Line x has a slope of -1/2. Line y is perpendicular to line x. What is the slope of line y?

Answer:

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

Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

The volume of a cone is given by the formula V = (1/3) * pi * r^2 * h, where r is the radius of the base and h is the height of the cone. In this case, the height of the cone is the radius of the circle, which is 10 inches, and the radius of the base is half the length of the circumference of the sector, which is (theta/360) * 2 * pi * 10 inches.

We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.

V = (1/3) * pi * r^2 * h

= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10

= (1/3) * pi * (theta/36)^2 * 100

dV/dtheta = (2/3) * pi * (theta/36) * (100/36)

= (2/3) * pi * theta/36

Setting dV/dtheta = 0 and solving for theta, we get theta = 0.

Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then

V = (1/3) * pi * r^2 * h

= (1/3) * pi * (10)^2 * 10

= (1/3) * pi * 100 * 10

= (1/3) * pi * 1000

= approximately 1047.19 cubic inches

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

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We want to find the value of theta that maximizes the volume of the cone. We can do this by taking the derivative of the volume formula with respect to theta, setting it equal to 0, and solving for theta.

V = (1/3) * pi * r^2 * h

= (1/3) * pi * ((theta/360) * 2 * pi * 10)^2 * 10

= (1/3) * pi * (theta/36)^2 * 100

dV/dtheta = (2/3) * pi * (theta/36) * (100/36)

= (2/3) * pi * theta/36

Setting dV/dtheta = 0 and solving for theta, we get theta = 0.

Since the magnitude of theta must be positive, the maximum volume occurs when theta = 0, which means that the entire circle is used to form the cone. The maximum volume of the cone is then

V = (1/3) * pi * r^2 * h

= (1/3) * pi * (10)^2 * 10

= (1/3) * pi * 100 * 10

= (1/3) * pi * 1000

= approximately 1047.19 cubic inches

So, the maximum volume of the cone is approximately 1047.19 cubic inches.

Answer:

7 and 5

Step-by-step explanation:

The present age of Khalil is 7 years and the present age of Angela is 2 years.

Given that, in five years, Angela will be the age that Khalil is now. In three years, Khalil will be twice as old as Angela.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the present age of Khalil be x-5.

In five years:

Khalil's age = x-5+5=x

Angela's age = Khalil's present age

Angela's age = x-5

So, present angle of Angela's age = x-5-5=x-10

In three years:

Khalil's age = x-5+3=x-2

Angela's age =x-10+3=x-7

So, x-2=2(x-7)

⇒ x-2 = 2x-14

⇒ x=12

Khalil's present age = x-5=7 years and Angela's present age = x-10=2 years.

Therefore, the present age of Khalil is 7 years and the present age of Angela is 2 years.

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The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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Answer:

Direct V:

y=3x

y=(2/7)x

-0.5x=y

Not direct V:

y=2.2x+7

x=-1

y=4

Step-by-step explanation:

That was the answer on edge2020 :))

Direct variation usually conform to the general formula : \(y = kx \) where k is the proportionality constant. Hence sorting the equation into tbe appropriate category :

Direct variation :

y = 3x

y = (2/7)x

y = -0.5x

Non - direct variation :

y = 2.2x + 7

y = 4 and x = - 1

Therefore, only three of the expressions exhibit direct variation while the other three do not.

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The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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The value of the angle U from the calculation is 88 degrees.

The sine rule can be applied in a variety of situations, such as determining a triangle's unknown side lengths or angles. The sine rule can be used to locate the missing side or angle if you know the lengths of two sides and the measure of an angle (not necessarily the included angle).

By the use of the sine rule;

u/Sin U = w/Sin W

Thus;

76/Sin U = 71/Sin 69

Sin U = 76Sin 69/71

U = Sin-1 (76Sin 69/71)

U = 88 degrees

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Answer:

d

Step-by-step explanation:

3(x - 9)

3×x - 3×9

3(x) - 3(9)

Answer:

No

Step-by-step explanation:

first one

2:8/3

Multiply by 3

6:8

Divide by 2

3:4

second one

2/3:6

Multiply by 3

2:18

Divide by 2

1:9

1:9 =\= 3:4

No

The density of the gasoline is 690 grams per litre.

The mass of the jerrycan when fully filled is 16.3 kg

He fills a 20 litre jerrycan with gasoline.

A volume  of gasoline of 1 litre has a mass of 690 grams and the empty jerrycan weighs 2.5 kg.

Therefore, the density of the gasoline can be calculated as follows:

density = mass / volume

Hence,

mass of the gasoline = 690 grams

volume of the gasoline = 1 litres

density of the gasoline = 690 / 1

density of the gasoline = 690 grams per litre.

The weight of the jerrycan when filled with gas can be calculated as follows:

1 litre of gas = 690 grams

20 litres gas = 13800 grams

Hence,

1000 grams  = 1kg

13800 grams = 13.8 kg

Therefore,

weight of the jerry can when filled with gas = 13.8 + 2.5 = 16.3 kg

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Answer:

1st one is 20  2nd one is 21

Step-by-step explanation:

Answer:

1: 20

2: 21

im not to sure tho

Answer:

- 0.964

Step-by-step explanation:

Given that Coefficient of determination (R^2) = 0.93

Slope of regression line = - 5.26

The linear correlation Coefficient =?

The Coefficient of determination (R^2) is used to obtain the proportion of explained variance of the regression line. It is the square of the linear correlation Coefficient (R).

Hence. To obtain the linear correlation Coefficient (R) from the Coefficient of determination (R^2); we take the square root of R^2

Therefore,

R = √R^2

R = √0.93

R = 0.9643650

R = 0.964

However, since the value of the slope is negative, this depicts a negative relationship between the variables, hence R will also be negative ;

Therefore, R = - 0.964

The linear correlation coefficient of the data is: -0.96

Recall:

Thus, given:

Coefficient of determination of a set of data points = 0.93

Slope of the regression line = -5.26

Therefore:

R² = 0.93

R = √0.93

R = 0.96

Since the slope the regression line is negative, R will be negative in this case.

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Answer: The value of x is 49.

Step-by-step explanation:

To find the value of x, you will first need to cross multiply the fractional variables together.

5x - 80 = 3x + 18

Then, move the numerical term 80 to the right side of this equation and add it to 18.

5x - 80 = 3x + 98

Move 3x to the left side of the equation and subtract it this time to the variable 5x.

2x = 98

Finally, you divide both of the equation's sides by 2 and you will get 49.

x = 49

When you actually add x to this problem, you would get 33/55.

49 - 16/49 +6 = 33/55

You can then simplify 33/55 and get the same answer 3/5.

3/5

Therefore, the value of x for this variable equation with the fractions would be equal to x = 49. Hope this helps!

-From 5th Grader Honors Student

Answer:

The missing number is 5

Step-by-step explanation:

Let x be the number

I hope this helps!

The length of each side of the square is  when the perimeter of 56 m.

The square is a four sided figure with all sides are equal in length .

The measure of all the angles of square is \(90^o\).

Given:

The perimeter of the square = 56 m

Let, the side of square be s m.

The side of the square can be calculated using the formula:

Perimeter of square = 4 \(\times\\\) s

56 = 4 \(\times\) s

The value of s can be obtained by dividing both sides by 4

\(\dfrac{56}{4}\) = s

s = 14

Thus, the length of each side is 14 m

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Answer:

√(2 + √3)/4

Step-by-step explanation:

Sine 5π/12 = Sine (5π/6)/2

Recall

π = 180°

Thus,

Sine (5π/6)/2 = Sine (5×180 /6)/2

= Sine 150/2

Recall

Sine θ/2 = √(1 – Cos θ)/2

Thus,

Sine 150/2 = √(1 – Cos 150)/2

But, Cosine is negative in the 2nd quadrant. Thus,

Cos 150 = – Cos 30 = –√3/2

Thus,

√(1 – Cos 150)/2 = √(1 – –√3/2 )/2

= √(1 + √3/2 )/2

= √[(2 + √3)/2 ÷ 2]

= √[(2 + √3)/2 × 1/2]

= √(2 + √3)/4

Therefore,

Sine 5π/12 = √(2 + √3)/4

Answers:

(a) x = 0.5

(b) Given Below.

Explanation:

(a)

\(4^x = 2\)

apply ln both sides

\(ln(4^x) = ln(2)\)

simplify

\(xln(4) = ln(2)\)

divide both sides by ln(4)

\(x = 0.5\)

(b)

Recall that rational numbers can be expressed in fractions a/b

\(4^x = 5\)

apply ln on both sides

\(ln( 4^x) = ln(5)\)

simplify

\(xln( 4) = ln(5)\)

divide both sides by ln(4)

\(x =\frac{ ln(5)}{ln(4)}\)

simplify

\(x =1.160964047...\)  The value is endless and continues.

The following cannot be expressed as a fraction or whole number.

Hence, the following value of x is irrational.

The probability that all the guinea pigs selected randomly are pregnant is 1/30 or 0.033

Given, we have 10 guinea pigs out of which 4 are pregnant. We know that probability of an event ⇒ P(E) = (No of favorable outcomes)/(No of all outcomes) . So, The probability of selecting pigs that are pregnant is :

⇒ 4/10

Now, 3 selections are made randomly. The probability that the 1st selected guinea pig will be pregnant = 4/10

The probability that the 2nd selected guinea pig will be pregnant = 3/9

The probability that the 3rd selected guinea pig will be pregnant = 2/8

Therefore, the probability of all the 3 selected guinea pigs being pregnant will be :

⇒  (4/10) x (3/9) x (2/8)

⇒ 1/30

Therefore, The probability of all the selections of pigs being pregnant without replacement rounded to 3 decimal places is 0.033 or 1/30

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The complete question will be :

In a scientific study there are 10 guinea pigs,4 of which are pregnant. if 3are selected at random without replacement, find the probability that all are pregnant. enter your answer as a fraction or a decimal rounded to 3 decimal places.

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

Answer:

2.25

so first  I think

Step-by-step explanation:

sorry if it didn't help

Answer:

x-intercept=(4,0)

y-intercept=(0,3)

Slope=-3/4

Step-by-step explanation:

the last number is the y-intercept. The y-intercept is 3. Starting at that point, you know that 3/4 is the slope. So count up 3 (rise is 3) and count left 4 (run is 4) to find x. X-intercept would meet at (4,0)

I've added a picture to give you a visual.

If you have any further questions, don't be afraid to reach out! Hope this helps!

Answer:

  (b)  22 in

Step-by-step explanation:

You want the perimeter of a rectangle with side lengths 4 inches and 7 inches.

The perimeter of a rectangle is the sum of the lengths of its sides. Your rectangle has two sides that are 4 inches, and two sides that are 7 inches. The perimeter is the sum of these lengths:

  P = 4 in + 4 in + 7 in + 7 in

  P = 22 in

The perimeter of the rectangle is 22 inches.

__

Additional comment

We can save a math operation by recognizing the sum can be arranged to ...

  P = (4 in +7 in) +(4 in +7 in) = 2(4 in +7 in)

This is evaluated using one sum and one product, rather than the three sums we need if we simply add the lengths of the four sides.

This is why the usual formula for the perimeter of a rectangle is ...

  P = 2(L +W)

Answer:

43.6 has 3 significant figures.

The original amount is: 13900

Discount rate is: 5%

After discount price is:

if price is 100 then after discount price is 95.

so original price is 13900

after discount the price is:

After 5% discount sale price is 13205

Then amount of discount is:

The discount of amount is 695.

Answer: 42

Step-by-step explanation: trust me

Step-by-step explanation:

Answer:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

Step-by-step explanation:

Standard equation of a circle:  \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2

(where (a, b) is the center and r is the radius of the circle)

Substitute the given center (-14, -5) into the equation:

Part A: Fraction of all students who does not like Lakers = 3/8.

Part B: Fraction of all student who likes the Clippers = 9/32

Part C: Fraction of all student who does not likes the Clippers =  23/32.

Part D: Fraction of all student who does not likes either the Clippers or Lakers : 35/32

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.

Given data:

Students who likes only Los Angeles Lakers = 5/8

Students who does not likes only Los Angeles Lakers: 1 - 5/8 = 3/8

From 3/8, only 3/4 like the Los Angeles Clippers.

= 3/8 * 3/4

= 9/32

Now,

Students who does not like the Los Angeles Clippers: 1 - 9/32 = 23/32.

Part A: Fraction of all students who does not like Lakers = 3/8

Part B: Fraction of all student who likes the Clippers = 9/32

Part C: Fraction of all student who does not likes the Clippers =  23/32.

Part D: Fraction of all student who does not likes either the Clippers or Lakers :

= 3/8 + 23/32

= 35/32

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Answer:

a) Range = 1.39

b) the sample variance is 0.1597

c) the sample standard deviation is 0.3996

Step-by-step explanation:

Given the data in the question;

a) Find the range.

To determine the range, we simple subtract the smallest value from the largest value. i.e

Range = largest value - smallest value

from data set; our smallest is 0.53 while our largest value is 1.92

so

Range = 1.92 - 0.53 = 1.39

b) Find the sample variance.

To determine our variance, we use the following formula;

∑(\(X_{i}\) - \(x_{bar}\))² / n - 1 = [ ∑\(X_{i}\)²/n-1 ] - [ \(\frac{n}{n-1}\)(\(x_{bar}\))²]

where \(x_{bar}\) =  ∑\(X_{i}\)/n

n is sample size = 14 so lets calculate ∑\(X_{i}\)

∑\(X_{i}\) = 0.99 + 1.92 + 1.23 + 0.85 + 0.65 + 0.53 + 1.41  + 1.12 + 0.63 + 0.67 + 0.69 + 0.60 + 0.60 + 0.66

∑\(X_{i}\)  =  12.55    

∑\(X_{i}\)² = 0.99² + 1.92² + 1.23² + 0.85² + 0.65² + 0.53² + 1.41²  + 1.12² + 0.63² + 0.67² + 0.69² + 0.60² + 0.60² + 0.66²

∑\(X_{i}\)² = 13.3253

so

our  \(x_{bar}\) =  ∑\(X_{i}\)/n = 12.55 / 14 = 0.8964

so our Variance  will be;

= [ ∑\(X_{i}\)²/n-1 ] - [ \(\frac{n}{n-1}\)(\(x_{bar}\))²]

= [ 13.3253 / 14-1 ] - [ \(\frac{14}{14-1}\) (0.8964)²]

= 1.025 - 0.8653

= 0.1597

Therefore, the sample variance is 0.1597

c) Find the sample standard deviation.

we know that standard deviation is the square root of variance;

standard deviation = √Variance

standard deviation = √0.1597

standard deviation = 0.3996

Therefore, the sample standard deviation is 0.3996