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3 years ago

Which of the following is the correct graph of the compound inequality 4p + 1 > −15 and 6p + 3 < 45?

Mathematics

1 answer:

rjkz [21]3 years ago

3 0

Answer:

4p + 1 > −15 or 6p + 3 < 45

has solution any number.

The graph looks like this

<~~~~~~~~~~~~~~~~~~~~~~~~~~~>

---------(-4)---------(7)-------------

The shading is everywhere from left to right.

Step-by-step explanation:

Let's solve this first:

4p+1>-15

Subtract 1 on both sides:

4p>-16

Divide both sides by 4:

p>-4

6p+3<45

Subtract 3 on both sides:

6p<42

Divide both sides by 6:

p<7

So our solution is p>-4 or p<7

So let's graph that

~~~~~~~~~~~~~~~~~~~~~~~~~~~~O

O~~~~~~~~~~~~~~~~~~~~~~~~~~~~ p>-4

---------------------(-4)---------------------(7)--------------------

or is a key word! or means wherever the shading exist for either is a solution.

So this shading is everywhere.

The answer is all real numbers.

The final graph looks like this:

<~~~~~~~~~~~~~~~~~~~~~~~~~~~>

---------(-4)---------(7)-------------

The shading is everywhere from left to right.

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Becky bought a bag of mixed chocolates that have either a toffee or nut center. Her and four friends pulled out the first eleven

denpristay [2]

Answer

Part A

Probability that the next chocolate will have a toffee center = (8/11)

Part B

Expected number of chocolates with nut centers = 18 nut centers

Part C

Probability of the picking three consecutive chocolates with nut centers

= (27/1331)

= 0.0203

Explanation

The first 11 chocolates had 8 toffee and 3 nut centers.

The result from these first 11 picks will be used to calculate the rest of the probability or make predictions.

So, for the first part of the question.

Probability that the next chocolate will have a toffee center

= (8/11)

Part B

If there are 66 chocolates left in the bag, how many do you expect to have a nut center?

Probability of picking a chocolate with nut center = p = (3/11)

Number of chocolates in total = n = 66

Expected number of chocolates with nut centers

= np

= (66) (3/11)

= 18 nut centers

Part C

What is the probability that the next 3 pulled do have a nut in the center?

Probability of picking a chocolate with nut center = (3/11)

Probability of the picking three consecutive chocolates with nut centers

= (3/11) × (3/11) × (3/11)

= (27/1331)

= 0.0203

Hope this Helps!!!

3 0

1 year ago

A spherical globe has a diameter of 10 inches. What is the approximate volume of the globe?

adelina 88 [10]

Answer:

523.33 in^3

Step-by-step explanation:

A sphere is a 3-dimensional version of a circle. An example of a sphere is a ball

Volume of a sphere = $\frac{4}{3}$ π $r^{3}$

Where

π = 3.14

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

diameter = 2r

Radius = 10 in / 2 = 5 inches

$\frac{4}{3}$ × 3.14 × $5^{3}$ = 523.33 $in^{3}$

6 0

3 years ago

12(1-x) = 36<br> what’s the equation

maks197457 [2]

Answer:

-12x + 12 = 32............................. the equation

Step-by-step explanation:

to determine the equation in this 12(1-x) = 36 expression is quite simple, you only need to open the bracket .

solution

12(1-x) = 36

12 - 12x = 32

-12x + 12 = 32............................. the equation

we can further evaluate for the value of x

-12x = 32 - 12

-12x = 20

divide both sides by the coefficient of x which is -12

-12x = 20

-12x/-12 = 20/-12

x = -1.67

3 0

3 years ago

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Given the line below.

Elza [17]

The slope of that line is -1, so m = -1.

The point you were told to use is (-2,2), so point-slope form starts as:

( y - 2 ) = -1 • ( x - (-2) )

But we'd clean up that x-(-2) to be x+2.

y - 2 = -1 ( x+2 )

7 0

3 years ago

Identify the polynomial.

Alexxandr [17]

Answer:

it's a trinomial

7 0

3 years ago