To avoid having her hours cut back at work, Bridgett must avoid performing in the lowest
40% of the distribution of workers at her job. Specifically, typical amount of items manufactured
at her job form a normal distribution with µ = 100 and o= 4. Bridgett needs to manufacture more than ____ items in order to avoid having her hours cut back at work.

Answer:

-12 + 4d

Step-by-step explanation:

(-3)4 - d(-4)

-12 - -4d

The digits are arranged in increasing order from left to right, and that each digit is used exactly once.

What is a number line?

A number line is a visual representation of numbers arranged in a straight line from left to right or from right to left. It is a tool commonly used in mathematics to help visualize numerical relationships, such as addition, subtraction, multiplication, and division.

A typical number line starts at zero in the middle and extends infinitely in both directions, with positive numbers increasing to the right and negative numbers decreasing to the left. The distance between any two points on the number line represents the absolute difference between the corresponding numbers.

Here's a number line using the digits 0-9 exactly once:

-9 --- -8 --- -7 --- -6 --- -5 --- -4 --- -3 --- -2 --- -1 --- 0 --- 1 --- 2 --- 3 --- 4 --- 5 --- 6 --- 7 --- 8 --- 9

Note that the digits are arranged in increasing order from left to right, and that each digit is used exactly once.

Therefore, the digits are arranged in increasing order from left to right, and that each digit is used exactly once.

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Answer:

Area = 78.54 sq. ft.  (25π)

Circumference = 31.42 ft.  (10π)

Step-by-step explanation:

Diameter of circle d = 10 ft
Radius r = Diameter/2 = 5

Area = πr² = π x 5² = π x 25 = 78.54 sq. ft. rounded to 2 decimal places

Circumference = πd = π x 10 = 31.42 ft. rounded to 2 decimal places.

Answer:

Step-by-step explanation:

To find the image of each point under the dilation, we need to apply the scale factor of 3 to the distances between the point and the center, and then add the coordinates of the center to get the new coordinates.

The center of dilation is (2,1), so we subtract 2 from the x-coordinates and 1 from the y-coordinates to get the distances from the center to each point:

X: (-3 - 2, 2 - 1) = (-5, 1)

Y: (0 - 2, 0 - 1) = (-2, -1)

Z: (2 - 2, 1 - 1) = (0, 0)

Next, we apply the scale factor of 3 to each distance:

X': (-5 × 3, 1 × 3) = (-15, 3)

Y': (-2 × 3, -1 × 3) = (-6, -3)

Z': (0 × 3, 0 × 3) = (0, 0)

Finally, we add the coordinates of the center (2,1) to each image:

X': (-15 + 2, 3 + 1) = (-13, 4)

Y': (-6 + 2, -3 + 1) = (-4, -2)

Z': (0 + 2, 0 + 1) = (2, 1)

Therefore, the coordinates of the image triangle X'Y'Z' are:

X' = (-13, 4)

Y' = (-4, -2)

Z' = (2, 1)

The area under the curve of the standard normal​ distribution is 98.61% of the area between equals negative 2. 2 and zequals2. 2

The area under the curve of a standard normal distribution between z = -2.2 and z = 2.2 is given by the integral of the normal distribution function from -2.2 to 2.2. This can be calculated using a table of standard normal probabilities or using a calculator with a normal distribution function.

The result is approximately 0.9861. To convert this to a percentage, simply multiply by 100: 0.9861 * 100 = 98.61%. Therefore, about 98.61% of the area is between z = -2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is also known as the z-distribution or the unit normal distribution. It is often used in statistical tests, such as the z-test, t-test, and chi-square test. It is also used to determine confidence intervals, to calculate probabilities, and to measure the probability of a given event.

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The required solution for the hypothesis testing is shown.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here, we have,

Part A:

The null hypothesis (H0) is that the company's claim is true, and the proportion of defective batteries is 5% or less.

The alternative hypothesis (Ha) is that the company's claim is false, and the proportion of defective batteries is greater than 5%.

H0: p ≤ 0.05

Ha: p > 0.05

where p represents the proportion of defective batteries.

Part B:

A Type I error in this context would be rejecting the null hypothesis (i.e., finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually true (i.e., the proportion of defective batteries is 5% or less). This would be a false positive result.

A Type II error would be failing to reject the null hypothesis (i.e., not finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually false (i.e., the proportion of defective batteries is greater than 5%). This would be a false negative result.

Part C:

If the hypothesis is tested at a 5% level of significance instead of 1%, this means that the criteria for rejecting the null hypothesis will be less stringent. In other words, it will be easier to find significant evidence that the company's claim is false. Therefore, increasing the level of significance from 1% to 5% will increase the power of the test.

Part D:

If the hypothesis is tested based on the sampling of 500 boxes of batteries rather than 100 boxes of batteries, this means that the sample size is larger. As a result, the standard error of the estimate will be smaller, and the test will be more precise. This increased precision will increase the power of the test.

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Answer:

  10x -25

Step-by-step explanation:

You want to simplify the expression ...

  3x+6+x-2+8(x-3)+-4-4+x+1+-2(x+2)+6+7x+-8x

First, we use the distributive property to eliminate parentheses:

  3x+6+x-2+8x-24+-4-4+x+1+-2x-4+6+7x+-8x

Now, we group x-terms and constant terms:

  (3 +1 +8 +1 -2 +7 -8)x +(6 -2 -24 -4 -4 +1 -4 +6)

Finally, we perform the sums:

  10x -25

__

Additional comment

This sort of problem can be described as "tedious, but not difficult."

Answer:

Step-by-step explanation:

Part A:

To create the table, we substitute each of the given values of x into the equation and solve for y:

x y = -1025x + 30,750

0         30,750

5         25,375

8         21,050

10         18,725

30         -7,500

Part B:

The altitude after 5 minutes can be found by substituting x=5 into the equation:

y = -1025(5) + 30,750 = 25,375

The altitude after 30 minutes can be found by substituting x=30 into the equation:

y = -1025(30) + 30,750 = -7,500

After 5 minutes, the altitude of the airplane is 25,375 feet. After 30 minutes, the altitude of the airplane is -7,500 feet, which means the airplane is on the ground. This is because the altitude is decreasing by 1,025 feet every minute, and after 30 minutes, the altitude has decreased to 0 feet, which is the ground level.

Part C:

The ordered pair (0, 30,750) represents the initial value, where x=0. The initial value represents the altitude of the airplane before it started descending. In this problem, the initial value of 30,750 feet represents the altitude of the airplane when it was at cruising altitude.

Part D:

The rate of change in this equation is -1025. The rate of change represents the speed at which the altitude of the airplane is changing per minute. In this problem, the rate of change of -1025 feet per minute means that the altitude of the airplane is decreasing by 1025 feet every minute it descends.

Answer:

1. The wholesale cost of the bike is $93.75.

2. Andre will pay $100 before tax.

The system of inequalities of the given question is x>0, y>0 and 24x+8y=160

When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalties.

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

We are given that;

Price per hour for tutoring=$24

Price per hour for clearing tables=$8

Earning no less than $160

Work no more than in tutoring= 8hr

Maximum working for clearing table=5hr

Now,

x = number of hours tutoring y = number of hours landscaping

We cannot have negative values for either x and y, so xo and

x+y= total hours worked for both jobs combined

This total cannot exceed 11 hours

x+y≤11

Either x+y= 11 or x+y < 11

22x amount of money made from tutoring only = By amount of money made from landscaping only 22x+8y = total amount made from both jobs

24k+By 160 since he must make at least $160 Either 24x+8y = 160 or 24x+8y> 160

Therefore, the system of inequalities will be x>0,y>0,24x+8y=160

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The original salary was approximately $45,180.72.

Prior to a percentage increase or decrease, one must ascertain the beginning value of an amount: The amount must be represented as a percentage of the initial sum. Determine one percent of the starting sum. The original value may be obtained by multiplying by 100 because 100% is the original sum.

We can use algebra to resolve this issue. Let x represent the starting wage.

The issue states that following a 66% raise, the new compensation is $75,000 Mathematically, this can be expressed as:

x + 0.66x = 75000

By merging similar phrases to simplify the left side, we obtain:

1.66x = 75000

Finally, by multiplying both sides by 1.66, we can find the value of x:

x = 75000/1.66

x ≈ 45,180.72

Hence, the initial wage was roughly $45,180.72.

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Answer:

Step-by-step explanation:

2X3x2Xx

The area of the Trepezium will be 60 feet².

What is a trepezium, exactly?

Trapezoids have two parallel sides and two oblique sides. It is also known as a Trapezium. A trapezoid is a four-sided closed shape or figure having a space-filling perimeter. It is a 2D figurine, not a 3D figure. The bases of a trapezoid are the sides that are parallel to one another. Legs, also known as lateral sides, are non-parallel sides. Its height is determined by the distance between its parallel sides.

Area of a trepezium=1/2*(a+b)*h

where h=height or distance between two parallel lines

a and b are two parallel lines.

Now,

Given that a=14 feet, b=10 feet and h=5 feet

then area=1/2*(10+14)*5

=24/2*5

=12*5

=60 ft²

hence,

              The area of the Trepezium will be 60 feet².

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The value of the expression is -3/2, So correct option is A.

In mathematics, a fraction represents a part of a whole. A fraction consists of two numbers separated by a horizontal line called a fraction bar or a division sign. The number above the bar is called the numerator, and the number below the bar is called the denominator.

The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator. This fraction represents three parts out of a total of four equal parts.

Fractions can be written in different forms, such as proper fractions, improper fractions, and mixed numbers.

A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.

An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.

A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.

Fractions are used in many real-life situations, such as cooking, measuring, and financial calculations. They are also an essential part of mathematics and are used in operations such as addition, subtraction, multiplication, and division.

We can start by simplifying the expression inside the absolute value bars:

|1/6 - 3/4| = |(2/12) - (9/12)| = |-(7/12)| = 7/12

Now we can substitute this back into the original expression and simplify:

(7/4 - 8/3) - |1/6 - 3/4|

= (21/12 - 32/12) - 7/12 (converting fractions to have a common denominator)

= -11/12 - 7/12

= -18/12

= -3/2

Therefore, the value of the expression is -3/2.

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Answer:

What is Fraction ?

A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fractio" which means 'to break'.

A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.

An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.

A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.

Fractions are used in cooking, measuring, and financial calculations.

We can start by simplifying the expression inside the absolute value bars:

|1/6 - 3/4| = |(2/12) - (9/12)| = |-(7/12)| = 7/12

Now we can substitute

(7/4 - 8/3) - |1/6 - 3/4|

= (21/12 - 32/12) - 7/12 (converting fractions to have a common denominator)

= -11/12 - 7/12

= -18/12

= -3/2

Therefore, the value of the expression is -3/2.

Answer:

f-1(x)=x4+3 this is your answer

It can be put as 40 / 100 as a fraction, which if you needed, it can be further simplified to 4 / 10, or even 8 / 20.

Answer: The side of the square is 20 miles

Step-by-step explanation:

Since the area of square= side *side

given, area =400 square miles

400 = side *side

400= side²

√400=side

20 miles=side

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Answer:

Third side > 13 - 8 = 5 cm. Therefore, the length of the third side is between 5 cm and 9 cm, respectively.

Step-by-step explanation:

Answer:21>c>5

Step-by-step explanation:

a+b>c>a-b

so,

13+8>c>13-8

21>c>5

Hyperbolic tan x is verified to equal to  

To verify the identity using the definitions of the hyperbolic functions, we start with the definition of hyperbolic tangent:

tanh x = sinh x / coxh x =  (e^x - e^-x) / (e^x + e^-x)

We can simplify this expression by multiplying the numerator and denominator by e^x:

tanh x = (e^x - e^-x) / (e^x + e^-x) * (e^x / e^x)

tanh x = (e^2x - 1) / (e^2x + 1)

We can see that this expression is equivalent to the given identity

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The constant of proportionality of the equation y = 1 / 3 x is 1/3.

Proportional relationships are relationships between two variables where their ratios are equivalent.  In other words, proportional relationship is one in which two quantities vary directly with each other.

Therefore, proportional relationship can be represented as follows:

y ∝ x

y = kx

where

Therefore, the constant of proportionality of y = 1 / 3 x is 1 / 3

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The monthly cost for 39 minutes of calls is $15.34.

We can use the two given data points to form two equations and then solve for the unknown coefficients of the linear function.

Let the monthly cost (in dollars) be denoted by C, and let the total calling time (in minutes) be denoted by T. Then we can write:

C = aT + b

where a is the slope of the line (representing the rate of change of cost per minute of calling time), and b is the y-intercept of the line (representing the fixed monthly cost).

Using the given data points (34, 14.69) and (57, 17.68), we can form the following two equations:

14.69 = 34a + b (equation 1)

17.68 = 57a + b (equation 2)

Subtracting equation 1 from equation 2, we get:

17.68 - 14.69 = 57a - 34a + b - b

2.99 = 23a

a = 2.99/23

a = 0.13 (rounded to two decimal places)

Substituting the value of a into equation 1 (or 2), we get:

14.69 = 34(0.13) + b

b = 14.69 - 4.42

b = 10.27

Therefore, the linear function that represents the monthly cost in terms of total calling time is:

C = 0.13T + 10.27

To find the monthly cost for 39 minutes of calls, we can substitute T = 39 into this function:

C = 0.13(39) + 10.27

C = 5.07 + 10.27

C = $15.34 (rounded to two decimal places)

Therefore, the monthly cost for 39 minutes of calls is $15.34.

The cost price (CP) is the original price paid to purchase a product or asset. It is the total cost incurred to acquire or produce the item, including all direct and indirect costs such as the cost of raw materials, labor, overhead expenses, transportation, taxes, etc.

The cost price is an important factor in determining the profitability of a business or investment, as it directly affects the profit margin. The profit margin is the difference between the selling price (SP) and the cost price (CP), expressed as a percentage of the cost price.

Profit Margin = (SP - CP) / CP * 100%

For example, if a product is sold for $100 and the cost price is $70, then the profit margin is:

Profit Margin = ($100 - $70) / $70 * 100%

Profit Margin = 30%

This means that for every $1 of cost, the business makes a profit of $0.30. The profit margin can be used to evaluate the efficiency and competitiveness of a business, and to compare the profitability of different products or investments.

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Using trigonometric ratio, the value of tan V is √7 / 8

To find the value of tan V, we have to use trigonometric ratio.

In the triangle, we have the opposite side and the hypothenuse. We can find the adjacent side using Pythagoras theorem.

Substituting the values into the formula;

w² = v² + x²

(√71)² = (√7)² + x²

71 = 7 + x²

x² = 71 - 7

x² = 64

x = √64

x = 8

The value of tan V;

tan V = opposite /adjacent

tan V = √7 / 8

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The speed of the person in miles per hour is S = 3 mph

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the speed of the person in miles per hour be S

Now , the distance traveled by the person D = 1/4 miles

The time taken by the person to travel ( 1/4 ) miles = 1/12 of an hour

Now , speed of the person in miles per hour S = distance traveled by the person D / time taken by the person to travel ( 1/4 ) miles

On simplifying , we get

The speed of the person in miles per hour S = ( 1/4 ) / ( 1/12 )

The speed of the person in miles per hour S = ( 1/4 ) x 12

The speed of the person in miles per hour S = 3 miles per hour

Hence , the speed is 3 mph

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Answer:

Step-by-step explanation:

The digit 3 in the number 4693 has a place value of 3 tens or 30. Therefore, the value of the number 3 in the number 4693 is 30.

Answer:

Add 1 to both sides. Add 11 and 1 to get 12. Divide both sides by 4. Divide 12 by 4 to get 3.

Answer:

x = 132°

Step-by-step explanation:

x and y lie on a straight line and sum to 180° , that is

x + y = 180°

x + 48° = 180° ( subtract 48° from both sides )

x = 132°

The solution of the trigonometric equation for θ is given as follows:

θ = 80º.

The trigonometric equation for this problem is defined as follows:

sin(θ - 70) = cos(θ).

When two angles are complementary, that is, the sum of their measures is of 90º, we have that the sine of one angle is equals to the cosine of the other angle.

The angles for this problem are given as follows:

As the sine of one is equals to the cosine of the other, they are complementary, hence the angle θ is obtained as follows:

θ - 70 + θ = 90

2θ = 160

θ = 160/2

θ = 80.

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The value of 1+1 is 2.

Addition is a fundamental operation in mathematics that involves combining two or more numbers or quantities to find a total or sum. The process of addition involves adding together individual digits, numbers, or quantities to find their sum or total.

In the simplest form of addition, two numbers are added together to find their sum. For example, 2 + 3 = 5, where 2 and 3 are the addends, and 5 is the sum. The order in which the addends are added does not affect the sum, so 3 + 2 = 5 as well.

Addition can be extended to more than two numbers by adding each pair of numbers in turn. For example, to find the sum of 2, 3, and 4, we can add 2 + 3 first, which equals 5, and then add 5 + 4 to get the final sum of 9.

Addition can be represented visually using symbols such as the plus sign (+) and the equals sign (=). The plus sign is used to indicate that two numbers are being added together, while the equals sign indicates that the sum has been found.

Addition is used in many different applications, from simple arithmetic to complex mathematical models. It is a fundamental skill that is taught early on in mathematics education and is essential for understanding more advanced concepts in algebra, calculus, and other branches of mathematics.

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The percentage of women with weights that are within the limits is:

60.93%

Can be calculated using the normal distribution formula. First, we need to find the z-scores for both the lower and upper limits:

z-score for lower limit = (132.4 - 168.7) / 48.8 = -0.74

z-score for upper limit = (217 - 168.7) / 48.8 = 0.99

Next, we can use a z-table to find the corresponding probabilities for these z-scores:

Probability for lower limit = 0.2296

Probability for upper limit = 0.8389

Finally, we can subtract the lower probability from the upper probability to find the percentage of women with weights that are within those limits:
Percentage = 0.8389 - 0.2296 = 0.6093

Therefore, approximately 60.93% of women have weights that are within the limits of 132.4 lb and 217 lb.

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Answer:

translation point a cross the coordinator