A researcher conducted a study investigating the effect of computer screen time on a person’s amount of REM sleep. The researcher randomly assigned 100 people into four groups. The first group was given 2 hours of computer screen time each day, the second group was given 4 hours each day, the third group was given 6 hours each day, and the fourth group was given 8 hours each day. The study was conducted for one week, and the amount of REM sleep for each person was measured. What is the explanatory variable in the study?

The correct answer is D. All natural numbers are integers, as natural numbers are part of the larger set of integers which includes all whole numbers both positive, negative, and zero.

Out of the options given, the true statement is: D. All natural numbers are integers. This is because natural numbers include all positive counting numbers from 1 upwards, which are also part of the integers set that includes all whole numbers both positive and negative, as well as zero.

Option A is incorrect because not all real numbers are rational. Real numbers include both rational numbers (which can be written as fractions of integers) and irrational numbers (which can't be expressed as fractions of integers).

Option B is incorrect because while all whole numbers are natural numbers, the set of whole numbers also includes 0 which is not considered a natural number.

Option C is incorrect since all integers are indeed whole numbers, but not all whole numbers are integers as integers also include negative numbers.

In addition to the answer, the commutative property of addition, which states that A+B=B+A was mentioned. This property holds true for the addition of ordinary numbers, such as 2 + 3 is the same as 3 + 2.

Answer:

Part 3) [tex]SA=288\ cm^2[/tex]

Part 4) [tex]64\ cm^2[/tex]

Step-by-step explanation:

Part 3) Calculate the total surface area of three 4 cm cubes

we know that

The surface area of a cube is equal to the area of its six square faces

[tex]SA=6b^2[/tex]

so

The surface area of three cubes is equal to the area of its 18 square faces

[tex]SA=18b^2[/tex]

where

b is the length side of the square face

In this problem

[tex]b=4\ cm[/tex]

so

The surface area of three cubes is

[tex]SA=18b^2[/tex]

substitute the given value

[tex]SA=18(4)^2[/tex]

[tex]SA=288\ cm^2[/tex]

Part 4) How much surface area would be lost if you glued three 4-cm cubes together to make a rod that is three cubes long and one cube wide?

In this case the total surface area of the three glued 4-cm cubes is equal to the area  of  its 14 square faces

so

The surface area lost is equal to

[tex]18b^2-14b^2=4b^2[/tex]

substitute

[tex]4(4)^2=64\ cm^2[/tex]

Gluing three 4-cm cubes together to form a rod results in a loss of 64 cm²of surface area because the areas of the glued faces are no longer exposed.

Each individual cube has 6 faces, so the surface area of one cube is 6 times the area of one face. With a side length of 4 cm, the area of one face is 4 cm  imes 4 cm = 16 cm². Thus, the total surface area for one cube is 6  imes 16 cm²= 96 cm². For three separate cubes, this would be 3  imes 96 cm² = 288 cm².

When the three cubes are glued together side by side to form a rod, they share faces. Each glue contact removes two faces worth of area (one from each cube). As there are two glue contacts, a total of 4 faces are lost. Therefore, the lost surface area is 4  imes 16 cm2 = 64 cm².

The original total surface area was 288 cm², so the new surface area after gluing is 288 cm² - 64 cm² = 224 cm². Hence, gluing the cubes together results in a loss of 64 cm² of surface area.

Answer:

4 is by SAS Postulate

5 is Definition of a Median

Step-by-step explanation:

hope this is right

Answer:

The total area of the farm land is  2520 sq. m

Step-by-step explanation:

Let us assume the total area of the farm land  = P sq. m

Now, two thirds of the area of a farm land was covered by wheat fields.

So, the area covered in Wheat field = [tex]\frac{2}{3}  \times P = (\frac{2}{3})P[/tex]

The area left which is not covered in wheat

= Total land - Land covered  in Wheat  

= [tex]P - (\frac{2}{3}) P =  (\frac{1}{3})P[/tex]

Also, the half of the remaining land is covered by pound.

So, the area covered in pound  = [tex]\frac{1}{2}  \times (\frac{P}{3} )  = (\frac{P}{6} )[/tex]

The other half is empty garden.

⇒The area empty garden  =   [tex]\frac{1}{2}  \times (\frac{P}{3} )  = (\frac{P}{6} )[/tex]

Also, the area of the garden = 420 sq. m

⇒[tex](\frac{P}{6})  =  420\\\implies  P = 6 \times 420 =  2520[/tex]

or, P  = 2520 sq. m

Hence, the total area of the farm land is  2520 sq. m

Answer:

y-y/x-x

1-7/5-9

= -6/-4

= 3/2

therefore, the slope is 3/2

Answer:

I m not an expert in maths but I m sure it is Option D

Final answer:

The midpoint of a segment can be found by averaging the x-coordinates and y-coordinates of the endpoints, with the formula M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2) representing the midpoint's coordinates.

Explanation:

The formula for finding the midpoint of a segment involves calculating the average of the x-coordinates and the average of the y-coordinates of the two endpoints of the segment.

If we have two points, A(x₁, y₁) and B(x₂, y₂), the coordinates of the midpoint M will be calculated as follows:

Thus, the coordinates of the midpoint M will be (Mx, My). This formula is essential when dealing with problems involving geometry, coordinate systems, or finding the center point between two given locations on a line segment.

She sold 98 small cups and 57 large cups

Step-by-step explanation:

Ashley had a summer lemonade stand

We need to find how many cups of each type she sold

Assume that Ashley sold x small cups and y large cups of lemonade

∵ Ashley sold x small cups of lemonade

∵ She sold y large cups of lemonade

∵ Ashley sold a total of 155 cups

∴ x + y = 155 ⇒ (1)

∵ The price of the small cup = $1.25

∵ The price of the large cup = $2.5

∵ The price of the all cups = $265

- Multiply x by 1.25 and y by 2.5 and add the two products,

  then equate the sum by 265

∴ 1.25x + 2.5y = 265 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -2.5 to eliminate y

∵ -2.5x - 2.5 y = -387.5 ⇒ (3)

- Add equations (2) and (3)

∴ -1.25x = -122.5

- Divide both sides by -1.25

∴ x = 98

- Substitute the value of x in equation (1) to find y

∵ 98 + y = 155

- Subtract 98 from both sides

∴ y = 57

She sold 98 small cups and 57 large cups

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Answer:

B

A

Step-by-step explanation:

[tex]f(x) = \left \{ \left \begin{matrix}5x-6,\ x<4\\x^{2}-2,\ 4 \leq x \leq 6\\4x+10,\ x>6 \end{matrix} \right } \right[/tex]

To find f'(x), take the derivative within each interval.  Clearly, it's 5 in the first one, 2x in the second one, and 4 in the third one.  But we need to determine if the derivative exists at the ends of each interval.

For a derivative to exist at a point x=a, the function must be continuous (f(a⁻) = f(a⁺)), and smooth (f'(a⁻) = f'(a⁺)).

Let's look at x=4.  On the left side:

f(4⁻) = 14, f'(4⁻) = 5

On the right side:

f(4⁺) = 14, f'(4⁺) = 8

So the function is continuous, but not smooth.  Therefore, the derivative doesn't exist there.

Let's try again with x=6.  On the left side:

f(6) = 34, f'(6) = 12

On the right side:

f(6⁺) = 34, f'(6⁺) = 4

Again, the function is continuous, but not smooth, so the derivative doesn't exist there either.

Therefore, f'(x) is:

[tex]f'(x) = \left \{ \left \begin{matrix}5,\ x<4\\2x,\ 4<x<6\\4,\ x>6 \end{matrix} \right } \right\ Domain:\ All\ real\ numbers,\ x\neq 4,6[/tex]

When we graph f(x) = (4x² − 1) / (x² − 9), we see f(x) has a horizontal tangent line at x=0.

desmos.com/calculator/6y3r1ju7jx

Two years ago, Sally had 5,000 dogs in her dog shelter. Now she has 24,575 dogs. The rate of change is 391.5 % increase

Solution:

Given that Two years ago, Sally had 5,000 dogs in her dog shelter

Now she has 24,575 dogs

To find: rate of change

A rate of change is a rate that describes how one quantity changes in relation to another quantity

[tex]\text {rate of change }=\frac{\text { new value }-\text {original value}}{\text {original value}} \times 100[/tex]

[tex]\begin{array}{l}{\text { rate of change }=\frac{24,575-5000}{5000} \times 100} \\\\ {\text { rate of change }=\frac{19575}{5000} \times 100=391.5}\end{array}[/tex]

Thus the rate of change is 391.5 % increase

Answer:

I think it's 22.2%

Step-by-step explanation:

There's 9 shirts in all and there's only 2 red shirts out of the 9. And 22.2% is the percentage of 2/9

Answer: 2 and 7/12

Step-by-step explanation: To subtract 4 - 1 and 5/12, first subtract the fractions. Since 4 has no fraction, imagine the fraction 0/12.

Notice however that we can't subtract 0/12 - 5/12.

So, let's rewrite 4 and 0/12 as 3 + 1 and 0/12 or 3 + 12/12 by changing 1 and 0/12 into an improper fraction.

Now we have 3 and 12/12 - 1 and 5/12.

Now we can subtract our fractions 12/12 - 5/12 and we get 7/12. Next we subtract our whole numbers 4 - 1 to get 3.

So 5 - 1 and 5/12 is 2 and 7/12.

Answer:

6/10

Step-by-step explanation:

Answer:

9/15 ur welcome!

Step-by-step explanation:

Answer:

2nd Option i.e M is the correct name of a plane.

Step-by-step explanation:

A plane is a flat surface which extends out in all direction without ending.

Just imagine the plane like taking a piece of paper except all the sides continue out forever and ever without ending.

For example, we have a plane as shown in attached figure a below. It extends out forever and ever without an ending. You must remember that planes do have infinite amount of points and lines on them.

Here, we identify point G, as shown in figure a. We can also indicate the line as well on this plane, and can put some points on this line, like V, D and Q.

There are several ways to name a plane. One way, we need at least three or more pints to name a plane. The only rule is that, those points you identify on the plane, cannot make a straight line. If they do, you cannot label the plane as those points.

So, lets pick three points that cannot make a straight line on a plane. As D, V and G cannot make a straight line as shown in figure a. So, DVG is one of the correct names of this plane. Since, order of points do not matter. So, DGQ can also be one of the correct names of this plane. Please remember, VDQ can not be the name of this plane, as these points make a straight line.

Now, planes could just be named with just a letter. Take this letter M written on a plane, as shown in figure a, but it doesn't have a point attach to it, meaning this letter is identifying the plane. Hence, we could just name this plane as just plane m.

So, from this entire discussion, and some rules and regulations necessary to identify a plane, we can safely say that 2nd Option i.e. M is the correct name of a plane.

Keywords: line, plane, point

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Answer:

A  increases slowly

B  decreases quickly

C  increases quickly

D  decreases slowly

Step-by-step explanation:

In the graph, the changes in the values of y for the values of x, are shown below.

A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used

In the given graph,

In interval A, the value of y increases slowly.

In interval B, the value of y decreases  quickly.

In interval C, the value of y increases quickly.

And in interval D, the value of y decreases slowly.

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Answer:

x = 6 ± i√23

Step-by-step explanation:

x² − 12x + 59 = 0

Use quadratic formula.

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ -(-12) ± √((-12)² − 4(1)(59)) ] / 2(1)

x = [ 12 ± √(144 − 236) ] / 2

x = (12 ± √-92) / 2

x = (12 ± 2i√23) / 2

x = 6 ± i√23

The values of x are 1.2 or 10.8.

The given equation is x²-12x+59=0.

We need to find the value of x.

The standard form of a quadratic equation is ax²+bx+c=0.

Use quadratic formula [tex]x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a}[/tex]

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

Now, a=1, b=-12 and c=59

[tex]x=\frac{12\pm\sqrt{(-12)^{2} -4\times 1\times 59} }{2\times 1}[/tex]

⇒x=1.2 or 10.8

Therefore, the values of x are 1.2 or 10.8.

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Answer:

It would have no last term

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

For $6 and 4 oranges the unit price per orange is $1.50,  and with $15 for 10 oranges the unit price per orange is also $1.50.

Answer: 18 whole times. Or if you want a specific answer, 18.75 times.

Step-by-step explanation: To calculate this, just do a bit of long division. 225 divided by 12 is 18.75. If you need a whole number, however, you round the decimal down to 18.

Hope this helped. ;)

Answer:

The total number of codes which can be assigned is, 55440 .

Step-by-step explanation:

According to the question, the home alarm system randomly assigns a five-character code for each customer.The code will not repeat a character and there are 11 distinct characters.

So, the total number of codes that can be randomly assigned is given by,

[tex]^{11}{P}_{5}[/tex]

= [tex]\frac {11!}{6!}[/tex]

= [tex]11 \times 10 \times 9 \times 8 \times 7[/tex]

= 55440

Answer:

[tex]y=2\text{cos}((\frac{2\pi}{3})t)[/tex]

Step-by-step explanation:

We have been given that an object oscillates 4 feet from its minimum height to its maximum height. The object is back at the maximum height every 3 seconds. We are asked to find the cosine function that can be used to model the height of the object.

We know that standard form of cosine function is [tex]y = A\cdot \text{cos}(Bt-C)+D[/tex], where,

|A| = Amplitude,

Period = [tex]\frac{2\pi}{|B|}[/tex],

C = Phase shift,

D = Vertical shift.

Since distance between maximum and minimum is 4, therefore, amplitude will be half of it, that is, [tex]A = 2[/tex].

Since objects gets back to its maximum value in every 3 seconds, therefore, period of the function is 3 seconds. We know that period is given by [tex]\frac{2\pi}{|B|}[/tex], therefore, we can write [tex]\frac{2\pi}{|B|}=3[/tex], therefore, [tex]B = \frac{2\pi}{3}[/tex].

We haven't been given any information about phase and mid-line, we can assume the values of C and D to be zero .

Therefore, our function required function would be [tex]y=2\text{cos}((\frac{2\pi}{3})t)[/tex].

Answer:

$10.52

Step-by-step explanation:

(1137.45 x 14.7%) / 12 - (1137.45 x 3.6%) /12 = 10.52

The amount of interest that your friend save compared to the credit card at the end of the first month is $10.5.

First step

Interest at 14.7% APR

Interest=(1137.45 x 14.7%) / 12

Interest=$13.9

Interest at 3.6% APR

Interest=(1137.45 x 3.6%) /12

Interest = $3.4

Second step

Interest saved=$13.9-$3.4

Interest saved=$10.5

Therefore the amount of interest that your friend save compared to the credit card at the end of the first month is $10.5.

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Yes it is. You would just plug in 10 for every instance of x so...

g(10) = 3(10)+4 = 30+4 = 34

answer: 34

Answer: g(10) = 34

Explanation: In this problem we are given the function g(x) = 3x + 4 and we are asked to find g(10).

In other words, if we put an x into our function, we get a 3x + 4 out so we are really being asked what happens if we put a 10 into the function.

Well if we put a 10 into the function, that's g(10) = and we get a 3(10) + 4 out.

Now all we have to do is simplify on the right side. 3 x 10 is 30 and 30 + 4 is 34. So g(10) = 34.

Q and S are parallel because the  93 degree and 87 degree angles are supplementary angles and when added together equal 180 degrees.

The answer is B.

Answer:

B

Step-by-step explanation:

if you move the angle 87 up to angle 93 on the line q they equall 180 showing you its parallel

Answer:

x = 3 or x = 4

Step-by-step explanation:

Given

x² + 12 = 7x ( subtract 7x from both sides )

x² - 7x + 12 = 0 ← in standard form

(x - 3)(x - 4) = 0 ← in factored form

Equate each factor to zero ( zero product property ) and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

American airlines made a total money of $ 4263

Solution:

Given that,

Cost of 1 first class ticket = $ 53

Cost of 1 coach ticket = $ 21

There were 139 passengers total

30% of the passengers composed of the first class, Which means 30 % of 139 are first class

Number of first class passengers = 30 % of 139

[tex]\rightarrow \frac{30}{100} \times 139 = 41.7[/tex]

Thus approximately 42 passengers are from first class

Number of coach class passengers = 139 - 42 = 97

So we have,

Number of first class passengers = 42

Number of coach class passengers = 97

To find: Total money made by American airlines

We can frame a equation as:

total money = (Number of first class passengers x Cost of 1 first class ticket) + (Number of coach class passengers x Cost of 1 coach ticket)

[tex]\text{ total money } = 42 \times 53 + 97 \times 21\\\\\text{ total money } = 2226 + 2037 = 4263[/tex]

Thus american airlines made a total money of $ 4263

Answer: The bike cost $ 329

Step-by-step explanation:

1. Ist sentence

The local bike shop sells a bike and accessories package for $376.

Let the cost of one bike be $b

Let the cost of the accessories be $a

b + a = 376 .........…...... eqn(1)

2. Second sentence.

If the bike is worth 7 times more than the accessories.

Equation;

b = 7a

3. Substitute b into eqn 1

7a + a = 376

8a = 376

a = 376/8

a= 47

b= 7a = 7× 47 = 329

Therefore The bike cost $ 329

Answer:(1) The distance Soo Lin walks is a function of time = True

(2) The time it takes soo- in to walk a certain distance is a function of distance = False

Step-by-step explanation:

Since the distance walked, e in miles= 3.17t

Where t is time

From the equation,

time t is an independent variable, it does not dependent on distance e

Also

distance e is a dependent variable that depend on time t

Therefore,

Distance e is a function of time t.

While time t is not a function of distance e.

Answer:

x=20, -5

Step-by-step explanation:

x^2-15x-100=0

factor out the trinomial,

(x-20)(x+5)=0

zero property,

x-20=0, x+5=0

x=0+20=20

x=0-5=-5