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Lunna [17]
4 years ago
15

There are 3 red and 9 blue counters in a box. A counter is chosen and then replaced. If you did this 144 times, how many times w

ould you expect to get a blue?
Mathematics
1 answer:
anygoal [31]4 years ago
3 0
If you do it 144 times that is (3+9)*12
This means that 12 times 3 red and 9 blue counters will be chosen that means that 9 blue counters will be chosen 12 times. 9*12 is 108.
This means blue counters will be chosen 108 times.
This can be checked as 108/3 would give you the number of red counters which is 36 and 108+36 is 144 

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GRAVITATION The height h(t) in feet of an object t seconds after it is propelled straight up from the ground with an initial vel
zhuklara [117]
<h3>Option B</h3><h3>At 2 second and 1.75 second, the object be at a height of 56 feet</h3>

<em><u>Solution:</u></em>

Given that,

<em><u>The height h(t) in feet of an object t seconds after it is propelled straight up from the ground with an initial velocity of 60 feet per second is modeled by the equation:</u></em>

h(t) = -16t^2 + 60t

<em><u>At what times will the object be at a height of 56 feet</u></em>

<em><u>Substitute h = 56</u></em>

56 = -16t^2 + 60t\\\\16t^2 - 60t + 56 = 0\\\\Divide\ the\ equation\ by\ 4\\\\4t^2 - 15t + 14=0

Solve the above equation by quadratic formula

\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

\mathrm{For\:}\quad a=4,\:b=-15,\:c=14\\\\x =\frac{-\left(-15\right)\pm \sqrt{\left(-15\right)^2-4\cdot \:4\cdot \:14}}{2\cdot \:4}\\\\Simplify\\\\x = \frac{15 \pm \sqrt{1}}{8}\\\\x = \frac{15 \pm 1}{8}\\\\We\ have\ two\ solutions\\\\x = \frac{15+1}{8} \text{ and } x = \frac{15-1}{8}\\\\x = 2 \text{ and } 1.75

Thus, at 2 second and 1.75 second, the object be at a height of 56 feet

5 0
4 years ago
Which of these points lies on the line described by the equation below? <br><br>y + 11 = -14(x - 2)
ladessa [460]
Here, we need to check for all pairs by substituting the value of x & y, 
1) 11 + 11 = -14(-2-2)
 sides are not equal.

2) -11 + 11 = -14(2 - 2)
 0 = 0
  sides are equal.

In Short, Your Answer would be Option 2

Hope this helps!
3 0
3 years ago
Can someone please check my answer? I really need help with this
Inessa05 [86]

Answer:

a = – 8

Step-by-step explanation:

From the question:

When P(x) = 2x³ – ax² + 4x – 4 is divided by x – 1, it gives a reminder of 10.

To obtain the value of a, we shall equate x – 1 to 0 as illustrated below:

x – 1 = 0

x = 0 + 1

x = 1

Next, we shall substitute the value of x into 2x³ – ax² + 4x – 4 and equating it to 10 as illustrated below:

2x³ – ax² + 4x – 4 = 10

x = 1

2(1)³ – a(1)² + 4(1) – 4 = 10

2 – a + 4 – 4 = 10

2 – a = 10

Collect like terms

– a = 10 – 2

– a = 8

Divide through by –1

a = – 8

Therefore, the value of a is –8.

5 0
3 years ago
Which expression is equivalent to StartFraction (3 m Superscript negative 1 Baseline n squared) Superscript negative 4 Baseline
koban [17]

Answer:

3m^{10}n^{-11}

Step-by-step explanation:

Given the expression \frac{(3m^{-1}n^{2})^{-4}   }{(2m^{-2}n)^{3}  }, we will use laws of indices to get the equivalent expression as shown below;

According to one of the law of indices,

\frac{a^{m} }{a^{n} } = a^{m-n}  \ and\ (a^{m})^{n} = a^{mn}

\frac{(3m^{-1}n^{2})^{-4}   }{(2m^{-2}n)^{3}  }\\= \frac{3m^{4}n^{-8}   }{2m^{-6}n^{3}  }\\= 3m^{(4-(-6))} * n^{-8-3}\\ = 3m^{10}n^{-11}

This gives the required expression

8 0
3 years ago
Read 2 more answers
Which is an equation of the line that has a slope of 1/2 and passes through the point (2, 4)?
irina1246 [14]

Answer:  y = \frac{1}{2}x +3  (Choice A)

Work Shown:

y - y_1 = m(x - x_1)\\\\y - 4 = \frac{1}{2}(x - 2)\\\\y - 4 = \frac{1}{2}x + \frac{1}{2}(- 2)\\\\y - 4 = \frac{1}{2}x - 1\\\\y = \frac{1}{2}x - 1+4\\\\y = \frac{1}{2}x +3\\\\

Explanation: I started with the point-slope form. Then I plugged in the given slope m = 1/2 and the point (x1,y1) = (2,4). Afterward I solved for y.

The answer is in slope-intercept form y = mx+b

3 0
1 year ago
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