A past survey of students taking a standardized test revealed that ​% of the students were planning on studying engineering in college. In a recent survey of students taking the​ SAT, ​% of the students were planning to study engineering. Construct a ​% confidence interval for the difference between proportions by using the following inequality. Assume the samples are random and independent.

The confidence interval is __

Answer:

the rate of change of the water depth when the water depth is 10 ft is;  [tex]\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}[/tex]

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft  is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the  rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at  a time t and r = radius of the cone shaped at a time t

Then the similar triangles  ΔOCD and ΔOAB is as follows:

[tex]\dfrac{h}{r}= \dfrac{20}{8}[/tex]    ( similar triangle property)

[tex]\dfrac{h}{r}= \dfrac{5}{2}[/tex]

[tex]\dfrac{h}{r}= 2.5[/tex]

h = 2.5r

[tex]r = \dfrac{h}{2.5}[/tex]

The volume of the water in the tank is represented by the equation:

[tex]V = \dfrac{1}{3} \pi r^2 h[/tex]

[tex]V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h[/tex]

[tex]V = \dfrac{1}{18.75} \pi \ h^3[/tex]

The rate of change of the water depth  is :

[tex]\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}[/tex]

Since the water is drained  through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

[tex]\dfrac{dv}{dt}= - 4 \ ft^3/sec[/tex]

Therefore,

[tex]-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}[/tex]

the rate of change of the water at depth h = 10 ft is:

[tex]-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}[/tex]

[tex]100 \pi \dfrac{dh}{dt} = -4 \times 6.25[/tex]

[tex]100 \pi \dfrac{dh}{dt} = -25[/tex]

[tex]\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}[/tex]

Thus, the rate of change of the water depth when the water depth is 10 ft is;  [tex]\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}[/tex]

Answer:

the rate of change of the water depth when the water depth is 10 ft is;  

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft  is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the  rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at  a time t and r = radius of the cone shaped at a time t

Then the similar triangles  ΔOCD and ΔOAB is as follows:

   ( similar triangle property)

h = 2.5r

The volume of the water in the tank is represented by the equation:

The rate of change of the water depth  is :

Since the water is drained  through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

Therefore,

the rate of change of the water at depth h = 10 ft is:

Thus, the rate of change of the water depth when the water depth is 10 ft is;  

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Yes.  They did exponents and grouping symbols first, then multiplication and division left to right.  Addition came before multiplication and division because it was inside a grouping symbol.

Answer:

c

Step-by-step explanation:

:)

Answer Choice 1

Take it step by step!

First find what sqrt(x-7) is like. Compare it to sqrt(x).

You can see that in sqrt(x), when x = 0, y = 0. However, in sqrt(x-7), when x = 7, y = 0. When y = 0, sqrt(x-7) is 7 more, which means it is shifted 7 units to the right.

Similarly, +8 means that whatever sqrt(x-7) is, you add 8 more to y. Adding on extra for y is just moving it up by 8 units.

Hope that helped,

-sirswagger21

Answer:

Y= 7.9 lb

X= 10.1 lb

Step-by-step explanation:

The chef orders 2.2 lb more carrots than celery. The two orders weigh 10.8 lb combined.

Let carrot= x

Let celery= y

X+y = 18...... equation one

X= 2.2 +y.... equation two

Substituting the value of x into equation one

2.2 +y +y =18

2y= 18-2.2

2y= 15.8

Y= 7.9 lb

Substituting the value of yinto equation 2

X= 2.2 +y

X= 2.2 + 7.9

X= 10.1 lb

Answer:

please mark my answer brainliest

Step-by-step explanation:

in tri ABD and bcd...

AD =DC ...given

AB =BC.....given

BD =BD.....common

therefore...both tri are congruent...by SSS CRITERION

therefore angle adb...and angle bdc are equal...cpct...

therefore angle bdc =32°

angle dbc =90°

therefore angle bcd =angle C=180- (90 +32) =58°

angle C=58°....answer

Answer:

The differences become smaller

Step-by-step explanation:

Normally, we use the t-distribution table rather than the normal distribution when the population standard deviation is unknown and when the sample size is small i.e. less than 30.

Now, as the sample size gets bigger, we will be getting closer to the point where we have to use the normal distribution.

This means that as the sample size increases, the values of the t-distribution will be getting close to that of the normal distribution because normal distribution is used when sample is more than 30.

For example the t-value for a sample of 25 people would be closer to the normal distribution value for a sample of 35 people while a t-value for a sample of 15 people will be far away from the normal distribution value for a sample of 35 people.

Thus, as the sample size increases, the differences between the t-distribution and standard normal distribution becomes smaller.

Answer:

4

Step-by-step explanation:

2×4 equals 8 4 papers in 8 hours

Answer:

0_10 =0_2

Step-by-step explanation:

Convert the following to base 2:

0_10

Hint: | Starting with zero, raise 2 to increasingly larger integer powers until the result exceeds 0.

Determine the powers of 2 that will be used as the places of the digits in the base-2 representation of 0:

Power | \!\(\*SuperscriptBox[\(Base\), \(Power\)]\) | Place value

0 | 2^0 | 1

Hint: | The powers of 2 (in ascending order) are associated with the places from right to left.

Label each place of the base-2 representation of 0 with the appropriate power of 2:

Place | | | 2^0 |  

| | | ↓ |  

0_10 | = | ( | __ | )_(_2)

Hint: | Divide 0 by 2 and find the remainder. The remainder is the first digit.

Determine the value of 0 in base 2:

0/2=0 with remainder 0

Place | | | 2^0 |  

| | | ↓ |  

0_10 | = | ( | 0 | )_(_2)

Hint: | Express 0_10 in base 2.

The number 0_10 is equivalent to 0_2 in base 2.

Answer: 0_10 =0_2

Answer:

A) It fulfills the condition of binomial experiment

B) P (x=12) =0.1678

C)P ( x ≥16)= 0.1011

d) P (x>17) =0.0096 < 0.5

Step-by-step explanation:

A. The binomial probability distribution has the following four properties

1. the outcomes of each trial maybe classified into success and failure.

2) the probability of success p remains constant for all trials.

3) the successive trials are all independent.

4) the experiment is repeated a fixed number of times ,n.

These all conditions are fulfilled by the given question so it is a  binomial experiment.

B) P (x=12) = 20C12 (0.64)^12 * (1-0.64)^8= 0.1678

C) P ( x ≥16) = P (x=16) + P (x=17) + P (x=18) + P (x=19)+ P (x=20)

where

P (x=16)= 20C16 (0.64)^16 * (1-0.64)^4= 0.0645

P (x=17)= 20C17 (0.64)^17 * (1-0.64)^3= 0.0270

P (x=18)= 20C18 (0.64)^18 * (1-0.64)^2= 0.0080

P (x=19)=20C19 (0.64)^10 * (1-0.64)^1= 0.0015

P (x=20)= 20C20 (0.64)^20 * (1-0.64)^0= 0.0001

so

P ( x ≥16)= 0.0645+ 0.0270 +0.0080+ 0.0015+0.0001= 0.1011

d) P (x>17)= P (x=17) + P (x=18) + P (x=19)+ P (x=20)

                    =0.0270 +0.0080+ 0.0015+0.0001

                         =0.0096

From this we see that the probability of  more than 17  people who flush public toilets with their foot is unusual because it is far away from the mean which is supposed to be somewhere 0.5 in a given distribution.

Answer:

the absolute value of -5 is 5, and the absolute value of 5 is also 5. ∣ a + b i ∣ = a 2 + b 2 . |a+bi| = \sqrt{a^2 +b^2}

please give me heart

Answer:

Debbie would need to purchase 2 1-gallon bottles of juice.

Step-by-step explanation:

So we have 20 cups and each cup holds 10 fluid ounces. 20 times 10 equals 200 fluid ounces. We need to see how many fluid ounces are in 1 gallon. There are 128 fluid ounces in 1 gallon. 200 divided by 128 equals to 1.56 gallons. Debbie needs more than 1 gallon. Since we have a decimal and 1 is on the left of the decimal, Debbie would need to purchase 2 1-gallon bottles of juice.

Answer:

It will be 1:50

Step-by-step explanation:

Answer:

11:50 + 2 hr. = 1:50 or 13:50 Military/European time

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

you clean 2 a hour so 7*2=14

Answer:

14 houses

Step-by-step explanation:

Answer:

You have 1/60 of the original hair color left

Step-by-step explanation:

Add up the fractions

1/3 + 1/4 + 2/5

Get a common denominator of 60

1/3 * 20/20    + 1/4 * 15/15    + 2/5 * 12/12

20/60 + 15/60 + 24/60

59/60

The total is 1 or 60/60

60/60 - 59/60

1/60

You have 1/60 of the original hair color left

Answer: Hi!

The place value of 6 in 37651 is equal to 600, as it is in the hundreds place.

All we need to do is multiply 600 by 11:

600 * 11 = 6600

Hope this helps!

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

So in 37,651, the 6 is in the hundreds place since it's the third digit (from right to left).

6 in the hundreds place is 600.

600 times 11 equals 6600.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

♡ Hope this helps! ♡

❀ 0ranges ❀

Answer:

a. 1120 is the area b. max # of ppl is 80

Step-by-step explanation:

a. Area= Length* width = 28 * 40 = 1120

(8,10) and (8,38) have 28 units between them

(8,10) and (48,10) have 40 units between them

b. Since the area is 1120 and they say that only one person is allowed per 14 square feet, you would divide 1120 by 14 to get 80 people

If each coordinate equals 1 foot then:

(8,10) to (48,10) is 40 feet (48-8)

(8,10) to (8,38) is 28 feet (38-10)

so now you got length 40 and width 28

40 x 28 = 1120

a. 1120ft^2

b. 1120 / 14 = 80

Answer:

The remainder is 87.

Step-by-step explanation:

By definition of remainder theorem, whenever a polynomial f(x) is divided by (x-b) the remainder will be: f(b)

Following the Remainder Theorem, in this question the remainder will be f(5).

In this case we were given f(x) as

f(x) = x^2 + 14x − 8

We're are to find the remainder when it is divided by (x-5)

Then(x-5)= 0

X=5

If we substitute x=5 into equation of f(x), we will have the remainder of

f(x) = x^2 + 14x − 8

f(4)= (5)^2 +14(5)-8

f(4)=25+70-8

f(4)=87

Hence, The remainder is 87.

Answer:

87

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Hello!

A function is a equation that every input has one output

To find if an equation is a function we put in a number for one variable and solve

I'll use 0

y^2 = 0^2 + 5(0) + 4

Simplify

y^2 = 0 + 0 + 4

Combine like terms

y^2 = 4

To remove the square from y you put 4 in the square root in both negative and positive

[tex]y=\sqrt{4}[/tex] [tex]y=-\sqrt{4}[/tex]

Simplify

y = 2, y = -2

For one input (0) we get two outputs (2 and -2) this means it is not a function. So the answer is B

Hope this Helps!

Answer:

$233.39

Step-by-step explanation:

Pants = $82, 2 Shirts = $53 * 2, Shoes = $120

Add all these values up to find the total cost of your order excluding tax.

82 + 53(2) + 120 = 308

Next find the price w/ tax. Multiply 308 by 8.25%, or 0.0825.

308 * 0.0825 = 25.41

Now you add the tax to the total value.

308 + 25.41 = 333.41

The total value including tax is $333.41. The online retailer is offering a 30% savings (discount), so multiply the total price including tax by 30% (0.30).

333.41 * 0.30 = 100.023

Now you subtract the discount from the total price.

333.41 - 100.023 = 233.38700

The question say the answer rounded to the nearest cent or hundredths, so your final answer is 233.39.

The final price of the clothing including all discounts and taxes is $233.39.

Answer:

the answer is -7

Step-by-step explanation:

m+9=2-9

-9

m=. -7

Answer:

Step-by-step explanation:

In this problem we are required to place flowers evenly across  3 flower vases.

Given that we have 25 flower to collect from and distribute evenly.

we are going to divide 25 by 3

We have

[tex]= \frac{25}{3}\\\\ =8\frac{1}{3}[/tex]

From the result in the improper fraction we can see the Darren can place 8 flowers evenly of the 25 flowers and there will be just one left over

Answer:

B. To test if the mean annual income of Ontarians is higher than that of British Columbians

E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.

Explanation:

The options chosen have two populations that are independent. For example in option B, the annual income of Ontarians is a different population from annual income of British Columbians and they are also independent. The two sample t test can only be used when the populations are independent, it can also be used when computing difference between the means of two populations

The scenarios where conducting a two-sample t-test for means be appropriate include:

It should be noted that the two sample t-test is used when the populations are independent band the sample size is small.

Therefore, it will be appropriate to test if there is a difference between the proportion of low-income families in British Columbia and a known national and the difference between the mean annual income of male British Columbians and that of female British Columbians.

Read related link on:

https://brainly.com/question/17042228

Answer:

B

Step-by-step explanation:

∠ U = ∠ F = 76° thus are congruent

Consider the ratios of corresponding sides

[tex]\frac{UW}{FH}[/tex] = [tex]\frac{9}{21}[/tex] = [tex]\frac{3}{7}[/tex]

[tex]\frac{UV}{FG}[/tex] = [tex]\frac{18}{42}[/tex] = [tex]\frac{3}{7}[/tex]

Thus Δ UVW ~ Δ FGH by the SAS postulate

Yes the given two triangles are similar.

The similarity statement is B) ΔUVW ∼ ΔFGH

The triangles that have similar shape but the sizes of the triangles may be different, are called similar triangles.

Here, in the given triangles,

∠U = ∠F = 76°

Therefore they are congruent.

The ratio of corresponding sides, [tex]\frac{UW}{FH} =\frac{9}{21} = \frac{3}{7}[/tex]

Again the ratio of corresponding sides, [tex]\frac{UV}{FG}=\frac{18}{42}=\frac{3}{7}[/tex]

Thus, ΔUVW ∼ ΔFGH by SAS rule of similarity.

Learn more about Similarity of triangle here :

https://brainly.com/question/14285697

#SPJ2

Answer:

£837.5

Step-by-step explanation:

Cost of slabs =  £16.75 / m²

Ordered amount = 50 m²

Total cost:

Total cost of slabs is  £837.5

Answer:16

Step-by-step explanation:

Given: 15% of 60 is 9.

so 9 kids are 15 year old.

and 1 other kid is 16 year old.

Thus, there are total of (15+1) kids that are either 15 or 16 year old. you can also draw venn diagram to find that.

Answer:

d) r = -65.

Step-by-step explanation:

The absolute value of r represents the relationship strength and the sign represents the relationship direction

Also if the relationship is nearest to 1 then it would be termed as positive correlated and if the relationship is nearest to -1 then it would be termed as negative correlated

Therefore based on the given options, the last option is correct

Answer:

(C) Maria's elevation increased between 9:00 and 12:00

Step-by-step explanation:

Looking at the graph, we can test each statement.

For A, it says Maria's elevation remained constant for 2 hours. Looking at the graph, we can see that it remained constant for just one hour, so this is eliminated.

For B, Maria's elevation decreased between 1:00 and 3:00, we can see that while x is between 1:00 and 3:00, the y is decreasing, meaning this statement is false - this is eliminated.

For C, Maria's elevation increased between 9:00 and 12:00, we can see that while x is between 9:00 and 12:00, the graph is increasing - which means this is correct.

For D, Maria spent more time decreasing her elevation than increasing, we can count how many hours were spent doing each. Comparing the x-axis, we can see that Maria spent 5 hours increasing and 3 hours decreasing, meaning that Maria spent more time INCREASING than decreasing, making this statement false.

Hope this helped!

Answer: C A B C D

Step-by-step explanation: I HAVE NONE IM JUST SMART

I THINK?