A rectangular box is 4 cm wide, 4 cm tall, and 10 cm long. What is the diameter of the smallest circular opening through which the box will fit? Round to the nearest tenth of a centimeter.

Answer:

[tex]z^{0.5}[/tex]

Step-by-step explanation:

So first simplify inside:

[tex]z^4z^{-1.5}=z^{2.5}[/tex]

Now divide that by 5:

[tex]z^{0.5}[/tex]

Answer:

5(4) + 5(8)

Step-by-step explanation:

Through destributive property, 5 is multiplied by both 4 and 8

Answer:

the person above is right thank and five star them

Step-by-step explanation:

Answer:  see boxed answers below

Step-by-step explanation:

(i) multiply the exponent to the coefficient then subtract 1 from the exponent.

[tex]y=\dfrac{3}{5x^3}+3x^4+2x^2-20\\\\\\\text{rewrite it as follows}: y=\dfrac{3}{5}x^{-3}+3x^4+2x^2-20x^0\\\\\\y'=(-3)\dfrac{3}{5}x^{-3-1}+(4)3x^{4-1}+(2)2x^{2-1}-(0)20x^{0-1}\\\\\\y'=-\dfrac{9}{5}x^{-4}+12x^3+4x^1-0\\\\\\y'=\large\boxed{-\dfrac{9}{5x^{4}}+12x^3+4x}[/tex]

(ii) Use the division formula:    [tex]y = \dfrac{a}{b}\rightarrow \quad y'=\dfrac{ab'-a'b}{b^2}[/tex]

[tex]a=5x^3+1\qquad \qquad a'=15x^2\\b=3x^5+4x^2\qquad \quad b'=15x^4+8x\\\\\\y'=\dfrac{(15x^2)(3x^5+4x^2)-(5x^3+1)(15x^4+8x)}{(3x^5+4x^2)^2}\\\\\\.\quad =\dfrac{45x^7+60x^4-75x^7-55x^4-8x}{(3x^5+4x^2)^2}\\\\\\.\quad =\large\boxed{\dfrac{-35x^7+5x^4-8x}{(3x^5+4x^2)^2}}[/tex]

Answer:

a. 336

b. 14.01%

c. 0.2%

Step-by-step explanation:

a. We have that the number of zinfandel bottles is 8 and that the number of zinfandel served is 3, therefore:

n = 8 and r = 3

we can calculate it by means of permutation:

nPr = n! / (n-r)!

replacing:

8P3 = 8! / (8-3)!

8P3 = 336

Which means there are 336 ways.

b. First we must calculate the ways to choose 2 bottles of each variety, through combinations:

nCr = n! / (r! * (n-r)!

We know that there are 8 bottles zinfandel, 10 of merlot, and 12 of cabernet, and we must choose 2 of each, therefore it would be:

8C2 * 10C2 * 12C2

8! / (2! * (8-2)! * 10! / (2! * (10-2)! * 12! / (2! * (12-2)!

28 * 45 * 66 = 83160

Now we must calculate the total number of ways, that is, choose 6 bottles of the 30 total (8 + 10 + 12)

30C6 = 30! / (6! * (30-6)! = 593775

Thus:

83160/593775 = 0.1401

In other words, the probability is 14.01%

c. In this case, we must calculate the number of ways of 8 bottles zinfandel, 10 of merlot, and 12 of cabernet choose 6, that is to say that they are all of the same variety, therefore:

8C6 + 10C6 + 12C6

8! / (6! * (8-6)! + 10! / (6! * (10-6)! + 12! / (6! * (12-6)!

28 + 210 + 924 = 1162

And that divide it by the total amount that we calculated the previous point, 30C6 = 593775

Thus:

1162/593775 = 0.002

In other words, the probability 0.2%

Answer:

10.03% probability of getting a cup weighing more than 8.64oz

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 8, \sigma = 0.5[/tex]

What is the probability of getting a cup weighing more than 8.64oz

This is the 1 subtracted by the pvalue of Z when X = 8.64. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8.64 - 8}{0.5}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a pvalue of 0.8997

1 - 0.8997 = 0.1003

10.03% probability of getting a cup weighing more than 8.64oz

Answer:

0.0004% probability that the student answers at least 9 questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses the correct answer, or he does not. All questions are answered independently. This means that we use the binomial distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

In this question, we have that:

[tex]n = 10, p = 0.2[/tex]

What is the probability that the student answers at least 9 questions correctly

[tex]P(X \geq 9) = P(X = 9) + P(X = 10)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} = 0.000004[/tex]

[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0 [/tex]

[tex]P(X \geq 9) = P(X = 9) + P(X = 10) = 0.000004 + 0 = 0.000004[/tex]

0.0004% probability that the student answers at least 9 questions correctly

Answer:

10.7 CM

Step-by-step explanation:

Correct on Edge 2020

Answer:

answer is C  10.7 cm

Step-by-step explanation:

got it right on edg 2020-2021

Answer:

x = 2 is the solution of the given equation

Step-by-step explanation:

Step(i):-

Given equation

  [tex]\sqrt{x+6-4} = x[/tex]

squaring on both sides , we get

[tex](\sqrt{x+2})^{2} = x^{2}[/tex]

⇒ x + 2 = x²

⇒x² - x -2 =0

Step(ii):-

  Given x² - x -2 =0

⇒ x² - 2x + x - 2 =0

⇒ x ( x-2) + 1(x - 2) =0

⇒ (x + 1) ( x-2) =0

⇒ x = -1 and x =2

x = 2 is the solution of the given equation

Verification:-

[tex]\sqrt{x+6-4} = x[/tex]

Put x= 2

[tex]\sqrt{2+6-4} = 2[/tex]

[tex]\sqrt{4} = 2[/tex]

 2 = 2

Answer:both sides will be equal

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Multiple (4)(2)= 8

-3(8) =24

Answer: Area = 490.87  meters

Step-by-step explanation:

A=πr2

r = 12.5 (1/2 of diameter)

A = 490.87  meters

Step-by-step explanation:

We know that the formula to find the area of a circle is πr^2 or in other words, pi times the radius squared. We have been given the diamter of 25 inches. We know that the diamater is double the radius. 25 divided by 2 will get us 12.5. If we write this in equation form (or substitute the variables) will be written as: (3.14)12.5^2, 3.14 being pi. Now, we would multiply the radius by radius (because it's squared) or in other words, (12.5*12.5) to equal 156.25. If we write this in equation form, we would get: 3.14(156.25). Now we finally multiply pi (3.14) times 156.25 to equal 490.625 or rounded to the tenth 490.6

Answer:

[tex]\frac{14}{125}\times 100=11.2\%[/tex]

Answer:

A score of 1920 has a z-score of 1.27.

A score of 1290 has a z-score of -0.74.

A score of 2220 has a z-score of 2.23.

A score of 1420 has a z-score of -0.32.

The score of 2220 is more than two standard deviations from the mean, so it is unusual.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If X is 2 or more standard deviations from the mean, it is considered unusual.

In this question, we have that:

[tex]\mu = 1521, \sigma = 314[/tex]

Score of 1920:

X = 1920. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1920 - 1521}{314}[/tex]

[tex]Z = 1.27[/tex]

A score of 1920 has a z-score of 1.27.

Score of 1290:

X = 1290. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1290 - 1521}{314}[/tex]

[tex]Z = -0.74[/tex]

A score of 1290 has a z-score of -0.74.

Score of 2220:

X = 1290. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2220 - 1521}{314}[/tex]

[tex]Z = 2.23[/tex]

A score of 2220 has a z-score of 2.23.

Since it is more than 2 standard deviations of the mean, the score of 2220 is unusual.

Score of 1420:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1420 - 1521}{314}[/tex]

[tex]Z = -0.32[/tex]

A score of 1420 has a z-score of -0.32.

Answer:

She can fit 9 cubic feet of clothing in the two boxes.

Step-by-step explanation:

She can fit a total of 3 cubic feet of clothing in one box, and the other she can fit a total 6 cubic feet.

3 + 6 = 9

Answer:

9 cu ft.

Step-by-step explanation:

That is the sum of the capacities of the 2 boxes

=  3 + 6

= 9 cu ft.

Answer:

260 stickers

Step-by-step explanation:

Let Gareth's stickers be x.

Hence Cheryl sticker is 160+x;

If Cheryl gave 185 stickers

to Gareth, it means:

Cheryl has at the moment;

160 + x - 185 = x - 25

At this time when Gareth receives 185 he now has:

x+ 185

Also when he receives x +185, he has 3 times Cherry's meaning:

x+185 =3(x-25)

x + 185 = 3x -75

185 + 75 = 3x-2x

260= x

x = 260.

Hence Gareth has 260 stickers

Answer:

[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659[/tex] and [tex]\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661[/tex]

Step-by-step explanation:

The equation of the isotope decay is:

[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]

14-Carbon has a half-life of 5568 years, the time constant of the isotope is:

[tex]\tau = \frac{5568\,years}{\ln 2}[/tex]

[tex]\tau \approx 8032.926\,years[/tex]

The decay time is:

[tex]t = 1315\,years + 2007\,years \pm 13\,years[/tex] (There is no a year 0 in chronology).

[tex]t = 3335 \pm 13\,years[/tex]

Lastly, the relative amount is estimated by direct substitution:

[tex]\frac{m(t)}{m_{o}} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\mp\frac{13\,years}{8032.926\,years} }[/tex]

[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{-\frac{13\,years}{8032.926\,years} }[/tex]

[tex]\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659[/tex]

[tex]\left(\frac{m(t)}{m_{o}} \right)_{max} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\frac{13\,years}{8032.926\,years} }[/tex]

[tex]\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661[/tex]

Step-by-step explanation:

178.25

The number 5 is in the place of one's so the value of 5 is 5

Answer:

  A.  G(x) = (x -3)^3 -(x -3)

Step-by-step explanation:

The graph before it was shifted left will be a right-shift of the equation shown. That is accomplished by replacing x with (x-1.5). Then the right-shifted equation is ...

  G(x) = ((x-1.5) -1.5)^3 -((x -1.5) -1.5)

  G(x) = (x -3)^3 -(x -3) . . . . matches choice A

Answer:

  (294π +448) cm³ ≈ 1371.6 cm³

Step-by-step explanation:

The half-cylinder at the right end has a radius of 7 cm, as does the one on top. Together, the total length of these half-cylinders is 8 cm + 4cm = 12 cm. That is equivalent in volume to a whole cylinder of radius 7 cm that is 6 cm long.

The cylinder volume is ...

  V = πr²h = π(7 cm)²(6 cm) = 294π cm³

__

The cuboid underlying the top half-cylinder has dimensions 4 cm by 8 cm by 14 cm (twice the radius). So, its volume is ...

  V = LWH = (4 cm)(8 cm)(14 cm) = 448 cm³

Then the total volume of the composite figure is ...

  (294π +448) cm³ ≈ 1371.6 cm³

Answer:

logₐ(420)

Step-by-step explanation:

Answer:

The answer is

[tex] log_{a}(420) [/tex]

Step-by-step explanation:

You have to use Logarithm Law,

[tex] log_{a}(b) + log_{a}(c) ⇒ log_{a}(b \times c) [/tex]

* Take note, number b and c can only be multiplied when they have the same base, a

So for this question :

[tex] log_{a}(6) + log_{a}(70) [/tex]

[tex] = log_{a}(6 \times 70) [/tex]

[tex] = log_{a}(420) [/tex]

Answer:

Step-by-step explanation:

For the null hypothesis,

H0 : p = 0.63

For the alternative hypothesis,

Ha : p < 0.63

This is a left tailed test

Considering the population proportion, probability of success, p = 0.63

q = probability of failure = 1 - p

q = 1 - 0.63 = 0.37

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 478

n = number of samples = 800

P = 478/800 = 0.6

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76

From the normal distribution table, the area below the test z score in the left tail 0.039

Thus

p = 0.039

Answer:

-3.66

Step-by-step explanation:

Answer:

GH¢. 18098.46

Step-by-step explanation:

Let the first investment giving 12% interest per annum be Bank A

Let the 2nd investment giving 10% per annum be bank B

Let the first amount invested be

GH¢. X and let the second amount invested be GH¢. X + 580

Thus; In bank A;

Principal amount in first = GH¢. x

rate = 12 %

time = 1 year

Formula for simple interest = PRT/100

Where P is principal, R is rate and T is time.

So, interest in his investment = 12X/100 = 0.12X

while in bank B;

principal amount = GH¢. X + 580

rate = 14%

time = 1 yr

So, interest in his investment = [(X + 580) × 14]/100

= 0.14(X + 580)

So, total accumulated interest is;

0.12X + 0.14(X + 580) = 0.12X + 0.14X + 81.2 = 0.26X + 81.2

Now, we are given accumulated interest = GH¢. 2,358.60

Thus;

2358.60 = (0.26X + 81.2)

2358.6 - 81.2 = 0.26X

X = 2277.4/0.26

X = 8759.23

So,

first amount invested = GH¢. 8759.23

Second amount invested = GH¢. 8759.23 + GH¢. 580 = GH¢. 9339.23

Total amount invested = GH¢. 8759.23 + GH¢. 9339.23 = GH¢. 18098.46

Answer:

25.75 %  interest rate

Step-by-step explanation:

Given:

Amount was invested = r% per quarter  

Amount invested = P

Rate of interest = r %  per quarter

Time (n) = 4  Quarters

Computation:

A = P(1 + r/100)ⁿ

According to question.

⇒ A = P + 1.5P  = 2.5P

⇒ 2.5P = P(1 + r/100)⁴

⇒ 2.5  = (1  + r/100)⁴

⇒ 1 + r/100  =  1.2575

⇒ r/100 = 0.2575

⇒ r = 25.75

25.75 %  interest rate

Answer:

22b+24

Step-by-step explanation:

If a box lunch costs b and a bag of chips is $2 extra then we would have:

box lunch = b dollars

box lunch with bag of chips = b + 2 dollars

Now, we need to find the expression for the cost of 12 lunches with chips and 10 lunches without chips, this would be:

12 lunches with chips = 12 (b + 2)

10 lunches without chips = 10b

Let's sum up and simplify these two expressions:

[tex]12(b+2)+10b\\12b+24+10b\\22b+24[/tex]

Thus, the cost of 12 lunches with chips and 10 lunches without chips is 22b+24

Answer:

4 1/2

Step-by-step explanation:

5 apples - 1/2 apple =

4 1/2 apple

or

9/2

Answer:

2/33

Step-by-step explanation:

Probability that a 3 is rolled on the die = 1/6 (equal chance of rolling any number)

Probability of choosing a red card = 8/22 (8 red cards, 22 cards in total)

8/22 = 4/11

Probability of rolling a 3 AND choosing a red card = 1/6 x 4/11

= 4/66

= 2/33

Answer:

(a) 17/20 b.5/18/25 c. 1.255

Answer:

B. No the ordered pair does not satisfy the equation

Step-by-step explanation:

y = -9x - 2

Substitute the point in and see if it is true

-37 = -9(4) -2

-37 = -36 -2

-37 = -38

This is not true so the point is not a solution

Answer:

4

Step-by-step explanation:

Set the height of the missing bar to 4 as there are 4 quantities between 21-25.

Answer:

a) 6

b) 10

Step-by-step explanation:

a) The area of a rhombus is half the product of the diagonals, meaning that the area of the shaded part is 4*3/2=6 square meters.

b) To find the area of the white background, you need to find the area of the full rectangle, and then to find the area of both rhombii. The area of the black rhombus is 2*4/2=4 square meters. The area of the full rectangle is 4*5=20 units. Subtracting the areas of the two rhombii, you get an area for the white background of 20-6-4=10 square meters. Hope this helps!