In general, the value measured by the
variable __________
axis is called the dependent

Answer:

  91/120

Step-by-step explanation:

It might be convenient to use the form ...

  (a/b) +(c/d) = (ad +bc)/(bd)

__

  -2/3 +4/5 +5/8 = (-2/3 +4/5) +5/8

  = (-10 +12)/15 +5/8

  = 2/15 +5/8

  = (16 +75)/120

  = 91/120

Answer:

Add 12 to the product of 13 and a number p.

Step-by-step explanation:

Given expression: 13p + 12

In the expression, 13 is multiplied by a number p, and 12 is added to the result. Therefore, a simple word phrase for the given expression would be: Add 12 to the product of 13 and a number p.

i.e 13 × p = 13p

Then add 12,

     =  13p + 12

Answer:

70g+74

Step-by-step explanation:

Answer:

= 70g + 74

Step-by-step explanation:

10 (7 + 7g) + 4

= 10(7g + 7) + 4

= 70 + 70g + 4

= 70g + 74

Answer:

-12a²+9a-5

Step-by-step explanation:

-7a²+3a-9 - (5a²-6a-4)=

-7a²+3a-9-5a²+6a+4=

-12a²+9a-5

Answer:

The data is skewed to the bottom and contains an outlier.  

Step-by-step explanation:

1. Test for outlier

An outlier is a point that is more than 1.5IQR below Q1 or above Q3.  

IQR = Q3 - Q1 = 74 - 51 = 23

1.5 IQR  = 1.5 × 23 = 34.5

51 - 15 = 36 > 1.5IQR

The point at 15 is an outlier.

2. Test for normal distribution

The median is not in the middle of the box.  

Rather, it cuts the box into two unequal parts, so the data does not have a normal distribution.

3. Test for skewness

The longer part is to the left of the median, so the data is skewed left.

Direct variation occurs when a variable varies directly with another variable. That is, as the x-variable increases, the y-variable also increases.

The ratio of between y-variable and x-variable would be constant.

Direct variation can be represented by the equation, [tex] y = xk [/tex], where k is a constant. Thus,

[tex] \frac{y}{x} = k [/tex]

From the table given, it seems, as x increases, y also increases. Let's find out if there is a constant of proportionality (k).

Thus, ratio of y to x, [tex] \frac{0.50}{1} = 0.5 [/tex]

k = 0.5.

If the given table of values has a direct variation relationship, then, plugging in the values of any (x, y), into [tex] \frac{y}{x} = k [/tex], should give us the same constant if proportionality.

Let's check:

When x = 2, and y = 1:

[tex] \frac{y}{x} = k [/tex],

[tex] \frac{1}{2} = 0.5 [/tex],

When x = 3, y = 1.5:

[tex] \frac{1.5}{3} = 0.5 [/tex],

When x = 5, y = 2.50:

[tex]\frac{2.5}{5} = 0.5[/tex],

The constant of proportionality is the same. Therefore, the relationship forms a direct variation.

Answer:

Direct variation occurs when a variable varies directly with another variable. That is, as the x-variable increases, the y-variable also increases.

Step-by-step explanation:

Answer:

[tex]2\sqrt{21}[/tex]

Step-by-step explanation:

We can multiply the two irrational terms, getting [tex]\sqrt{84}[/tex].

We see that 4 is a factor of 84, so we can rewrite [tex]\sqrt{84}[/tex] as [tex]\sqrt{4 (21) }[/tex]. We can take the 4 out, getting [tex]2\sqrt{21}[/tex].

Answer: 7

Explanation:

List out the factors of 120 until we hit a gap

1,2,3,4,5,6,8

Note that 7 is not shown above. We can see that 120/7 = 17.14 approximately meaning that 7 doesn't go evenly into 120. So this is why 7 isn't a factor. Something like 3 is a factor because 120/3 = 40 is a whole number result.

Also, 7 is prime. The only factors of 7 are 1 and itself. This means that 7 and 120 do not have any common factors other than 1. The GCF of 7 and 120 is 1, leading to the two numbers being relatively prime

Side note: The term "coprime" is sometimes used in place of "relatively prime"

Answer:

3 cm

Step-by-step explanation:

A line from the centre of the circle at right angles to the chord is a perpendicular bisector.

Thus a right triangle is formed with legs d , the line from centre to chord and 4 , half the length of the chord. The radius 5 is the hypotenuse.

Using Pythagoras' identity in the right triangle.

4² + d² = 5², that is

16 + d² = 25 ( subtract 16 from both sides )

d² = 9 ( take the square root of both sides )

d = [tex]\sqrt{9}[/tex] = 3

Thus the chord is 3 cm from the centre of the circle.

OB = 3 cm

AO = radius = 5 cm

AB = 8cm/2 = 4 cm

Pythagora

OB² = AO² - AB²

= (5cm)² - (4cm)²

= 25cm² - 16cm²

= 9 cm²

OB = √9cm²

= 3 cm

Answer:

The correct option is (a).

Step-by-step explanation:

The general least square regression line is given by,

[tex]\hat Y=a+bX[/tex]

Here,

X = independent variable

Y = dependent variable.

b = slope (or regression) coefficient

a = intercept

The main purpose of the least square regression line is to predict the value of the dependent variable when the independent variable is known.

So, the correct interpretation is:

A least squares regression line can be used to predict a value of y if the corresponding x value is given.

The correct option is (a).

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two given points is given by

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(10,5) and (-2, -10)

The midpoint of points is

We have the final answer as

Hope this helps you

Answer:

(x + y) - 2     or    x + y - 2

Step-by-step explanation:

"sum of x and y"

may be expressed mathematically as (x + y)

"two less than sum of x and y", can thus be written:

(x + y) - 2  or x + y - 2

Answer:

2.16 gallons

Step-by-step explanation:

Area to be painted:

9 ft × 12 ft = 108 ft²

Pain required:

===============================================

Explanation:

Notice how inscribed angles x and y subtend (or cut off) the same minor arc measure. This means that x = y. So if we find x, we found y also.

The vertical line is a diameter of the circle. The blue angle marked in the diagram below is a right angle due to Thales Theorem, which is a special case of the inscribed angle theorem. Thales Theorem says that any inscribed angle in a semicircle is 90 degrees.

Therefore the triangle marked in red (same diagram) is a right triangle, allowing us to say

x+47+90 = 180

x+137 = 180

x = 180-137

x = 43

So y = 43 as well.

Answer:

B. sen α = BC/b

Step-by-step explanation:

Las identidades trigonométricas se utilizan para resolver problemas de ángulos rectos.

En un ángulo recto, el lado al que se hace referencia como opuesto es el lado opuesto al ángulo, el lado al que se hace referencia como adyacente es el lado siguiente al ángulo (entre el ángulo y el ángulo recto) mientras que la hipotenusa es el lado más largo (opuesto al ángulo recto)

De identidades trigonométricas:

[tex]sen\ \alpha=\frac{lado\ opuesto}{hipotenusa} \\\\lado\ opuesto=BC=a\\\\hipotenusa=b\\\\sen\ \alpha=\frac{lado\ opuesto}{hipotenusa} =\frac{BC}{b} \\\\sen\ \alpha =\frac{BC}{b}[/tex]

Answer:

The correct option is (a).

Step-by-step explanation:

The complete question is:

A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool.

Solution:

The first hose takes 6 hours to fill the pool.

So, work done per hour by the first hose is, 1/6.

Suppose the second hose takes x hours to fill the pool.

So, work done per hour by the second hose is, 1/x.

The work done per hour by the two hoses together is, [1/6 + 1/x] = (x + 6)/6x.

Together the two hoses can fill the pool in, 6x/(x + 6) hours.

It is provided that, the second hose needs 3 more hours to fill the pool than the two hoses combined.

That is:

6x/(x + 6) = x - 3

6x = (x - 3)(x + 6)

6x = x² + 3x - 18

x² - 3x - 18 = 0

x² - 6x + 3x - 18 = 0

x (x - 6) + 3 (x - 6) = 0

(x + 3)(x - 6) = 0

x = 6

Then the time taken by the two hoses together is,

6x/(x + 6) = x - 3 = 6 - 3 = 3 hours

So, each hose takes 6 hours and together they take 3 hours to fill the pool.

This implies that the second hose takes 3 hours more than the 3 hours together to fill the pool.

Thus, the correct option is (a).

Answer:

[tex] \sqrt{2} [/tex]

Step-by-step explanation:

[tex]2 \sqrt{2} \times \frac{1}{2} = \frac{ 2\sqrt{2} }{1} \times \frac{1}{2} = \frac{2 \sqrt{2} }{2} = \sqrt{2} [/tex]

Hope this helps ;) ❤❤❤

Answer:

Step-by-step explanation:

If x represents Caitlyn's age, then  can be used to represent Carl's age, and  can be used to represent Daryl's age.

The product of Caitlyn and Daryl's ages is at least 160. Use this information to set up an inequality to represent this situation.

The answer is x squared +9x+14 is greater than or equal to 160.

The inequality that represents the given situation where x is the age of Caitlyn will be (X+2) (x+7) ≥ 160.

The inequality equation is a representation of the relation between two or more expressions that are not equal, not equal to, less than, or greater than.

Represented by:

Solution:

It is given that,

Caitlyn's age = x,

Carl's is two years older than Caitlyn, therefore,

Carl's age = x + 2

And, Daryl is 5 years older than Carl, therefore,

Daryl's age = Carl's age + 5

= (x + 2) + 5

= x + 7

The last condition is that the product of Carl and Daryl's age is at least 160, at least is represented as ≥ which mean that value either equal or greater than.

Therefore, the inequality would be (x+2) (x+7) ≥ 160

Learn more about inequality:

https://brainly.com/question/16826399

Answer:

h = 61.83 feet

Step-by-step explanation:

length of string from Hector to kite = c = 86 feet.

and 4 feet off the ground.

angle A = 42° 15' 30"

req'd:  how high is the kite?

angle A = 42° + 15' (1° / 60') + 30"(1° / 3600'')

angle A = 42.26

to get the side a (height of kite) 4 feet above ground: use Sin(A) = opp / hyp

Sin(A) = a / c

Sin(42.26) = a / 86

a = Sin(42.26) * 86

a = 57.83 feet

therefore, the height of the kite from the ground = h = 57.83 + 4

h = 61.83 feet

Step-by-step explanation:

(A) (In the fig. triangle represented by small triangle with angle of elevation 30° and height h1 ) ( Using this explanation since the figure is not marked)

[tex]tan30 = \frac{h1}{40} [/tex]

[tex]h1 = \frac{40}{\sqrt{3} } m[/tex]

(B) (In the fig. triangle represented by small triangle with angle of depression 58° and height h2 )

[tex]tan58 = \frac{h2}{40} [/tex]

[tex]h2 = 64m[/tex]

(C)

[tex]Height \: of \: Building \: A = h2 = 64m[/tex]

[tex]Height \: of \: Building \: B = h1+h2 = (64 + \frac{40}{ \sqrt{3} } )= 87m[/tex]

Given that,

Voltage = 34 volt

Current = 3i mA

We need to calculate the complex number to represent the impedance

Using ohm's law

[tex]V=IR[/tex]

[tex]R=\dfrac{V}{I}[/tex]

Where, V = voltage

I = current

R = impedance

Put the value into the formula

[tex]R=\dfrac{34}{0.003i}[/tex]

[tex]R=\dfrac{34}{0+0.003i}\times\dfrac{0-0.003i}{0-0.003i}[/tex]

[tex]R=\dfrac{0.102i}{0.9\times10^{-5}}\ \Omega[/tex]

(b). Given that,

Voltage = 13 volts

Current = 2.4 mA

We need to calculate the complex number to represent the impedance

Using ohm's law

[tex]R=\dfrac{V}{I}[/tex]

Put the value into the formula

[tex]R=\dfrac{13}{0.00024i}[/tex]

[tex]R=\dfrac{13}{0.00024i}\times\dfrac{-0.00024i}{-0.00024i}[/tex]

[tex]R=\dfrac{0.00312i}{5.76\times10^{-8}}\ \Omega[/tex]

Hence, (a). The complex number to represent the impedance is [tex]\dfrac{0.102i}{0.9\times10^{-5}}\ \Omega[/tex]

(b). (a). The complex number to represent the impedance is [tex]\dfrac{0.00312i}{5.76\times10^{-8}}\ \Omega[/tex]

Answer:

m = -6

Step-by-step explanation:

3m= 5(m + 3)-3

Distribute

3m = 5m +15 -3

Combine like terms

3m = 5m +12

Subtract 5m

3m-5m = 5m+12-5m

-2m = 12

Divide by -2

-2m/-2 = 12/-2

m = -6

Answer:

1  5/9  

Step-by-step explanation:

Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.

Answer:

1/31381059609

Step-by-step explanation:

Answer:

100/360

Step-by-step explanation:

A complete turn of a circle is 360 degrees

Therefore, 100 degrees turn is 100 out of 360

Answer:

  4,834

Step-by-step explanation:

  $14,500/($3 / pizza) = 4833.3 pizzas

MOD Pizza must sell 4,834 pizzas to cover the cost of the oven.

Answer:

4

Step-by-step explanation:

The equation of a line can be written as y = mx + b where m is the slope.

In this case, m = 4 since the equation is y = 4x + 12.

Answer: The slope is  4

Step-by-step explanation:

The slope of a  y intercept form equation which uses the formula y=mx+b is  the number acting as the coefficient.

Answer:

2x3+9x2+8x+4x2+18x+16

2x3+13x2+26x+16