For each of the following research scenarios, decide whether the design uses a related sample. If the design uses a related sample, identify whether it uses matched subjects or repeated measures.
1. You are interested in a potential treatment for compulsive hoarding. You treat a group of 50 compulsive hoarders and compare their scores on the Hoarding Severity scale before and after the treatment. You want to see if the treatment will lead to lower hoarding scores. The design described__________a, b, or c________.
a. uses a related sample - repeated measures
b. uses a related sample - matched subjects
c. does not use a related sample
2. John Caccioppo was interested in possible mechanisms by which loneliness may have deterious effects of health. He compared the sleep quality of a random sample to lonely people to the sleep quality of a random sample of nonlonely people. The design described______a, b, or c_______.
a. does not use a related sample
b. uses a related sample (repeated measures)
c. uses a related sample (matched subjects)

Answers

Answer 1

Answer:1. uses a related sample - repeated measures

2. . does not use a related sample--a

Step-by-step explanation:

Question 1.

step1  A repeated measure design is a design which measures a given sample repeatedly over a given time using different conditions or related measures.

step 2:In the treatment for compulsive hoarding, Here, measures are taken two times ie before and after treatment on the same 50 hoarders which shows a repeated measure, also the design is a within related sample of the same 50 hoarders to give measurement at different conditions  of treatment for  high and low hoarding scores so the design describes  a related sample - repeated measures

Question 2:

step 1 ; An unrelated sample  occurs when Samples being measured do not depend on each other  

Step 2;  1st Sample for comparison by John are random lonely people  and Second Sample are random non lonely people. so the two samples are independent on each other and will give different  measurement based on quality of sleep.   So the design does not use a related sample


Related Questions

A tree diagram is simply a way of representing a sequence of events. True or False.

Answers

Answer:

True.

Step-by-step explanation:

A tree diagram is a diagram used in general mathematics, statistics, and probability to show a sequence of events. This tool is used to calculate the number of possibilities of an event to occur. Commonly, the tool of a tree diagram is used to find the possibility of outcome while flipping a coin. It is a diagram in which connections between the events is shown using the strucure of branching connecting lines.

So, the given statement is true, that is a simple way of showing events in a sequence.

Which rule represents the translation from he pre-image, ABCD, to the image, A’B’C’D’?

Answers

Answer:

Option (4)

Step-by-step explanation:

From the figure attached,

Quadrilateral ABCD has been translated to form an image A'B'C'D' by shifting 'a' units right and 'b' units up.

Let the rule for translation is,

(x, y) → (x + a, y + b)

Coordinates of point A is (-4, 4) and the coordinates of the image A' are (-2, 5).

So, (-4, 4) → [(-4 + 2), (4 + 1)]

Therefore, the translation can be represented by [tex]T_{2, 1}(x, y)[/tex] (shifted 2 units right and 1 unit up).

Option (4) will be the answer.

Answer:

T2,1(x,y)

Step-by-step explanation:

What is the area of a rectangle with a base of 23 feet and a height of 6 feet

Answers

Answer:

Step-by-step explanation:

Area of rectangle = l × b

= 23 × 6

= 138 feet

hope this helps

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Find the SURFACE AREA of this composite solid.

Answers

FINDING THE SURFACE AREA OF A COMPOSITE SOLID

About "Finding the surface area of a composite solid"

Finding the surface area of a composite solid :

A composite solid is made up of two or more solid figures.

To find the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Finding the surface area of a composite solid - Examples

Example 1 :  

Daniel built the birdhouse shown below. What was the surface area of the birdhouse before the hole was drilled ?

Solution :  

Step 1 :

Identify the important information.

• The top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

• The bottom is a rectangular prism with h = 18 cm. The base is a 30 cm by 24 cm rectangle.

 

• One face of each prism is not on the surface of the figure.

Step 2 :  

Find the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

Step 3 :  

Find the area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Step 4 :  

Find the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Step 5 :  

Add. Then subtract twice the areas of the parts not on the surface.

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

 

The surface area before the hole was drilled was 3,720 sq.cm.

The surface area before the hole was drilled was; 3,720 sq.cm.

What is composite solid?

A composite solid is made up of two or more solid figures.

To determine the surface area of a composite solid, find the surface area of each figure. Subtract any area not on the surface.

Given that the top is a triangular prism with h = 24 cm. The base is a triangle with height 8 cm and base 30 cm.

The bottom is a rectangular prism with h = 18 cm.

The base is a 30 cm x 24 cm rectangle.

One face of each prism is not on the surface of the figure.

Then the surface area of each prism.

Add the areas. Subtract the areas of the parts not on the surface.

The area of the triangular prism.

Perimeter  =  17 + 17 + 30  =  64 cm

Base area  =  (1/2)(30)(8)  =  120 sq.cm

Surface area  =  Ph + 2B

Surface area  =  64(24) + 2(120)

Surface area  =  1,776 sq.cm

Now the area of the rectangular prism.

Perimeter  =  2(30) + 2(24)  =  108 cm

Base area  =  30(24)  =  720 sq.cm

Surface area  =  Ph + 2B

Surface area  =  108(18) + 2(720)

Surface area  =  3,384 sq.cm

Now,

Surface area  =  1,776 + 3,384 - 2(720)  =  3,720 sq.cm

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Lily paints 3 trees for a wall mural. The middle tree is 2 1/2 ft tall. The tree on the left is 3/4 as tall as the middle tree. The tree on the right is 1 3/4 times as tall as the middle tree. How tall is each tree?

Answers

Answer:

middle is 2.5 ft

right is 4375 ft

left is 1875 ft

Step-by-step explanation:

(12 /`15) ÷ (25/ 16) =

Answers

Answer:

[tex]\frac{64}{125}[/tex]

Step-by-step explanation:

[tex]\frac{12}{15} \div \frac{25}{16}[/tex]

[tex]\frac{12}{15} \times \frac{16}{25}[/tex]

[tex]\frac{12 \times 16}{15 \times 25}[/tex]

[tex]\frac{192}{375}[/tex]

[tex]\frac{64}{125}=0.512[/tex]

Answer:

[tex]\frac{64}{125}[/tex]

Step-by-step explanation:

=> [tex]\frac{12}{15} / \frac{25}{16}[/tex]

Changing the division sign into multiplication and inverting the term after the sign.

=> [tex]\frac{12}{15} * \frac{16}{25}[/tex]

=> [tex]\frac{12*16}{15*25}[/tex]

=> [tex]\frac{192}{375}[/tex]

=> [tex]\frac{64}{125}[/tex]

This is the required form.

Arsha predicted that she would sell 225 magnets. She actually sold 240 magnets. What are the values of a and b in the table below? Percent Error Item Approximate value Exact value Error Absolute error Ratio Percent error Magnets 225 240 a b a = Negative StartFraction 15 over 225 EndFraction; b = negative 6.7 percent a = Negative StartFraction 15 over 240 EndFraction; b = negative 6.25 percent a = StartFraction 15 over 240 EndFraction; b = 6.25 percent a = StartFraction 15 over 225 EndFraction; b = 6.7 percent

Answers

Answer:cStep-by-step Explanation:PLZS MARK BRAINLIEST PLZS PLZSMARK BRAINLIEST

Answer:

c

Step-by-step explanation:

Mr. Azu invested an amount at rate of 12% per annum and invested another amount, 580 ghana cedis more than the first at 14% . if Mr. Azu had total accumulated amount of 2,358.60, how much was his total investment? ​

Answers

Answer:

  2082.12 was the total invested

Step-by-step explanation:

Let x represent the amount invested at 14%. Then the amount invested at 12% was (x-580). The total accumulated amount was ...

  112%(x -580) +114%(x) = 2358.60

  2.26x -649.60 = 2358.60

  2.26x = 3008.20 . . . add 649.60

  x = 1331.06 . . . . . . divide by 2.26

  x -580 = 751.06

The total invested was 1331.06 +751.06 = 2082.12 cedis.

__

Check

The investment at 12% was 751.06, so the accumulated amount of that investment was 751.06×1.12 = 841.19.

The investment at 14% was 1331.06, so the accumulated amount of that investment as 1331.06×1.14 = 1517.41.

The accumulated total amount was 841.19 +1517.41 = 2358.60.

Please help. I keep getting this problem wrong . I need help please . I’ll mark you as brainliest if correct . Only answer if you know. Thank you

Answers

Answer:

The real number 'a' = 32

The real number 'b' = 0

Step-by-step explanation:

Product of a number of a number and its conjugate = a + bi

The number is = -4 + 4i

Conjugate of this number is = -4 - 4i

Product of the number and it's conjugate

= (-4 + 4i)(-4 - 4i)

= -4(-4 - 4i) + 4i(-4 - 4i) [By distributive property]

= 16 + 16i - 16i - 16i²

= 16 - 16(-1)

= 16 + 16

= 32

a + bi = 32 + (0)i

By comparing both the sides,

a = 32

b = 0

The sales price of a single family house in Charlotte is normally distributed with mean $210,000 and standard deviation $35,000. 1. A random sample of 49 single-family houses in Charlotte is selected. Let X ¯ be the mean sales price of the sample. What is the mean of X ¯?

Answers

Answer:

E(X ¯)=210,000.

Step-by-step explanation:

A sampling distribution for samples of size n=49 from a population with means μ=210,000 and standard deviation σ=35,000, has the following means anda standard deviation:

[tex]\mu_s=\mu=210,000\\\\\sigma_s=\sigma/\sqrt{n}=35,000/\sqrt{49}=35,000/7=5,000[/tex]

If X ¯ is the mean sales price of the sample, it will have a mean value of E(X ¯)=210,000.

A rectangle has a length of 60 in and a width of 8 in. Given a scale factor of 4in:5ft. What is the area of the rectangle?

Answers

Answer:

750ft²

Step-by-step explanation:

Area of rectangle = L*B

Before we find the area of the given rectangle, we need to convert the dimensions using the given scale.

Thus, dimensions of the given rectangle using the scale factor of 4in:5ft would be:

==> Length = 60in = (60*5)/4 = 75ft

Breadth or Width = 8in = (8*5)/4 = 10ft

Therefore, area of rectangle = L * B

= 75ft * 10ft

= 750 ft²

Area of rectangle = 750ft²

Solve the inequality.
-3(x-1) > -3x - 2​

Answers

Answer:

all real x

Step-by-step explanation:

-3(x-1) > -3x - 2​

Distribute

-3x +3> -3x -2

Add 3x to each side

-3x +3 +3x > -3x+3x - 2​

3 > -2

This is always true so the inequality is true for all x

1/x=1/2 / 4/5
Solve for x.
X =

Answers

Answer:

1/x = 1/2÷4/5

1/x=1/2 x 5/4

1/x=5/8

5x=8

x=1.6

1. Ryan budgets $35 a week for lunch for 5 days. What
is his average lunch expense each day?

Answers

Answer: $7

Step-by-step explanation:

35/ 5 = 7

Answer:

$7

Step-by-step explanation:

Bc/ 35/5=7

Find the constant of variation for the relation and use it to write and solve the equation.

if y varies directly as x and as the square of z, and y=25/9 when x=5 and z=1, find y when x=1 and z=4

Answers

Answer:

When x = 1 and z = 4,   [tex]y=\frac{80}{9}[/tex]

Step-by-step explanation:

The variation described in the problem can be written using a constant of proportionality "b" as:

[tex]y=b\,\,x\,\,z^2[/tex]

The other piece of information is that when x = 5 and z = 1, then y gives 25/9. So we use this info to find the constant "b":

[tex]y=b\,\,x\,\,z^2\\\frac{25}{9} =b\,\,(5)\,\,(1)^2\\\frac{25}{9} =b\,\,(5)\\b=\frac{5}{9}[/tex]

Knowing this constant, we can find the value of y when x=1 and z=4 as:

[tex]y=b\,\,x\,\,z^2\\y=\frac{5}{9} \,\,x\,\,z^2\\y=\frac{5}{9} \,\,(1)\,\,(4)^2\\y=\frac{5*16}{9}\\y=\frac{80}{9}[/tex]

A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars form this company have an average gas mileage of 25.5 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?

Answers

Answer:

[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]  

Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense

Step-by-step explanation:

Information given

[tex]\bar X=25.5[/tex] represent the sample mean

[tex]s=1[/tex] represent the sample standard deviation

[tex]n=8[/tex] sample size  

[tex]\mu_o =26[/tex] represent the value to verify

[tex]\alpha=0.06[/tex] represent the significance level  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Hypothesis to est

We want to test if the true mean is at least 26 mpg, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 25.5[/tex]  

Alternative hypothesis:[tex]\mu < 25.5[/tex]  

The statistic for this case is given by;

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we got:

[tex]t=\frac{25.5-26}{\frac{1}{\sqrt{8}}}=-1.414[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=8-1=7[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(7)}<-1.414)=0.100[/tex]  

Since the p value is higher than the significance level of 0.06 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 25.5 and then the claim makes sense

Which graph represents the solution set for
-X2 + 8x - 12 > 0?

Answers

Answer:
Here is how it should be graphed.

Answer:

B

Step-by-step explanation:

Please answer this correctly I have to finish this today as this is my deadline

Answers

Answer:

r = 1.499619733762 m  There is no such thing a quarter radius!

C = 9.4223886775301 m

A = 7.065 m^2

Step-by-step explanation:

Calculate r and C | Given A

Given the area of a circle calculate the radius and circumference

r = √(A / π)

C = 2πr

Agenda:

r = radius

C = circumference

A = area

π = pi = 3.1415926535898

√ = square root

What’s the correct answer for this question?

Answers

Answer:

B:

Step-by-step explanation:

Measure of ARC AFB is 180°

Why?

This is because AB is a diameter.

B is the correct answer

Which expression is equivalent to 4+2(1+3x)

Answers

Answer:

I'm glad you asked!

Step-by-step explanation:

OK,let's simplify the number for a equivalent expression.

[tex]4+2(1+3x)[/tex]

Distribute:

[tex]=4+(2)(1)+(2)(3x)[/tex]

[tex]= 4+2+6x[/tex]

Combine Like Terms:

[tex]=4+2+6x[/tex]

[tex]=(6x)+(4+2)[/tex]

[tex]=6x+6[/tex]

The Final Answer is : [tex]6x+6[/tex]

The expression that is equivalent to 4+2(1+3x) is 6x+6.

What is an Algebraic expression?

Mathematical expressions that are made up of constants, variables, and coefficients that are combined using algebraic operations such as multiplication, addition, subtraction, and division are called Algebraic expressions.

How do simplify the algebraic expression?

Given, 4+2(1+3x)

Firstly distribute 2(1+3x) to get 2+6x then,

4+2(1+3x)

=4+2+6x

=6x+6

Thus, 4+2(1+3x)=6x+6

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work out the weekly mean number of 50 kg bags of flour used in these 5 weeks

Kim is a baker, she buys flour in 50kg bags.
weeks 1 2 3 4

NO of bags of flour 7 14 8 13

Kim will make 2400 loaves in week 5
Each of these loaves will need 250g of lour

Kim works out weekly mean number of 50kg bags of flour used in these 5 weeks.
she will use the figure for future orders.

Answers

Answer:

Weekly Mean Number of 50-kg bags =10.8 bags

Step-by-step explanation:

In Week 1, Kim uses 7  50kg bags of flour

In Week 2, Kim uses 14  50kg bags of flour

In Week 3, Kim uses 8 X 50kg bags of flour

In Week 4, Kim uses 13 X 50kg bags of flour

In Week 5, Kim will make 2400 loaves.

Each of these loaves will need 250g of flour.

Total Mass of flour that will be used =2400 X 250=600,000 grams

[tex]600,000$ grams=600,000 \div 1000$ kg =600kg\\Number of 50-kg bags =600 \div$ 50 =12 bags[/tex]

In Week 5, Kim will use 12 bags.

Therefore:

Weekly Mean number of 50kg bags of flour used in these 5 weeks.

[tex]=\dfrac{7+14+8+13+12}{5}\\\\ =\dfrac{54}{5}\\\\=10.8 \\ \approx 11$ bags[/tex]

Solve the inequality 2(4x-3)>-3(3x)+5

Answers

Answer:

48x>+2

Step-by-step explanation:

Some scientists believe there is a limit to how long humans can live. One supporting argument is that during the past​ century, life expectancy from age 65 has increased more slowly than life expectancy from​ birth, so eventually these two will be​ equal, at which​ point, according to these​ scientists, life expectancy should increase no further. In​ 1900, life expectancy at birth was 45 ​years, and life expectancy at age 65 was 75 yr. In​ 2010, these figures had risen to 78.7 and 84.5​, respectively. In both​ cases, the increase in life expectancy has been linear. Using these assumptions and the data​ given, find the maximum life expectancy for humans.

Answers

Answer:

The maximum life expectancy for humans is approximately 87 years.

Step-by-step explanation:

We have to calculate the point in which both linear functions (Life expectancy from birth and Life expectancy from age 65) intersect, as this is the point in which is estimated to be the maximum life expectancy for humans.

NOTE: to simplify we will consider t=0 to the year 1900, so year 2010 becames t=(2010-1900)=110.

The linear function for Life expectancy from birth can be calculated as:

[tex]t=0\rightarrow y=45\\\\t=110\rightarrow y=78.7\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{78.7-45}{110-0}=\dfrac{33.7}{110}=0.3064\\\\\\y=0.3064t+45[/tex]

The linear function for Life expectancy from age 65 can be calculated as:

[tex]t=0\rightarrow y=75\\\\t=110\rightarrow y=84.5\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{84.5-75}{110-0}=\dfrac{9.5}{110}=0.0864\\\\\\y=0.0864t+75[/tex]

Then, the time t where both functions intersect is:

[tex]0.3064t+45=0.0864t+75\\\\(0.3064-0.0864)t=75-45\\\\0.22t=30\\\\t=30/0.22\\\\t=136.36[/tex]

The time t=136.36 corresponds to the year 1900+136.36=2036.36.

Now, we can calculate with any of both functions the maximum life expectancy:

[tex]y=0.0864(136.36)+75\\\\y=11.78+75\\\\y=86.78\approx87[/tex]

The maximum life expectancy for humans is approximately 87 years.

Find the circumference of each circle, use 3.14 for . Include units and round to the nearest tenth. Show work





7. The circumference of a circle is 34.54 cm. What is the diameter and radius of the circle? (Show work)




8. What is the circumference of a circle in terms of , if it has a radius of 3.5 in?
(in terms of means do not substitute 3.14 for pi, leave the symbol in the final answer)

Answers

Answer:

Answer:-

a) The circumference of the circle  C = 21.98 m

b) The circumference of the circle  C = 37.68 ft

c)  The circumference of the circle  C = 40.82 km

d) The radius of the circle = r = 11 c.m

    The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m

e) The circumference of the circle = 21.98 inches

  Step-by-step explanation:

a)  In First diagram

Given radius of the circle 'r' = 7.1 m

  The circumference of the circle  C = 2πr

                                                            C = 2 (3.14) (7.1)

                                                            C = 21.98 m

The circumference of the circle  C = 21.98 m

b) In second diagram

Given diameter of the circle 'd' = 12 ft

   The circumference of the circle  C = 2πr

                                                            C = π(2 r)

                                       Diameter = 2 X radius

                                               d = 2 r

 The circumference of the circle  C = πd

                                                          C = 3.14 ×12

The circumference of the circle  C = 37.68 ft

c)

Given diameter of the circle 'd' = 13 km

   The circumference of the circle  C = 2πr

                                                            C = π(2 r)

                                       Diameter = 2 X radius

                                               d = 2 r

 The circumference of the circle  C = πd

                                                          C = 3.14 ×13

 The circumference of the circle  C = 40.82 km

   

7) The circumference of the circle  C = 2πr

    Given The circumference of a circle is 34.54 cm

          Now       2πr = 34.54

                   2(3.14) r = 34.54

                           [tex]r = \frac{34.54}{3.14} = 11[/tex]

   The radius of the circle = r = 11 c.m

    The Diameter of the circle 'd' = 2(r) = 2(11) =22 c.m

8) Given radius of the circle 'r' = 3.5 inches

   The circumference of the circle  C = 2πr

                                                            C = 2 (3.14) (3.5)

                                                            C = 21.98

  The circumference of the circle = 21.98 inches

 

Help meee please 15 points!!

Answers

Answer:

B.

Step-by-step explanation:

B.

- 9 ≤ - 3x - 6 ≤ 6

1 part.

- 9  +6 ≤ - 3x - 6 +6

- 3/(- 3) ≤ - 3x/(- 3)

1 ≥ x

2d part

- 3x - 6 +6≤ 6 + 6

- 3x ≤ 12

- 3x/(-3) ≥ 12/(-3)

x ≥ - 4

x ≥ - 4 and x≤ 1

round 0.004198223 to 3 significant figures

I will give brainliest

Answers

Answer:

0.00420 is the answer

Step-by-step explanation:

The definition of sig figs is each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.

The rounding number of 0.004198223 to 3 significant figures is 0.0042

Here,

The number is 0.004198223.

We have to find,  0.004198223 to 3 significant figures.

What is Rounding number?

Rounding means making a number simpler but keeping its value close to what it was.

Here,

The number is 0.004198223.

To find 3 significant figures,

We round a number to three significant figures in the same way that we would round to three decimal places.

Then, We count from the first non-zero digit for three digits. We then round the last digit.

Here, the digit is 9 then it will be round.

We get, the number is;

0.0042

We fill in any remaining places to the right of the decimal point with zeros.

So, The rounding number of 0.004198223 to 3 significant figures is 0.00420

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A standard​ 52-card deck has four​ 13-card suits:​ diamonds, hearts,​ clubs, and spades. The diamonds and hearts are​ red, and the clubs and spades are black. Each​ 13-card suit contains cards numbered from 2 to​ 10, a​ jack, a​ queen, a​ king, and an ace. An experiment consists of drawing 1 card from the standard deck. Find the probability of drawing a black jack of diamonds.

Answers

Answer:

0

Step-by-step explanation:

In a suit of 52 cards

The Red Cards are: diamonds and heartsThe Black cards are: clubs and spades

The experiment consists of drawing 1 card from the standard deck.

Since diamonds are red, there is no black jack of diamonds.

Therefore:

P(drawing a black jack of diamonds)

[tex]=\dfrac{0}{52}\\\\ =0[/tex]

Answers:

In photo below

Explanation:

I got it correct in my test :)

Suppose that a large mixing tank initially holds 100 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 4 lb/gal, determine a differential equation (in lb/min) for the amount of salt A(t) (in lb) in the tank at time t > 0. (Use A for A(t).)

Answers

Answer:

dA/dt = 12 - 2A/(100 + t)

Step-by-step explanation:

The differential equation of this problem is;

dA/dt = R_in - R_out

Where;

R_in is the rate at which salt enters

R_out is the rate at which salt exits

R_in = (concentration of salt in inflow) × (input rate of brine)

We are given;

Concentration of salt in inflow = 4 lb/gal

Input rate of brine = 3 gal/min

Thus;

R_in = 4 × 3 = 12 lb/min

Due to the fact that solution is pumped out at a slower rate, thus it is accumulating at the rate of (3 - 2)gal/min = 1 gal/min

So, after t minutes, there will be (100 + t) gallons in the tank

Therefore;

R_out = (concentration of salt in outflow) × (output rate of brine)

R_out = [A(t)/(100 + t)]lb/gal × 2 gal/min

R_out = 2A(t)/(100 + t) lb/min

So, we substitute the values of R_in and R_out into the Differential equation to get;

dA/dt = 12 - 2A(t)/(100 + t)

Since we are to use A foe A(t), thus the Differential equation is now;

dA/dt = 12 - 2A/(100 + t)

Triangle JKL was dilated using the rule D Subscript M, one-third. The image, triangle J'K'L', is the result of the dilation. Point M is the center of dilation. Triangle J K L is dilated to form smaller triangle J prime K prime L prime. The length of M L prime is 2.5. What is L'L? 5 units 7.5 units 10 units 12.5 units

Answers

Answer: the answer is A 5 units

The length of L'L in the dilated figure is 5 units.

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the increase or decrease in size of a figure.

Triangle JKL was dilated by 1/3 with M as the center of dilation to form J'K'L'.

Given that ML' = 2.5 units, hence:

L'L = (2.5 * 3) - 2.5 = 5 units

The length of L'L in the dilated figure is 5 units.

Find out more on transformation at: https://brainly.com/question/1620969

what is the solution to this problem

x-17= -5

Answers

Hi

X-17 = -5

X = -5+17

X = 12

Answer:

Step-by-step explanation:

I'm pretty sure that you have to add 17 on both sides to keep the final number, not negative.  

So like:

x-17=-5

+17   +17

x-0=12            

and because 0 is nothing really, x=12

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