessing, what is the probability of no correct decisions in seven trials? d. now suppose the psychic has esp and p
a. The probability of a correct decision on each trial is 0.1.
b. The expected number of correct decisions in seven trials is 0.7.
c. The probability of no correct decisions in seven trials is approximately 0.478.
d. The probability that the psychic guesses incorrectly in all seven trials is approximately 0.0078.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
a. If the psychic is guessing (i.e., does not possess ESP), there are 10 boxes, and only one of them contains the crystal.
Therefore, the probability of a correct decision on each trial is -
p = 1/10 = 0.1
b. If the psychic is guessing, the expected number of correct decisions in seven trials can be found by multiplying the probability of a correct decision on each trial (0.1) by the number of trials (7) -
E(X) = np = 7 × 0.1 = 0.7
Therefore, the number of correct decisions is 0.7.
c. If the psychic is guessing, the probability of no correct decisions in seven trials can be found using the binomial distribution formula -
\(P(X=0) = (n\ choose\ x) \times p^x \times (1-p)^{(n-x)}\)
In this case, n = 7, x = 0, and p = 0.1.
Substituting these values into the formula, we get -
\(P(X=0) = (7\ choose\ 0) \times 0.1^0 \times 0.9^7 = 0.478\)
Therefore, the probability value is 0.478.
d. If the psychic has ESP and p = 0.5, the probability of guessing incorrectly on any trial is -
q = 1 - p
q = 1 - 0.5
q = 0.5
The probability of guessing incorrectly in all seven trials can be found using the binomial distribution formula -
\(P(X=7) = (n\ choose\ x) \times p^x \times q^{(n-x)}\)
In this case, n = 7, x = 7, p = 0.5, and q = 0.5.
Substituting these values into the equation, we get -
\(P(X=7) = (7\ choose\ 7) \times 0.5^7 \times 0.5^0 = 0.0078\)
Therefore, the probability value is 0.0078.
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The Tampa bay skeptics performed an experiment to see whether an acclaimed psychic has extrasensory perception (ESP). A crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table. The experiment was repeated seven times, and x, the number of decisions, was recorded. (Assume that the seven trials are independent.)
a. If the psychic is guessing (i.e., if the psychic does not possess ESP), what is the value of p, the probability of a correct decision on each trial?
b. If the psychic is guessing, what is the expected number of correct decisions in seven trials?
c. If the psychic is guessing, what is the probability of no correct decisions in seven trials?
d. Now suppose the psychic has ESP and p=.5. What is the probability that the psychic guesses incorrectly in all seven trials.
In the diagram, PN is perpendicular bisector of AB and is also the ange bisector of
Find the volume of each solid
Answer:
the answer is
13 cm:y
5 cm:x
2 cm:z
There were two exhibitions at the nec on sunday.3816 people went to one of the exhibitions and 13427 people went to the other exhibition how many people went to the nec,in total on sunday/
Using basic mathematical operations such as addition, there was a total of 17,243 people who went to the NEC on Sunday.
Basic mathematical operations include addition, subtraction, multiplication, and division.
Addition is combining two or more values to come up with a total or sum.
If there were two exhibitions at the NEC on Sunday, and 3816 people went to one of the exhibitions and 13427 people went to the other exhibition, then the sum of these numbers are the total number of people who went to the NEC on Sunday.
total number of people = 3816 + 13427
total number of people = 17,243
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place the numbers 2 , 6 , 7 , 8 , and 9 in the circles so that the sums across (horizontally) and down (vertically) are equal. which number will you place in the middle?
The number 7 will be placed in the middle circle.
To place the numbers 2, 6, 7, 8, and 9 in the circles so that the sums across and down are equal, you can use the following method:
1. Place the median number (7) in the middle circle.
2. Place the two smallest numbers (2 and 6) on either side of the median number.
3. Place the two largest numbers (8 and 9) in the top and bottom circles.
Here is a list of them. Each group of three numbers makes up a side of the triangle. Of course, within a side you can replace round numbers that are not on a corner, but that does not really give any new solutions.
So, the final arrangement would be:
6 2 7
9 8 7
6 2 7
Therefore, the number 7 will be placed in the middle circle.
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In an introductory psychology class with n = 50 students, there are 9 freshman males, 15 freshman females, 8 sophomore males, 12 sophomore females, and 6 junior females. A random sample of n = 2 students is selected from the class. If the first student in the sample is a male, what is the probability that the second student will also be a male?
a. 8/14
b. 12/20
c. 20/44
d. 20/50
Answer: Total number of males= C
Step-by-step explanation:
Half a number added to the number gives 240.What is the number?
Answer:
Step-by-step explanation:
Let number be "n".
Half a number added to the number = 240
This means
0.5n + n = 240
1.5n = 240
Divide both sides by 1.5
n = 240/1.5 = 160
find two numbers whose difference is 108 and whose product is a minimum.
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
Roberto' employer offer a liding paid vacation. When he tarted work, he wa given three paid day of vacation. For each ix-month period he tay at the job, hi vacation i increaed by two day. Let x repreent the number of 6-month period worked and y repreent the total number of paid vacation day. Write an equation that mode the relationhip between thee two variable
An equation that mode the relationship between thee two variable is y=2x+3 .
Let x represent the number of 6-month period worked
Let y represent the total number of paid vacation day
According to the question,
When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.
Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19
An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).
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Nai's dog eats about 1(3)/(4) cups of dog food per day. If Nai has 12(1)/(3) cups of dog food left, about how many days can Nai feed his dog before having to buy more?
Answer:
7 days
Step-by-step explanation:
What you have to do is divide 12(1)/(3) by 1(3)/(4)... the best way to do that is first turn them into exact form.
12(1)/(3) --> 12*3 plus 1= 37/3 (the denominator stays the same)
1(3)/(4) --> 1*4 plus 3= 7/4
Then you have (37/3) over (7/4), from this point you switch the numerator and the denominator on the second fraction so that you can multiply both equations. (7/4) --> (4/7)
(37/3) * (4/7) = (148/21)
When simplified... 7(1)/(21)... and since you want to know full days, you only take 7
HELP I will give Brainliest!
Find the measure of the angle indicated.
Answer:
45
Step-by-step explanation:
Given the number of rows and the number of columns, write nested loops to print a rectangle.
Answer:
You need to use a nested for loop. Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows.
Step-by-step explanation:
Use the range() builtin to produce an iterable sequence. The outer for loop should iterate over the number of rows overtime.
Most times screening tests are not perfect. What might be the benefits and drawbacks of having a test with high sensitivity and medium specificity vs. a test with high specificity and medium sensitivity.
High sensitivity and medium specificity: Detect more true positives, but have more false positives.
High specificity and medium sensitivity: Reduce false positives, but may miss some cases.
What are the advantages and drawbacks of tests with high sensitivity and medium specificity versus high specificity and medium sensitivity?Screening tests with high sensitivity and medium specificity can effectively identify a large number of individuals with the condition, including those in the early stages.
This early detection allows for timely interventions and treatment, potentially improving patient outcomes.
However, this increased sensitivity also leads to a higher number of false positives, where individuals without the condition are incorrectly identified as positive.
This can result in unnecessary follow-up tests, interventions, and psychological distress for the individuals involved.
Conversely, tests with high specificity and medium sensitivity offer increased accuracy for negative results, providing individuals who test negative with a higher level of confidence.
The reduced false positives help avoid unnecessary follow-up tests and interventions.
However, the drawback lies in the potential for false negatives, where individuals with the condition are incorrectly identified as negative.
This can delay diagnosis and treatment, potentially leading to negative health outcomes and missed opportunities for early intervention.
In conclusion, the choice between a screening test with high sensitivity and medium specificity or high specificity and medium sensitivity depends on various factors,
including the specific context, the consequences of false positives and false negatives, and the goals of the screening program or diagnostic process.
High sensitivity and medium specificity in a screening test offer the benefit of detecting a high proportion of true positive cases, but at the cost of increased false positives.
On the other hand, high specificity and medium sensitivity reduce false positives, but may result in missed cases and delayed intervention.
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write 3/4 as a decimal
Answer:
0.75
Step-by-step explanation:
Answer:
0.75
Step-by-step explanation:
do 3 divided by 4!
Find the positive value of x that satisfies x=3.7cos(x).
Give the answer to six places of accuracy.
x≈
and to calculate the trig functions in radian mode.
The positive value of x that satisfies the equation x = 3.7cos(x) can be found using numerical methods such as the Newton-Raphson method. The approximate value of x to six decimal places is x ≈ 2.258819.
To solve the equation x = 3.7cos(x), we can rewrite it as a root-finding problem by subtracting the cosine term from both sides: x - 3.7cos(x) = 0. The objective is to find the value of x for which this equation equals zero.
Using the Newton-Raphson method, we start with an initial guess for x and iterate using the formula xᵢ₊₁ = xᵢ - f(xᵢ)/f'(xᵢ), where f(x) = x - 3.7cos(x) and f'(x) is the derivative of f(x) with respect to x.
By performing successive iterations, we converge to the value of x where f(x) approaches zero. In this case, starting with an initial guess of x₀ = 2.25, the approximate value of x to six decimal places is x ≈ 2.258819.
It's important to note that trigonometric functions are typically evaluated in radian mode, so the value of x in the equation x = 3.7cos(x) is also expected to be in radians.
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PLEASE HELP!
Multiple Choices. Which of the following fractions is equivalent to 6/15
A. 2/7
B. 4/10
C 1/2
D 1/4
Answer: 4/10
Step-by-step explanation:
what is the value of x?
Answer:
x = 51°
Step-by-step explanation:
The image of the triangle is an isosceles triangle. Since it is an isosceles triangle, ∠DFE = ∠FDE.
78 + x + x = 180
=> 2x = 102
=> x = 51°
Hoped this helped.
write the statements using summation or product notation. 1/2*4/4*9/8*16/16*25/32*36/64*49/128
4+5/2! + 6/3! + 7/4! + 8/5! + 9/6!
The required expressions in summation and product notations are: ∏(n = 1 to 7) [(n + 1)²] / (2 × 4 × 8 × 16 × 32 × 64 × 128) and ∑ (n = 0 to 5) n + (n + 5) / (n + 2)
The given expression is 1/2 × 4/4 × 9/8 × 16/16 × 25/32 × 36/64 × 49/128
To express the given expression using product notation, let's consider the numerators and the denominators separately.
Product of the numerators = 1 × 4 × 9 × 16 × 25 × 36 × 49
Product of the denominators = 2 × 4 × 8 × 16 × 32 × 64 × 128
Therefore, the given expression in the product notation is:
∏(n = 1 to 7) [(n + 1)²] / (2 × 4 × 8 × 16 × 32 × 64 × 128)
Now, let's consider the second expression.
The given expression is: 4 + 5/2! + 6/3! + 7/4! + 8/5! + 9/6!
To express this given expression in the summation notation, we can write it as:
∑ (n = 0 to 5) n + (n + 5) / (n + 2)!
Therefore, the required expressions in summation and product notations are:
∏(n = 1 to 7) [(n + 1)²] / (2 × 4 × 8 × 16 × 32 × 64 × 128) and ∑ (n = 0 to 5) n + (n + 5) / (n + 2)
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a card dealer lays out five cards, face down, from a single deck of 52 cards. what is the probability that at least one of them is an ace?
The probability that at least one person receives exactly one aces in their 52 cards is 4/52= 1/13
We define the following events:
A: person A receives exactly two aces in their five cards.
B: person B receives exactly two aces in their five cards.
C: person C receives exactly two aces in their five cards.
We need to calculate P(A∪B∪C). According to the principle of inclusion and exclusion:
P(A∪B∪C)= P(A)+P(B)+P(C)-P(A∩B)-P(A∩C)-P(B∩C)+P(A∩B∩C)
Total outcomes is equal to because there 52 cards and we select 5 of them.
The probability of each event is given by:
P(A)=P(B)=P(C)===0.0399
where the possible outcomes are 2 aces and 3 of the other cards.
Then, the intersections of the events mean that one player gets 2 aces and the other gets 2 aces too.
P(A∩B)=P(B∩C)=P(A∩C)==0.0001
Finally,
P(A∩B∩C)=0 because it is not possible that the three events occur at the same time due to there are only 4 aces.
P(A∪B∪C)= 0.0399+0.0399+0.0399-0.0001-0.0001-0.0001+0
P(A∪B∪C)=0.1194
The probability that at least one person receives exactly two aces in their five cards is 0.1194.
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10 pens for $8.99 answer is
Answer: the cost of each pen would be 0.899
Step-by-step explanation:
PLEASE HELP PLEASE HELP!!!!
You run m miles on Monday, the same amount on Tuesday, and 3 miles on Wednesday. Write an expression in the simplest form that represents the total amount in each situation.
(please show work)
The mean, or average, is equal to the sum of all the miles divided by the number of terms you added together. We have 4 terms that will be added, but are missing one term. We will solve for the missing term by setting up an equation for the average and solving for x, the number of miles you must run on Thursday.
3 = (2 + 3 + 4 + x) / 4
12 = 2 + 3 + 4 + x
12 = 9 + x
x = 3 miles