in a recent study on the effects of sleep and test​ results, volunteers took a math test. the volunteers who had 8 hours of sleep were three times more likely to answer questions correctly on the math test than were​ sleep-deprived volunteers. complete parts a through d.

The probability that a student who can drive is a college student is 0.2771 or 27.7%

It will be sooved using Baye's theorem -

P(college) = P(C) / 1/5 = 0.2

P(high school students) = P(H) = 4/5 = 0.8

P(college drives) = 0.23

P(high school drives) = 0.15

We have to find, probability that a student who drives is a college student.

That is, we have to find P(C/D).

P(C/D) = P(C ∩ S)/P(S)

Since P(C ∩ S) is an independent event.

P(C ∩ S) = P(C) × P(S)

P(C ∩ S) = 0.2 × 0.23

= 0.046

Using bayes's theorem, we will get

P(C/D) = 0.2771 or 27.7%

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Answer:

3/4 x 8 1/2 = 6.375

The segment AB is perpendicular to the segment CD because the two angles it creates are each 90 degrees .

A line is said to be perpendicular to another line if the two lines intersect at a right angle . The segment AB can be called the perpendicular from A to the segment CD . The point B is called the foot of the perpendicular from A to segment CD or simply , the foot of A on CD .If a first line is perpendicular to a second line , then the second line is also perpendicular to the first .

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The volume of water in the sink after x minutes can be represented by a function V(x) = 0.25 x and its domain is 0 ≤ x ≤ 10

After x minutes, the volume of water in the sink will be:

   V = filling rate ⨉ time interval

Information from the problem:

filling rate = 0.25 gallons per minute

time interval = x

Substitute these parameters into the formula:

   V = 0.25 x

The domain of a function is the set of all possible inputs, of which the function is defined.

In this problem, the function is the volume, which is a function of x.

V(x) = 0.25 x

To determine its domain, check the minimum and maximum values of V(x).

When the sink is empty, V = 0.

Then,

V(x) = 0.25 x

  0   = 0.25 x

  x   = 0

When the sink is full, V = 2.5.

Then,

V(x) = 0.25 x

 2.5 = 0.25 x

  x   = 10

Since V(x) has value 0 ≤ V(x) ≤ 2.5, its corresponding input should be  0 ≤ x ≤ 10. This is the domain.

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Here is the completed table:

x       y            y/x

3       30          10 / 1

5       50           10 / 1

7        70           10 / 1

9       90             10 / 1

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s). The sign used to represent ratios are :.

The ratio of y to x : change in value of y / change in the value of x

(50 - 30) / (5 - 3) = 20 / 2 = 10 / 1

(70 - 50) / (7 - 5) = 20 / 2 = 10 / 1

(90 - 70) / (9 - 7) = 20 / 2 = 10 / 1

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Answer:

-5

Step-by-step explanation:

Let's assume the you are moving horizontally along the number line. If you start at -4 and jump to -6, you have made 2 jumps to the left(-4;-5;-6). So halfway between them (the midpoint) is 1 jump (half of 2 jumps).

1 jump to the left of -4.... You land at -5.

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The weight of each bag is 23.25 pounds.

For given question,

Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags.

If all the bags were identical, we need to find the weight of each bag.

Let 'm' be the weight of each bag.

As Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags and all the bags were identical, we get an expression.

8 × m = 187.6

now we solve above expression to find the value of m i.e., to find the weight of each bag.

⇒ 8 × m = 187.6

⇒ m = 187.6 / 8

⇒ m = 23.25 pounds

Therefore, the weight of each bag is 23.25 pounds.

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60-100 bpm and that is the range of a 16 year old heart beat

Answer:

Step-by-step explanation:

Lower limit of range:

H = [tex]\frac{7}{10}[/tex](220-a)

a = 16 [given]

∴ H = [tex]\frac{7}{10}[/tex](220-16)

H = [tex]\frac{7}{10}[/tex](204)

H = [tex]\frac{7}{10}[/tex]×[tex]\frac{204}{1}[/tex]

H = [tex]\frac{1428}{10}[/tex]

H = 142.8

H = 143 beats per minute [as an integer]

The ratios are equivalent

Ratio shows the relationship that exists between values. It shows the proportion of one value in another value.

In other words, ratios says how much of one thing there is compared to another thing.

Therefore,

Ratio of peanuts to raisins in the first version = 3 : 2

divide both numbers by 2

1.5 : 1

Ratio of peanuts to raisins in the second version = 4.5 : 3

divide both numbers by 3

1.5 : 1

The ratios of the first and second trail mix are equivalent because they are both 1.5 : 1

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42 pieces of candy because math

Answer:

18.48

7.39 divided by 0.4 is 18.475

rounded to hundredth is 18.48 because 5 or above you round up

Answer:2.909

Step-by-step explanation:hope this helps

the image of the point ( 0 , - 9 ) after a translation of right 5 units and down 1 unit will be ( 5 , - 10 ).

We are given a point:

( 0 , - 9 )

We will first translate it to the 5 units right.

So, we get that:

( 0 + 5 , - 9)

= ( 5 , - 9)

Now, we will translate it 1 unit to the down.

So, we get that:

= ( 5 , - 9 - 1)

= ( 5 , - 10 )

Image will become:

( 5 , - 10 )

Therefore, we get that, the image of the point ( 0 , - 9 ) after a translation of right 5 units and down 1 unit will be ( 5 , - 10 ).

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Answer:

hola

Step-by-step explanation:

Using the vertical angles theorem, the value of x = 2.

Given that angles A and B are vertical angles pair, based on the vertical angles theorem, both angles are congruent to each other.

Therefore:

m<A = m<B [vertical angles theorem]

m<A = (5x + 1)°

m<B = (4x + 3)°

Substitute

(5x + 1)° = (4x + 3)°

Solve for x

5x + 1 = 4x + 3

5x + 1 - 1 = 4x + 3 - 1

5x = 4x + 2

5x - 4x = 4x + 2 - 4x

x = 2

Therefore, using the vertical angles theorem, the value of x = 2.

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Answer:

0.7¢

Step-by-step explanation:

         [tex]8 \cdot 7 = 56\\= 56 - 56\\= 0.7\:\mathrm{R0}[/tex]

The x-intercept of the line is -3

y-intercept: None

From the question, we are to find the y-intercept and x-intercept of the given line

The x-intercept of a line is the point where the line crosses the x-axis on a cartesian plane

The y-intercept of a line is the point where the line crosses the y-axis on a cartesian plane

From the graph, we can observe that the line only crosses the x-axis at the point (-3, 0). That is, at the point where x = -3

Thus,

The x-intercept of the line is -3

The graph does not cut through the y-axis

Thus,

There is no y-intercept

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The solution to the system of equations is (-7, 5)

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2x + y = -9

3x + 5y = 4

Make y the subject in 2x + y = -9

So, we have

y = -2x - 9

Substitute y = -2x - 9 in 3x + 5y = 4

So, we have

3x + 5(-2x - 9) = 4

Open the bracket

So, we have

3x - 10x - 45 = 4

Evaluate the like terms

-7x = 49

Divide both sides by -7

x  = -7

Substitute x  = -7 in y = -2x - 9

y = -2(-7) - 9

Evaluate

y = 5

Hence, the solution to the system of equations is (-7, 5)

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[tex]\sin^2\left(\frac{\pi }{6}-x \right)\implies \left[ ~~ \sin\left(\frac{\pi }{6}-x \right) ~~ \right]^2 \\\\\\ \stackrel{\textit{\LARGE Chain Rule}}{2\left[ ~~ \sin\left(\frac{\pi }{6}-x \right) ~~ \right]^1 \left[ ~~ \cos\left(\frac{\pi }{6}-x \right) ~~ \right] (-1)}\implies \boxed{-2\sin\left(\frac{\pi }{6}-x \right)\cos\left(\frac{\pi }{6}-x \right)}[/tex]

The dimension of the smallest flowering plant is 59/2500 in. long and 129/10,000 in. wide.

To convert Decimal into Fraction form:

Do the following Steps:

Step 1: Make a fraction with the decimal number as the numerator and a 1 as the denominator.

Step 2: Remove the decimal places by multiplication.

Step 3: Reduce the fraction.

Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Given,

The smallest flowering plant is the flowering aquatic duckweed found in Australia.

And it is 0.0236 inch long and 0.0129 inch wide.

Here we need to write these dimensions as fractions in simplest form.

Rewrite the decimal number as a fraction with 1 in the denominator

So,

=> 0.0236/1 and 0.0129/1

Now, Multiply to remove 4 decimal places. Here, you multiply top and bottom by 10⁴ = 10000.

Then we get,

=> 236/10000 and 129/10000

Now, reduce the fraction by dividing both numerator and denominator by GCF = 4,

=> 59/2500

But the fraction 129/10000 is not reducible.

Therefore, the fraction form is,

=> 59/2500 in. long and 129/10,000 in. wide.

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The water in the rectangular pool which has a depth of 3/4 of the pool's depth has a volume of 2250 cubic feet.

If the depth of the water is 3/4 of the depth of the pool and the depth of the pool is 60 inches, then

depth of the water = 3/4 of the depth of the pool

depth of the water = 3/4(60 inches)

depth of the water = 45 inches = 3.75 feet

Volume is defined as the amount of space any object occupies. The volume for a rectangular prism is given by the formula:

V = lwh

where v is the volume

l is the length

w is the width

h is the height

Since the water occupies the inside of the rectangular pool, to solve the volume of the water, use the formula for the volume of a rectangular prism.

V = lwh

V = 20 feet(30 feet)(3.75 feet)

V = 2250 cubic feet

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Statement a : "The standard deviation measures the variation of the data. If the standard deviation is 0, then there is some variation, so all the data are different" is false.

Statement b : "All the data must be equal to the mean because the sum of the squares of the differences of the data from the mean is 0. So, all the data take the same value" is true

This is a term in statistics that represent the amount of variation in a data set or simply put the spread of the data set. Standard deviation is solved from the mean of the data, that is we get mean first before solving for standard deviation.

From the definition, if all the data is the same then the data should be equal to the mean. If the data is equal to the mean there will be no spread or variation leading to a zero standard deviation.

Hence we can conclude that statement b is true and statement a is false

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By using the fact that EBC and ABE are supplementary angles, we will see that the measure of angle EBF is 106 degrees.

First, we can notice that angles EBC and ABE are supplementary angles, which means that their measures add up to 180°.

Then we can write:

m∠EBC + m∠ABE = 180°

Replacing what we know we get:

3y + 10 + 2y - 20 = 180°

Now we can solve this linear equation for y, we will get:

5y - 10 = 180

5y = 180 + 10

y = 190/5 = 38

Then we have that:

EBC = 3*38 + 10 = 124°

ABE = 2*38 - 20 = 56°

Now, in the image it says that:

ABE = 2b = 56°

then b = 56°/2 = 28°

And ABF = 7b - 24 = 162°

Then:

EBF = ABF - ABE = 162° - 56° = 106°

We conclude that the measure of angle EBF is 106 degrees.

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Answer: -15

Step-by-step explanation:

x=-5

g(-5)=3(-5)

g(-5)=-15

The car with the speed of 50 Km/h travels the fastest.

We have given with three choices for selecting the fastest speed from them. The three choices are

First choice is 50 Km/h.

Second Choice is  car b travels a distance of d kilometers in h hours, based on the equation 55 h = d , h, equals, d.. So from this be can conclude that this car is moving with the speed of (1/55)km/h.

Third choice is  car c travels 135 kilometers in 3 hours. So from this be can conclude that this car is moving with the speed of (135/3) Km/h i.e., 45 Km/h.

So, from the given choices we can conclude that the car with the speed of 50 Km/h travels the fastest.

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The evaluation of  (2-a)³+(2-b)³+(2-c)³-3(2-a)(2-b)(2-c) is mathematically given as

a^3+3 a b c-b^3-c^3+6 a^2-6 a b-6 a c+6 b^2-6 b c+6 c^2

This is further explained below.

(2-a)^3+(2-b)^3+(2-c)^3-3(2-a)(2-b)(2-c)

Use the Binomial Theorem.

2^3+3 * 2^2(-a)+3*2(-a)^2+(-a)^3 +(2-b)^3+(2-c)^3  -3(2-a)(2-b)(2-c)

8-12 a+6 a^2-a^3+(2-b)^3+(2-c)^3 -3(2-a)(2-b)(2-c)

Use the Binomial Theorem.

8-12 a+6 a^2-a^3+2^3+3 * 2^2(-b)+3 * 2(-b)^2+(-b)^3+(2-c)^3-3(2-a)(2-b)(2-c)

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +(2-c)^3-3(2-a)(2-b)(2-c)

Use the Binomial Theorem.

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+2^3+3 \cdot 2^2(-c)+3 \cdot 2(-c)^2+(-c)^3-3(2-a)(2-b)(2-c)

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +8-12 c+6 c^2-c^3-3(2-a)(2-b)(2-c)

Apply the distributive property.

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3+(-3 * 2-3(-a))(2-b)(2-c)

Multiply -3 by 2 .

&8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3 +(-6-3(-a))(2-b)(2-c)

Multiply -1 by -3.

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3 +8-12 c+6 c^2-c^3 +(-6+3 a)(2-b)(2-c)

Expand (-6+3 a)(2-b) using the FOIL Method.

Combine the opposite terms in

8-12 a+6 a^2-a^3+8-12 b+6 b^2-b^3+8-12 c+6 c^2-c^3-24+12 c+12 b-6 b c+12 a-6 a c-6 a b+3 abc

8+6 a^2-a^3+8+6 b^2-b^3+8+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 abc

Simplify by adding numbers.

6 a^2-a^3+6 b^2-b^3+24+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 abc

Combine the opposite terms in

6 a^2-a^3+6 b^2-b^3+24+6 c^2-c^3-24-6 b c-6 a c-6 a b+3 a b c

6 a^2-a^3+6 b^2-b^3+6 c^2-c^3-6 b c -6 ac-6 ab+3 abc

Re odrder

a^3+3 a b c-b^3-c^3+6 a^2-6 a b-6 a c+6 b^2-6 b c+6 c^2

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The coordinates of the translated points if the translation sequence is repeated n times according to the task content is; (nc, nd).

It follows from the task content that the point in discuss is at the origin. Hence, the point is; (0, 0).

Also, since the point is repeatedly translated c units horizontally and d units vertically, it follows from transformations that the resulting point is;

((0+c), (0+d))

Ultimately, when the translation sequence is repeated n times; the resulting pair of coordinates is; ((0+nc), (0+nd)).

And upon simplification, we have; (nc, nd).

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The derivative is f'(x) = 5.

The limit definition of the derivative tells us that the derivative of a function is f is

f' (x) = [tex]\lim_{h \to \0} 0[/tex] [tex]\frac{f(x+h)-f(x)}{h}[/tex]

For this, f(x) = 5x and f(x + h) = 5(x + h)

So:

f'(x) = [tex]\lim_{h \to \}0[/tex] [tex]\frac{5(x+h)-5x}{h}[/tex]

        = [tex]\lim_{h \to \}0[/tex] [tex]\frac{5x+5h-5x}{h}[/tex]

       = [tex]\lim_{h \to \}0[/tex] [tex]\frac{5h}{h}[/tex]

       = [tex]\lim_{h \to \}0[/tex] 5

       = 5

So, when f(x) = 5x , we see that its derivative is f'(x) = 5.

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a) r>0 is the domain of A. b) r = (4/2π + 16)^1/2 - 4

A(r) is a function representing the surface area of a cylinder of height = 8inches and radius = r.

A(r) = 2п[tex]r^{2}[/tex] + 16пr

r must be a positive number, as we can't have a radius of negative length, so the domain of A(r)  is r>0.

Solving for r in terms of A is an odd question, and a little challenging but possible using completing the square:

A/2п = [tex]r^{2}[/tex] + 8r

A/ 2п + 16 = [tex]r^{2}[/tex] + 8r + 16

A/2п + 16 = [tex](r + 4)^{2}[/tex]

r =( A/2п + 16) ^1/2 - 4

Therefore we get to know the range of r i.e., r>0 and radius = (A/2п + 16 )^1/2 - 4

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