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Alex777 [14]
2 years ago
15

Use absolute value notation to represent the distance between x and 8 is no more than 4

Mathematics
1 answer:
ivanzaharov [21]2 years ago
3 0
The distance: use absolute value
Between x and 8: x-8

The distance between x and 8: | x-8 |

“is no more than” means it can be that or be less than that, so use ≤

The distance between x and 8 is no more than 4

| x-8 | ≤ 4
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A bookstore buys Algebra 1 books at a wholesale price of $23 each. It marks up the price by 92% and then sells the Algebra 1 boo
IceJOKER [234]

Answer:

The mark up is $21.16 and the final selling price is $44.14

Step-by-step explanation:

To find the mark up price, you simply multiply the cost by the mark up percentage. This will give you the mark up.

$23 * 92% = $21.16

Now to find the total selling price, we add the cost and the mark up together.

$23 + $21.16 = $44.16

5 0
3 years ago
Find the area of the following figure.
11Alexandr11 [23.1K]

Answer:

\large \boxed{\text{60 units}^{2}}

Step-by-step explanation:

You haven't given us a diagram of your figure. Assume it is like the one in the image below.

The formula for the area of a parallelogram is

A = bh

1. Determine the height of the parallelogram

Notice that the angle is 45°. That makes the triangle an isosceles right triangle, so we can use Pythagoras' Theorem.

h² + h² = (6√2)²

    2h² = 36 × 2 = 72

      h² = 36

        h = 6

2. Calculate the area of the parallelogram

\begin{array}{rcl}A & = & bh\\A & = & 10 \times 6\\& = & \textbf{60 units}^{\mathbf{2}}\\\end{array}\\\text{The area of the figure is $\large \boxed{\textbf{60 units}^{\mathbf{2}}}$}

3 0
3 years ago
Read 2 more answers
The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed.
Anton [14]

Answer:

a) The evidence suggest the true mean life of a biomedical device > 5500

b) (5487.94, +∞)

c) There is evidence to support that the mean is equal to 5500

Step-by-step explanation:

Here we have

(a) To test the hypothesis we have the claim that the mean life of biomedical devices > 5500

Therefore, we put the null Hypothesis which is the proposition that a difference does not exist. That is

H₀:  μ = 5500

Therefore, the alternative hypothesis will be

Hₐ:  μ > 5500

The test statistic is then found by;

t=\frac{\bar{x}-\mu }{\frac{s }{\sqrt{n}}} =\frac{5617.8-5500 }{\frac{234.5 }{\sqrt{15}}} \approx 1.95

The P value from the T table at df = n - 1 = 15 - 1 = 14 is

0.025 < P < 0.05

The P value is given as 0.036 from the T distribution at 14 derees of freedom df

Therefore, since P < α or 0.05, we reject the null hypothesis. That is we fail to reject Hₐ:  μ > 5500. The evidence suggest the true mean life of a biomedical device > 5500

(b) The 95% confidence interval is given as

CI=\bar{x}\pm t_\alpha \frac{s}{\sqrt{n}}

Which gives    t_\alpha =  \pm2.145

CI=5617.8\pm 2.145 \times \frac{234.5}{\sqrt{15}}

The confidence interval of the lower bound on the mean is then

(5487.94, +∞)

c) From the above result, we find that the mean of 5500 is contained in the range of the lower confidence on the mean. We can therefore, accept the null hypothesis. That is there is evidence to support that the mean is equal to 5500.

6 0
3 years ago
Complete the identity sin(2θ) sin(4θ) cos(2θ) cos(4θ) = ?
Novay_Z [31]

Answer:

Step-by-step explanation:

Factor the left hand side as a difference of squares:

(

cos

2

θ

+

sin

2

θ

)

(

cos

2

θ

−

sin

2

θ

)

=

cos

2

θ

−

sin

2

θ

Apply the pythagorean identity  

cos

2

θ

+

sin

2

θ

=

1

:

1

(

cos

2

θ

−

sin

2

θ

)

=

cos

2

θ

−

sin

2

θ

cos

2

θ

−

sin

2

θ

=

cos

2

θ

−

sin

2

θ

L

H

S

=

R

H

S

Hopefully this helps!

4 0
3 years ago
Help please I’m tired
xxTIMURxx [149]

15.25-7.14=8.11

3.4x2.1=7.14

5 0
3 years ago
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