If a tank holds 4500 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as V = 4500 1 − 1 50 t 2 0≤ t ≤ 50. Find the rate at which water is draining from the tank after the following amounts of time.a) 5 min 855 x gal/min b) 10 min 160 x gal/min c) 20 min 120 x gal/min d) 50 min gal/min

Answer:

The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 150, \pi = \frac{17}{150} = 0.1133[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 - 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.0531[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 + 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.1735[/tex]

The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).

Answer:

Step-by-step explanation:

Corresponding true average energy expenditure of shovel with conventional blade and true average energy expenditure of shovel with perforated blades form matched pairs.

The data for the test are the differences between the true average energy expenditures of the shovels.

μd = true average energy expenditure of shovel with conventional blade minus true average energy expenditure of shovel with perforated blades.

Conventional perforated diff

0.0011 0.0011 0

0.0014 0.0010 0.0004

0.0018 0.0019 -0.0001

0.0022 0.0013 0.0009

0.0010 0.0011 -0.0001

0.0016 0.0017 -0.0001

0.0028 0.0024 0.0004

0.0020 0.002 0

0.0015 0.0013 0.0002

0.0023 0.0017 0.0006

0.0017 0.002 -0.0003

0.0020 0.0013 0.0007

0.0014 0.0013 0.0001

Sample mean, xd

= (0 + 0.0004 - 0.0001 + 0.0009 - 0.0001 - 0.0001 + 0.0004 + 0 + 0.0002 + 0.0006 - 0.0003 + 0.0007 + 0.0001)/13 = 0.0002077

xd = 0.0002077

Standard deviation = √(summation(x - mean)²/n

n = 13

Summation(x - mean)² = (0 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2+ (0.0009 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2 + ( - 0.0001 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (0 - 0.0002077)^2 + (0.0002 - 0.0002077)^2 + (0.0006 - 0.0002077)^2 + (- 0.0003 - 0.0002077)^2 + (0.0007 - 0.0002077)^2 + (0.0001 - 0.0002077)^2 = 0.00000158923

Standard deviation = √(0.00000158923/13

sd = 0.00035

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 13 - 1 = 12

The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (0.0002077 - 0)/(0.00035/√13)

t = 2.14

We would determine the probability value by using the t test calculator.

p = 0.027

Since alpha, 0.05 > than the p value, 0.027, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the true average energy expenditure using the conventional shovel does not exceed that using the perforated shovel.

Answer:

x = 1/9

Step-by-step explanation:

3^ (x+1) = 9 ^ (5x)

Replace 9 with 3^2

3^ (x+1) = 3^2 ^ (5x)

We know that a^b^c = a ^(b*c)

3^ (x+1) = 3^(2 * (5x))

3^ (x+1) = 3^(10x)

The bases are the same so the exponents are the same

x+1 = 10x

Subtract x from each side

x+1-x = 10x-x

1 = 9x

Divide each side by 9

1/9 = 9x/9

1/9 =x

Answer:

the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]

Step-by-step explanation:

The probability of the density function of the total claim amount for the health insurance policy  is given as :

[tex]f_x(x) = \dfrac{1}{1000}e^{\frac{-x}{1000}}, \ x> 0[/tex]

Thus, the expected  total claim amount [tex]\mu[/tex] =  1000

The variance of the total claim amount [tex]\sigma ^2 = 1000^2[/tex]

However; the premium for the policy is set at the expected total claim amount plus 100. i.e (1000+100) = 1100

To determine the approximate probability that the insurance company will have claims exceeding the premiums collected if 100 policies are sold; we have :

P(X > 1100 n )

where n = numbers of premium sold

[tex]P (X> 1100n) = P (\dfrac{X - n \mu}{\sqrt{n \sigma ^2 }}> \dfrac{1100n - n \mu }{\sqrt{n \sigma^2}})[/tex]

[tex]P(X>1100n) = P(Z> \dfrac{\sqrt{n}(1100-1000}{1000})[/tex]

[tex]P(X>1100n) = P(Z> \dfrac{10*100}{1000})[/tex]

[tex]P(X>1100n) = P(Z> 1) \\ \\ P(X>1100n) = 1-P ( Z \leq 1) \\ \\ P(X>1100n) =1- 0.841345[/tex]

[tex]\mathbf{P(X>1100n) = 0.158655}[/tex]

Therefore: the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]

Answer:82

Step-by-step explanation:

a+b+c+d+e+f/6=72

a+b+c+d+e+f=6*72

a+b+c+d+e+f=432

a+b+c+d+e+f+g+h/8=74.25

a+b+c+d+e+f+g+h=594

g=80

h=?

432+80+h=594

512+h=594

h=82

hope it helps brainleast plz...

Answer: 5h/3

Step-by-step explanation:

12 hours passed, and 20 degrees dropped.

Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.

Hope that helped,

-sirswagger21

Answer:

5h 3

Step-by-step explanation:

12 hours passed, and 20 degrees dropped.

Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.

Hope that helped,

-sirswagger21

Answer:

The answer is y = -3x - 2.

Step-by-step explanation:

Given that in slope-form equation, m represents gradient and c is y-intercept. So you have to sbustitute the values into the equation :

[tex]y = mx + c[/tex]

[tex]let \: m = - 3 \\ let \: c = - 2[/tex]

[tex]y = - 3x - 2[/tex]

Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.

If two angles is said to create a linear pair, the angles are then regarded as supplementary and it is said that their measures often add up to 180°.

Note that Vertical angles are said to be pair of nonadjacent angles created by the crossing or the intersection of any two straight lines.

Since vertical angles are seen if "X" created by two straight lines then when you look at the image attached, you can see that the angle that can from this is Angle EFA.

Therefore, Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.

Learn more about vertical pair from

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Answer:

x <= 48

Step-by-step explanation:

Subtract 3 from both sides

x/12 <= 4

Multiply by 12

x <= 48

Answer:

Step-by-step explanation:

a)4a-6a                   d)2x+4y-10x

   =-2a.                     =-8-+4y

b)14-1-10

=3

c)2+8

=10

e)answer is 6 x raised to the power 3

f)7x raised to the power 2-5x-y

The answer is 1 7/20

2/5 x 4/4 + 7/10 x 2/2 + 1/4 x 5/5

=  8/20 + 14/20 + 5/20

= 27/20

= 1 7/20

Answer:

27/20 or 1 and 7/20

Step-by-step explanation:

All you do is find common factors.

Answer:

Brainelist?

Step-by-step explanation:

7-4i

just use a online calculator

Answer:

7-4i

Step-by-step explanation:

(2 - 3i)(2 + i)​

FOIL

first 2*2 = 4

Outer: 2i

Inner: -3i*2 = -6i

Last: -3i*i = -3i^2 = -3(-1) = 3

Add them together

4+2i-6i+3

7-4i

Answer:

C

Step-by-step explanation:

The range of a data set is the difference between the biggest and smallest values, so to find it, you just subtract the minimum from the maximum.

Answer:

Step-by-step explanation:

5

Answer:

If we have a cone-shape candle with r=2 cm and h=3 cm, then the amount of paper needed is 18.84 cm^2 and the amount of plastic needed is 12.56 cm^2.

Step-by-step explanation:

The question is incomplete: no numerical values for the dimensions of the cone are given.

A right cone is defined by the radius r of the base and the height h.

The base area is the area of a circle with radius r:

[tex]A_b=\pi r^2[/tex]

The lateral area is calculated as:

[tex]A_l=\pi \cdot r\cdot l[/tex]

As the values for r and h are not given, we will use an example with r=2 and h=3.

Then, the amount of paper needed is:

[tex]A_l=\pi \cdot r\cdot l=3.14\cdot (2\,cm)\cdot (3\, cm)=18.84\,cm^2[/tex]

The amount of plastic needed is:

[tex]A_b=\pi r^2=3.14\cdot (2\,cm)^2=3.14\cdot 4\,cm^2=12.56\,cm^2[/tex]

Answer:

Step-by-step explanation:

The bottom (or top) of the U is called the vertex, or the turning point. The vertex of a parabola opening upward is also called the minimum point. The vertex of a parabola opening downward is also called the maximum point.

The x-intercepts are called the roots, or the zeros. To find the x-intercepts, set ax^2 + bx + c = 0.

The parabola is symmetric (a mirror image) about a vertical line drawn through its vertex (turning point). This line is called the axis of symmetry.

If possible, please mark brainliest

The quadratic function can be expressed in the form of vertex form and the parabola is symmetric about the line which is passing through focus.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The important features for the graph of a quadratic function will be

The parabola is symmetric about the line which is passing through focus.

The quadratic function can be expressed in the form of vertex form.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

More about the quadratic equation link is given below.

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Not necessarily, the more correct definition is opposite reciprocal slopes.

The example used is how horizontal and vertical lines are parallel. Horizontal lines have a slope of 0, also written as 0/1. However, vertical lines have an undefined slope, which isn't necessarily negative. It has a slope of 1/0, which is undefined. In this case, the reciprocal isn't negative.

In all other cases (1 and -1, 2 and -1/2, etc.) yes, the perpendicular pairs are negative and reciprocal.

Answer:

Step-by-step explanation:

From the news story, we are told that:

The odds are 1 in 150 that a piece of Skylab will hit someone.

However, 4 billion people live in the zone in which pieces could fall.

Therefore, any one person’s chances of being struck are:

[tex]=\dfrac{1}{150} \times 4$ billion\\=\dfrac{1}{37.5}$ billion\\\\=26,666,667 million[/tex]

Therefore, the odds are one in approximately 27 million.

The inaccuracy presented in this reasoning was that the odds are one in 600 billion.

Answer:

Step-by-step explanation:

1/10*5 is the answer i think...

Answer:

Top right option

Step-by-step explanation:

Answer:

10,15.20.25

Step-by-step explanation:

+5 in each number

Answer:

1.5 meters

Step-by-step explanation:

The formula for the area of a trapezoid is h * (a+b)/2, where a is the first base and b is the second base. Now, we can work backwards to determine the height of the trapezoid:

3.75=h*(1.7+3.3)/2

3.75=h*2.5

h=3.75/2.5=1.5

Hope this helps!

Answer:

Step-by-step explanation:

use the formula and rearrange for h.

1/2 x h x  (a + b) = A

1/2 x (1.7 + 3.3) x h = 3.75

2.5 x h = 3.75

h = 1.5

hope this helps! :)

Answer:

a= -3/8

b= 1/8

Step-by-step explanation:

To remove i from the denominator, we need to multiply the numerator and denominator by -i

[tex]\frac{(-1-3i)(-i)}{8i(-i)}[/tex]

This simplifies to

[tex]\frac{i+3i^{2} }{-8i^{2} }[/tex]

This further simplifies to

[tex]\frac{i-3}{8}[/tex]

This can be rewritten as

[tex]-\frac{3}{8} +\frac{1}{8} i[/tex]

a= -3/8

b= 1/8

Answer:

[tex] a = - \frac{3}{8} \\ \\ b = \frac{1}{8} [/tex]

Step-by-step explanation:

[tex] \frac{ - 1 - 3i}{8i} \\ \\ = \frac{ - 1 - 3i}{8i} \times \frac{i}{i} \\ \\ = \frac{( - 1 - 3i)i}{8i \times i} \\ \\ = \frac{ -1 \times i - 3 {i}^{2} }{8 {i}^{2} } \\ \\ = \frac{ - i - 3 ( - 1)}{8 ( - 1) } \\ \\ = \frac{ - i + 3}{ - 8} \\ \\ = \frac{ i - 3}{ 8} \\ \\ = \frac{ - 3 + i}{ 8} \\ \\ = \frac{ - 3}{8} + \frac{i}{8} \\ \\ \purple{ \bold{ = - \frac{3}{8} + \frac{1}{8} i}} \\ equating \: it \: with \: a + bi \\ \\ a = - \frac{3}{8} \\ \\ b = \frac{1}{8} \\ [/tex]

By rounding of the following number to the nearest thousand is 2000.

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

'

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

Round the following number to the nearest thousand

2385

= 2000

Thus, by rounding of the following number to the nearest thousand is 2000.

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Answer:

250

Step-by-step explanation:

if x=50

5(x)=5*50=250

Hope it helps..Pls mark as Brainliest!!

Answer:

52300

Step-by-step explanation:

When you multiply by ten the decimal dot moves one space to the right, so here you multiply by ten four times, so you move the dot four spaces to the right and you get 52300

Answer:

Which earns more interest = Account B

How much more = $1,306.60

Step-by-step explanation:

Given;

Principal P = $2,000

Interest rate r = 5% = 0.05

Time t = 20 years

For account A;

Simple interest = P×r×t

Substituting the values;

Simple interest = 2,000 × 0.05 × 20 = $2000

Interest on account A = $2,000

For account B;

Compound interest

Final amount = P(1 + r)^t

Since it's compounded annually

Substituting the values;

Final amount = 2000(1+0.05)^20

Final amount = $5306.60

Interest = final amount - principal = $5306.60 -$2000

Interest = $3,306.60

Therefore, account B earns more interest.

Difference = account B interest - account A interest

Difference = $3,306.60 - $2,000

Difference = $1,306.60

Answer:

n = 3 or n = 4

Step-by-step explanation:

Let the unknown number be n.  

Then:

n² = 7n - 12

In standard quadratic form, we have:

n² - 7n + 12 = 0

In factored form, we have:

(n - 3)(n - 4) = 0, and so

n = 3 and n = 4