Solve the rational equation quantity 3 times x minus 5 end quantity divided by 7 equals four sevenths.

The fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.

We assume the drop in the level of water to be d cm.

Since the container is cylindrical in shape, its volume is given as:

V = πr²h, where V is the volume, r is the radius, and h is the height.

In the question, we are given that the diameter of the can is 30 cm.

Hence its radius = 30/2 = 15 cm.

The capacity of the container is given to be 30 liters or 30*1000 = 30000 cm³.

The volume of the oil used = 1 liter or 1*1000 = 1000 cm³.

Thus, substituting V = 1000, r = 15, and h = d, in the formula of the volume, V = πr²h, we get:

1000 = π(15)²(d),

or, d = 1000/(225π) = 1.4147.

Thus, the fall in the water level is 1.4147 cm.

Therefore, the fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.

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Answer:

17a^2b

Step-by-step explanation:

Difference = subtracting

12a ^2b - (-5a^2b)

12a ^2b + 5a^2b

17a^2b

The computation of the decimals are illustrated below.

1. 7/4 + √5

= 1.75 + 2.24

= 3.99

2. -✓2 + 9

= -1.41 + 9

= 7.59

3. 2 - 5/4

= 2 - 1.25

= 0.75

4. 7.93 + 1/7

= 7.93 + 0.14

= 8.07

5. π + ✓5

= 3.14 + 2.24

= 5.38

6. ✓2 + 13/4 - 3

= 1.41 + 3.25 - 3

= 1.66

7. 8.5 - 12.65

= -4.15

8. 4 + ✓3 - 11/3

= 4 + 1.73 - 3.67

= 2.06

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We have that x = 3, LM = 14 and LN = 2. options A, C and E

We known that the three sides are on a straight line

LM  + MN = LN

Let's substitute the values, we have

3x + 5 + 4x = 11x - 7

Collect like terms

3x + 4x - 11x = -7 -5

-4x = -12

x = -12/ -4

x = 3

LM = 3x + 5 = 3(3) + 5 = 14

LN = 11x - 7 = 11(3) -7 = 33 -7 = 26

Thus, we have that x = 3, LM = 14 and LN = 2.  options A, C and E

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Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

Dilation is the increase or decrease in the size of a figure.

Figure A maps to figure B with a scale factor of 4/9, hence:

4/9 * x = 16

x = 54

Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54

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Answer: Mustafa is incorrect. He made a mistake in step 2.

Step-by-step explanation: Mustafa was certainly correct in step 1 that x(9x+3) + 3(x+3) is 9x^2 + 6x + 9. However when he was factoring, he made a mistake.

(3x + 3)^2 is NOT equal to 9x^2 + 6x + 9. Rather, (3x + 3)^2 is equal to 9x^2 + 18x + 9. If you want to double check this, use FOIL.

The correct factoring of 9x^2 + 6x + 9 is actually 3(3x^2 + 2x + 3). So, Mustafa made a mistake in step 2.

The linear regression model obtained by fitting the data points is Y = 0.0914X1 - 0.3741.

x = test score

y = average sleep

Slope = 0.0914

intercept = - 0.3741

The test score of a student that sleeps 8 hours

y = 8

8 = 0.0914X1 - 0.3741

8 + 0.3741 = 0.0914X1

X = 8.3741 / 0.0914

X = 91.62

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Answer:

its 5 5+4=9

Step-by-step explanation:

Answer: 55°

Step-by-step explanation:

Hi!

since an angle bisector splits it in half,

110°, being the entire angle divided by 2 = 110/2 = 55°

Answer:

-1/2

Step-by-step explanation:

slope is change in y / change in x

change in y is -5 bc y decreases by 5

change in x is 10 bc x increases by 10

-5/10 simplifies to -1/2

Answer:

The value of y for the system of equation is -1/2 .

A system of equation is a set of equation that have common solution

The set of equation given is

3x+4y=4

2x−4y=6

To solve the system , Elimination method will be used

Add equation 1 and 2 to eliminate y

5x  = 10

x = 2

Substitute the value of x in equation 1 to determine y

3x +4y = 4

6 + 4y = 4

4y = -2

y = -1/2

Therefore the value of y for the system of equation is -1/2 .

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If line J is perpendicular of line K, they should cross to make an X. If the slope of line K is -5, Line J would be 5.

Answer:

Vertical angles are equal

Step-by-step explanation:

-

[tex]vertical \: angles \: are \: equal[/tex]

[tex]3y = 150[/tex]

The sum of two supplementary angles equals 180 degrees

Therefore 6x +150=180

At least 832 teenagers must be interviewed.

It is given that the standard deviation is of 1.24 liters.

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2}[/tex] = 0.005

Now, we have to find z in the Ztable as such z has a p-value of [tex]1-\alpha[/tex].

So it is z with a p-value of [tex]1-0.005 = 0.995[/tex], so [tex]z= 2.575[/tex]

Now, find the margin of error M as such

[tex]M = Z * \frac{SD}{\sqrt{n} }[/tex]

In which SD is the standard deviation of the population and n is the size of the sample.

How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liters when constructing a 99% confidence interval?

At least n teenager must be interviewed.

n is found when M = 0.1.

We have that SD = 1.12

So

[tex]0.1 = 2.575*\frac{1.12}{\sqrt{N} }[/tex]

[tex]\sqrt{n} = \frac{2.575*1.12}{0.1}[/tex]

[tex]n = 831.7[/tex]

So rounding up to at least 832 teenagers must be interviewed.

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Answer:

a) 1/30

b) 1/6

Step-by-step explanation:

a) There are 10 people total and a group of 3 is being chosen. However, they all need to be women:

For the first person, the probability of it being a woman is 4/10

For the second person, the probability of it being a woman (with the prerequisite that the first was a woman) is 3/9

For the third (with the same requirements) is 2/8

If we multiply all of the fractions together, we get: [tex]\frac{1}{30}[/tex]

b) There are 10 people total and a group of 3 is being chosen. However, two of them need to be men, and 1 needs to be a woman:

For the first person, the probability of it being a man is 6/10

For the second person, the probability of it being a man (with the prerequisite that the first was a man as well) is 5/9

For the third person, the probability of it being a woman (because it can only be two men) is 4/8

If we multiply all the fractions together, we get: [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

The radians is just the length of the arc, so if you had a unit circle where the radius was 1, the length of that entire circle would be [tex]2\pi[/tex] since the circumference of any circle is [tex]2\pi r[/tex] except r is 1 so the length is just [tex]2\pi[/tex]. So if you take 1/4 of this you get [tex]\frac{2\pi}{4}[/tex] which can be simplified to  [tex]\frac{\pi}{2}[/tex]

Answer:

Step-by-step explanation:

Comments

You need to get the radian measure of the circle.

The radian measure of the entire circle is 2 * pi

To get the radian measure of 1/4 of the circle, just divide by 4.

2 pi / 4 = pi/2

The central angle is = to 1/4 of the circumference of the circle.

So the central angle is also pi/2

Answer: pi/2

Answer:

see below

Step-by-step explanation:

you can use cosine law

(3 sqrt3)^2 + (4 sqrt3)^2 - 2(3 sqrt3)(4sqrt3)cos60 = AC^2

AC = sqrt39

The mean of the heights of roller coaster is 27.92 feet, median is 21, mode is 16 and mid range is 35.5.

Given heights in feet of 14 roller coaster 11,12,13,14,16,21,25,26,31,40,51,55,60.

We have to calculate the mean, median, mid range and mode for the data.

Mean is the sum of numbers divided by the numbers.

Mean=∑X/n

∑X=11+12+13+14+16+21+25+26+31+40+51+55+60

=391

n=14

Mean=391/14

=27.92 feet.

Median is the central value of the data given.

Median=(n/2)th term ,when  n is even, ( n/2)th term, (n+1)/2th term when n is odd.

Median=14/2th term=7th term which is 21.

Mode is the number which has higher frequency.

Mode is 16 because it comes 2 times.

Mid range is the sum of upper value and lower value of data divided by 2.

Mid range=(11+60)/2==35.5.

Hence the mean is 27.92 feet, median is 21 feet, mid range is 35.5 feet, mode is 16 feet.

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Question is incomplete as the values of height should be included as under:

11,12,13,14,16,16,21,25,26,31,40,51,55,60.

Answer:

80π

Step-by-step explanation:

Circle O with radius IO:

large radius = IO = 12 = R

Circle O with diameter JK

IJ = JK = KL = 2 × IO = 24

IJ = JK = KL = 24/3 = 8

small radius = 8/2 = 4 = r

The shaded area is a semicircle of radius 12 minus a semicircle of radius 4 plus two semicircles of radius 4.

That is the same as

1 semicircle of radius 12 plus 1 semicircle of radius 4

A = πR²/2 + πr²/2

A = π(12² + 4²)/2

A = 160π/2

A = 80π

Answer:

Just look at the other answer

Step-by-step explanation:

Answer:

f is always positive on the interval.

Step-by-step explanation:

Answer:

1.(6*4) + (18*6) + (6*4)

1.(6*10) + (6*6) + (6*10)

Step-by-step explanation:

there are two ways to break this shape into three rectangles:

1.Top right rectangle, Top left rectangle, Bottom long rectangle

2. Left rectangle, Middle square, Right rectangle.

The sample size that gives 99% confidence level and estimate will be within 3 ounces is 0.7386[tex](standard deviation)^{2}[/tex].

Given  confidence level 99% and margin of error is 3 ounces of true mean.

Margin of error is the difference between the actual values and the calculated value of mean.

Sample size is the number of items taken from the population as a sample for research.

We have to find the sample size.

First we have to find the z value for the corresponding p value of 0.99.

z value=2.58

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

3=2.58σ/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex]=2.58/3 σ

Squaring both sides

n=[tex]2.58^{2}[/tex]σσ

Hence the sample size needed is 2.58 ([tex](standard deviation)^{2}[/tex].

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The statements that are true are B, C, and F.

Here we have the exponential function:

[tex]f(x) = 4*5^x[/tex]

We can see that the initial value is 4, and the base is 5. Because the base is larger than 1, this is an exponential growth function.

The statements that are true are:

B: The domain of an exponential function is always the set of all real numbers.

C: Is an exponential growth, so yes, it is increasing.

F: The y-intercept is given by evaluating the function in x = 0, when you do that, you get the initial value, which is 4. So the y-intercept is (0, 4).

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The first four terms of the sequence are 8,12,16 and 20.

Given the function is f(n) = (2n+2)2

Now, we want first four terms, therefore, putting 1, 2, 3, 4 in the sequence we get:

f(1) = (2*1+2)2 = 8

f(2) = (2*2+2)2 = 12

f(3) = (2*3+2)2 = 16

f(4) = (2*4+2)2 = 20

Hence, The first four terms of the sequence are 8,12,16 and 20.

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Neither 2 nor 7 have inverses mod 6 or 7, respectively, so the expressions in (a) and (b) cannot really evaluated... At least we can evaluate (c) :

[tex]5\times3 \equiv 15 \equiv 1 \pmod 7 \\\\ \implies 3\times2\div5 \equiv 3\times2\times3 \equiv18 \equiv \boxed{4 \pmod{7}}[/tex]

Length = 7 + 2x [L]

Breadth = 6 + x [B]

So, Area = L × B

=> Area = (7 + 2x) (6 + x)

=> Area = 7 × 6 + 7x + 2x × 6 + 2x²

=> Area = 42 + 7x + 12x + 2x²

=> Area = 2x² + 19x + 42

Option B is correct.

Any questions, you may ask.

Answer: b.) 2x² + 19x + 42

Area of rectangle:

⇒ Length × Width

⇒ (6 + x) × (7 + 2x)

⇒ 6(7) + 6(2x) + x(7) + x(2x)

simplify

⇒ 42 + 12x + 7x + 2x²

arrange

⇒ 2x² + 19x + 42

Answer:

The answer is  4×4+5×2−3.

Step-by-step explanation:

This is because, in the original amount, they had 4 tanks with 4 fish and 5 tanks with 2 fish. 4x4 is 16 and 5x2 is 10. Then you add them together to get 26. But, you have to subtract 3 because of the order of 3 fish, which equals 23. The equation 4×4+5×2−3 shows that.

Answer: [tex]\frac{3 +- \sqrt{23}i}{2}[/tex] If using complex numbers, or undefined if using all real numbers

Step-by-step explanation:

Moving -8 to the left side of the eq by adding both sides by 8=

x^2-3x+8=0

The quad formula:[tex]\frac{-b +- \sqrt{b^2-4ac}}{2a}[/tex]

a=1 b=-3 c=8

Inserting a b c values into formula: [tex]\frac{-(-3) +- \sqrt{(-3)^2-4(1)(8)}}{2(1)}[/tex]

Simplifying: [tex]\frac{3 +- \sqrt{9-32}}{2}[/tex]

[tex]\frac{3 +- \sqrt{-23}}{2}[/tex]  Since the square root of a negative number doesn't exist in the set of real numbers, the equation is undefined.

OR

[tex]\frac{3 +- \sqrt{23}i}{2}[/tex] Using complex numbers i, to replace the negative number created by subtracting 9-32.