a machine in a factory makes 20 gadgets every 1/4 hour. How many gadgets are made every hour?

Answer:

Step-by-step explanation:

Pat believes that [tex]\sqrt{2}+\sqrt{8}=(2)(2)^{\frac{1}{2}}[/tex]

[tex]\sqrt{2}+\sqrt{8}=\sqrt{2}+\sqrt{4\times 2}[/tex]

             [tex]=\sqrt{2}+2\sqrt{2}[/tex]

             [tex]=3\sqrt{2}[/tex]

             [tex]=3(2)^{\frac{1}{2} }[/tex]

But [tex]2(2)^{\frac{1}{2}}\neq 3(2)^{\frac{1}{2}}[/tex]

Therefore, Pat's belief is not correct.

Camilla believes that [tex]\sqrt{2}+\sqrt{8}=3\sqrt{2}[/tex]

Which is correct as we have calculated above.

Therefore, [tex]\sqrt{2}+\sqrt{8}=3\sqrt{2}[/tex] will be the correct answer.

Answer:

[tex]b=-3[/tex]

Step-by-step explanation:

We have:

[tex]25^b\cdot 125^{b+2}=125^b[/tex]

Notice that 125 is the same as 5³. So:

[tex]25^b\cdot ((5)^3)^{b+2}=((5)^3)^b[/tex]

Also, 25 is the same as 5². So:

[tex]((5)^2)^b\cdot ((5)^3)^{b+2}=((5)^3)^b[/tex]

Power of a power property:

[tex]5^{2b}\cdot 5^{3(b+2)}=5^{3b}[/tex]

Power of a product property:

[tex]5^{2b+3(b+2)}=5^{3b}[/tex]

Since they have the same base, the exponents are equal. So:

[tex]2b+3(b+2)=3b[/tex]

Solve for b. Distribute on the left:

[tex]2b+3b+6=3b[/tex]

Combine like terms on the left:

[tex]5b+6=3b[/tex]

Subtract 5b from both sides:

[tex]6=-2b[/tex]

Divide both sides by -2. So, the value of b is:

[tex]b=-3[/tex]

And we're done!

Answer: a

Step-by-step explanation:

Answer:

$8,978.36

Step-by-step explanation:

Answer:

negative 3

Step-by-step explanation:

Answer:

6.25 gallons

Step-by-step explanation:

Answer:

6.25

Step-by-step explanation:

Answer:

(a) 2/3

(b) 45

Step-by-step explanation:

(a)

The "ratio of shirts to skirts" means "the number of shirts divided by number of skirts."

10 shirts

15 skirts

shirts : skirts = 10/15 = 2/3

Answer: 2/3

(b)

In the simplified ratio, there are 2 shirts for every 3 skirts.

Add 2 + 3 = 5.

The ratio of skirts to total number of items of clothing is 3:5.

There are 3 skirts to each 5 items of clothing.

Set up a proportion.

3/5 = x/75

5x = 3 * 75

x = 3 * 15

x = 45

Answer: 45

Answer:

The answer is f ( x )  =  −  6 x  +  57

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

1. Set up a equation.

2. X is the first, so the ones after x are x+2, x+4, x+6, x+8, and x+10.

3. That means that x+x+2+x+4+x+6+x+8+x+10=204.

4. Simplify. You would get that 6x+30=204.

5. Solve for x. 6x=174, so x=29.

6. Get the fourth number in the sequence. 29+6=35.

Answer: The fourth number in this sequence is 35.

Answer:

35 days

Step-by-step explanation:

Andrew brings juice for lunch every 5 days and Hannah brings juice every 7 days

Find the lowest common multiple of 5 and 7

Andrew (every 5 days) = 10, 15, 20, 25, 30, 35, 40, 45, 50

Hannah (every 7 days) = 14, 21, 28, 35, 42, 49, 56

The lowest common multiple of 5 and 7 is 35

Therefore, if Andrew and Hannah both brought juice today, it will take 35 days before they will both bring food again on the same day.

Step-by-step explanation:

12x+6(24-x)=7*24

12x+144-6x=168

12x-6x =168-144

6x=24

/6

x=4 ounces 12.00%

20 ounces 6.00%

Answer:

7/9 of the work was done by Victoria.

Step-by-step explanation:

8/9-1/9=7/9

Answer:

40

Step-by-step explanation:

In 50 times Juan will jump 40 times.

Unitary method is first finding the value of a single unit and then deriving the required units from the given data.

For example - : A can eat 2 bananas in 2 seconds.So he can eat one banana in 1 second.From this we can calculate how many bananas he can eat in any given time.

According to the given question Juan jumped 24 times in 30 seconds.

∴ In 1 sec Juan will jump 24/30 times which is

= 4/5 times.

So, in 50 secs Juan will jump ( 4/5 × 50 ) = 40 times.

learn more about unitary method here :

https://brainly.com/question/21648365

#SPJ2

Answer:

X times 3 + 4 =22

X=6

Step-by-step explanation:

22-4=18

18/3=6

Answer:15

Step-by-step explanation:

Apex

Answer:

Jose

Step-by-step explanation:

Jose:

Step 1:

42 × 15        Equation

Step 2:

$630     Multiply

Fernando:

Step 1:

38 × 16      Equation

Step 2:

$608    Multiply

Answer:

Jose earns more

Hope This Helps :)

Answer:

-8x+4

Step-by-step explanation:

Answer:

-8x+4

Step-by-step explanation:

Answer:

-x + 2

Step-by-step explanation:

Answer:

3 trillion

Step-by-step explanation:

because just do the math bu bl I really dk

Answer:

Half of a ton

Step-by-step explanation:

2/3 of the elevator are already full and the elevator already weighs 1/3 of ton.The elevator needs 1/3 more of people to make the elevator full so that would be half of 1/3 of a ton which is a sixth.So add 1/6 and 1/3 together ams you get 1/2.

Answer:

b=60

Step-by-step explanation:

Add 8 to both sides to receive the equation of 20=b/3

Multiply all sides by 3 to get 60 as b

Answer:

a) the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204

b) the probability that the sample proportion will be within 0.04 of the population proportion is 0.95

c) sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061

d) the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088

e) gain in precision is 0.1402.

Step-by-step explanation:

a) Let p represent the

Given that

population proportion of complaints settled for new car dealers p = 0.75.

and n = 450

mean of the sampling distribution of the sample proportion is the population proportion p

i.e  up° = p

mean of the sampling distribution of the sample proportion p° = 0.75

so standard error of the proportion is;

αp° = √(p( 1-p ) / n)

we substitute

αp° = √(0.75 ( 1-0.75 ) / 450)

=√(0.1875 / 450

= √0.0004166

= 0.0204

therefore the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204

b)

(p° - p) is within 0.04

so lets consider

p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 450)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 450))

= p( -0.04/0.0204 ≤ z ≤ 0.04/0.0204)

= p ( -1/96 ≤ z ≤ 1.96 )

= p( z < 1.96 ) - p( z < -1.96 )

now from the S-normal table,

area of the right of z = 1.96 = 0.9750

area of the left of z = - 1.96 = 0.0250

p( -0.04 ≤ p°- p ≤ 0.04)  =  p( z < 1.96 ) - p( z < -1.96 ) = 0.9750 - 0.0250

= 0.95

therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.95

c)

population proportion of complaints settled for new car dealers p = 0.75.

n = 200

mean of the sampling distribution of the sample proportion p°.

i.e up° = p

mean of the sampling distribution of the sample proportion p° = 0.75

Sampling distribution of the sample proportion p is determined as follows

αp° = √(p( 1-p ) / n)

we substitute

αp° = √(0.75 ( 1-0.75 ) / 200)

=√(0.1875 / 200

= √0.0009375

= 0.03061

therefore sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061

d)

(p° - p) is within 0.04

so lets consider

p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 200)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 200))

= p( -0.04/0.03061≤ z ≤ 0.04/0.03061)

= p ( -1.31 ≤ z ≤ 1.31 )

= p( z < 1.31 ) - p( z < -1.31 )

now from the S-normal table,

area of the right of z = 1.31 = 0.9049

area of the left of z = - 1.31 = 0.0951

p( -0.04 ≤ p°- p ≤ 0.04)  =  p( z < 1.31 ) - p( z < -1.31 ) = 0.9049 - 0.0951

= 0.8098

therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088

e)  

From b), the sample proportion is within 0.04 of the population proportion; with the sample of 450 complaints involving new car dealers is 0.95.

sample proportion is within 0.04 of the population proportion; with the sample of 200 complaints involving new car dealers is 0.8098.

measured by the increase in probability, gain in precision occurs by taking the larger sample in part (b)

i.e

Gain in precision will be;

0.9500 − 0.8098

= 0.1402

therefore  gain in precision is 0.1402.

Answer: C

Step-by-step explanation:

Answer:

a) Mean is 12.9

b) Standard Error

i) n = 16, Standard Error = 1

The shape of the sampling distribution means is not normal

ii) n = 49 , Standard Error = 0.5714285714

The shape of the sampling distribution means is normal

iii) n = 121, Standard Error = 0.3636363636

The shape of the sampling distribution means is normal

c)Describe the pattern as n increases

As the number of random samples(n) increases the value for the standard error decreases

Step-by-step explanation:

Central Limit Theorem states that

if the sample size is large (generally n ≥ 30), and the standard deviation of the population is finite, then the distribution of sample means will be approximately normal.

a) 16 residents

Mean = 12.9

Standard Error = Standard Deviation /√n

= 4/√16

= 4/4

= 1

n < 30, hence, The shape of the sampling distribution means is not normal

b) 49 residents

= Mean = 12.9

Standard Error = Standard Deviation /√n

= 4/√49

= 4/7

= 0.5714285714

n > 30, hence, The shape of the sampling distribution means is normal

c) 121 residents

Mean = 12.9

Standard Error = Standard Deviation /√n

= 4/√121

= 4/11

= 0.3636363636

n > 30, hence, The shape of the sampling distribution means is normal

Describe the pattern as n increases

As the number of random samples(n) increases the value for the standard error decreases

Answer:

1

Step-by-step explanation:

didn't mulitiply by -2

Answer:

I believe it is 4

Step-by-step explanation:

Answer:

5÷100

=0.05

0.05×60

=3

Answer:

1200 readers

Step-by-step explanation:

Let x = number of readers

x* 5% = 60

Change to decimal form

x* .05 = 60

Divide each side by .05

x * .05/.05 = 60/.05

x =1200

Answer:

y=-7

Step-by-step explanation:

if g(x)  is g(-2) that means that x=-2 so we plug that in so 5*-2+3

5*-2+ -10  

-10+3+ -7

so y=-7

Answer:

6x²y³ I think n hope it's right

Answer:

7

Step-by-step explanation:

Median is the middle value in a list of values arranged in increasing order.

The values given are :2,8,7,8,6,15,6,8,3

Arrange values in ascending order as: 2,3,6,6,7,8,8,8,15

The middle value is: 2,3,6,6,7,8,8,8,15

Median is 7