100 points please help

100 Points Please Help

Answers

Answer 1
That’s not 100 but take the sqrt of the function and you get 9x+10
Answer 2

Answer:(9x + 10)(9x - 10)

Step-by-step explanation:


Related Questions

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

Answers

-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:

Question is down below

Answers

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.

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?

Answers

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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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)

Answers

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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please help thanks !!!

Answers

Answer:

boron

particle 1

Step-by-step explanation:

boron is number 5 on the periodic table of elements.

mass - protons= neutrons

11(rounded up) - 5 = 6 neutrons

ions are when an atom is positively or negatively charged. for example electrons are higher than protons or vice versa.

The Good Fruit stand sells baskets of cherries for $4 and baskets of blueberries for $3.

Its daily sales goal is $720

Answers

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.

Work out
25
% of
401. 16
m
Give your answer rounded to 2 DP

Answers

2 decimal point of 25% of 401.16 is 100.29



How to calculate 2 DP of 25% of 401.16 ?

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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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​

Answers

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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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.

Answers

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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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

Answers

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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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)

Answers

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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Using a calculator, work out
(3.5 × 107)
107) + (7.1 × 10⁹)
Give your answer in standard form.

Answers

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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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.

Answers

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.

Use the order of operations to simplify 19×33−2(16+23) .

Answers

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:

ParenthesesExponentsMultiplicationDivisionAdditionSubtraction

To simplify the expression 19×33−2(16+23) using the order of operations, first solve the operations inside the parentheses:

16 + 23 = 39

Now we multiply:

2 × 39 = 78

The expression now looks like this:

19 × 33 − 78.

Perform the multiplication before the subtraction:

19 × 33 = 627

Now that we have done the multiplication, we can subtract:

627 - 78 = 549

Therefore, the expression simplified is 549.

Answer:

b

Step-by-step explanation:

A puppy weighed 4 kg. Later, he weighed 5 kg. What is the percentage increase?

Answers

Mathematically, this can be expressed as follows: Percentage Increase = (15 - 10) / 10 x 100= 5 / 10 x 100= 50%.

The percentage increase can be calculated by taking the difference between the two weights and dividing it by the original weight. In this case, the percentage increase is 25%. Mathematically, this can be expressed as follows: Percentage Increase = (5 kg - 4 kg) / 4 kg x 100= 1 kg / 4 kg x 100= 25%In a broader sense, the formula for calculating the percentage increase of any quantity is given by: Percentage Increase = (Final Value - Initial Value) / Initial Value x 100This formula can be used to determine the percentage increase of any quantity, not just weight. For example, if the price of a product increases from $10 to $15, then the percentage increase in the price can be calculated using the same formula. In this case, the percentage increase would be 50%. Mathematically, this can be expressed as follows: Percentage Increase = (15 - 10) / 10 x 100= 5 / 10 x 100= 50%.

Step 1: Calculate the difference between the two weights:

5 kg - 4 kg = 1 kg

Step 2: Calculate the percentage increase:

(1 kg / 4 kg) x 100 = 25%

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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

Answers

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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Dani spends 1520 total to create
2 treat bags. How much more
would she have to spend to make
5 more similar bags?

Answers

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.

4.02 Lesson check ! (7)

Answers

100 is the common difference of the given sequence

Determining the common difference of a  sequence

An 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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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?

Answers

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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factirise fully.

[tex]2x + 4x { \\ }^{2} [/tex]

Answers

2x(1+2x) is the answer
This is algebraic this is only Ana

someone help me please

Answers

Answer:

Step-by-step explanation:

Knowing that we have a Right triangle find the third angle first, 53 + 90 =180 which the answer will be 37 degrees then add that answer to 41 to get you the second degree of your whole triangle, which will be 78 degrees. Then you can find the last angle by adding 78 + 53 = 180, the answer is 49 degrees. Now you have enough information to find the second triangles hypotenuse, using the law of sines which will end up being 12 inches approximately then you can use law of sines again but this time for the 1st triangle on the left. Giving you an answer of 15 inches for the whole side on the top of the triangle, but then you must subtract 8 inches, giving you the FINAL answer of 7 inches.

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

Answers

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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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

Answers

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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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

Answers

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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Sam spent $23.00 to buy 12 flowers for his mother.

Answers

Answer:

$1.92

Step-by-step explanation:

We take

23 / 12 = $1.92 per flower

So, it costs $1.92 per flower.

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.)

Answers

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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5x+6/1 1/3=3x/0.4


PLEASE HELP ME!!!!!!!!!!!!!!

Answers

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.

Interquartile range for 1 1 1 3 4 5

Answers

Answer:

3

Step-by-step explanation:

Can someone help me out?

Answers

Answer:

rar

Step-by-step explanation:

rar

Answer: 666

Step-by-step explanation:

y is inversely proportional to x.
When y = 6, x = 8
a) Work out an equation connecting y and x.

Answers

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{y varies inversely with x}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=8\\ y=6 \end{cases} \\\\\\ 6=\cfrac{k}{8}\implies 48=k\hspace{10em}\boxed{y=\cfrac{48}{x}}[/tex]

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