If P is directly proportional to Q. And Q = 30 when P = 40. Find Q when P = 70

Step-by-step explanation:

1)

SOLUTION

5(x+5) = 6. (6 +9)

90 = 5x + 25

13 = x

2)

SOLUTION

x (3) = (4) (6)

3x = 24

x= 8

3)

SOLUTION

3 (3 + x + 2) = (x+1)(x + 1 + x – 1) Use Theorem

3x + 15=2x²+2x

0 = 2x² – x – 15

0 = (x – 3) (2x + 5) Solve for x

3 = x Use positivesolution

Using the normal distribution, it is found that 84 people would be expected to have BP > 160.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Researching the problem on the internet, the mean and the standard deviation for the BPs are given, respectively, by:

[tex]\mu = 122, \sigma = 22[/tex].

The proportion of adults with BP > 160 is given by one subtracted by the p-value of Z when X = 160, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{160 - 122}{22}[/tex]

Z = 1.73

Z = 1.73 has a p-value of 0.9582.

1 - 0.9582 = 0.0418.

Out of 2000 people:

0.0418 x 2000 = 83.6.

Rounding to the nearest integer, 84 people would be expected to have BP > 160.

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Answer:

1.09

Step-by-step explanation:

9.81÷3=3.27 This shows the cost of 1 yard

3.27÷3= 1.09 since theres 3 feet in a yard, when you divide by 3 it shows how much 1 foot costs

Answer:

C.

Step-by-step explanation:

-3 7/8 rounds down to -4

4.63 rounds up to 5

-4 x 6 + 5

-24 + 5

-19

her answer (-19.14) also rounds to -19

So yes, it is reasonable and the correct response is C.

Answer:

max could still add 135 minutes of music into his playlist

Step-by-step explanation:

180 - 45 = 135

Answer:

So we know that Max's playlist can have at most 180 minutes of music meaning that our amount of music cannot exceed that number.  We are also given that Max already has 45 minutes of music on there so we need to subtract that from 180 minutes to see how much we have left.

[tex]180\ minutes - 45\ minutes[/tex]

[tex]135\ minutes[/tex]

Max still has 135 minutes left on his playlist that he can fill up.

Hope this helps!  Let me know if you have any questions

Step-by-step explanation:

since there are answer options we don't need to formally solve the system of equations, we only need to try the first point of every option, and see, where the equations are true.

if we cannot find it for the first point, then we would need to try the same thing for the serving points.

let's put (0, 6) into the first equation :

-2×0² + 6 = 6

6 = 6 true

let's put it into the second equation ;

4×0² + 3×6 = 28

18 = 28 false

that eliminates the first 2 answers.

let's put (-1, 4) into the first equation :

-2×(-1)² + 4 = 6

-2×1 + 4 = 6

-2 + 4 = 6

2 = 6 false

that eliminates the third answer.

let's put (-1, 8) into the first equation :

-2×(-1)² + 8 = 6

-2 + 8 = 6

6 = 6 true

let's put it into the second equation :

4×(-1)² + 3×8 = 28

4 + 24 = 28

28 = 28 true

and because the square function delivers the same result for -1 and +1, it is also true for the second point.

and the 4th answer is therefore correct.

Question 1 ) A ray has one endpoint and continues forever in the opposite direction

Question 2)

⇒

IG

Question3)

⇒

DC

Hope this helps!

The best approximation of the factor by which the population increases over a ten years period will be 6.19.

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

A certain buffalo population increases by a factor of 1.2 each year.

Then the best approximation of the factor by which the population increases over a ten years period will be

→ 1.2¹⁰

→ 6.1917

→ 6.19

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Answer:

the vertex is (-3 , -3)

Step-by-step explanation:

[tex]\frac{1}{2} x^{2}+3x+\frac{3}{2}[/tex]

[tex]=\frac{1}{2} \left( x^{2}+6x+3\right)[/tex]

[tex]=\frac{1}{2} \left[ \left( x+3\right)^{2} -9+3\right][/tex]

[tex]=\frac{1}{2} \left( x+3\right)^{2} -3[/tex]

then the vertex is (-3 , -3)

Answer:

[tex]6 \frac{2}{13} [/tex]

Step-by-step explanation:

4:12 there are four vowels and 12 letters?

Answer:

30° and 60°

Step-by-step explanation:

Let the interior angles be ∠x₁ (smaller) and ∠x₂ (larger), and the exterior angle ∠X.

Making the statements into equations :

Size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles ⇒ ∠X + ∠x₁ + ∠x₂ = 180° [Equation 1]

Greater of the opposite interior angles exceeds smaller by 30° :

⇒ ∠x₂ = ∠x₁ + 30° [Equation 2]

By exterior angle property :

⇒ ∠x₁ + ∠x₂ = ∠X [Equation 3]

Substituting Equation 3 in Equation 1 :

⇒ ∠x₁ + ∠x₂ + ∠x₁ + ∠x₂ = 180°

⇒ 2 (∠x₁ + ∠x₂) = 180°

⇒ ∠x₁ + ∠x₂ = 90°

⇒ ∠x₂ = 90° - ∠x₁ [Equation 4]

Substituting Equation 4 in Equation 2 :

⇒ 90° - ∠x₁ = ∠x₁ + 30°

⇒ 2∠x₁ = 60°

⇒ ∠x₁ = 30°

Substituting the value of ∠x₁ in Equation 2 :

⇒ ∠x₂ = 30° + 30°

⇒ ∠x₂ = 60°

The measures of the interior angles are 30° and 60°

Answer:

first 2 I'm not sure about. for the first one I think its 0.5 if that's an option

Answers:

bio = 258

sociology = 169

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

Work Shown:

x = number of bio textbooks

y = number of sociology textbooks

x+y = 427 books sold total

y = x-89 since 89 less sociology textbooks were sold compared to bio

Apply substitution to get the following

x+y = 427

x+x-89 = 427 ... replace y with x-89

2x-89 = 427

2x = 427+89

2x = 516

x = 516/2

x = 258 bio textbooks were sold

y = x-89

y = 258-89

y = 169 sociology textbooks were sold

Answer: 160 seconds

Step-by-step explanation:

First let us find the number of seconds per rotation

52 second/65 rotations

52/65

0.8 seconds/1 rotation

0.8 seconds per rotation

Now let us multiply 0.8 by 200 to get our answer

0.8 * 200

160

It takes 160 seconds to do 200 rotations

Answer:

160 seconds

Step-by-step explanation:

We have 65 rotations in 52 seconds, let's represent it like this:

[tex]\frac{52 seconds}{65 rotations}[/tex]

Now, let's multiply this by 200 rotations, and cancel out the rotations on the bottom:

[tex]\frac{52 seconds}{65 rotations} * 200 rotations[/tex]

See how there is rotations on both the top and bottom? This cancels both of them and leaves seconds!

Multiply the above equation and we get:

160 seconds or 2 minutes 40 seconds.

Hope this helps! Good luck and if you have questions please leave them in the comments!

Answer:

Ok I can walk you through if you comment the questions ok?

Step-by-step explanation:

Trust me :-)

Answer:

1. obtuse

2.straight

3.right

4. acute

5. <EAF

6. <DAF

7. <BAF

8. They are perpendicular to each other

Answer: Option (c) is correct.

68% of the data points lie between 10 and 18.

Step-by-step explanation: Given :  a normal distribution with a standard deviation of 4 and a mean of 14

We have to choose the  sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.

Since, given 68% data.

We know mean of data lies in middle.

And standard deviation is distribute equally about the mean that is 50% of values less than the mean  and 50% greater than the mean.

So, 68% of data lies

mean - standard deviation = 14 - 4 = 10

mean + standard deviation = 14 + 4 = 18

So, 68% of the data points lie between 10 and 18.

Answer:

C? Not 100% sure

Step-by-step explanation:

Answer: [tex]b^{2}(1-21a^{3})[/tex]

Step-by-step explanation:

[tex]b^{2} - 21a^{3} b^{2} \\b^{2}(1-21a^{3})[/tex]

[tex]y = 3x-2\\\\~~~=3(-5) -2\\\\~~~= -15-2\\\\~~~= -17[/tex]

Answer:

y = -17

Step-by-step explanation:

Given values :

⇒ x = -5

Let's substitute in the expression to find y :

⇒ y = 3(-5) - 2

⇒ y = -15 - 2

⇒ y = -17

To write 28 + 24 as a product of two factors, we need to determine the HCF of the addends (28 and 24). This can be done by listing the factors of the addends. The greatest factor that is common in 28 and 24 is the HCF.

If the number is in bolded text, the number is a common factor.

Since 4 > 2 > 1, the HCF is 4.

Now, let us put the provided expression between parentheses.

Finally, factor four out of the expression, as it is the GCF of 28 and 24.

Therefore, 28 + 24 as a product of two factors is 4(7 + 6).

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Step-by-step explanation:

that means the opposite ...

the opposite of

x > 39

is

x <= 39

Answer:

120ft

Step-by-step explanation:

The Equation for the launch of the yellow bird is y = -0.1( x - 26 )² + 20

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values

Given:

Starting position of the bird = ( 10 , 0 )

Final position of the bird = ( 42 , 0 )

Maximum Height of the bird = 20 yards

To find: Equation that represent this condition.

Clearly, Birds flight path is not a straight line. It has a curved path.

So, the path bird follow is a PARABOLA.

Standard Equation of the parabola in vertex form, y = a( x - h )² + k

where ( h , k ) is the vertex of the parabola.

In our Question , vertex is the point at the highest position.

Vertex will be 20 yard above the mid point of the starting and final position.

Using Mid-Point Formula,

Mid-Point of ( 10 , 0 ) & ( 42 , 0 ) =

Now, the vertex = ( 26 , 0 + 20 ) = ( 26 , 20 )

⇒ Equation, y = a( x - 26 )² + 20

Now, we find value of by substituting value of (10 , 0) in the equation,

⇒ 0 = a( 10 - 26 )² + 20

a( -16 )² = -20

a(256) = -20

a = -20/256

a = −0.078125

a ≈ -0.1

Therefore, The Equation is y = -0.1( x - 26 )² + 20

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