Determine the
percent of the population for the following given that μ = 100 and
σ = 15. Draw a picture and record the Z values, showing your
work.
I.
83.2 ≤ X ≤
133.15
J.
77.5 ≤ X ≤
138.

Answer:

Given:

Profit of every sandwich = $2

Profit of every wrap = $3

x = sandwich

y = wrap

Last month:  2x + 3y = 1,470

Next month: 2x + 3y = 1,593

Based on the given equation:

Both still have the same profit. $2 for sandwiches and $3 for wraps.

The only reason why there is a difference in the total amount is the change in the number of sandwich or wrap sold in a given month.

Since, next month's total sale is higher than last month's total sale, it is safe to assume that the sale of sandwich or wrap is higher than last month's sale.

The graph of the functions for the two moths are similar because both conditions have same slope and they are different because they have different \(y-\) intercept.

What is slope intercept form?

The graph of the linear equation   is a line with \(m\) as slope, \(m\) and \(b\)   as the \(y-\) intercept. This form of the linear equation is called the slope-intercept form, and the values of \(m\) and \(b\) are real numbers.

It is given that, the profit amount is \($\$2$\) for each sandwich and \($\$3$\) for each wrap and total profit is \($\$1593$\).

So, the equation is,

\(2x+3y=1593\)

Change the equation in slope intercept form \(y=mx+b\)

So,

\(2x+3y=1593\)

Subtract \(2x\) in both sides.

\(2x+3y-2x=1593-2x\)

\(3y=1593-2x\)

Divide each side by \(3\).

\($\frac{3y}{3}=\frac{1593}{3} -\frac{2x}{3}\)

\($\therefore y=-\frac{2x}{3}+531$\)

So, the equation is,

\(y=-\frac{2x}{3}+531$\)

The graph of the equation is shown below.

From the below graph, we will have two step down and three step right.

So, slope looks like rise over run.

So, the graphs represents, how many wraps and sandwiches were sold.

Both will have same slope, because if we will make the equation for this, it is like,

\($2x+3y=1593$\)

The calculation is follow for both condition is same.

Since, both conditions have same slope but different \(y-\) intercept.

Hence, next month's total sale is greater than last month's total sale, it is safe to consider that the sale of sandwich or wrap is greater than last month's sale.

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Answer:

The answer to 17 is -8. 2+ = 10 - 12 = -2*4 = -8.

The answer to 18 is 28. 4^2 = 16, 7 + 1 = 9 + 3 = 12, 16 + 12 = 28.

Step-by-step explanation:

Answer:

0 < t ≤ 8  (in hours)

Up to (and including) 8 hours

Step-by-step explanation:

Let t = number of hours the room is rented

Given:

Create an equation using the given information and solve for t:

⇒ 39 + 9.8t ≤ 117.4

Subtract 39 from both sides:

⇒ 9.8t ≤ 78.4

Divide both sides by 9.8

⇒ t ≤ 8

Therefore, the possible amounts of time for which they could rent the meeting room is 0 < t ≤ 8  (in hours)

Answer:

8 is the very maximum number of hours the room can be rented. As long as 8 is not exceeded, the room is rentable for what money the math club has.

Step-by-step explanation:

Givens

Formula

payment ≥ 39 + 9.80*t                where t is in hours.

Solution

117.40 ≥ 39 + 9.80*t                      Subtract 39 from both sides.

117.40 - 39 ≥9.80*t

78.40 ≥ 9.80*t                               Divide by 9.8

78.40/9.80 ≥ 9.80*t/9.80

8 ≥ t    

Answer t≥ 8

Perceived lack of anonymity is the source of bias that is most relevant to the given situation.

The data collected in the study, which is Mood on a Happy/OK/Sad scale, is qualitative or categorical data.

This describes an observational study.

What is Statistics?

Statistics is a field of study that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and statistical methods to extract meaningful insights from data and to draw conclusions or make decisions based on the findings.

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Answer:

See Below.

Step-by-step explanation:

We are given that ∠A = ∠D, and we want to prove that ΔACB ~ ΔDCE.

Statements:                                    Reasons:

\(1) \text{ $\angle A=\angle D$}\)                                    \(\text{Given}\)

\(2) \text{ }\angle BCA=\angle ECD\)                        \(\text{Vertical Angles Are Congruent}\)

\(3) \text{ } \Delta ACB \sim \Delta DCE\)                        \(\text{AA (Angle-Angle) Similarity}\)

\( \angle \: A = \angle D\)

ACB ~ DCE

Given,

\( \bf\angle \: A = \angle D \)

\( \bf \angle \: BCA= \angle \: ECD\)

[ vertical angles ]

\( \therefore \: ACB \sim DCE\)

By AA Criterion of similarity

The exact value of sin(π/6) is 1/2.

To find the exact value of sin(π/6), we can use the unit circle or the trigonometric identity for the sine function. In the unit circle, π/6 corresponds to an angle of 30 degrees, which lies in the first quadrant.

At this angle, the y-coordinate of the corresponding point on the unit circle is 1/2. Since sin(θ) represents the ratio of the opposite side to the hypotenuse in a right triangle, for an angle of 30 degrees, sin(π/6) is equal to 1/2.

Alternatively, we can use the trigonometric identity sin(θ) = cos(π/2 - θ). Applying this identity, we have sin(π/6) = cos(π/2 - π/6) = cos(π/3). Now, π/3 corresponds to an angle of 60 degrees, which lies in the first quadrant.

At this angle, the x-coordinate of the corresponding point on the unit circle is 1/2. Therefore, cos(π/3) = 1/2. Substituting this value back into sin(π/6) = cos(π/3), we get sin(π/6) = 1/2.

In both approaches, we find that the exact value of sin(π/6) is 1/2, indicating that the sine function of π/6 radians is equal to 1/2.

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Answer:

5

Step-by-step explanation:

If Lisa has x quarters and Brenda has 3x quarters, we can write:

80% * 3x = 4 + (20% * 3x + x) -- We write 4 because 1 dollar =  4 quarters

0.8 * 3x = 4 + (0.2 * 3x + x)

2.4x = 4 + 1.6x

0.8x = 4

x = 5

Answer:

48.67

Step-by-step explanation:

31 divided by 2 = 15.5 which is the radius

15.5 times by 3.14(pi) = 48.67

Answer:

m>5

Step-by-step explanation:

Let's solve your inequality step-by-step.

m+4>9

Step 1: Subtract 4 from both sides.

m+4−4>9−4

m>5

Answer:

m > 5

Step-by-step explanation:

m + 4 > 9

m + 4 - 4 > 9 - 4

m > 5

Answer:

ans=12

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

=(

18

1

)(

2

3

)

=

(18)(2)

(1)(3)

=

36

3

=12

Answer:

3

Step-by-step explanation:

72/9 = 8 ( The quotient of 72 and 9)

8-5 = 3 (Decrease by 5)

True. The 3px, 3py, and 3pz orbitals are similar in shape but differ in their orientation or direction.

The p orbitals are one type of orbital that corresponds to the angular momentum number l = 1. These p orbitals are designated as 3px, 3py, and 3pz to indicate their orientations along the x, y, and z axes, respectively.

The p orbitals have a  shape with a node at the nucleus. They consist of two lobes of electron density, one on either side of the nucleus, separated by a region of zero electron density. The lobes are oriented along the designated axes. The 3px orbital points along the x-axis, the 3py orbital points along the y-axis, and the 3pz orbital points along the z-axis. Although they have different orientations, their shapes and sizes are the same.

So, while the 3px, 3py, and 3pz orbitals differ in their orientation in space, they share the same overall shape and size.

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To model the cost of renting an economy car for x days, you can use a linear equation. A linear equation can be represented in the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. In this case, y represents the cost of renting the car, and x represents the number of days.

To find the equation of the line, we need to use the given information to find the slope and y-intercept. We know that the cost of renting the car increases by a certain amount for each additional day, so the slope will be the daily rate. We also know that the cost of renting the car for 1 day is $90, which means that $90 is the y-intercept.We can use the two points (1, 90) and (3, 170) to find the slope:Slope = (y2 - y1) / (x2 - x1)

Slope = (170 - 90) / (3 - 1)Slope = 80 / 2Slope = 40Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:y - y1 = m(x - x1)We can use the point (1, 90) as our reference point:y - 90 = 40(x - 1)Simplifying this equation gives y = 40x + 50Thus, the function to model the cost of renting an economy car for x days is given by the equation y = 40x + 50, where y represents the cost and x represents the number of days.

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The probability that a professional would accept the promotion is 0.7435.

The total row represents the sum of the probabilities of each event for all the categories, and in this case, the probability of accepting the promotion is the sum of the probabilities of accepting the promotion for each category, which is 0.276 + 0.3145 + 0.1530 = 0.7435.

This means that if we randomly select a professional, there is a 0.7435, or 74.35%, chance that they would accept the promotion. The probability is calculated by taking the sum of the probabilities for each category that corresponds to accepting the promotion and dividing it by the total number of professionals surveyed.

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Validation of the model and answering the question "what are my options" occur in the design phase of the IDC (Intelligence, Design, and Choice) framework.

The IDC framework is a decision-making process that consists of three phases: Intelligence, Design, and Choice. Each phase corresponds to a specific set of activities and objectives.

In the intelligence phase, the focus is on gathering information, identifying the problem or decision to be made, and understanding the factors and variables involved. This phase involves data collection, analysis, and exploration to gain insights and knowledge about the problem domain.

In the design phase, the emphasis is on developing and evaluating potential options or solutions to address the problem or decision at hand. This phase involves creating models, prototypes, or simulations to represent the problem and exploring different alternatives.

Validation of the model is an important aspect of this phase to ensure that the proposed solutions align with the problem requirements and objectives.

The question "what are my options" is a fundamental question that arises during the design phase. It implies the exploration and generation of various possible choices or solutions that can be evaluated and compared.

Therefore, the design phase of the IDC framework encompasses the activities of validating the model and answering the question "what are my options." It involves refining and testing potential solutions to make informed decisions in the subsequent choice phase.

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Answer:

it is 1265 ?!?!?!!?!?!!?

Step-by-step explanation:

work out

Answer: 240 feet

Step-by-step explanation:

Since the scale used was 1 inch = 2 feet

Then, length = 10 inches = 10 × 2 = 20 feet

Width = 6 inches = 6 × 2 = 12 feet

Area = Length × Width

Area = 20 × 12

Area = 240 feet

Answer:

77 years old

Step-by-step explanation:

The strain that exists under a maximum-stress condition is 9.27 × 10^-3.

Given data: Minimum cross-sectional area of femur= 4.4×10^-4 m^2

Compressional force to fracture= 6.100×10^4 N

We need to find the maximum stress that this bone can withstand.

Maximum stress = compressive force / minimum cross-sectional area

                            = 6.1×10^4 / 4.4×10^-4=1.39×10^8 N/m^2

Now, we need to find the strain that exists under a maximum-stress condition.

Since stress = Young’s modulus × strain,

Strain = stress / Young's modulus

Maximum stress = 1.39×10^8 N/m^2

Young's modulus for bone = 1.5 × 10^10 N/m^2

Strain = 1.39×10^8 / 1.5 × 10^10= 0.00927= 9.27 × 10^-3

Therefore, the strain that exists under a maximum-stress condition is 9.27 × 10^-3.

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The curve is y = In(sec(x)) and we have to find its length. We are given the range as 0 ≤ x ≤ π/4. So, the formula for the length of the curve is given as:

To solve for the length of the curve of y = In(sec(x)), we use the formula,

`L = ∫[a,b] √[1+(f′(x))^2] dx`.Where, `a = 0` and `b = π/4`. And `f′(x)` is the derivative of `In(sec(x))`.

We know that:`f′(x) = d/dx[In(sec(x))]`

Using the formula of logarithm differentiation, we can write the above equation as:

`f′(x) = d/dx[In(1/cos(x))]`

So,`f′(x) = -d/dx[In(cos(x))]`

Therefore,`f′(x) = -sin(x)/cos(x)`

Substituting the values, we get:

`L = ∫[a,b] √[1+(f′(x))^2] dx`

`L = ∫[0,π/4] √[1+(-sin(x)/cos(x))^2] dx`

`L = ∫[0,π/4] √[(cos^2(x)+sin^2(x))/(cos^2(x))] dx`

`L = ∫[0,π/4] sec(x) dx`

Now, `L = ln(sec(x) + tan(x)) + C` where `C` is a constant.

We calculate the constant by substituting the values of `a = 0` and `b = π/4`:

`L = ln(sec(π/4) + tan(π/4)) - ln(sec(0) + tan(0))`

`L = ln(√2 + 1) - ln(1 + 0)`

`L = ln(√2 + 1)`

Thus, the exact length of the curve is `ln(√2 + 1)` units.

Thus, the exact length of the curve of y = In(sec(x)), 0≤x≤π/4 is `ln(√2 + 1)` units.

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Answer:

A. The slope is 7/2, The y-intercept is (0,-3)

Step-by-step explanation:

The slope of a line passing through two points P=(x1,y1) and Q=(x2,y2) is given by m=y2−y1x2−x1.

We have that x1=0, y1=−3, x2=2, and y2=4.

Plug the given values into the formula for a slope: m=4−(−3)/2−0=72.

Now, the y-intercept is b=y1−mx1 (or b=y2−mx2, the result is the same).

b = -3 - (7/2) × (0) = -3

Finally, the equation of the line can be written in the form y=b+mx:

y = 7/2x - 3

Answer:

\(HD=5.5\)

Step-by-step explanation:

\(4(HD)=22 \implies HD=5.5\)

The standard deviation of 4:

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

In descriptive statistics, the standard deviation measures how widely the data points vary from the mean. It describes how values are distributed throughout the data sample and measures how widely apart data points are from the mean. The square root of the variance is used to calculate the standard deviation of a sample, statistical population, random variable, data collection, or probability distribution.

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The percent of rural neighborhoods in the county is 37.5%.

What is Ratio to Percentage Conversion?

It is given that the ratio of urban to rural neighborhoods in a county is 5 : 3.

\(\implies \frac{\text Urban}{Rural} =\frac{5}{3}\)      -----(1)

The total neighborhoods can be given as,'

5 + 3 = 8 neighborhoods.

Thus, 5/8 parts are urban neigborhoods and 3/8 parts are rural neighborhoods.

Converting the ratio of rural neighborhoods to percentage, we get

\(\frac{3}{8} \times 100 =37.5 \%\)

Therefore, the percent of rural neighborhoods in the county is 37.5%.

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Answer:

58*

Step-by-step explanation:

We know a full circle is 360* and the rest of the triangle is 293* so 360-293 is 67. Now 67 minus 23 which is 44. 58-14 is 44.

Given :

A mountain climber started his climb at 50 feet above see level .

He then raised 3 feet to rest in his cot to make his final 10 feet climb down.

To Find :

An expression to find his position relative to his final position.

Solution :

Let , final position is h .

h is given by :

\(h=\text{(Initial position)-(initial descended)+(height raised to rest)-(final descended)}\\\\h=50 -28 +3-10\ feet\\\\h=15\ feet\)

So , his final position is 15 feet .

Hence , this is the required solution .

Answer: B, $16.26 per 6 yards

Step-by-step explanation:

$11.04/ 4 yd is $2.76 a yd

$16.26/ 6 yd is $2.71 a yd

$19.11/ 7 yd is $2.73 a yd

$13.85/ 5 yd is $2.77 a yd

Answer: 151,515

Step-by-step explanation:

555+333= 888

333÷888 = .375

.375 × 404040 = 151,515

Answer:

its 15

Step-by-step explanation:

Answer:

1

4

3 6

2.8

-----

+ 288

+ 720

---------

100.8

This is a horizonal line going through y = 4.

Horizontal lines are of the form

Where

a is a number

Slope is rise over run, or, the change in y divided by change in x.

No matter what the change in x is, the change in y is always zero (horizontal line). Thus, the slope is always 0 as well.

1.

The slope of the line is 0

2.

The slope intercept form is:

Since the slope is zero, m = 0 and y intercept (b) is 4, we have: