What's the length? Please help. Thanks.

Part A. Let the total number of patrons be x. Then the number of patrons that liked reading sci-fi novels is x-35. Now

x-35 is 80%

35 is 100%-80%=20%.

Mathematically, you can write a proportion:

[tex]\dfrac{x-35}{80}=\dfrac{35}{20},\\ \\x-35=\dfrac{35\cdot 80}{20},\\\\x-35=140,\\\\x=175.[/tex]

Part B. The total nuber of patrons is 175, 35 did not like the sci-fi novels, then 140 liked.

Final answer:

To find the total number of library patrons, set up an equation using the given information. Then, solve the equation to determine the number of patrons who enjoy reading sci-fi novels.

Explanation:

Part A: Let's represent the total number of patrons at the library as 'x'. Since Celine observed that 80% of the patrons liked reading sci-fi novels, we can say that 80% of 'x' patrons enjoy reading sci-fi novels.

Therefore, the equation to find the total number of patrons can be written as: 0.8x = x - 35.

Part B: To find the number of patrons who enjoy reading sci-fi novels, we can solve the equation from Part A. First, let's simplify the equation: 0.8x = x - 35.

Then, we'll subtract 'x' from both sides of the equation: 0.8x - x = -35.

Combining like terms, we have: -0.2x = -35.

Finally, we'll divide both sides of the equation by -0.2 to solve for 'x': x = (-35)/(-0.2).

Plugging in the values, we get: x = 175. Therefore, there are 175 patrons who enjoy reading sci-fi novels.

x = [tex]\frac{3}{4}[/tex]

distribute the parenthesis on left side of equation and simplify

5x - 2x - 2 = [tex]\frac{1}{4}[/tex]

3x - 2 = [tex]\frac{1}{4}[/tex] ( add 2 to both sides )

3x = [tex]\frac{1}{4}[/tex] + 2 = [tex]\frac{9}{4}[/tex] ( divide both sides by 3 )

x = [tex]\frac{9}{4}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{3}{4}[/tex]

MN = 6 in

add the parts of the ratio, 1 + 2 + 3 = 6

divide AB by 6 to find 1 part of the ratio

[tex]\frac{18}{6}[/tex] = 3 ← 1 part

AM = 3 in ← 1 part

MN = 2 × 3 = 6 in ← 2 parts

NB = 3 × 3 = 9 in ← 3 parts

and 3 + 6 + 9 = 18 in = AB

h(6) = 8

reading vertically from x = 6 , we get , horizontally that y = 8

The correct answer is "His teacher advised it because he did not have time to tutor Euler privately." I just did the assignment and got it correct.

While in college, Euler work through advanced math books on his own because his teacher advised it because he did not have time to tutor Euler privately.    

Leonhard Euler was a renowned Swiss mathematician who made significant contributions to various branches of mathematics. While in college, Euler worked through advanced math books on his own not because of his father or the quality of education, but because his tutor, Johann Bernoulli, advised it. Bernoulli recognized Euler's talent and encouraged him to pursue mathematics independently, as Bernoulli did not have enough time to tutor Euler privately.

Parallel lines have the same slope, so the slope of the new line is 1/2.

The line passes through (0,4), and this gives the y-intercept, which would equal 4.

The equation now would be: y = 1/2x + 4

(a)

his profits increase annually by 2.5%, thus the profits each year form a geometric sequence with r = 1.025

that is 100 + 2.5 = 102.5% = 1.025

[tex]a_{n}[/tex] = 35000 × [tex](1.025)^{n-1}[/tex] ← explicit rule

(b)

[tex]a_{12}[/tex] = 35000 × [tex](1.025)^{11}[/tex] = 45923....

Profits after 12 years ≈ $46000

A graph quickly shows the solution to be ...

... A. x=3 and y=-10

_____

There are a couple of different strategies you can employ to eliminate possibilities.

1. Since the equations involve fractions, you can look only at answers that deal well with the fractions. That is, look for x-values that are multiples of 3 and y-values that are multiples of 5. Right away, this suggests you are not interested in choices B and C.

2. You can look at the general nature of the equations to see where the lines lie on a graph. It can be handy to know that intercept form is ...

... x/a + y/b = 1

where a and b are the x- and y-intercepts, respectively. That is, you can divide by the constant on the right (or just pay attention to its sign) to check the signs of the intercepts. For the first equation, the intercepts are both negative. Hence there cannot be any 1st-quadrant solutions. (That line never goes through the first quadrant—eliminating choices C and D.)

Likewise, the intercepts for the second equation are both positive, so it will never go through the third quadrant—eliminating choice B.

I would add 7 to get ...

... 2x² = 16

then divide by 2 to get

... x² = 8

Now, I would take the square root, recognizing that both positive and negative values will solve the problem.

... x = ±√8

The root can be simplified, so we have ...

... x = ±2√2

_____

The above method seemed the most obvious method to me. One could use the quadratic formula, but that seems to involve more operations.

... 2x² -16 = 0 . . . . subtract 9

... x = (-0 ± √(0² -4·2·(-16)))/(2·2) . . . . put the coefficients into the formula

... x = ±(√128)/4 = ±√8 = ±2√2 . . . . . simplify the result

Sample Response/Explanation: I would use the square root property of equality. Because there is no x term, I would just add and divide to get x2 by itself. Then I would take the square root.

This would just be 7 1/5 + 3/5 since the negative sign gets distributed and makes (-3/5) into a positive number.

From there you have basic math and you get 7 4/5.

The subtraction of the given expression will be [tex]7\dfrac{4}{5}[/tex].

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The subtraction will be calculated as:-

[tex]=7\dfrac{1}{5}-(-\dfrac{3}{5})[/tex]

[tex]= \dfrac{36}{5}+\dfrac{3}{5}\\\\\\= \dfrac{39}{5}\\\\\\= 7\dfrac{4}{5}[/tex]

Therefore subtraction of the given expression will be [tex]7\dfrac{4}{5}[/tex].

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2/11 is 0.181818 as a decimal so closest to 0.

Answer:

The answer is the first one which is 0

Answer:

about 36.3 feet

Step-by-step explanation:

Let x represent the height of the kite in feet. Then (x-22) is the horizontal distance to the kite. The Pythagorean theorem tells you the string length is related to these distances by ...

... 39² = x² + (x-22)²

... 2x² -44x -1037 = 0 . . . . rearrange to standard form

Using the quadratic formula, the positive solution is ...

... x = (-b+√(b²-4ac))/(2a) . . . . for a=2, b=-44, c=-1037

... x = (44 + √((-44)² -4(2)(-1037)))/(2·2)

... x = 11 + √639.5 ≈ 36.288

The kite is about 36.3 feet above the ground.

top left choice is correct. 0.002 g is 10^(-3) time the approximate number of seed in the jar 4*10^4 (40000) = 10

Separate the equation like this:

(4x2) (10^-3 x 10^4)

Then multiply the first and add the powers:

Final Answer: 8 x 10^1

hope that helps :)

Answer:

Total liters of salt in [tex]2.64*10^20[/tex] liters of water is [tex]9.24*10^18[/tex].

Step-by-step explanation:

If 1 liter of water contains [tex]3.5*10^-2[/tex] amount of salt,

Then,

[tex]2.64*10^20[/tex] liters of water will contain,

[tex]3.5*10^-2[/tex] should be multiplied by [tex]2.64*10^20[/tex].

Therefore,

Total liters of salt in [tex]2.64*10^20[/tex] liters of water is [tex]9.24*10^18[/tex].

Divide the total amount she has by how much she needs per batch.

When dividing fractions, flip the second one over and then multiply straight across.

9/10 / 1/4 becomes: 9/10 x 4/1

9/10 x 4/1 = 36/10 = 3 6/10 = 3 3/5

She can make 3 more batches and have 3/5 of a teaspoon left over.

Answer:

a) Error: Moving the decimal point without changing the exponent changes the value of the number. The final number reported is different from the one computed.

b) Correct work: (see below)

... Correct solution: 1.035×10¹¹

Step-by-step explanation:

a) When the decimal point is moved to the left in the mantissa, its value is divided by 10 for each place the decimal point is moved. To keep the overall value of the number the same, the power of 10 must be increased to compensate. The increase in the exponent is the number of places the decimal point is moved left.

In this problem, the decimal point is moved 1 place left, so the exponent needs to be increased from 10 to 11.

b) Correct work:

[tex]\displaystyle(7.14\cdot 10^{10})+(3.21\cdot 10^{10})=(7.14+3.21)\cdot 10^{10}\\\\=10.35\cdot 10^{10}=1.035\cdot 10^{11}[/tex]

Charlotte will need 3 buffet menus to host 75 people!

x = 10

[tex]\frac{x-2}{4}[/tex] = 2 ( multiply both sides by 4 to eliminate fraction )

x - 2 = 4 × 2 = 8 ( add 2 to both sides )

x - 2 + 2 = 8 + 2

x = 10

Answer:

b = 24

d = 10

f = 32

g = 34

h = 46

Step-by-step explanation:

From the given table we find that students who are in band = 48

So 24 + b = 48

b = 48 - 24

b = 24

Total students who do not play sports = h

And h = students in band + students not in band

h = b + 22

h = 24 + 22 = 46

h = 46

Total students who play sports and who do not play sports = 80

g + h = 80

g + 46 = 80

g = 80 - 46 = 34

g = 34

Total students who are not in band and not in band = 80

48 + f = 80

f = 80 - 48

f = 32

Students who are not in Band but either play sports or do not play sports = f

d + 22 = f

d + 22 = 32

d = 32 - 22 = 10

d = 10

Using the change of subject, the values of the alphabet b, d, f g, h calculated from the table are 24, 10, 32, 34, and 46 respectively.

To find b :

24 + b = total

24 + b = 48

b = 48 - 24

b = 24

To find h :

b + 22 = total

b + 22 = h

24 + 22 = 46

h = 46

To find g :

g + h = 80

g + 46 = 80

g = 80 - 46

g = 34

To find d :

24 + d = g

24 + d = 34

d = 34 - 24

d = 10

To find f :

d + 22 = f

10 + 22 = f

f = 32

Therefore, the values of b, d, f g, h are 24, 10, 32, 34, and 46 respectively.

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Let T represent the fifth test score. The average is the sum of scores divided by their number.

... 82 = (83 +75 +93 +67 +T)/5

... 410 = 318 +T . . . . . . . multiply by 5

... 92 = T . . . . . . . . . . . . subtract 318

The fifth score was 92.

_____

One of the ways I like to work problems like these is to add the differences from the mean. Those are ...

1, -7, 11, -15

so their sum is -10.

The final score must be 10 above the mean in order for this total to be zero. 10 above the mean is 92.

x Greater-than-or-equal-to 12

A closed circle is used on the graph.

The arrow on the graph points right.

The inequality representation is x ≤ 2.6 and has been graphed.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of before example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

The graph of inequality has a closed circle at 2.6, and the ray moves to the left.

The closed circle represents that point x = 2.6 is included.

Suppose the variable is x then x ≤ 2.6 represents the inequality.

Hence "The inequality representation is x ≤ 2.6 and has been graphed".

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( anything )² = anything × anything

5² = 5 × 5 = 25

The table can be filled in as follows:

[tex]\begin{array}{r|cccc}x(days)&1&2&3&4\\g(x)=3^x&3&9&27&81\\f(x)=3x+5&8&11&14&17\end{array}[/tex]

After 3 days, Kim's savings already exceeds Ben's, and is increasing at a faster rate. The appropriate descriptor is ...

... Kim will save more than Ben

_____

An exponential function increases faster than any polynomial function. (A linear function is a polynomial function.)

If Kim keeps up her savings for 28 days, her account balance will exceed the US Gross National Product of more than $20 trilliion. (Exponential functions tend to increase very rapidly!) Meanwhile, Ben's savings will be $89 on day 28.

_____

Please note the discrepancy in the problem statement. The verbiage says "days", but the table shows "years".

"It is decreased by $80,000" is the one among the following choices given in the question that would be an immediate effect on the money supply. The correct option among all the options that are given in the question is the first option or option "A". I hope that this is the answer that has actually come to your desired help.

mark brainliest plssss

The expected value of business profit is the sum of probability times profit:

... 0.2×(-10,000) + 0.4×0 + 0.3×5,000 + 0.1×8,000

... = -2000 + 1500 + 800

... = 300 . . . dollars

The expected value of the business return is slightly positve, so Claire should invest in the business.

Answer:

The answer above is correct

[tex]\sqrt{5}=2.23607, \sqrt{13}=3.60555, \sqrt{21}=4.58258, \sqrt{38}=6.16441[/tex]

These are all approximate decimal versions of the given numbers' square roots. If you need help rounding the decimals to a certain number of digits, let me know.

I hope this helps :)

Answer:

B. x = 5 and y = -13

Step-by-step explanation:

Equating real parts, we have ...

... x + 4 = 9

... x = 9 - 4 . . . . subtract 4

... x = 5

___

Equating imaginary parts, we have ...

... yi +9i = -4i

... yi = -4i -9i = -13i . . . . subtract 9i

... y = -13 . . . . . . . . . . . divide by i

[tex](x+yi)+(4+9i)=9-4i \\\\x+4+yi+9i=9-4i\\\\x+4+(y+9)i=9-4i\\\\x+4=9 \wedge y+9=-4\\\\x=5 \wedge y=-13 \Rightarrow \text{B}[/tex]

x < -  [tex]\frac{13}{7}[/tex]

add [tex]\frac{4}{7}[/tex] to both sides

- 3x > [tex]\frac{4}{7}[/tex] + [tex]\frac{35}{7}[/tex]

- 3x > [tex]\frac{39}{7}[/tex] ( divide both sides by - 3 )

note that when we divide/ multiply by a negative quantity we must reverse the inequality symbol

x < - [tex]\frac{13}{7}[/tex]

slope = [tex]\frac{4}{3}[/tex] and equation of line is

y = [tex]\frac{3}{2}[/tex] x + 3

calculate the slope m using the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = 2, 7 ) and (x₂, y₂ ) = (- 1, 3 )

m = [tex]\frac{3-7}{-1-2}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

calculate m using the gradient formula

with (x₁, y₁ ) = (- 4, - 3) and (x₂, y₂ ) = (0, 3 )

m = [tex]\frac{3+3}{0+4}[/tex] = [tex]\frac{6}{4}[/tex] = [tex]\frac{3}{2}[/tex]

the line crosses the y-axis at (0, 3 ) hence c = 3

y = [tex]\frac{3}{2}[/tex] x + 3 ← equation of line