Sketch the area under the standard normal curve over the indicated interval and find the specified area. (You can use the probability table or software. Round your answer to four decimal places.)

a) The area to the right of z = 1.35 is [a]

b) The are to the left of -0.47 is [b]

c) The are between z = -1.72 and z = 1.16 is [c]

Answer:

14 base 10

Step-by-step explanation:

Remember what the digits mean in the base 10 system we use.

For example, the number 539 (base 10) means:

The 5 in the hundreds place means 5 × 100 = 500.

The 3 in the tens place means 3 × 10 = 30.

The 9 in the ones place means 9 × 1 = 9.

The number 539 means

5 × 100 + 3 × 10 + 9 × 1 = 500 + 30 + 9 = 539

Also keep in mind one more thing. The ones digit means the number of ones. 1 = 10^0. The number in the ones digit means the number if 10^0 you have.

The ten digits is the digit of 10^1.

The hundreds digit is the digit of 10^2 since 10^2 = 100.

In other words, the ones digit is the number of 10^0 you have.

The tens digit is the number of 10^1 you have.

The hundreds digit is the number of 10^2 you have.

Now let's look at base 5.

Here, each place to the left is a successively higher power of 5 instead of a power of 10.

Think of the number 432 base 5.

The 2 is in the units place. it represents the number of 5^0 or ones you have. In this case, it is 2 × 5^0 = 2 × 1 = 2

The 3 is in the 5^1 place. It represents the number of fives you have.

3 × 5 = 15

The 4 is in the 5^2 place. It represents the number of 25's you have.

4 × 25 = 100

The number 432 base 5 means:

4 × 5^2 + 3 × 5^1 + 2 × 5^0

= 4 × 25 + 3 × 5 + 2 × 1

= 100 + 15 + 2

= 117 base 10

In other words, 432 base 5 = 117 base 10.

Now we do the same with your number, 24 base 5.

24 base 5 =

= 2 × 5^1 + 4 × 5^0

= 2 × 5 + 4 × 1

= 10 + 4

= 14

1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .

The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.

The length of my book in when measured in millimeters is 280 mm.

In centimeters, this is therefore:

= 280 mm / 10 cm /mm

= 28 cm

Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.

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Answer:

224

Step-by-step explanation:

360.-136.

The probability of getting 3 successes is 0.00463 Or 0.46%.

In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment). The binomial probability is \(P(x) = ^nC_xp^xq^{n-x}\) if the likelihood of success on a given trial is p.

Given, A fair die is rolled three times. Getting a 4 is considered 'success', while all other outcomes are 'failures'.

So, The probability(p) of getting a 4 on a die is (1/6), and hence the probability of failure(q) = 1 - 1/6 = 5/6.

Also given, n = 3.

Therefore, The probability of getting 3 successes is,

\(P(x = 3) = ^3C_0(1/6)^3\times(5/6)^0\).

\(P(x = 3) = 1\times\frac{1}{216}\times1\)

\(P(x = 3) = \frac{1}{216}\).

So, the probability of 3 successes is 1/216.

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Step-by-step explanation:

\(\frac{63}{7}=\frac{l}{9}\)

\(l=81\text{ ml}\)

Answer:

D

Step-by-step explanation:

We are given that the volume of water in a vase is proportional to the depth of the water. In other words, we can write that:

\(\displaystyle V = kd\)

Where V is the volume, d is the depth of the water, and k is the constant of proportionality.

When there are 63 mL of water in the vase, the depth is 7 cm. Hence, V = 63 when d = 7:

\(\displaystyle (63) = k(7)\)

Solve for k:

\(\displaystyle k = \frac{63}{7} = 9\)

Hence, our equation is:

\(V = 9d\)

Then when the depth of the vase is 9 cm:

\(\displaystyle V = 9(9) = 81\text{ mL}\)

There will be 81 mL of water in the vase.

Hence, our answer is D.

Answer:

f(x) = 15x + 1,000

Step-by-step explanation:

y = mx + b

the 15 is the slope or rate and 1000 is the fixed value ( y intercept)

Answer:

Shorter leg = 20 cm.

Longer leg = 21cm.

Hypotenuse = 29 cm

Step-by-step explanation:

Let the shorter leg be x cm long

Then longer leg = x + 1 and hypotenuse = x + 9 cm long

So by Pythagoras:

x^2 + (x + 1)^2 = (x + 9)^2

0 = x^2 + 18x + 81 - x^2 - (x^2 + 2x + 1)

x^2 + 18x + 81 - x^2 - x^2 - 2x - 1 = 0

-x^2 + 16x + 80 = 0

x^2 - 16x - 80 = 0

(x - 20)(x + 4) = 0

So x = 20   (we ignore the negative root).

So longer leg = 20 + 1 and hypotenuse = 20 + 9.

Answer:

b = 4

Step-by-step explanation:

4/6 is equivalent to 2/3, so with the slopes and y-intercepts being the same, there will be infinitely many solutions

The absolute maximum and minimum values obtained from the graph of the functions are;

Absolute maximum of g; [1, 4]

Absolute minimum of g; [4, -3]

Absolute maximum h; [4, 3]

Absolute minimum of h; (-4, -5)

The absolute maximum and minimum of a function are the coordinates of the highest and lowest points on the graph of the function, within the specified domain.

The points on the graph of the functions indicates that the maximum and minimum values of the functions are;

Graph of g; Absolute maximum of g = (1, 4)

Absolute minimum of g ; [4, -3]

Graph of h

Absolute maximum of h; [4, 3]

Absolute minimum of h; (-4, -5)

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Answer:

Ok

Step-by-step explanation:

To add these two fractions, you have to find a common denominator. The closest one is 8, so to get to that it is 1/4*2. That is equal to 2/8 + 1/8. that is 4/8, and when multiplied by 2 it equals 8/16, not 5/16.

Notice that segment GA is part of line AB that intersects the circle at points A and B, therefore AB is a secant. Segment GA is outside the circle, therefore, it is true that GA is an external part of a secant segment.

Answer: Third Option.

The true statement based on the relationship depicted in the Venn diagram is that no rhombuses are trapezoids (option D).

To identify the true statement using the relationship represented in the Venn diagram, we need to analyze the overlapping regions and the properties of the shapes involved.

A trapezoid is a quadrilateral with at least one pair of parallel sides, while a rhombus is a quadrilateral with all sides of equal length. Let's evaluate the options:

A. All trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region between the trapezoids and rhombuses shows that there are trapezoids that are not rhombuses. Therefore, option A is incorrect.

B. All rhombuses are trapezoids: This statement is true based on the diagram. The entire region representing rhombuses is also included within the region representing trapezoids. Every rhombus can be considered a trapezoid because it has at least one pair of parallel sides. Thus, option B is correct.

C. No trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region indicates that there are trapezoids that are indeed rhombuses. Therefore, option C is incorrect.

D. No rhombuses are trapezoids: This statement is true based on the diagram. There is no overlap between the regions representing rhombuses and trapezoids, implying that no rhombus can be considered a trapezoid. Hence, option D is correct.

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Answer:

Yes, y = \(\frac{1}{5}\) x represents a proportional relationship and the constant of proportionality is \(\frac{1}{5}\)

Step-by-step explanation:

The Proportional is a relationship between two quantity one of them equals the product of the other and a constant, where this constant called the constant of proportionality

Let us solve the question

∵ y = \(\frac{1}{5}\) x

→ It the same as the form of the proportional equation above

∵  \(\frac{1}{5}\)  is a constant

∴ y is the product of x and constant

∴ y =  \(\frac{1}{5}\) x represents a proportional relationship

Substitute x by 0 to find y and show it represented by a line passing through the origin

∵ x = 0

∴ y = \(\frac{1}{5}\) (0) = 0

→ That means point (0, 0) lies on the line which represents the equation

∴ The line which represents this relation is passing through the origin

∴ y = \(\frac{1}{5}\) x represents a proportional relationship

∵ y = kx, k is the constant of proportionality

∵ y = \(\frac{1}{5}\) x

∴ k =  \(\frac{1}{5}\)

∴ The constant of proportionality is \(\frac{1}{5}\)

Answer:

a

Step-by-step explanation:

the perimeter (P) of a square is the sum of the 4 congruent sides.

the area of a square is calculated as

area = s² ( s is the length of a side )

here area is 36 , then

s² = 36 ( take square root of both sides )

s = \(\sqrt{36}\) = 6

then

P = 4s = 4 × 6 = 24 cm

Median of the set is 34, as it is the middle value of the ordered set (32, 33, 33, 33, 34, 35, 35, 36, 38).

To find the middle of a bunch of numbers, the initial step is to organize the numbers all together from least to most prominent. For this situation, the arranged set is: 32, 33, 33, 33, 34, 35, 35, 36, 38.

The middle is the center number in the arranged set. On the off chance that there is an odd number of values, the middle is the center worth. On the off chance that there is a considerably number of values, the middle is the normal of the two center qualities.

For this situation, there are nine qualities in the set, which is an odd number. The center worth is the fifth worth, which is 34. Thusly, the middle of the set is B. 34.

To confirm, we can count four qualities before 34 and four qualities after 34 in the arranged set. Since there are an equivalent number of values when the middle, we can infer that 34 is for sure the middle.

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Answer:

3072

Step-by-step explanation: you just need to multiply .32 by 9600.

Answer:

24

Step-by-step explanation:

Basically, for every 5 boys there is 3 girls. A simple way to solve this, but longer, yet the one I personally use count up, go 5*2 3*2 and find which one adds up to 64. Once you get to 64, total including the product of both, you will have the amount of boys and girls. In this case

5*8 and 3*8 = 64

3*8 = 24

5*8 = 40

There are 24 girls

The value of angle RPQ in the circle is 115 degrees.

The intersecting chords theorem, also known as the chord theorem, is an elementary geometry statement that describes a relationship between the four line segments formed by two intersecting chords within a circle.

If two chords intersect inside a circle, then the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore,

∠RPQ = 1  / 2 (arc angle RQ + arc angle SA)

arc angle RQ = 175 degrees

arc angle SA = 55 degrees

Hence,

∠RPQ  = 1 / 2 (175 + 55)

∠RPQ  = 1 / 2 (230)

∠RPQ  = 115 degrees.

The angle is 115°.

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The basketball is a sphere of radius(r) 4.5 inches.

By formula,

Area of a Sphere is given below:

The exact material needed for each basketball is 254.57 square inches

b. The surface area of each box is a cuboid.

The surface Area of a cuboid is given by the formula below:

Thus, the square inches of cardboard needed for each box is 680 square inches.

Answer:

1:4

Step-by-step explanation:

A ratio can be written like this: 15:60, but it can also be written as the fraction 15/60, which can be simplified to 1/4, or 1:4.

Answer:

A

Step-by-step explanation:

x=5, y=0

The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;

1. The area is about 15.16 units²

2. The coordinates of the points are;

(i) B(5, 8)

(ii) C(8.58, 4)

(ii) D(8,58, 1.21)

A quadrilateral is a four sided polygon.

1. The coordinate of the point C can be found as follows;

Let (x, y) represent the coordinates of the C, we get;

(x + 8)/2 = 5

x = 2 × 5 - 8 = 2

(y + 8)/2 = 6

y = 2 × 6 - 8 = 4

The coordinates ot the point C (2, 4)

The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)

Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)

The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13

CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;

(4 - y)/(2 - x) = -(5 - x)/(6 - y)

y - 4 = (-4/7)(x - 2)

y - 6 = (7/4)(x - 5)

(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6

x = (17/5) = 3.4

y = (7/4)((17/5) - 5) + 6 = 3.2

The coordinates of the point E is (3.4, 3.2)

The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)

Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)

Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)

Area of the figure is therefore;

2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))

y - 6 = (1/3)·(x + 1)

y = (1/3)·(x + 1) + 6

The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2

Slope of the segment BE = -1/(-1/2) = 2

Equation of BE is; y - 4 = 2·(x - 3)

y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6

Therefore, x = 5

y = (1/3)·(5 + 1) + 6 = 8

(ii) Area of the triangle EBC = 24 unit²

EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20

Therefore;

BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)

(x - 5)² + (y - 8)² = 28.8

y = 4, therefore;

(x - 5)² + (4 - 8)² = 28.8

(x - 5)² = 28.8 - (4 - 8)² = 12.8

x = √(12.8) + 5

(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)

x = √(12.8) + 5

Therefore;

y - 4 = (-1/2)((√(12.8) + 5) - 3)

y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21

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The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.

Note that At the point H, there is  found to be an intersection between the distance taken by both people involve so:

Y (a)= 10 + 2x ------ Josiah

Y (0) = 3x   ----- Chana

If  Y (a)= Y (0)

Then:

10 + 2x = 3x

x = 10

F = x = 20

Y (o) = 60

If x = 20

= then Y(0) = 3 x 20

= 60

Therefore, The point that is labeled H on this graph is that at 25th second, Josiah is 60 meter distance from the starting line.

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Answer: B

Step-by-step explanation:

Oki so I know this becaue I study to much and because if there was an answer saying this : y=6x+3 it would be wrong because it is adding to the constant

So y=6x is proportinal because it is allways constant. I forgot this was an example sorry.

Answer:

B. since x can equal anything, but nine is in front therefore, it can be what you want, so it is B.

The expression 48 − 8 × 48−8x48 is factored to give an equivalent expression 8(6 − x) × 48, where 8, 6, and x are terms of the expression. Factoring is the method of expressing a polynomial as the product of other polynomials. The term minus refers to subtraction, and the operation of subtraction is used to subtract 8 × 48 from 48 to get a result of 16.

The expression to factor is 48 − 8 × 48−8x48. Factoring the expression 48 − 8 × 48−8x48 gives an equivalent expression 8(6 − x) × 48, where 8, 6, and x are terms of the expression.

In mathematics, factoring is the method of expressing a polynomial as the product of other polynomials. The factored expression 8(6 − x) × 48 can be expanded back to the original expression by multiplying the individual factors with each other.

The term minus refers to subtraction. In this context, the operation of subtraction is used to subtract 8 × 48 from 48, yielding a result of 16. This result is multiplied by 48 − 8x48 to get the original expression 48 − 8 × 48−8x48.

Therefore, the equivalent expressions are 48 − 8 × 48−8x48 and 8(6 − x) × 48, where 8, 6, and x are terms of the expression.

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9514 1404 393

Answer:

  13, 22

Step-by-step explanation:

Let s represent the smaller. The sum of the numbers is ...

  s + (s+9) = 35

  2s = 26 . . . . . . subtract 9

  s = 13

  s+9 = 22

The two numbers are 13 and 22.

_____

Additional comment

As you can see, the smaller number is half the difference of the sum and difference: s = (35-9)/2. This is the generic solution to a "sum and difference" problem.

Answer:0.6

Step-by-step explanation:

We can grab 2 points in this table and plug this into the slope formula: (y2-y1)/(x1-x2). The 2 easiest points would be (0,0) and (2, 1.2). Doing this would get us (1.2-0)/(2-0). Simplifying this would get us 1.2/2, or .6.

The profit function is given by Profit(x) = 80x - 5040, where x speaks to the number of tires delivered.

The profit function is characterized as the distinction between the income and the fetched. In this case, the income work is R(x) = 105x and the taken a toll work is C(x) = 25x + 5040, where x speaks to the number of tires delivered.

To calculate the benefit work, we subtract the fetched work from the income work:

Profit(x) = R(x) - C(x)

Substituting the given income and fetched capacities, we have:

Profit(x) = 105x - (25x + 5040)

Rearranging the expression, we get:

Profit(x) = 105x - 25x - 5040

Combining like terms, we have:

Profit(x) = 80x - 5040

This condition permits us to calculate the benefit made from creating a certain number of tires, taking under consideration the income and the taken a toll related with generation.

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Answer:

C

......................................................

a) The distance of the stone above ground level at time t :

d(t)= -4.9t² + 950

b) It takes 13.92 seconds the stone to reach the ground

c)  With 136.42 m/s velocity the stone strikes the ground.

d) If the stone is thrown downward with a speed of 8 m/s, it will take 13.13 seconds to reach the ground

Here, a  stone is dropped from the upper observation deck of a tower, 950 m above the ground.

(a)  the distance of the stone above ground level at time t would be,

d(t)  = 0.5 (-9.8) t² + v(0) t + d(0)

      = (-4.9)t² + 0t + 950

      = -4.9t² + 950

(b) Now we find the time the stone takes to reach the ground.

i.e., the value of 't' when d = 0

Substituting d(t) = 0 in the above equation.

-4.9t² + 950 = 0

t² = (-950) / (-4.9)

t² = 193.88

t = 13.92 seconds

(c) We need to find the velocity the stone takes to strike the ground

i.e., the velocity when t  = 13.92 seconds

v(t) = v(0) + gt      

v(13.92) = 0 + (9.8)(13.92)

v = 136.42 m/s

(d) here, v(0) = -8 m/s  

Velocity is negative because stone is being thrown downward.

d(t) = 0

(-4.9)t² + v(0) t + d(0) = 0

(-4.9)t² -8t + 950 = 0

Using the quadratic formula we solve above equation for,

t = -14.76, 13.13

We can disregard the negative solution

So, we get t = 13.13 seconds.

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