The mean of the given probability distribution is 0.2007.
The probability distribution table for the given scenario can be completed as follows:
| x | P(x) |
|---|------|
| 0 | 0.8036 |
| 1 | 0.1929 |
| 2 | 0.0036 |
| 3 | 0.0000 |
The probabilities are calculated using the hypergeometric distribution formula:
P(x) = (C(N-K, n-x) * C(K, x)) / C(N, n)
Where N is the total number of items (14), K is the number of items that are not correctly calibrated (2), n is the number of items selected (3), and x is the number of items that are not correctly calibrated in the selection.
For x = 0:
P(x) = (C(14-2, 3-0) * C(2, 0)) / C(14, 3) = (C(12, 3) * C(2, 0)) / C(14, 3) = (220 * 1) / 364 = 0.8036
For x = 1:
P(x) = (C(14-2, 3-1) * C(2, 1)) / C(14, 3) = (C(12, 2) * C(2, 1)) / C(14, 3) = (66 * 2) / 364 = 0.1929
For x = 2:
P(x) = (C(14-2, 3-2) * C(2, 2)) / C(14, 3) = (C(12, 1) * C(2, 2)) / C(14, 3) = (12 * 1) / 364 = 0.0036
For x = 3:
P(x) = (C(14-2, 3-3) * C(2, 3)) / C(14, 3) = (C(12, 0) * C(2, 3)) / C(14, 3) = (1 * 0) / 364 = 0.0000
The mean of this probability distribution can be calculated by multiplying each value of x by its corresponding probability and summing the results:
mean = (0 * 0.8036) + (1 * 0.1929) + (2 * 0.0036) + (3 * 0.0000) = 0.2007
Therefore, the mean of this probability distribution is 0.2007.
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Brian is 2 years older than Bod who is 7 years older than Mark. If their combined age is 61 years, find the age of each person. (4)
Bod is 22 years old, Brian is 24 years old, and Mark is therefore 15 years old.
what is variables ?A variable in mathematics is a symbol or letter that denotes a possible number or quantity. It frequently serves as a placeholder for an unknowable number that needs to be calculated or solved for in mathematical expressions or equations. For instance, the factors x and y are used in the equation y = 3x + 5. The value of x, which can be any integer, determines the value of y. If we know the number of x, we can find a solution for y.
given
Let's indicate their ages with variables:
Mark's age: M
Body Age: B Equals M + 7
Br = B + 2 = (M + 7) + 2 = M + 9 is Brian's age.
Their total age is 61, so we can create the following equation:
M + (M + 7) + (M + 9) = 61
M is simplified to 3M Plus 16 and the answer is 61.
3M = 45
M = 15
Bod is 22 years old (15 + 7), Mark is 15 years old (15 + 7), and Brian is 24 years old (22 + 2).
Bod is 22 years old, Brian is 24 years old, and Mark is therefore 15 years old.
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find the surface area to the nearest tenth of a cylinder 61.7 ft tall that has a diameter of 38 ft
The surface area of the cylinder to the nearest tenth is approximately 9617.9 [tex]ft^{2}[/tex].
The surface area of a cylinder is given by the formula:
Surface area = 2π[tex]r^{2}[/tex] + 2πrh
where r is the radius of the cylinder, h is its height, and π is a constant equal to approximately 3.14159.
To solve this problem, we first need to find the radius of the cylinder. The diameter of the cylinder is given as 38 ft, so the radius is half of that:
radius = diameter / 2 = 38 ft / 2 = 19 ft
The height of the cylinder is given as 61.7 ft.
Now, we can plug in these values into the surface area formula:
Surface area = 2π[tex]r^{2}[/tex] + 2πrh
Surface area = 2π[tex](19ft)^{2}[/tex]+ 2π(19 ft)(61.7 ft)
Surface area = 2π(361[tex]ft^{2}[/tex]) + 2π(1168.3 [tex]ft^{2}[/tex])
Surface area = 722π [tex]ft^{2}[/tex] + 2336.6π [tex]ft^{2}[/tex]
Surface area = 3058.6π[tex]ft^{2}[/tex]
We can approximate π to 3.14159 and evaluate the expression:
Surface area ≈ 3058.6 × 3.14159
Surface area ≈ 9617.9 [tex]ft^{2}[/tex]
Therefore, the surface area of the cylinder to the nearest tenth is approximately 9617.9 [tex]ft^{2}[/tex].
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Using a calculator, work out
(3.5 × 107)
107) + (7.1 × 10⁹)
Give your answer in standard form.
The addition of the two numbers in scientific notation is given as follows:
[tex](3.5 \times 10^7) + (7.1 \times 10^9) = 7.135 x 10^9[/tex]
What is scientific notation?A number in scientific notation is given by the notation presented as follows:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.
The addition operation for this problem is given as follows:
[tex](3.5 \times 10^7) + (7.1 \times 10^9)[/tex]
To add two terms, they must have the same exponent, hence I am going to convert 3.5 x 10^7 to exponent 9, as follows:
[tex]3.5 \times 10^7 = 0.35 \times 10^8 = 0.035 \times 10^9[/tex]
Two add two terms, we add the bases and keep the exponents, hence:
[tex](0.035 \times 10^9) + (7.1 \times 10^9) = 7.135 \times 10^9[/tex]
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Jessica graphed point G on the coordinate grid. She will graph point H 5 units away from point G. Which ordered pair could represent the location of point H if point G was (-4,3)? A) (-4,5) B) (-9,8) C) (1,3) D) (-4,-1)
The ordered pair for point H would be (-9,8).
What is graph?Graph is a mathematical structure used to model pairwise relations between objects. It consists of a set of nodes, which represent the objects, and a set of edges, which represent the relations between pairs of objects. Graphs can be used to represent networks, flows, and even data structures such as trees or linked lists. They are also used in various optimisation problems, such as route finding and scheduling.
The correct answer is B) (-9,8). To find the location of point H, Jessica needs to move 5 units to the left on the x-axis, which would put it at -9. She then needs to move 5 units up on the y-axis, which would put it at 8. Therefore, the ordered pair for point H would be (-9,8).
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The ordered pair for point H would be (-9,8).
What is graph?Graph is a mathematical structure used to model pairwise relations between objects. It consists of a set of nodes, which represent the objects, and a set of edges, which represent the relations between pairs of objects.
The correct answer is B) (-9,8). To find the ordered pair for point H, you need to add 5 units to the x-coordinate of point G, and 5 units to the y-coordinate of point G. Since the x-coordinate of point G is -4 and the y-coordinate of point G is 3, the x-coordinate of point H would be -4 + 5 = -9 and the y-coordinate of point H would be 3 + 5 = 8. Therefore, the ordered pair for point H would be (-9,8).
The correct answer is B) (-9,8). To find the location of point H, Jessica needs to move 5 units to the left on the x-axis, which would put it at -9.
She then needs to move 5 units up on the y-axis, which would put it at 8. Therefore, the ordered pair for point H would be (-9,8).
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Which is more economical: purchasing the economy size of a detergent at 2 kilograms for $3. 15 or purchasing the regular size at 920 grams for 60?
The economy size is more economical, as you will get 2kg for $3.15, which comes out to be $1.58 per kg, while the regular size will cost you $0.65 per gram.
To determine which option is more economical, we need to calculate the cost per unit of weight for each detergent.
For the economy size, the cost per kilogram is:
Cost = $3.15
Weight = 2 kg
Cost per kilogram = Cost / Weight = $3.15 / 2 kg = $1.575/kg
For the regular size, the cost per kilogram is:
Cost = $0.60
Weight = 920 g = 0.92 kg
Cost per kilogram = Cost / Weight = $0.60 / 0.92 kg = $0.652/kg
Therefore, the regular-size detergent is more economical as it has a lower cost per kilogram.
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The diameter of a circle is 14 feet. What is the circle's circumference?
Use 3.14 for л.
Answer
43.96
14 x 3.14 = 43.96
hope this helped!
D
Question 15
Which of the following lines is parallel to the line graphed below?
O
y=x+3
O4x+3y=6
Oy=-3x+2
O-4x+y=7
B
-4x + y = 7 is the line parallel tο the line graphed. Optiοn D is cοrrect.
What is parallel?Parallelism is a writing style that uses similar grammatical structures, phrases, οr wοrds tο make a pοint. It is used tο emphasize a pοint and make the writing mοre interesting and easier tο understand. Parallelism is used in different types οf writing such as persuasive writing, pοetry, stοries, and legal dοcuments.
Parallelism can alsο be used in speech, allοwing the speaker tο emphasize their pοint. It creates balance and structure in the writing, making it mοre οrganized and easier tο read. Parallelism can alsο be used tο create rhythm in the writing. By creating rhythm, the writing becοmes mοre memοrable and easier tο understand.
The line parallel will have a same slοpe
Lets find the slοpe
Any two pοints form the graph are, (1, 1) and (0, -3)
Slope m = [tex]$ \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Slope m = [tex]$ \frac{-3 -1}{0 - 1}[/tex]
m = 4
Nοw, frοm the given οptiοns,
a. y=x+3 is nοt parallel as it have a οppοsite slοpe.
b. 4x + 3y = 6, write in y-intercept fοrm
y = (-4x + 6)/y. Nοt parallel
c. y =- 3x+2 is nοt parallel as it have a οppοsite slοpe.
d. -4x + y = 7, write in y-intercept fοrm
y = 4x + 7, That is parallel as the slοpe is same.
Therefοre, -4x + y = 7 is the line parallel tο the line graphed.
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Complete question:
Maxine wants to bake and needs to buy flour. She will need 1 3/4
cups of flour to make a chocolate cake. She will also need 2 1/3
cups of flour for chocolate chip cookies. Finally, Maxine will need
1 2/3 cups of flour for brownies. Maxine wants to buy enough
flour to bake with and only wants to have less than two cups left
over.
Based on the information provided, Maxine needs to buy a total of 6 cups of flour.
How to calculate the amount of flour Maxina needs to buy?The total of flour can be calculated by adding the numbers provided; however, to make it easier let's simplify the numbers:
Chocolate cake: 1 3/4 = 1.75
Chocolate chip cookies: 2 1/3 = 2.33
Brownies: 1 2/3 = 1.66
Now, let's add the amounts given:
1.75 + 2.33 + 1.66 = 5.74 which can be rounded as 6 cups, which means she will need to buy a 6 or 7-cup bag.
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Of the top 10 cars and trucks based on gas mileage, 4 are Hondas, 3 are Toyotas, and 3 are Volkswagens. If you choose one at random, what is the probability that the car is Japanese or German?
Of the top 10 cars and trucks based on gas mileage, 4 are Hondas, 3 are Toyotas, and 3 are Volkswagens. Therefore, The probability that the car is Japanese or German is 01.
Probability:
The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of an event that will definitely occur is 1. The probabilities of two complementary events A and B (A or B) add up to 1.
A simple example is tossing a fair (fair) coin. If a coin is fair, both possible outcomes ("heads" and "heads") are equally likely; since the two outcomes are complementary and the probability of "heads" is equal to the probability of "heads" Probability, so the probability of each of the two outcomes is equal to 1/2 (which can also be written as 0, 5 or 50%).
According to the Question:
Given that:
Total cars = 10
Honda cars = 04
Toyota Cars = 03
and, Volkswagens cars = 03
From the above list the Japanese cars are : Toyota
German cars are: Honda and Volkswagens.
(a) Let P(J or G) = probability of getting Both Japanese and German car.
Probability of Getting Japanese or German car :
P(J or G) = Total number of Japanese and German car / Total number of cars.
⇒ P(J or G) = 4 + 3 + 3/ 10
⇒ P(J or G) = 10/10
⇒ P(J or G) = 1
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The length of the hypotenuse of
an isosceles triangle is 40 inches.
How long is each leg of the
triangle? Round your answer to
the nearest tenth if necessary.
Answer: 28.3 inches long
Step-by-step explanation:
Since the triangle is isosceles, the two legs have the same length. Let's call the length of each leg "x". We can use the Pythagorean theorem to solve for x:
x^2 + x^2 = 40^2
2x^2 = 1600
x^2 = 800
x ≈ 28.3
Therefore, each leg of the triangle is approximately 28.3 inches long.
Sam spent $23.00 to buy 12 flowers for his mother.
Answer:
$1.92
Step-by-step explanation:
We take
23 / 12 = $1.92 per flower
So, it costs $1.92 per flower.
factirise fully.
[tex]2x + 4x { \\ }^{2} [/tex]
Leah invests in an account paying a simple interest of 8% per year. If no money will be added or removed from the investment, what should she multiply her current balance by to find her total balance in a year in one step
Leah should multiply her current balance by 1.08 to find her total balance in one year.
To find Leah's total balance in one year, we can use the simple interest formula:
Simple Interest = Principal x Rate x Time
where:
Principal is the amount of money invested
Rate is the interest rate per year
Time is the time period in years
In this case, we know that Leah's account pays a simple interest rate of 8% per year, and no money will be added or removed from the account during the year. Hence, we may condense the formula to:
Total Balance = Principal + Simple Interest
Total Balance = Principal + (Principal x Rate x Time)
Total Balance = Principal x (1 + Rate x Time)
So to find Leah's total balance in one year, she should multiply her current balance by (1 + 0.08 x 1), which simplifies to 1.08:
Total Balance = Current Balance x 1.08
For example, if Leah currently has 1,000 in her account, her total balance in one year would be:
Total Balance = 1,000 x 1.08
Total Balance = 1,080
So Leah should multiply her current balance by 1.08 to find her total balance in one year.
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Dani spends 1520 total to create
2 treat bags. How much more
would she have to spend to make
5 more similar bags?
Answer: 2280 more
Step-by-step explanation:
We need to first find out how much Dani spends to make one treat bag:
1520/2 = 760
Now we can find out how much it would cost to make 5 more bags:
760 x 5 = 3800
Therefore, Dani would have to spend 3800 - 1520 = 2280 more to make 5 more similar bags.
WHOEVER DOES MOST ASAP GETS AN EXTRA 50
Fraction value [tex]16\frac{17}{27}[/tex] as a percentage is [tex]1662\frac{26}{27} %[/tex] %
Fraction value [tex]16\frac{17}{27}[/tex] as a decimal is 16.629629
What is percentage, decimal, and fraction?Percentage, decimal, and fraction are all ways of representing numbers that are related to each other. Here's a brief explanation of each:
Percentage: A percentage is a number expressed as a fraction of 100, with the symbol % (percent) added. For example, 50% is the same as 50/100 or 0.5.
Decimal: A decimal is a way of representing fractions using the base-10 numbering system. It is written with a decimal point between the whole number and the fractional part. For example, 0.5 is the same as 5/10 or 50/100 or 50%.
Fraction: A fraction is a way of representing a part of a whole or a ratio of two numbers. It is expressed as a ratio of two integers, with the numerator (top number) representing the number of parts being considered, and the denominator (bottom number) representing the total number of equal parts. For example, 1/2 is the same as 0.5 or 50%.
Fraction value [tex]16\frac{17}{27}[/tex] as a percentage is [tex]1662\frac{26}{27} %[/tex] %
Fraction value [tex]16\frac{17}{27}[/tex] as a decimal is 16.629629
For other values see the below figure.
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A, B & C form the vertices of a triangle. ∠ CAB = 90°, ∠ ABC = 65° and AB = 8. 6. Calculate the length of BC rounded to 3 SF
The length of BC rounded to 3 significant figures is approximately 3.62 units.
We can use trigonometric function to find the length of BC. First, we can use the fact that ∠CAB = 90° to determine that ∠ACB = 25° (since the angles in a triangle sum to 180°).
Next, we can use the law of sines to relate the lengths of the sides and angles of the triangle:
sin(∠ABC) / AB = sin(∠ACB) / BC
Substituting in the values we know:
sin(65°) / 8.6 = sin(25°) / BC
Solving for BC:
BC = sin(25°) × 8.6 / sin(65°) ≈ 3.62
Rounding to 3 significant figures, we get BC ≈ 3.62 units
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Tom wishes to purchase a property that has been valued at $300,000. He has 25% of this amount available as a cash deposit, and will require a mortgage for the remaining amount. The bank offers him a 25-year mortgage at 2% interest. Calculate his monthly payments
Tom's monthly mortgage payment will be $984.84 As Tom has a cash deposit of 25% of $300,000 which is $75,000.
Therefore, he needs to borrow $225,000 from the bank to purchase the property.
Using the formula for calculating the monthly payment for a mortgage, we get:
M = [tex]P [ i(1 + i)^n ] / [ (1 + i)^{n-1}][/tex]
Where:
P = Principal amount borrowed = $225,000
i = monthly interest rate = 2%/12 = 0.001667
n = total number of monthly payments = 25 years x 12 months/year = 300
Plugging in these values, we get:
M = $225,000 [0.001667[tex](1 + 0.001667)^{300[/tex]] / [[tex](1 + 0.001667)^{300[/tex] – 1] = $984.84
Therefore, Tom's monthly mortgage payment will be $984.84.
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Suppose you wish to estimate the difference between the mean acidity for rainfalls at two different locations, one in a relatively unpolluted area and the other in an area subject to heavy air pollution. If you wish your estimate to be correct to the nearest 0.2 pH, with probability near 0.90, approximately how many rainfalls (pH values) would have to be included in each sample? (Assume that the variance of the pH measurements is approximately 0.35 at both locations and that the samples will be of equal size. Round your answer up to the nearest whole number.)
Approximately 21 pH values would have to be included in each sample to estimate the difference between the mean acidity for rainfalls at the two different locations to the nearest 0.2 pH, with probability near 0.90.
What is the standard error?
Standard error is a measure of the variability or uncertainty of a statistic. It is the standard deviation of the sampling distribution of a statistic, and it estimates how much the sample statistic may vary from the true population parameter due to random sampling error.
To estimate the difference between the mean acidity for rainfalls at two different locations, we can use the formula for the standard error of the difference between means:
[tex]SE = \sqrt{[(s1^2 / n1) + (s2^2 / n2)]}[/tex]
where s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and SE is the standard error of the difference between means.
We want our estimate to be correct to the nearest 0.2 pH, with probability near 0.90. This means we want to find the sample size n that will give us a margin of error of 0.2 pH with a confidence level of 90%.
We can use the following formula to find the sample size:
[tex]n = [(z*\sigma / E)^2][/tex]
where z is the z-score for the desired confidence level (0.90), σ is the population standard deviation (0.35), and E is the margin of error (0.2).
First, we need to find the z-score for a 90% confidence level. This can be found using a standard normal distribution table or calculator. For a 90% confidence level, the z-score is approximately 1.645.
Substituting these values into the formula, we get:
n = [(1.645*0.35 / 0.2)^2]
= 20.95
Rounding up to the nearest whole number, we get a sample size of n = 21 for each sample.
Therefore, approximately 21 pH values would have to be included in each sample to estimate the difference between the mean acidity for rainfalls at the two different locations to the nearest 0.2 pH, with probability near 0.90.
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Work out
25
% of
401. 16
m
Give your answer rounded to 2 DP
2 decimal point of 25% of 401.16 is 100.29
In the question, we are ask to calculate the percentage of 25 multiplied by 401.16 and then round the answer to 2 decimal point
The first step is to work of 25%. This can be done by dividing 25 by 100
= 25/100
= 0.25
The next step is to multiply this value (0.25) by 401.16
= 0.25 × 401.16
= 100.29
The answer rounded to 2 decimal point is 100.29
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Question is down below
Answer:
C is the answer.
Step-by-step explanation:
Answer:
The answer is A and C
Step-by-step explanation:
The answer is A and C because as you can see the angles of the triangles are both the same. If you took the smaller triangle or triangle A and enlarged it, it would be the same triangle.
A block exerts a force of 9 N on the ground. Calculate the pressure the block exerts on the ground, in N/m², when it is a) flat on the ground, so that the area of its base is 0.04 m². b) standing up on its side, so that the area of its base is 0.015 m². a) base area = 0.04 m² b) base area = 0.015 m² Not drawn accurately
The pressure exerted by the block on the ground is 225 N/m² and 600 N/m² respectively.
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
The equation for pressure is:
Pressure = Force / Area
A block exerts a force of 9 N on the ground
a) If the area of its base is 0.04 m², hence:
Pressure = Force / Area = 9 N / 0.04 m² = 225 N/m²
a) If the area of its base is 0.015 m², hence:
Pressure = Force / Area = 9 N / 0.015 m² = 600 N/m²
The pressure exerted on the ground is 225 N/m² and 600 N/m² respectively.
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10 How many ways can a company select 3 candidates to interview from a shortlist of 15? (2 Points) a. 555 b. 455 c. 444 d. None of them
Therefore , the solution of the given problem of unitary comes out to be the response is option b 455.
An unitary method is what?By combining what was learned and implementing this variable technique, which also includes all supplemental information from two people who used a particular tactic, the task can be finished. In other words, if the desired result occurs, either the entity specified in the expression will also be identified, or both crucial procedures will actually skip the colour. A refundable fee of Rupees ($1.01) may be needed for forty pens.
Here,
The following combination formula determines how many ways a company can choose three candidates from a shortlist of fifteen:
=> C(15,3) = 15! / (3! (15-3)!)
=> (15 x 14 x 13) / (3 x 2 x 1)
=> 455
Consequently, the response is (b) 455.
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The Good Fruit stand sells baskets of cherries for $4 and baskets of blueberries for $3.
Its daily sales goal is $720
The Good Fruit stand needs to sell 180 baskets of cherries and 240 baskets of blueberries to reach their daily sales goal of $720.
1 cherry = $4
1 blueberry = $3
60 cherry basket:
60 × 4
= 240
Goal amount = $720
Bw day selling blueberry basket
Money:
= 720 - 240
= 480
Blueberry basket = 480 ÷ 3
Cherry = 60
Blueberry = 160
Sales goals are measurable objectives that sales reps and teams use to guide them through their day-to-day sales activities and help them make big-picture strategic decisions. Sales goals are usually based on KPIs and specific sales metrics.They are data-driven and are meant to provide a blueprint for sellers and organizations on how to achieve new levels of success. Sales goals bring clarity and control to the sales process while also mitigating risk.
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Question:
The Good Fruit stand sells baskets of cherries for $4 and baskets of blueberries for $3. Its daily sales goal is $720. Write and graph the linear equation that describes the problem. Use the graph to find how many baskets of blueberries it must sell to reach its goal if 60 baskets of cherries are sold.
Use the order of operations to simplify 19×33−2(16+23) .
Answer:
549
Step-by-step explanation:
What is the order of operations?The order of operations is a sequence in which operations should be performed to evaluate a mathematical expression correctly. A common way to remember is PEMDAS:
ParenthesesExponentsMultiplicationDivisionAdditionSubtractionTo simplify the expression 19×33−2(16+23) using the order of operations, first solve the operations inside the parentheses:
16 + 23 = 39Now we multiply:
2 × 39 = 78The expression now looks like this:
19 × 33 − 78.Perform the multiplication before the subtraction:
19 × 33 = 627Now that we have done the multiplication, we can subtract:
627 - 78 = 549Therefore, the expression simplified is 549.
Answer:
b
Step-by-step explanation:
Select the correct answer. Given the following formula, solve for y. w=x-y/2-z
After answering the presented question, we can conclude that expressions Therefore, the answer is: y = -2w + 2x + 2z
what is expression ?In mathematics, you can double, divide, add, or subtract something. The following is an expression: Expression, numerical value, and math operator A mathematical expression is made up of numbers, parameters, and functions. Opposing sentences and expressions are possible. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and a mathematical action between them. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical sign +.
To solve for y
[tex]w = x - y/2 - z\\2w = 2x - y - 2z\\2w - 2x - 2z = -y\\y = -2w + 2x + 2z[/tex]
Therefore, the answer is:
y = -2w + 2x + 2z
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Interquartile range for 1 1 1 3 4 5
Answer:
3
Step-by-step explanation:
Factorise the following 9x²-14x+16
Answer: The given quadratic expression is:
9x² - 14x + 16
To factorize it, we can use the quadratic formula:
x = [-(-14) ± √((-14)² - 4(9)(16))] / 2(9)
Simplifying under the square root:
x = [-(-14) ± √(4)] / 18
x = [14 ± 2] / 18
x = (16/18) or x = (12/18)
Simplifying:
x = (8/9) or x = (2/3)
So the roots of the quadratic are x = 8/9 and x = 2/3. Therefore, we can factorize the quadratic expression as:
9x² - 14x + 16 = 9(x - 8/9)(x - 2/3)
Step-by-step explanation:
5x+6/1 1/3=3x/0.4
PLEASE HELP ME!!!!!!!!!!!!!!
Answer:
x=0.8
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
x=0.8
Answer:
x = 1.2
Step-by-step explanation:
see image. If the problem is two big, ugly fractions equal to each other, then you can cross-multiply. There are lots of different ways to solve it. This is just one way. I think the problem is to help you practice dealing with decimals and mixed numbers, multiplying and/or dividing with fractions, and distributive property. See image.
assuming the population has an approximate normal distribution, if a sample size has a sample mean with a sample standard deviation , find the margin of error at a 95% confidence level. round the answer to two decimal places.
The margin of error for a sample mean at a 95% confidence level can be calculated using the formula
E = (1.96 * (sample standard deviation/√sample size).
Therefore, the margin of error is E = (1.96 * (sample standard deviation/√sample size)) = (1.96 * (s/√n)).
Round the answer to two decimal places, and the margin of error is [tex]E = (1.96 * (s/√n)) = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = (1.96 * (s/√n)) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n) = E = 1.96 * (s/√n).[/tex]
Therefore, the margin of error at a 95% confidence level is E = 1.96 * (s/√n).
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4.02 Lesson check ! (7)
100 is the common difference of the given sequence
Determining the common difference of a sequenceAn ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is the number of elements.
Given the sequence below
8, 108, 208, 308...
The nth term of an arithmetic sequence is given as Tn = a + (n-1)d
The common difference is the difference between the preceding and the succeeding term.
First term = 12
Second term = 20
Common difference = 108 -8 = 208 - 108
Common difference = 100
Hence the common difference of the sequence is 100
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