Determine the area under the standard normal curve that lies to the left of (a) Z=-1.66, (b) Z= -0.03, (c) Z=-0.26, and (d) Z=1.08.

The area to the left of Z= -1.66 is__

(Round to four decimal places as needed.)

The area of the polygons arranged in order of increasing Area is:

A polygon is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.

The area of the triangle is given as:

[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2

Where Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.

Hence given:

A(-4-3), B(1, -3), C(-1,2)

we have

[-4(-3-2) + (1(2-(-3)) + (-1(-2-(-3))]/2

= 24/2

= 12

Hence the area of the triangle is 12.

To calculate the area of the rectangle, we use the distance formula. The equation for this is given as:

d² = (x₂ - x₁)² + (y₂-y₁)²

Where (x₁, x₂) are the coordinates of the first point and

(y₁, y₂) are the coordinates of the second point.

Assuming that the vertices are labeled as follows:

A (7,9), B(6,9), C(6,5), D(7,5), then

AB² = (6-7)² + (9-9)²
AB² = 1 + 0

AB = 1

BC² = (6-6)² + (5-9)²

BC² = 0² + -4²

BC = 4

CD² = (7-6)² +(5-5)²

CD² = 1² + 0²

CD = 1

DA² = (7-7)² + (9-5)²

DA² = 0² +4²

DA = 4

From the above, we can tell as is typical of a rectangle, that AB = CDand BC = DA

Since the Area of the rectangle is AB x CD OR BC x DA

The area of the rectangle =

4 x 1 = 4

Using the distance methods we can also arrive at the length of the sides of the square.

Since the area of a square is given as L² we only need the lenght one one side.

Hence,

AB = 3.60555

Hence the area of the square =

3.60555²

= 12.9999908025

Area of the square [tex]\approx[/tex] 13.

Thus the polygons arranged in order of increasing area are:

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The commutative law of addition makes the expressions as,

35 + 82 → 82 + 35

7 + (-3) → (-3) + 7

15 - 9 = 6 → -9 + 15 = 6

27 + 13 = 40 → 13 + 27 = 40

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The commutative law of addition states that,

a + b = b + a

Now,

Using the commutative law we get,

35 + 82 = 82 + 35

7 - 3:

7 + (-3) = (-3) + 7

15 - 9 = 6

15 + (-9) = 6

(-9) + 15 = 6

-9 + 15 = 6

27 + 13 = 40

13 + 27 = 40

Thus,

The commutative law of addition makes the expressions as,

35 + 82 → 82 + 35

7 + (-3) → (-3) + 7

15 - 9 = 6 → -9 + 15 = 6

27 + 13 = 40 → 13 + 27 = 40

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The  frequency table formed using tally marks can be analyzed by using the numbers indicated by the tally  marks as follows;

The true statements are as follows;

Tally marks makes use of vertical lines to represent data, in which the fifth count is represented by a diagonal line across four vertical lines;

The data in the table are as follows

The number of students that prefer red = 5 + 1 = 6

The number of students that prefer yellow = 2

The number of students that prefer Blue = 5

The number of students that prefer purple = 3

The number of students that prefer Green = 6

Therefore;

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Answer: Quadrant 1, y-axis

Step-by-step explanation:

Answer:

A is (3,4) B. is 18,4

Step-by-step explanation:

Check the picture below.

The probability that it stops working in less than 2 years is 0.40.

Given:

the probability that a new microwave oven will stop working in less than 2 years is 0.05. the probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. the probability that a new microwave oven is damaged during delivery is 0.10.

here

P ( A ∩ B ) = 0.04

P ( A ) = 0.10

we know that,

According to conditional probability:

P ( B / A ) = P ( A ∩ B ) / P ( A )

substitute values

= 0.04 / 0.10

= 004 / 100 / 010/100

= 4 / 100 * 100 / 10

= 4 * 100 / 100 * 10

= 4 * 1 / 10 * 1

= 4 / 10

= 0.40

Therefore the probability that it stops working in less than 2 years is 0.40.

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A good half a mile time is totally good, if a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile.

In the given question, we have to explain, what is a good half a mile time.

First, some background is required for 5:43 for half a mile. When did you start running? Was that time calculated using a full effort, or was it only the distance covered without walking? Don't worry about if it's good if you're spanking new. Use it as a foundation.

Second, like with most things in life, practise makes perfect, and running performance is no exception. If a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile. The goal is to gradually push your boundaries until you consistently cross that threshold and then push your limits even farther.

Your body will be encouraged to adapt to the challenge, grow to it, and become prepared for when the challenge gets harder.

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Answer:

y = -x + 8

Step-by-step explanation:

x + y = 5

y = -x + 5

y = -x + b

0 = -(8) + b

b = 8

y = -x + 8

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A linear problem is always convex, because anything linear is convex.

What is linear programming?

A mathematical model whose requirements are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming.

A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.

Every linear function has a concave shape. However, only convex polygons (possible sets of linear programs) exist.

A linear problem is always convex, because anything linear is convex.

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Answer:

  45 eggs

Step-by-step explanation:

You want to know the number of eggs left after 27 have been eaten from a supply of 6 crates having 12 eggs each.

If each of 6 crates had 12 eggs, the number of eggs bought was ...

  (6 crates) × (12 eggs/crate) = 72 eggs

If 27 of those 72 were eaten, the number remaining is ...

  72 -27 = 45

45 eggs are left.

A spherical snowball is melting and its radius decreases from 7 cm to 6.8 cm. Its approximate change in volume is 123.2 cm³.

The approximated value can be obtained using derivative approach.

The volume of the sphere is given by:

V = 4/3 πr³

dV/dr = 4 . πr²

Suppose the change of the radius is Δr, using the above derivative, the change of volume can be approximated as:

ΔV = 4 . πr² Δr

Parameters given:

r = 7 cm

Δr = 7 - 6.8 = 0.2 cm

Hence,

ΔV = 4 . π7² (0.2)

ΔV = 4 . π7² (0.2)

ΔV = 123.2 cm³

Therefore, the approximate change in volume is 123.2 cm³

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The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.

A financing model is a planned, institutionalized strategy for creating a steady income stream to sustain an organization's core services and operations. Nonprofits need funding because it enables them to make investments in their operations and increase their overall effect. Securing funding is crucial to keeping your organization operational because nonprofits frequently rely on grants to assist with operational costs. Grants of all kinds are available to nonprofit organizations.

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The volume of the solid tetrahedron is [tex]\frac{1}{144}[/tex] cubic units.

T's base is a triangle in the xy-plane (z= 0), with one edge being the line y=x, z= 0; the front side is a triangle in the vertical plane x= 1; the left side is a triangle in the xz-plane (y= 0); and the top is the plane xyz= 0 (this plane contains the three points (0,0,0), (1,1,0), (1,0,1).

The equation must be ax+by+cz+d=0 and must be satisfied by the three points as well as the edge (x=y, z=0).

T is thus described as 0≤z≤(xy), 0≤y≤x, 0≤x≤1.

for which it is suitable to used V=dzdydx.

[tex]\int\limits\int\ \int\limits{xyz} \, dV=\int\limits^1_0 \int\limits^x_0 \int\limits^{x-y}_0 {xyz} \, dxdydz\\ \\ =\int\limits^1_0 \int\limits^x_0[\frac{1}{2}xyz^2]\limits^{x-y}_0 dydx\\\\=\frac{1}{2}\int\limits^1_0 \int\limits^x_0(x^3y-2x^2y^2+xy^3)dydx\\\\=\frac{1}{2}\int\limits^1_0 [\frac{1}{2}x^3y^2-\frac{2}{3}x^2y^3+\frac{1}{4}xy^4]\limits^x_0dx\\\\=\frac{1}{2}\int\limits^1_0\frac{1}{12}x^5dx\\\\=\frac{1}{2}[\frac{1}{72}x^6]\limits^1_0\\\\=\frac{1}{144}[/tex]

Thus, the volume of the solid tetrahedron is [tex]\frac{1}{144}[/tex] cubic units.

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Using mathematical operation, the value of stock on Friday is $341.04

To find the value of the stock on Friday, the value of the stock on Monday is $24.42. Since he own 12 shares, we can multiply 12 by $24.42.

This can be done using a mathematical operation called multiplication.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

The value of the stock is 12 * 28.42 = 341.04

The stock value on Friday will $341.04

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After 1.67 minutes, the Ferris wheel will be higher than 12 meters.

Given,

The Ferris wheel has a 16-meter diameter.

The circumference of a circle with a diameter of 16 meters, which is calculated as follows, is the distance travelled by the Ferris wheel in one rotation; 16π meter

The Ferris wheel makes one revolution in 7 minutes, hence the following is true:

16π meter = 7 minutes

1 meter = (7/16π) minutes

12 meters = (7 ×12)/16π minutes

12 meters = 1.67 minutes

Therefore,

The Ferris wheel will be above 12 meters after 1.67 minutes.

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Answer:

2 1/6 more cups

Step-by-step explanation:

Answer: 2 1/6

Step-by-step explanation:

2 1/6

The 90 % Prediction interval on the wall thickness of next bottle tested is (4.41, 4.99).

A prediction interval is a form of confidence interval (CI) used with regression analysis predictions; it is a range of values that forecasts the value of a new observation based on your existing model.

Confidence intervals and predictions are frequently used interchangeably. They are not exactly the same thing, though.

A confidence interval is a set of values connected to a population parameter. the population's mean, as an illustration.

Where you anticipate an upcoming number to fall is called a prediction interval.

The Interval Uncertainties

It doesn't imply that you can forecast with confidence where a single number will fall, just like with most things in statistics.

Confidence intervals are usually accompanied with a confidence level, which represents the amount of uncertainty.

How to solve?

X=4.7

s=0.7

n=25

The tabulated value of t at 24 degree of freedom is 2.06

t24=2.064

The 90 % Prediction interval on the wall thickness of next bottle tested is given by:

=(4.7±t24×0.7√25)

=(4.7−2.064×0.75,4.7+2.064×0.75)

=(4.7−0.28896,4.7+0.28896)

=(4.41,4.99)

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For the correct statement of the p-value, we would reject the null hypothesis.

There are two main methods for interpreting the statistical significance of a hypothesis test;

1) compare the p-value to the level of significance or

2) compare test statistics to a critical value.

Either method is acceptable, and is chosen by the researcher based upon which one is most typical in their field of research.

Under a hypothesis test we reject the null hypothesis if our p-value is less than the level of significance (p<α), and fail to reject the null hypothesis otherwise. Under the question, we are given a level of significance of 0.05 and a p-value of 0.01, where

p = 0.01 <α = 0.05

hence we would reject the null hypothesis. Thus the statement is TRUE.

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Answer:

the correct answer is B

Step-by-step explanation:

$2.29 is the cost of a notebook.

Here, we have,

given that,

Jack bought 3 pencils and 4 notebooks and paid a total of $10.93. Sara bought 5 pencils and 2 notebooks and paid a total of $7.53.

let, the cost of a notebook = n

the cost of a pencil = p

we would solve this with simultaneous equations,

so if we write it as:

4n + 3p = 10.93

2n + 5p = 7.53

=> we get,

multiplying the equations by 5 and 3, we get,

20n + 15p = 54.65

6n + 15p = 22.59

(subtract)

14n = 32.06

divide both sides by 14,

14n ÷ 14 = 32.06÷ 14

n = 2.29

notebooks = 2.29

So the final answer is notebooks are $2.29.

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The probability for the given condition is, 0.56.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given:

11 black balls and 14 white balls are placed in an urn. two balls are then drawn in succession.

We have to find the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball.

P(white ball) = 14 / (11 + 14) = 14 / 25

P(2nd ball is white) = P(first ball is white)*P(2nd ball is white) + P(first ball is black)*P(2nd ball is white)

= (14 / 25) * (13 / 24) + (11 / 25) * (14 / 24)

=0.56

Hence, the probability for the given condition is, 0.56.

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The largest possible value of the expression (12 - x)/3x is 3.

Expression

In algebra, expression is the combination of variables, numbers and constants.

Given,

Here we have the expression (12 - x)/3x.

Now we have to find the  largest possible integer value.

As we have given in the question that the x takes only the non negative integer, then the values must be 1, 2, 3, ….

So, we have to apply the values on the given expression ,

Then we get the values,

=> x = 1 = > (12 - 1)/3(1) = 11/3 = 3.6

=> x = 2 => (12 - 2) / 3(2) = 10/6 = 1.6

=> x = 3 => (12 - 3) / 3(3) = 9/9 = 1

Therefore, the resulting value is 3.

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Answer: I believe it is 2/12. tell me if I am wrong.

Step-by-step explanation: Hope this helps!

Answer:The property used in 7 + 8 = 8 + 7 is Commutative property under addition

Step-by-step explanation:

Answer:

The identity property is a=a, so it is identity property

Step-by-step explanation:

???

Answer:

Step-by-step explanation:

574.35/35=16.41

276.16/32=8.63

16.41 + 8.63 = 25.04

Answer: y=3x-1

Step-by-step explanation:

1st subtract 1 from 16 so 15 then do 15/5 to get 3 seconds

Answer: =3x+6

Step-by-step explanation:

The percentage is 10% who did not complete the marathon. It can be calculted using the formula of percentage.

What is percentage?

It is way of writting any number as a fraction of 100. Its symbol is % . It is a dimention less qunatity.

Total participants = 270

Number of participants completed the marathon = 243

Number of participants gave up = 19

Number of participnats disqualified = 8

Total number of participants who did not completed the merathon is the sum of participants who gave up and who did not qualified = 19 + 8 =27

Now, percentage of participants who did not complete the marathon is,

[tex]\frac{\text{Number of participants did not complete}}{\text{Total participants}}\times100\\=\frac{27}{270}\times100\\=10\%[/tex]

Hence, 10% did not complete the marathon.

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