Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 15 ft high

Answer:

D. Two-sample chi-square

Step-by-step explanation:

A chi-square test is a test used to compare the data that is observed, from the data that is expected.

In a two-sample chi-square test the observed data should be similar to the expected data if the two data samples are from the same distribution.

The hypotheses of the two-sample chi-square test is given as:

H0: The two samples come from a common distribution.

Ha: The two samples do not come from a common distribution

Therefore, in this case, the best statistical test to utilize is the two-sample chi-square test.

Answer:

2. Precise but not accurate

Step-by-step explanation:

In a high precision, low accuracy case study, the measurements are all close to each other (high agreement between the measurements) but not near/or close to the center of the distribution (how close a measurement is to the correct value for that measurement)

Answer:

16

Step-by-step explanation:

X^2 + 8x= 11

Take the coefficient of x

8

Divide by 2

8/2 =4

Square it

4^2 = 16

Add 16 to each side

Answer:  24

Step-by-step explanation:

Let's find one solution:

3x² + 7x + c = 0

a=3 b=7  c=c

First, let's find c so that it has REAL ROOTS.

⇒ Discriminant (b² - 4ac) ≥ 0

                         7² - 4(3)c ≥ 0

                         49 - 12c ≥ 0

                               -12c  ≥ -49

                                [tex]c\leq\dfrac{-49}{-12}\quad \rightarrow c\leq \dfrac{49}{12}[/tex]      

Since c must be a positive integer, 1 ≤ c ≤ 4

Example: c = 4

3x² + 7x + 4 = 0

(3x + 4)(x + 1) = 0

x = -4/3, x = -1         Real Roots!

You need to use Quadratic Formula to solve for c = {1, 2, 3}

Valid solutions for c are: {1, 2, 3, 4)

Their product is: 1 x 2 x 3 x 4 = 24

Answer:

$3x^2+7x+c=0$

comparing above equation with ax²+bx+c

a=3

b=7

c=1

using quadratic equation formula

[tex]x = \frac{ - b + - \sqrt{b {}^{2} - 4ac} }{ 2a} [/tex]

x=(-7+-√(7²-4×3×1))/(2×3)

x=(-7+-√13)/6

taking positive

x=(-7+√13)/6=

taking negative

x=(-7-√13)/6=

Answer:

z=0

x= -5

y=4

Step-by-step explanation:

Check the attachment please

Hope this helps :)

Step-by-step explanation:

x + 2y − z = 3

x + y − 2z = -1

There are three variables but only two equations, so this system of equations is undefined.  We cannot solve for the variables, but we can eliminate one of them and reduce this to a single equation.

Double the first equation:

2x + 4y − 2z = 6

Subtract the second equation.

(2x + 4y − 2z) − (x + y − 2z) = (6) − (-1)

2x + 4y − 2z − x − y + 2z = 7

x + 3y = 7

Answer:

50%

Step-by-step explanation:

Cost of 3 bananas= Rs. 5 ⇒ cost of 1 banana= Rs. 5/3

Selling price of 2 bananas= Rs. 5 ⇒ selling price of 1 banana= Rs. 5/2

Gain= Rs. (5/2- 5/3)= Rs. (15/6- 10/6)= Rs. 5/6

Gain %= 5/6÷5/3 × 100%= 50%

Answer:

-2w - 4

Step-by-step explanation:

What is the simplest form of this expression

2(w - 1) + (-2)(2w + 1) =

= 2w - 2 - 4w - 2

= -2w - 4

Answer: -2w-4

Step-by-step explanation:

subtract 4w of 2w

2w-2-4w-2

subtract 2 of -2

-2w-2-2

final answer

-2w-4

Answer:

yes it is little different  from the confidence interval (30.4 ≤μ≤ 32.8) changes statistics

90% confidence interval estimate of the mean is

(30.1048 , 33.0952)

Step-by-step explanation:

Step(I):-

Given sample size 'n' = 153

Given mean of the sample x⁻ = 31.5

Sample standard deviation 'S' = 7.1 h g

90% confidence interval estimate of the mean is determined by

[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]

Degrees of freedom

ν = n-1 = 153-1 =152

t₀.₀₅ =1.9757

Step(ii)

90% confidence interval estimate of the mean is

[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]

[tex](31.5 - 1.9757 } \frac{7.1}{\sqrt{153} } , 31.5 + 1.9757 \frac{7.1}{\sqrt{153} } )[/tex]

( 31.5 - 1.1340 , 31.5 + 1.1340)

(30.366 , 32.634)

90% confidence interval estimate of the mean is

(30.4 , 32.6)

b)

Given sample size 'n' = 15

Given mean of the sample x⁻ = 31.6

Sample standard deviation 'S' = 2.7 h g

90% confidence interval estimate of the mean is determined by

[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]

Degrees of freedom

ν = n-1 = 15-1 =14

t₀.₀₅ =2.1448

90% confidence interval estimate of the mean is

[tex](x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]

[tex](31.6 - 2.1448 } \frac{2.7}{\sqrt{15} } , 31.6 + 2.1448 \frac{2.7}{\sqrt{15} } )[/tex]

( 31.6 - 1.4952 , 31.6 + 1.4952)

(30.1048 , 33.0952)

Conclusion:-

yes it is little different  from the confidence interval (30.4 ≤μ≤32.8)

The probability of picking greens on both occasions will be 5/18.

The probability of picking greens cards will be:

= 5/9 × 4/8

= 5/18

The probability of picking at least one green will be:

= 1 - P(both aren't green)

= 1 - (4/9 × 3/8)

= 1 - 1/6.

= 5/6

From the tree diagram, the probability as a fraction of P(G2 | G1) will be:

= 4/8 = 1/2

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Answer:

Hey!

Your answer is YES!

AKA the Last Option on your screen!

Step-by-step explanation:

It is this because...

They both have the angles 105 in it...

And looking at the other angle on the smaller one (25)

50 + 25 = 75 ... 180 - 75 = 105

WE HAVE 105 as an angle on the larger triangle...which makes them SIMILAR but congruent Angles!

It cant be the "corresponding sides" as we do not have the notations (lines intersecting the sides) that let us know that the lines are the same.

Hope this helps!

Answer:

0.3174

Step-by-step explanation:

Z-score:

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 area under the normal curve to the left of Z. Subtracting 1 by the pvalue, we find the area under the normal curve to the right of Z.

Left of z = -1

z = -1 has a pvalue of 0.1587

So the area under the standard normal curve to the left of z = -1 is 0.1587

Right of z = 1

z = 1 has a pvalue of 0.8413

1 - 0.8413 = 0.1587

So the area under the standard normal curve to the right of z = 1 is 0.1587

Left of z = -1 or right of z = 1

0.1587 + 0.1587 = 0.3174

The area is 0.3174

Answer:

The second question

Step-by-step explanation:

The orca starts at -25 meters. She goes up 25 meters.

up 25 = +25

-25+25=0

Answer:

Option 2

Step-by-step explanation:

The orca swims at the elevation of -25 meters. The orca swims up 25 meters higher than before.

-25 + 25 = 0

Answer:

7

Step-by-step explanation:

2x-3=11

Move the -3 to the right side by adding 3 to both sides of the equation

2x=14

Divide both sides by 2 to get x by itself

x=7

Answer:

  7

Step-by-step explanation:

2x -3 = 11

2x = 14 . . . . add 3

x = 7 . . . . . . divide by 2

The number 7 makes the equation true when substituted for x.

Answer:

A 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].

Step-by-step explanation:

Since in the question only 9 random scores are given, so I am performing the calculation using 9 random scores.

We are given that the scores of bowlers in particular league follow a normal distribution such that the standard deviation of the population is 6.

The accompanying data set of 9 random scores in ascending order is given as; 75, 86, 86, 88, 89, 93, 93, 98, 107

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean score = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{815}{9}[/tex] = 90.56

            [tex]\sigma[/tex] = population standard deviation = 6

            n = sample of random scores = 9

            [tex]\mu[/tex] = population mean score for all bowlers

Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\bar X-\mu}[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] =  [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                                          = [ [tex]90.56-1.96 \times {\frac{6}{\sqrt{9} } }[/tex] , [tex]90.56+1.96 \times {\frac{6}{\sqrt{9} } }[/tex] ]

                                          = [86.64 , 94.48]

Therefore, a 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].

Answer:

104.93 in

Step-by-step explanation:

When we draw out a picture of our triangle, we should see that we need to use sin∅ to solve:

sin23° = 41/x

xsin23° = 41

x = 41/sin23°

x = 104.931

Answer:

after 9 weeks it would become 9*1+10=19 inches

and after w weeks it will be w*1+10 inches tall

hope this helps

Step-by-step explanation:

Answer:

a) 19 inches

b) 10+w inches

Step-by-step explanation:

The equation for this problem is 10 + w.  In the first part, w = 9, so the plant is 19 inches tall.

Answer:

This question is about:

sin(A/2) and cos(A/2)

First, how we know when we need to use the positive or negative signs?

Ok, this part is kinda intuitive:

First, you need to know the negative/positve regions for the sine and cosine function.

Cos(x) is positive between 270 and 90, and negative between 90 and 270.

sin(x) is positive between  0 and 180, and negative between 180 and 360.

Then we need to see at the half-angle and see in which region it lies.

If the half-angle is larger than 360°, then you subtract 360° enough times such that the angle lies in the range between (0° and 360°)

and: Tan(A/2) = Sin(A/2)/Cos(A/2)

So using that you can infer the sign of the Tan(A/2)

Now, why these relationships use the two signs?

Well... this is because of the square root in the construction of the relationships.

This happens because:

(-√x)*(-√x) = (-1)*(-1)*(√x*√x) = (√x*√x)

For any value of x.

so both -√x and √x are possible solutions of these type of equations, but for the periodic nature of the sine and cosine functions, we can only select one of them.

So we should include the two possible signs, and we select the correct one based on the reasoning above.

Answer:

A discrete data set because there are a finite number of possible values.

Step-by-step explanation:

We are given the following data set below;

When a car is randomly selected, it is found to have 8 windows.

Firstly, as we know that the discrete data is that data that have countable or finite values, and also we can observe at a point value.

On the other hand, the continuous data is that data in which there is a range of values and we can't count or observe each and every value.

So, in our question; as we can observe that we can count all the windows and it is also a finite number which means that the given data set is a discrete data set because there are a finite number of possible values.

Answer:

The length of the third side of fence is 11.4 m

Step-by-step explanation:

Solution:-

- We are to mow a triangular piece of land. We are given the description of motion and the orientation of land-mower while fencing.

- From one corner of the triangular land, the land-mower travels H1 = 5.7 m at θ1 = 0.3 radians north of east. We will use trigonometric ratios to determine the amount traveled ( B1 ) in the east direction.

                                  [tex]cos ( theta_1 ) = \frac{B_1}{H_1}[/tex]

Where,

                          B1: Is the base length of the right angle triangle

                          H1: Hypotenuse of the right angle triangle

Therefore,

                                [tex]B_1 = H_1*cos ( theta_1 )\\\\B_1 = 5.7*cos ( 0.3 )\\\\B_1 = 5.44541 m[/tex]

- Similarly, from the other corner of the triangular land. The land-mower moves a lateral distance of H2 = 9m and directed θ2 = 0.9 radians north of west. We will use trigonometric ratios to determine the amount traveled ( B2 ) in the west direction.

                                [tex]cos ( theta_2 ) = \frac{B_2}{H_2} \\[/tex]

Where,

                          B2: Is the base length of the right angle triangle

                          H2: Hypotenuse of the right angle triangle

Therefore,

                                 [tex]B_2 = H_2*cos ( theta_2 )\\\\B_2 = 9*cos(0.9)\\\\B_2 = 5.59448 m[/tex]

- The total length of the third side of the fence would be the sum of bases of the two right angles formed by the land-mower motion at each corner.

                                [tex]L = B_1 + B_2\\\\L = 5.44541 + 5.59448\\\\L = 11.4 m[/tex]

Answer:

1 year

Step-by-step explanation:

1. Convert 10% into a z-score, using a calculator or whateva

2. Z = -1.281551 ( you can find this by doing the following equation: (x - mean) / (standard deviation)

3. Hence -1.281551 = (x - 4) / 2 or, x = 1.436898, ( rounded to the nearest year ) = 1 year

Answer:

18/90=9/x and to find x use proportion so first 90*9=18x and 810=18x and x-45

Step-by-step explanation:

Answer:

45 stores are at University Mall

Step-by-step explanation:

The ratio of malls that sell shoes at North Area mall are 18 out of 90, which simplifies to one fifth of stores. Since the same ratio holds for the University Mall, and 9 is half of 18, the amount of stores at University Mall is 45 because 45 is half of 90.

Answer:

(-2 ,3)

Step-by-step explanation:

Step 1: Rewrite first equation

x = 4 - 2y

-2x + y = 7

Step 2: Substitution

-2(4 - 2y) + y = 7

Step 3: Solve y

-8 + 4y + y = 7

-8 + 5y = 7

5y = 15

y = 3

Step 3: Plug in y to find x

x + 2(3) = 4

x + 6 = 4

x = -2

Answer:

aaaaha pues

Step-by-step explanation:

Answer:

what happened

Step-by-step explanation:

Answer:

y = 2x + 3

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope-Intercept Form: y = mx + b

Step 1: Find slope m

m = (-1 - 3)/(-2 - 0)

m = -4/-2

m = 2

y = 2x + b

Step 2: Rewrite equation

y = 2x + 3

*You are given y-intercept (0, 3), so simply add it to your equation.

Part A

g(x) = 3x+1

g(-4) = 3(-4)+1 ... every x replaced with -4

g(-4) = -12+1

g(-4) = -11

Plug this into the f(x) function

f(x) = x^2 - 2x

f( g(-4) ) = (g(-4))^2 - 2( g(-4) )

f( g(-4) ) = (-11)^2 - 2(-11)

f( g(-4) ) = 121 + 22

====================================================

Part B

Plug the g(x) function into the f(x) function

f(x) = x^2 - 2x

f( g(x) ) = ( g(x) )^2 - 2( g(x) ) ... replace every x with g(x)

f( g(x) ) = (3x+1)^2 - 2(3x+1)

f( g(x) ) = (9x^2+6x+1) + (-6x-2)

f( g(x) ) = 9x^2+6x+1-6x-2

Note that we can plug x = -4 into this result and we would get

f( g(x) ) = 9x^2-1

f( g(-4) ) = 9(-4)^2-1

f( g(-4) ) = 9(16)-1

f( g(-4) ) = 144-1

f( g(-4) ) = 143 which was the result from part A

====================================================

Part C

Replace g(x) with y. Then swap x and y. Afterward, solve for y to get the inverse.

[tex]g(x) = 3x+1\\\\y = 3x+1\\\\x = 3y+1\\\\3y+1 = x\\\\3y = x-1\\\\y = \frac{1}{3}(x-1)\\\\y = \frac{1}{3}x-\frac{1}{3}\\\\g^{-1}(x) = \frac{1}{3}x-\frac{1}{3}\\\\[/tex]

Answer:

1000

Step-by-step explanation:

=> [tex]\frac{1}{10^{-3}}[/tex]

According to the law of exponents, [tex]\frac{1}{a^{-m}} = a^{m}[/tex]

So, it becomes

=> [tex]10^{3}[/tex]

=> 1000

Answer: the answer is d sin30degrees equal 5/x because sin is opposite over hyponuese

Answer:

[tex] P(X \geq 3)= 1- P(X<3)= 1-P(X \leq 2)= 1- [P(X=0) +P(X=1) +P(X=2)][/tex]

And we can find the individual probabilites using the probability mass function and we got:

[tex] P(X=0) = (15C0) (0.08)^{0} (1-0.08)^{15-0}=0.286 [/tex]

[tex] P(X=1) = (15C1) (0.08)^{1} (1-0.08)^{15-1}=0.373 [/tex]

[tex] P(X=2) = (15C2) (0.08)^{2} (1-0.08)^{15-2}=0.227 [/tex]

And replacing we got:

[tex] P(X\geq 3) = 1-[0.286+0.373+0.227 ]= 0.114[/tex]

Step-by-step explanation:

For this case we can assume that the variable of interest is "drivers were involved in a car accident last year" and for this case we can model this variable with this distribution:

[tex] X \sim Bin (n =15, p =0.08)[/tex]

And for this case we want to find this probability;

[tex] P(X \geq 3)[/tex]

and we can use the complement rule and we got:

[tex] P(X \geq 3)= 1- P(X<3)= 1-P(X \leq 2)= 1- [P(X=0) +P(X=1) +P(X=2)][/tex]

And we can find the individual probabilites using the probability mass function and we got:

[tex] P(X=0) = (15C0) (0.08)^{0} (1-0.08)^{15-0}=0.286 [/tex]

[tex] P(X=1) = (15C1) (0.08)^{1} (1-0.08)^{15-1}=0.373 [/tex]

[tex] P(X=2) = (15C2) (0.08)^{2} (1-0.08)^{15-2}=0.227 [/tex]

And replacing we got:

[tex] P(X\geq 3) = 1-[0.286+0.373+0.227 ]= 0.114[/tex]

Answer:

C

Step-by-step explanation:

102.35-20-33.33-52.80+25+24.75

45.97