Weekly wages at a certain factory are
normally distributed with a mean of
of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makesbetween
$400 and $450.
[? ]%

[tex]\sqrt[3]{4 a^4 b^5} = \sqrt[3]{4 \times 4^4 \times 2^5} = \sqrt[3]{(4\times 2)^5} = \sqrt[3]{(2^2\times2)^5} = \sqrt[3]{(2^3)^5} = \sqrt[3]{2^{15}} = \sqrt[3]{(2^5)^3} = 2^5 = 32[/tex]

[tex]\dfrac{a-c}{(b+c)^2} = \dfrac{4-(-5)}{(2+(-5))^2} = \dfrac{4+5}{(2-5)^2} = \dfrac9{(-3)^2} = \dfrac99 = 1[/tex]

Then the expression evaluates to 32 + 1 = 33.

The value of the expression

[tex]$\sqrt[3]{4a^4b^5} + \dfrac{a - c}{(b+c)^2}$[/tex]

is 33 when $a = 4$, $b = 2$, and $c = -5$.

Let's substitute the given values into the expression and calculate the result:

Given:

$a = 4$

$b = 2$

$c = -5$

Substituting the values:

[tex]$\sqrt[3]{4a^4b^5} + \dfrac{a - c}{(b+c)^2} = \sqrt[3]{4(4)^4(2)^5} + \dfrac{4 - (-5)}{(2+(-5))^2}$[/tex]

Calculating the values within the cube root:

[tex]$\sqrt[3]{4(4)^4(2)^5} = \sqrt[3]{4 \cdot 256 \cdot 32} = \sqrt[3]{32768} = 32$[/tex]

Calculating the values within the fraction:

[tex]$\dfrac{4 - (-5)}{(2+(-5))^2} = \dfrac{4 + 5}{(-3)^2} = \dfrac{9}{9} = 1$[/tex]

Now we can substitute the calculated values back into the expression:

[tex]$\sqrt[3]{4a^4b^5} + \dfrac{a - c}{(b+c)^2} = 32 + 1 = 33$[/tex]

Therefore, the value of

[tex]\sqrt[3]{4a^4b^5} + \frac{a - c}{(b+c)^2} \: is \: 33 \: when \: a = 4, \: b = 2, and \: c = -5[/tex]

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Answer:

A complementary angle is 63 degrees and supplementary angle is 153 degrees.

Step-by-step explanation:

Complementary angle:

A complementary angle adds up to 90 degrees, so you have to subtract 27 from 90.  90-27=63

Supplementary angle:

A supplementary angle adds up to 180 degrees, so you have to subtract 27 from 180. 180-27=153

Answer:

90

Step-by-step explanation:

x/15=66/11

x/15=6

multiply by 15 on both sides to get the variable by itself

x=90

Answer:

5.

Step-by-step explanation:

Have you heard of something called reading?

Answer:

1.a) 90 1.b) 32

Step-by-step explanation:

1.) 1^2 + 2^3 + 3^4

Squared means how much times to multiply the same number.

So, 1^2= 1x1=1

2^3=2x2x2=8

3^4=3x3x3x3=81.

So, 81+8+1=90

2. 4^2=4x4=16+2^4=2x2x2x2=16

16+16=32

Please mark me brainliest :)

Answer:

11/3

Step-by-step explanation:

convert the 7 1/3 to 22/3 then convert the 3 2/3 to 11/3 and subtract.

From the definition, we have

[tex]\displaystyle f'(10) = \lim_{x\to0} \frac{f(x) - f(10)}{x - 10}[/tex]

With [tex]f(x)=\sqrt{x-1}[/tex], we get [tex]f(10)=\sqrt{10-1}=\sqrt9=3[/tex]. So the limit we want to compute is

[tex]\displaystyle f'(10) = \lim_{x\to0} \frac{\sqrt{x-1} - 3}{x - 10}[/tex]

Rationalize the numerator by multiplying by its conjugate:

[tex]\displaystyle \frac{\sqrt{x-1} - 3}{x - 10} \times \frac{\sqrt{x-1}+3}{\sqrt{x-1}+3} = \frac{\left(\sqrt{x-1}\right)^2-3^2}{(x-10)\left(\sqrt{x-1}+3\right)} = \frac{x-10}{(x-10)\left(\sqrt{x-1}+3\right)}[/tex]

x is approaching 10, which is to say x ≠ 10, so we can cancel the factors of x - 10 and remove the discontinuity.

Then we're left with

[tex]\displaystyle f'(10) = \lim_{x\to0} \frac1{\sqrt{x-1}+3} = \frac1{\sqrt{10-1}+3} = \frac1{\sqrt9+3} = \frac1{3+3} = \boxed{\frac16}[/tex]

evaluated by direct substitution, which we can do since the limand is continuous.

Answer:

$19,260

Step-by-step explanation:

1 year = 12 months

5 × 12 = 60

5 years = 60 months

$321 × 60 = $19,260

Hi!

The words "y varies inversely as x" automatically means we can write:

[tex]y=\cfrac{k}{x}[/tex]

Note that this is a fraction because it said "inversely". If it had said "jointly" or "directly", it would have been [tex]y=kx[/tex].

Now, we plug in the given values to solve for k.

We are given:

[tex]y = 0.4[/tex]

[tex]x = 0.8[/tex]

Plug those in and we have:

[tex]0.4=\cfrac{k}{0.8}[/tex]

Multiply both sides by [tex]0.8[/tex]:

[tex]0.32=k[/tex]

Now, with the value of [tex]k[/tex] solved for, we put it back into the original equation, and that's your answer:

[tex]y=\cfrac{0.32}{x}[/tex]

For a similar problem, see:

https://brainly.com/question/2315806

Answer:

a. (53, 12)

b. I couldn't find this without making a graph myself, hopefully someone will find it or you can figure it out for yourself using the answer I did provide.

Answer:

Describe a set of transformations that would map triangle FGH onto F'G'H

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

41.65

Step-by-step explanation:

First do 5.5*20.7 because of PEMDAS or GERMDAS which is basically saying the order of how to solve expressions/equations

5.5*20.7=113.85

Then subtract 113.85 from 155.5

155.5-113.85=41.65

Answer:

B. 486,732

__________________________________________________________

To solve digit problems, multiply the value of the digit example: tens place, hundreds place by 10 to get to the next digit, and then you will have your answer.

[tex]600 * 10 = 6,000~-- > ~thousands~place[/tex]

Therefore, the answer would be B. because it has a 6 in the thousands place.

__________________________________________________________

Ask in comments.

486,732 is the number in which the  digit 6 have a value that is 10 times as great as the value of the digit 6 in 283,691. Option B is correct.

To find the number in which the digit 6 has a value that is 10 times as great as the value of the digit 6 in 283,691, we need to compare the place values of the digit 6 in both numbers.

In the number 283,691:

The 6 is in the hundreds place.

Now let us multiply this place with 10.

100×10 = 1000.

Find the number in which the digit is in 1000 place.

In the number 486732, the 6 is in 1000 place.

Hence, Option B is correct. 486,732 is the number in which the  digit 6 have a value that is 10 times as great as the value of the digit 6 in 283,691.

To learn more on Number system click:

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[tex] \alpha + \beta = 90[/tex]

[tex] \beta + 4 \alpha = 180[/tex]

[tex] - \alpha - \beta = - 90[/tex]

[tex] \beta + 4 \alpha = 180[/tex]

[tex]3 \alpha = 90[/tex]

[tex] \alpha = 30[/tex]

[tex] \beta = 90 - \alpha = 90 - 30 = 60[/tex]

[tex]( \alpha = 30) < = > ( \beta = 60)[/tex]

Answer:

The answer is B

Step-by-step explanation:

Btw if its wrong im sorry

Answer:

Mean - 12

Median - 9

Mean - Median = 3

Step-by-step explanation:

math

Answer:

A

Hope This Helps! :)

Answer:

B. 4 inches

Step-by-step explanation:

(24)(1) / 6 = 4

1. As you can tell from the function definition and plot, there's a discontinuity at x = -2. But in the limit from either side of x = -2, f(x) is approaching the value at the empty circle:

[tex]\displaystyle \lim_{x\to-2}f(x) = \lim_{x\to-2}(x-2) = -2-2 = \boxed{-4}[/tex]

Basically, since x is approaching -2, we are talking about values of x such x ≠ 2. Then we can compute the limit by taking the expression from the definition of f(x) using that x ≠ 2.

2. f(x) is continuous at x = -1, so the limit can be computed directly again:

[tex]\displaystyle \lim_{x\to-1} f(x) = \lim_{x\to-1}(x-2) = -1-2=\boxed{-3}[/tex]

3. Using the same reasoning as in (1), the limit would be the value of f(x) at the empty circle in the graph. So

[tex]\displaystyle \lim_{x\to-2}f(x) = \boxed{-1}[/tex]

4. Your answer is correct; the limit doesn't exist because there is a jump discontinuity. f(x) approaches two different values depending on which direction x is approaching 2.

5. It's a bit difficult to see, but it looks like x is approaching 2 from above/from the right, in which case

[tex]\displaystyle \lim_{x\to2^+}f(x) = \boxed{0}[/tex]

When x approaches 2 from above, we assume x > 2. And according to the plot, we have f(x) = 0 whenever x > 2.

6. It should be rather clear from the plot that

[tex]\displaystyle \lim_{x\to0}f(x) = \lim_{x\to0}(\sin(x)+3) = \sin(0) + 3 = \boxed{3}[/tex]

because sin(x) + 3 is continuous at x = 0. On the other hand, the limit at infinity doesn't exist because sin(x) oscillates between -1 and 1 forever, never landing on a single finite value.

For 7-8, divide through each term by the largest power of x in the expression:

7. Divide through by x². Every remaining rational term will converge to 0.

[tex]\displaystyle \lim_{x\to\infty}\frac{x^2+x-12}{2x^2-5x-3} = \lim_{x\to\infty}\frac{1+\frac1x-\frac{12}{x^2}}{2-\frac5x-\frac3{x^2}}=\boxed{\frac12}[/tex]

8. Divide through by x² again:

[tex]\displaystyle \lim_{x\to-\infty}\frac{x+3}{x^2+x-12} = \lim_{x\to-\infty}\frac{\frac1x+\frac3{x^2}}{1+\frac1x-\frac{12}{x^2}} = \frac01 = \boxed{0}[/tex]

9. Factorize the numerator and denominator. Then bearing in mind that "x is approaching 6" means x ≠ 6, we can cancel a factor of x - 6:

[tex]\displaystyle \lim_{x\to6}\frac{2x^2-12x}{x^2-4x-12}=\lim_{x\to6}\frac{2x(x-6)}{(x+2)(x-6)} = \lim_{x\to6}\frac{2x}{x+2} = \frac{2\times6}{6+2}=\boxed{\frac32}[/tex]

10. Factorize the numerator and simplify:

[tex]\dfrac{-2x^2+2}{x+1} = -2 \times \dfrac{x^2-1}{x+1} = -2 \times \dfrac{(x+1)(x-1)}{x+1} = -2(x-1) = -2x+2[/tex]

where the last equality holds because x is approaching +∞, so we can assume x ≠ -1. Then the limit is

[tex]\displaystyle \lim_{x\to\infty} \frac{-2x^2+2}{x+1} = \lim_{x\to\infty} (-2x+2) = \boxed{-\infty}[/tex]

Answer:

B) r = -0.35

Step-by-step explanation:

Correct me if I'm wrong

Answer:

y=5

x=31

Step-by-step explanation:

5y=25

y=5

25+25+10x=360

50+10x=360

x=31

Answer:

17. 125 ft^2

18. 9.4 in^2

Step-by-step explanation:

Both 17 and 18 are similar. You split that it into pieces.

Area of Rectangle/Square: Area = Length * Width

Area of a Triangle: Area = 1/2 * Base * Height.

17.

Area Rectangle:

Area = Length * Width

Area = 10 ft * 6 ft = 60 ft^2

Area Triangle:

Area = 1/2 * Base * Height

Area = 1/2 * 10 ft * 13 ft = 65 ft^2

Total Area = 60 ft^2 + 65 ft^2 = 125 ft^2

18.

Area Rectangle:

Area = Length * Width

Area = 2.7 in * 2 in = 5.4 in^2

Area Triangle:

Area = 1/2 * Base * Height

Area = 1/2 * 2 in * 4.4 ft = 4.4 ft^2

Total Area = 5.4 ft^2 + 4.4 ft^2 = 9.4 ft^2

Answer:

D=3h+5

Step-by-step explanation:

Given: The rate of increasing speed  = 3 miles per hour

The distance she traveled before stopping = 5 miles

Let h represents the number of additional hours for hiking.

Then the equation that models the total distance 'D' Sarah travels after hiking for an additional h hours is given by :-

D=3h+5

Answer:

D = 3h + 5

Step-by-step explanation:

Answer:

1962.5 m^2

Step-by-step explanation:

area of the entire circle = pi (50^2)

subtract the large area

pi 50^2 -   4.71 /2pi   pi 50^2 =

Answer:

Step-by-step explanation:

from Cyrus' to Jane's ,  the distance is  D= [tex]\sqrt{8^{2} +21^{2} }[/tex] = 22.47 mi

from Adriana's to Madisyn's , the dist. is D =[tex]\sqrt{21^{2} +14^{2} }[/tex] = 25.24 mi

Answer:

95.45%

Step-by-step explanation:

Honestly I looked it up I hope it helps though and best of luck! : )

Answer:

47.5% I just took it

Answer:

AB = 23, BC = 13

Step-by-step explanation:

[tex]5x - 7 = 23[/tex]

[tex]5x = 30[/tex]

[tex]x = 6[/tex]

AB = 23, BC = 3(6) - 5 = 18 - 5 = 13

Answer:

164 ft

Step-by-step explanation:

The TIME of maximum height   (this is a dome shaped parabola)

        will be given by t = -b/2a = - 64 / (2)(-16) = 2 sec

Putting in t = 2   into the equation will give the max height

-16 (2^2) + 64(2) + 100 = max = 164 ft

Answer:

(x = 0, y = 0) and (x = 3, y = 0)

Step-by-step explanation:

Let's test out each pair by substituting the values into the inequalities.

Case 1: x = 0, y = 0

0 <= 6

0 < 6

It works!

Case 2: x = -5, y = -15

-15 <= 10 + 6 = 16

-5 + 15 = 10 < 6

It doesn't work.

Case 3: x = 4, y = -2

-2 <= -8 + 6 = -2

4 + 2 = 6 < 6

It doesn't work.

Case 4: x = 3, y = 0

0 <= -6 + 6 = 0

3 < 6

It works!

Case 5: x = 10, y = 0

0 <= -20 + 6 = -14

From here we can already see that it doesn't work

Case 1 and 4 work!