18dp - 17b + 17dm - 14dm - 3b + 12dp - 12b

Answer: the original slope is 3/2

The perpendicular slope is -2/3

Slope is rise/run

Step-by-step explanation: For the original slope get  

Find coordinates where the graphed line crosses the grid lines at the intersections. Here, (0,-2) and (2,1) Count the number of squares vertically. That is the rise. It is the difference in y-values. It is the numerator of the fraction. Then count the squares horizontally to get the run. That is the denominator of the fraction.

It is possible to use the expression \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\) to calculate the slope.

\(\frac{1-(-2)}{2-0} = 3/2\)

To find the perpendicular slope, reverse the sign and use the reciprocal of the original fraction.

The reciprocal of 3/2 is 2/3. The opposite sign is negative. -2/3

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw is 0.39.

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, can be calculated using conditional probability.

P(A|B) = P(A and B) / P(B)

P(A and B) = P(T or P on second draw and F on first draw) = P(T on second draw and F on first draw) + P(P on second draw and F on first draw)

= (3/9) x (4/10) + (2/9) x (4/10) = 14/90

To find P(B), we know that it is 0.4.

Therefore, the conditional probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is:

P(A|B) = P(A and B) / P(B) = (14/90) / 0.4 ≈ 0.39

So the probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is approximately 0.39.

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The area of the surface is (2/3)π.

We can solve this problem using a double integral. First, we need to find the limits of integration for x and y. From the equation x + y + z = 1, we get:

z = 1 - x - y

Substituting this into the equation x² + 7y² ≤ 1, we get:

x² + 7y² ≤ 1 - z² + 2xz + 2yz

Since we want to find the area of the surface, we need to integrate over x and y for each value of z that satisfies this inequality. The limits of integration for x and y are given by the ellipse x² + 7y² ≤ 1 - z² + 2xz + 2yz, so we can write:

∫∫[x² + 7y² ≤ 1 - z² + 2xz + 2yz] dA

where dA is the area element.

To evaluate this integral, we can change to elliptical coordinates u and v, defined by:

x = √(1 - z²) cos u

y = 1/√7 √(1 - z²) sin u

z = v

The limits of integration for u and v are:

0 ≤ u ≤ 2π

-1 ≤ v ≤ 1

The Jacobian for this transformation is:

J = √(1 - z²)/√7

So the integral becomes:

∫∫[u,v] (x² + 7y² )J du dv

Substituting in the values for x, y, z, and J, we get:

∫∫[u,v] [(1 - z²) cos² u + 7/7 (1 - z²) sin² u] √(1 - z²)/√7 du dv

Simplifying, we get:

∫∫[u,v] [(1 - z²) (cos² u + sin² u)] (1/√7) dz du dv

= ∫∫[u,v] [(1 - z²)/√7] dz du dv

= (2/3)π

Therefore, the area of the surface defined by x + y + z = 1, x² + 7y² ≤ 1 is (2/3)π.

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An organized group of integers with a shared variance among each succeeding word is known as an arithmetic sequence. Hence, the right response is (b). 1/3, 1/9, 1/15, 1/21, 1/27.

Which collection of numbers doesn't fit the definition of an arithmetic sequence?

The following instances don't constitute arithmetic sequences: 1.) 2,4,8,16 is not true since the first with second terms differ by 2, while the third and fourth terms differ by 4, and the fifth and sixth terms differ by 8. There are no shared differences, hence the sequence is not arithmetic.

Is the number sequence 2 2 2 2 2 arithmetic?

The series cannot be an arithmetic sequence, however it may be defined. It does, nevertheless, have a common ratio across succeeding words, namely 1, which results in its geometric growth.

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Answer:

if I'm correct I think it's B

Answer:QUESTION 13 10 points Save Answer Benzene (CSForal = 0.055 mg/kg/day) has been identified in a drinking water supply with a concentration of 5 mg/L. Assume that adults drink 2 L of water per day and children drink 1 L of water per day. Assume that an adult male weighs 70 kg, a female adult weighs 50 kg, and a child weighs 10 kg.

Step-by-step explanation:

To find the least number of terms, we need to solve the inequality a_n+1 ≥ 0.03 for n. This will give us the smallest value of n that ensures the partial sum is within 0.03 of s

To guarantee a partial sum within 0.03 of s for an alternating series, the least number of terms that must be summed can be found using the alternating series error bound formula.

The alternating series error bound formula is given by:

|Error| ≤ a_n+1

where a_n+1 is the absolute value of the next term in the series. Since the series alternates, the absolute value of the next term is a smaller bound for the error. Rearranging the formula, we get:

a_n+1 ≥ |Error|

We want the error to be less than or equal to 0.03, so we can set |Error| = 0.03. Substituting this into the formula, we get:

a_n+1 ≥ 0.03

We need to find the least value of n for which a_n+1 is less than or equal to 0.03. Once we find that value of n, we can sum the first n terms of the series to guarantee a partial sum within 0.03 of s.

Therefore, to find the least number of terms, we need to solve the inequality a_n+1 ≥ 0.03 for n. This will give us the smallest value of n that ensures the partial sum is within 0.03 of s

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Answer:

11

Step-by-step explanation:

r=6+5

=11

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Answer:

r = 11

Step-by-step explanation:

Add 5 to both sides of the equation:

6 + 5 = r - 5 + 5

Add the numbers

11 = r - 5 + 5

11 = r

Move the variable to the left

r = 11

Sherry used 3/8 of her sugar to make sweet tea, which is the fraction obtained by subtracting 1/2 from 7/8.

The fraction of sugar that Sherry used to make sweet tea, we need to subtract the amount of sugar she used from the total amount of sugar she had.

Sherry had $7/8$ of a cup of sugar in her kitchen, and she used $1/2$ of a cup of sugar to make sweet tea.

To find the remaining amount of sugar, we subtract $1/2$ from $7/8$:

$7/8 - 1/2$

To subtract fractions, we need a common denominator. In this case, the common denominator is 8. We can rewrite $1/2$ as $4/8$:

$7/8 - 4/8$

Now we can subtract the numerators:

$3/8$

Therefore, Sherry used $3/8$ of her sugar to make sweet tea.

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Answer:

9y+6

Step-by-step explanation:

The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.

An ordered pair consists of two items. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it might be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.

The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

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Answer:

D

Step-by-step explanation:

Answer:

2:5 12:30(?)

Step-by-step explanation:

the first ones right I'm not sure about 12:30

The cost of 2 pounds of cherries without the coupon would be $6.50 x 2 = $13.

With the coupon, Madeline would have to pay $13 - $1 = $12 for 2 pounds of cherries.

The expression for the cost of buying x pounds of cherries with the coupon is:

(6.5*x) - 1

The length of the straw is 3.74 inches.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

In rectangular box,

Length (l) = 2 inches

Width (w) = 1 inches

Height (h) = 3 inches

Here, The straw is said to fit into the box diagonally from the bottom.

So, the length (s) of the straw is calculated as:

⇒ s = √ l² + w² + h²

⇒ s = √ 2² + 1² + 3²

⇒ s = √ 4 + 1 + 9

⇒ s = √ 14

⇒ s = 3.74 inches

Thus, The length of straw = 3.74 inches

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The length of the straw will be 3.7416  inches long in radical form.

If a cuboid has length = l units, breadth = b units, and height = h units, then we can evaluate the length of the diagonal of a cuboid using the formula : X²=l²+b²+h²

Here,

As per the question the length of the straw is equal to length of the diagonal of Rectangular box.

l= 3 inch , b= 2 inch , h= 1 inch

Let us consider the length of the straw be 'x'.

As, Diagonal of Cuboid is,

X²=14

X=√14

i.e. X=3.7416

We get, X= 3.7416 (in radical form)

Hence, the length of the straw will be  5.91607 inches.

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Answer:

40,60,80

Step-by-step explanation:

let 2x 3x and 4x

9x=180

x=20

2x=40

3x=60

4x= 80

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(a) Example question: "How often do you look at social media while doing schoolwork?

(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.

(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.

(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.

(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."

(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.

(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.

To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.

Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.

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If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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Answer:

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Step-by-step explanation:

x=2

1/2(x) + 4

1/2(2) +4

1+4 = 5

x + 6 -1/2(x) -2

2+6 -1/2(2) -2

8 - 1 -2 = 5

Hope i helped you out :)

Answer:

102°

Step-by-step explanation:

<3+<4=180°

<3+78°=180°

<3=180°-78°

<3= 102°

hope it helps

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Answer:

8 \(\frac{2}{3}\)

Step-by-step explanation:

Find the LCD of the two fractions, which is six

3\(\frac{1}{2}\) = 3 \(\frac{3}{6}\)

---------------------------------------------------------------------------------------------------------------

5\(\frac{1}{6}\) + 3 \(\frac{3}{6}\) = 8\(\frac{4}{6}\)

The next step is to reduce:

8\(\frac{4}{6}\) = 8\(\frac{2}{3}\)

---------------------------------------------------------------------------------------------------------------

Have a great summer :)

Answer:

Step-by-step explanation:

\(5\frac{1}{6} +3\frac{1}{2} =\frac{31}{6} +\frac{7}{2} \\=\frac{31+21}{6}\\=\frac{52}{6} \\=\frac{26}{3} \\=8\frac{2}{3}\)

In mathematics, "\(a^2\)" denotes the square of a number or variable "a." It is calculated by multiplying "a" by itself.

4For example, if "a" is 5, then a^2 would be 5*5, which equals 25. When "a" represents a positive number, its square is always positive.

If "a" is negative, its square is still positive since a negative multiplied by a negative results in a positive.

In geometrical terms, if "a" represents the length of the side of a square, then a^2 represents the area of that square. This notation is part of the general concept of exponentiation.

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The Question in English

What does a^2 mean in mathematics

something you should keep in mind is that all three angles in a triangle always add up to 180 degrees.

so, here, since you know the two other angles, you can find the third.

180 - 106 - 42 will give you the measure of that third angle.

your answer will be 32.

hope i helped, good luck!

Answer:

32

Step-by-step explanation:

as you triangle angle add up to 180 so you add 106 by 42 which gives you 148 then

you take 180 -148 which it will give you =32

Answer:

360 tons

Step-by-step explanation:

Coke burned : cast iron = 15 : 16

The smelter produces 384 tons of cast iron a day

Let x = tons of coke burned

Coke burned : cast iron = x : 384

Equate both ratios

15 : 16 = x : 384

15/16 = x/384

Cross product

15 * 384 = 16 * x

5,760 = 16x

x = 5,760/16

x = 360

x = tons of coke burned = 360 tons

Answer:

Step-by-step explanation:

Please refer to the attachement. I defined the height (H), width (W), and length (L) and set:

H = 4m and W = (1/3)L. The total cost of 640 Rs/m^2 is divided by the rate cost of Rs 5/m^2 to give 128 m^2 that was plastered. The total area of the walls must be 128 m^2, so then calculate the total wall area: The walls for the length are 2*LH and for the width are 2*WH. Substituting, we have a total of 8*L + (4/3)L = 128 m^2. Solve for L to obtain L = 12m. W is 1/3L, or 4m. The room is (W,L,H) 4, 12, and 4 meters. The floor is W*L, or 48m^2. At Rs 250/m^2, the rug will cost Rs 12000. Ouch.

Answer:

Domain:[-4,∞)

Range:[0, ∞)

Thus, choice C is the exact answer

James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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The equation used to find the distance of the flowerbed from the hive is called the "time equation".

The flowerbed is 900 feet far from the hive.

Find the traveling time

The bee spends 12 minutes hunting down the nectar in the flowerbed. Since it was away from the hive for a total of 16 minutes, the traveling time is

16min - 12min = 4 min

Convert the Minutes to seconds

1 minute = 60 seconds

4 minutes = 4*60 = 240 seconds

Find the time each way

The total time is 240 seconds, but it is not divided evenly.

Let the time there = t

Let the time back = 240 - t

The distances are the same

r = 10 m/s

r1 = 6 m/s

t1 = t

t2 = 240 - t

dthere = dback

d = rate * time

10 m/s *t = 6 m/s (240 - t)      

Remove the brackets on the right.

10 * t = 6*240 - 6t                

Combine the like terms on the right.

10t = 1440 - 6t                        

Add 4t to both sides

10t + 6t = 1440 - 6t + 6t          

Combine

16t = 1440                            

Divide both sides by 16

16t/16 = 1440/16                    

Do the division

t = 90                                    

Find the height

d = ?

r = 10 m/s

t = 90 second

d = r*t

d = 10 * 90 = 900 feet

The flowerbed is 900 feet far from the hive.

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The complete question is:

A babe flies at 10 feet per second directly to a flowerbed from its hive. the bee stays at the flowerbed for 12 minutes and then flies directly back to the hive at 6 feet per second. It is away from the hive for a total of 16 minutes.

What equation can you use to find the distance of the flowerbed from the hive?

Answer:

the length of a line s3gment is 13 units then its 169

Answer:

3/10 || 7/10

Step-by-step explanation:

Answer:

30%

70%

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Step-by-step explanation: