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Masteriza [31]
3 years ago
7

Which of the following is the graph of the solution set of t – 4 ≥ 4t + 8 or 3t >14 – 4t?

Mathematics
1 answer:
Stells [14]3 years ago
4 0

Answer:

Option (C)

Step-by-step explanation:

There are two inequalities,

t - 4 ≥ 4t + 8 ------(1)

3t > 14 - 4t ------(2)

By simplifying inequality (1),

t - 4 ≥ 4t + 8

t ≥ 4t + 8 + 4

t ≥ 4t + 12

t - 4t ≥ 12

-3t ≥ 12

t ≤ \frac{12}{(-3)}

t ≤ -4

By solving inequality (2),

3t > 14 - 4t

3t + 4t > 14

7t > 14

t > \frac{14}{7}

t > 2

From the given graphs, Option (C) will be the answer.

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Given the graph, find an equation for the parabola.
Sauron [17]

Answer:

\Large \boxed{\sf \bf \ \ y=\dfrac{1}{16}(a-3)^2-2 \ \  }

Step-by-step explanation:

Hello, please consider the following.

When the parabola equation is like

y=a(x-h)^2+k

The vertex is the point (h,k) and the focus is the point (h, k+1/(4a))

As the vertex is (3,-2) we can say that h = 3 and k = -2.

We need to find a.

The focus  is (3,2) so we can say.

2=-2+\dfrac{1}{4a}\\\\\text{*** We add 2. ***}\\\\\dfrac{1}{4a}=2+2=4\\\\\text{*** We multiply by 4a. ***}\\\\16a=1\\\\\text{*** We divide by 16. ***}\\\\a=\dfrac{1}{16}

So an equation for the parabola is.

\large \boxed{\sf y=\dfrac{1}{16}(a-3)^2-2 }

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

4 0
3 years ago
Two​ shooters, Rodney and​ Philip, practice at a shooting range. They fire rounds each at separate targets. The targets are mark
Sedaia [141]

Complete Question

Answer:

a

  SE  = 0.66}

b

-3.29 <  \mu_1 - \mu_2 <  -0.70  

Step-by-step explanation:

From the question we are told that

  The sample size is  n  = 60

   The first sample mean is  \= x _1  =  8

    The second sample mean is   \= x _2  =  10

    The first variance is  v_1 =  0.25

    The first variance is  v_2 =  0.55

Given that  the confidence level is 95% then the level of significance is 5% =  0.05

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.96

Generally the first standard deviation is  

     \sigma_1 =  \sqrt{v_1}

=>   \sigma_1 =  \sqrt{0.25}

=>   \sigma_1 =  0.5

Generally the second standard deviation is

     \sigma_2 =  \sqrt{v_2}

=>   \sigma_2 =  \sqrt{0.55}

=>   \sigma_2 =  0.742    

Generally the first standard error is

     SE_1  =  \frac{\sigma_1}{\sqrt{n} }

      SE_1  =  \frac{0.5}{\sqrt{60} }

     SE_1  =  0.06

Generally the second standard error is

     SE_2  =  \frac{\sigma_2}{\sqrt{n} }

      SE_2  =  \frac{0.742}{\sqrt{60} }

     SE_2  =  0.09

Generally the standard error of the difference between their mean scores is mathematically represented as    

      SE  =  \sqrt{SE_1^2 + SE_2^2 }

=>     SE  =  \sqrt{0.06^2 +0.09^2 }

=>     SE  = 0.66}

Generally 95% confidence interval is mathematically represented as  

      (\= x_1 -\= x_2) -(Z_{\frac{\alpha }{2} } *  SE) <  \mu_1 - \mu_2 <  (\= x_1 -\= x_2) +(Z_{\frac{\alpha }{2} } *  SE)

=> (8 -10) -(1.96 *  0.66) <  \mu_1 - \mu_2 <  (8-10) +(Z_{\frac{\alpha }{2} } *  0.66)  

=>  -3.29 <  \mu_1 - \mu_2 <  -0.70  

 

5 0
3 years ago
Kelsey keeps track of how much money she makes each time she babysits. For the last 10 jobs she made:
Alex777 [14]

Answer:

Mean = sum of all elements/number of elements

          = (7.5 + 10.5 + 5 + 4.5 + 3.5 + 7.5 + 4 + 10 + 7.5 + 5)/10

          = 6.5

=> Option C is correct

Hope this helps!

:)

8 0
3 years ago
Find the vertex of the function given below y=x^2-2x+1
Ymorist [56]

Hey there! :)

Answer:

(1, 0).

Step-by-step explanation:

Convert from standard form to vertex form by completing the square:

y = x² - 2x + 1

Move 1 to the other side:

-1 = x² - 2x

Complete the square. Remember to add to both sides:

-1 + (1) = x² -2x + 1

Simplify:

0 = (x - 1)²

The function in vertex form is:

y = (x - 1)²

Therefore, the vertex is:

(1, 0).

3 0
3 years ago
Tomas wants to spend less than $100 for a new soccer ball and
Morgarella [4.7K]

Answer:

x+24<100

Step-by-step explanation:

7 0
3 years ago
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