A company manufacturing computer chips finds that 8% of all chips manufactured are defective. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. A hypothesis test is performed to determine if the additional training was effective in lowering the defect rate. The correct value of the Z-statistic is

Answer:

y = x - 3

Step-by-step explanation:

1. slope-intercept form: y = mx + b
given: m = 1;  (-4, -7)

2. plug in the values from the given point [(x, y) --> (-4, -7)] into the linear equation of the slope-intercept form.
y = mx + b
-7 = 1(-4) + b
-7 = -4 + b
b = -3

3. construct the final equation in slope-intercept form.
y = mx + b
y = x - 3

Therefore, number of pages of study guide Gloria have=9

In mathematics, an equation is a formula that uses the equals symbol (=) to represent how two expressions are equivalent. the act of comparing two things or "the equation of science with objectivity."

given

no. of  study guides for language art= 3

no. of  pages in each study guides=3

so no. of pages of study guides= no. of  study guides for language art*

no. of  pages in each study guides

3*3=9

therefore, number of pages of study guide Gloria have=9

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Answer:

x=3

Step-by-step explanation:

7-3=4 or 4+3=7

In the given equation, Y = 3x is at (0, 3) and a line passes through (-3, 0).

A mathematical statement known as equation is given by joining two expressions with the equal sign. For instance, 3x - 5 = 16 is an equation. This equation can be solved, and the result shows that the value of the variable x is 7.

A mathematical equation links the two phrases on either side of the sign. It typically only contains an equal sign and one variable. similar to 2x - 4 = 2.

Either identities or conditional equations can be used to classify equations. Each value of the variables corresponds to a specific identity. A conditional equation can only be true for a certain range of variable values. An equation is represented by two expressions being separated by the equals sign ("=").

A line goes through (- 3, 0) and (0, 3)

The equation is

y - y1 = y2 - y1/ x2- x1

y - 0 = 3 - 0 / 0 - (-3) (x - (-3)

y = x + 3

y = 3x

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Answer:

It's 6 and -5.

Step-by-step explanation:

:D

Answer:

Step-by-step explanation:

If the weight of Ram and Sam are in the ratio 4:7, and the weight of Aari and Ram are in the ratio 3:2, you can use this information to set up a system of equations to represent the weights of the three people. Let's say that Ram weighs x kilograms. Then, the weight of Sam is 7x/4 kilograms, and the weight of Aari is 3x/2 kilograms.

The maximum difference in weight between any two people is 15 kilograms, so we can set up the following equation to represent this constraint:

|x - (7x/4)| <= 15

|x - 3.5x| <= 15

|-2.5x| <= 15

|x| <= 6

This equation tells us that the weight of Ram (x) must be less than or equal to 6 kilograms or greater than or equal to -6 kilograms.

Since the weight of a person cannot be negative, the maximum weight for Ram is 6 kilograms. Therefore, the maximum weight for Sam is 7x/4 = 76/4 = 10.5 kilograms, and the maximum weight for Aari is 3x/2 = 36/2 = 9 kilograms.

Thus, the maximum weight of the three people is 6 + 10.5 + 9 = 25.5 kilograms.

Based on the definition of isosceles triangle, the value of x is: 25.

An isosceles triangle has two base angles that are equal and are opposite two equal sides.

The image shows an isosceles triangle that is inscribed in the circle. Therefore, the two base angles will each equal (2x - 5).

To find the value of x, create the equation below:

2(2x - 5) + 90 = 180

4x - 10 + 90 = 180

4x + 80 = 180

Subtract 80 from both sides:

4x + 80 - 80 = 180 - 80

4x = 100

Divide both sides by 4:

4x/4 = 100/4

x = 25

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Hannah drove 450 miles to her brother's house at an average speed of 60 miles per hour. How long did she take? (Time)

[tex]t=\dfrac{Distance}{Speed}[/tex]

[tex]t=\dfrac{450}{60}[/tex]

[tex]t=7.5hours[/tex]

Remember, time must be converted to seconds as it is the unit for time.

7.5 hours to seconds

1 hour = 3600 seconds

3600 seconds * 7.5 hours

[tex]=\fbox{27000 seconds}[/tex]

Answer:

-----------------------

Initial number of sports team:

Number after new members joined:

60% of 150 members are men, number  of men is:

Number of women:

Number of newly joined women:

Perimeter of the rectangle:

Area of rectangle:

New dimensions:

New perimeter:

New area:

New perimeter is same as previous one but new area is smaller.

Answer:

140.69

Step-by-step explanation:

I hope this helps

The probability that the student is

(a) enrolled in mathematics is equal to [tex]\frac{3}{10}[/tex]

(b) enrolled in English is equal to [tex]\frac{11}{20}[/tex].

(c) enrolled in both is equal to [tex]\frac{11}{80}[/tex].

(d) enrolled in mathematics or English is equal to [tex]\frac{57}{80}[/tex].

(e) enrolled in English but not in mathematics is equal to [tex]\frac{33}{10}[/tex].

(f) not enrolled in English or is enrolled in mathematics is equal to [tex]\frac{23}{80}[/tex].

What is probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The total number of students in college is 400.

Students enrolled in Mathematics = 120.

Students enrolled in English = 220.

Students enrolled in both Mathematics and English = 55.

(a) The probability that the student is enrolled in mathematics is the Number of students enrolled in mathematics divided by the total number of students which is equal to [tex]\frac{120}{400} =\frac{3}{10}[/tex].

(b) The probability that the student is enrolled in English is the Number of students enrolled in English divided by the total number of students which is equal to [tex]\frac{220}{400} =\frac{11}{20}[/tex].

(c) The probability that the student is enrolled in Both is equal to the number of students enrolled in Both divided by the total number of students which is equal to [tex]\frac{55}{400} =\frac{11}{80}[/tex].

(d)  The probability that the student is enrolled in mathematics or English is the Number of students enrolled in mathematics or English that is the Number of students in (Maths+English - Both) divided by the total number of students which is equal to [tex]\frac{120+220-55}{400} =\frac{285}{400}=\frac{57}{80}[/tex].

(e) The probability that the student is enrolled in English but not in mathematics is the Number of students enrolled in (English- enrolled in both) divided by the total number of students which is equal to [tex]\frac{220-55}{400} =\frac{165}{400}=\frac{33}{80}[/tex].

(f) The probability that the student is neither enrolled in mathematics nor English is the Total Students - (Maths+English-both) divided by the total number of students which is equal to [tex]\frac{400-(120+220-55)}{400} =\frac{115}{400}=\frac{23}{80}[/tex].

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Answer:

a) 3193.75

b)39,693.75

The hypotenuse is always the longest side of a right triangle, hence it will always be across from the biggest angle, which is a right angle.

The hypotenuse of a right triangle is occasionally across from the right angle, therefore it will only be across from the smallest angle when the right angle is the smallest angle of the triangle.

The hypotenuse is never the longest side of any triangle, and the longest side of any triangle is always across from the smallest angle of the triangle.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.

Here,

It is always true that The hypotenuse is the longest side of a right triangle, so it will be across from the largest angle, which is a right angle.

It is sometimes true that The hypotenuse is across from the right angle of a right triangle, so it will only be across from the smallest angle when the right angle is the smallest angle of the triangle.

It is never true that The hypotenuse is the longest side and the longest side of any triangle is across from the smallest angle of the triangle.

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Answer:

YES

Step-by-step explanation:

For country A , the doubling time = 26

For country B , the growth rate = 1.5

Define growth rate?

The growth rate is the fractional change per unit time, ∆x. x. ∆t , the fractional change divided by the length of the time period.

For Country A :

      Formula for doubling time,

      T = [tex]\frac{log 2}{log (1 + \frac{k}{100} )}[/tex]

The given growth rate , k% = 2.7%

T = [tex]\frac{log 2}{lod (1 + \frac{2.7}{100} )}[/tex]

  = [tex]\frac{log 2}{log (1 + 0.027)}[/tex]

  = [tex]\frac{log 2}{log (1.027)}[/tex]

  = 26.017

  ≅ 26

Therefore, the doubling time (T) = 26 years

For Country B :

        Formula for growth rate

           k = 100 [tex][2^{1/T} - 1][/tex]

k = 100 [tex][2^{1/46} - 1 ][/tex]        (Since T = 46 years)

k = 100 [1.01518 - 1]

k = 100 [0.01518]

k = 1.518

k ≅ 1.5

Therefore, the growth rate is 1.5 % per year.

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Answer:

Using the inclusion and exclusion principle, we can calculate the percentage of members who play all three sports as follows:

60% of members play Tennis, 50% of members play Cricket, and 70% of members play Football.

Therefore, 60% + 50% + 70% = 180% of members play at least one of the sports.

However, this count includes members who play more than one sport, so we need to subtract out the members who play two sports and add back in the members who play all three sports.

20% of members play Tennis and Cricket, 40% of members play Cricket and Football, and 30% of members play Football and Tennis.

Therefore, 20% + 40% + 30% = 90% of members play at least two sports.

Subtracting this number from the total number of members who play at least one sport gives us 180% - 90% = 90% of members who play at least one sport but not all three sports.

To find the number of members who play all three sports, we need to subtract this number from the total number of members who play at least one sport:

180% - 90% = 90% of members who play at least one sport but not all three sports

180% - 90% = 90% of members who play all three sports

Therefore, according to the inclusion and exclusion principle, 90% of members play all three sports.

If someone claimed that 20% of members play all three sports, this would be incorrect based on the calculations using the inclusion and exclusion principle. The correct number of members who play all three sports is 90%, not 20%. This can be verified by using the given information about the percentage of members who play each individual sport and the percentage of members who play two sports in combination.

To clarify, the inclusion and exclusion principle states that to find the number of elements in a union of sets (in this case, the number of members who play at least one sport), we can add the number of elements in each set (the percentage of members who play each individual sport) and then subtract the number of elements that are counted multiple times (the percentage of members who play two sports in combination). We then add back in the elements that were subtracted out in the previous step (the percentage of members who play all three sports).

Using this principle, we were able to calculate that 90% of members play all three sports, rather than the 20% claimed by someone.

Step-by-step explanation:

Answer:

Only X = X - ( (X∩Y - X∩Y∩Z) + X∩Y∩Z + (Z∩X - X∩Y∩Z) )

Only X = 600 - ( (200-200) + 200 + ( 300-200) )

Only X = 600 - (0 + 200 + 100)

Only X = 600 - (300)

Only X = 300

Only Y = Y - ( (Y∩Z - X∩Y∩Z) + X∩Y∩Z + (X∩Y - X∩Y∩Z) )

Only Y = 500 - ( (400-200) + 200 + ( 200-200) )

Only Y = 500 - (200 + 200 + 0)

Only Y = 500 - (400)

Only Y = 100

Only Z = Y - ( (Y∩Z - X∩Y∩Z) + X∩Y∩Z + (Z∩X - X∩Y∩Z) )

Only Z = 500 - ( (400-200) + 200 + ( 300-200) )

Only Z = 500 - (200 + 200 + 100)

Only Z = 500 - (500)

Only Z = 200

Step-by-step explanation:

The correct answer is: mean = 10.44/30 = 0.348, standard error (9.2/30)^2 = 0.094

When you take random samples of 30 pennies and find the mean age in each sample, the distribution of the sample means will have a mean that is equal to the mean of the population (10.44 years in this case) divided by the sample size (30 in this case). This is known as the sampling distribution of the mean.

The standard error is a measure of the spread or dispersion of the sampling distribution. It is calculated as the standard deviation of the population divided by the square root of the sample size. In this case, the standard error would be (9.2/30)^2 = 0.094.

The other options do not correctly describe the center and spread of the sampling distribution of the means. Option A gives the mean and standard deviation of the population, not the sampling distribution. Option B gives the correct standard error, but the mean is incorrect. Option D gives the correct mean, but the standard error is incorrect.

∴ The correct answer is: mean = 0.348, standard error = 0.094.

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Answer: 15

Step-by-step explanation:

To solve this problem, we first need to translate the given information into a system of equations. Let's call the first number x and the second number y. Since the sum of the two numbers is 22, we know that x + y = 22.

The second statement says that three times one number increased by five is the same as twice the other number decreased by four. We can translate this into an equation by substituting x and y for the two numbers and using the given information:

3x + 5 = 2y - 4

Now that we have a system of equations, we can solve for x and y. First, we'll solve for x by adding four to both sides of the second equation:

3x + 9 = 2y

Then, we can divide both sides by three to get the value of $x$:

x = {2y - 9} / {3}

Next, we can substitute this expression for x into the first equation to solve for y:

y + {2y - 9} / {3} = 22

We can simplify this equation by multiplying both sides by three:

3y + 2y - 9 = 66

Combining like terms on the left side, we get:

5y - 9 = 66

Then, we can add nine to both sides to solve for y:

5y = 75

Finally, we can divide both sides by five to find the value of y:

y = 15

Now that we know the value of $y$, we can substitute it back into the expression for $x$ to find the value of $x$:

x = \frac{2 \cdot 15 - 9}{3} = \frac{27}{3} = 9

Since we want the larger of the two numbers, the answer is 15

Using the principle of proportional relationship, the time taken by the turtle to walk one mile is 2.1667 hours

What is proportional relationship?

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

Creating a system of proportional expression :

Cross multiply :

1.5t = (3.25 × 1)

1.5t = 3.25

Divide both sides by 1.5

t = (3.25 ÷ 1.5)

t = 2.1667 hours

Therefore, the time taken per mile is 2.1667 hours

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The turtle needs 2.16 hours to move a mile using the proportional relationship principle.

What does the word "proportional" mean?

Proportional relationships form when the ratios of two variables are equal. The fact that one variable is consistently equal to the constant value of the other in a proportionate connection is another way to think of them. The "constant of proportionality" is the name of this constant.

For instance, the time it takes a train to travel 50 kilometers per hour is equal to the time it needs to travel 250 kilometers in 5 hours. e.g., 250km/5 hours at 50 km/h.

Establishing a proportional expression system

Cross multiply :

1.5t = (3.25 × 1)

1.5t = 3.25

t = (3.25 ÷ 1.5)

t equals 2.16 hours

Consequently, the time required for each mile is 2.16 hours.

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The exact value of the expression cos(arcsin(15/17)) is 1.

The inverse sine function, denoted as arcsin, gives the angle whose sine is a given value. Since the range of the sine function is -1 to 1, the range of the arcsin function is -90 degrees to 90 degrees.

In this case, the value of the expression is given by cos(arcsin(15/17)). To find the exact value of this expression, we can first use the definition of the inverse sine function to find the value of arcsin(15/17). Since the sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle, we can set up the following equation:

Since the sine function has a period of 180 degrees, we can add or subtract multiples of 180 degrees to the angle x to find the value of the expression for all possible angles. For example,

Using this information, we can find the values of the expression for all possible angles:

x = arcsin(15/17) => cos(arcsin(15/17)) = cos(x)

                                                           = √(1 - sin^2(x))

                                                           = √(1 - (15/17)^2)

                                                           = √(289/289)

                                                           = 1

x + 180 = arcsin(15/17) + 180 => cos(arcsin(15/17) + 180) = cos(x + 180)

                                                                                         = -cos(x)

                                                                                         = -1

x - 180 = arcsin(15/17) - 180 => cos(arcsin(15/17) - 180) = cos(x - 180)

                                                                                       = -cos(x)

                                                                                       = -1

Since the cosine function has a period of 360 degrees, the values of the expression for all possible angles can be expressed as:

cos(arcsin(15/17) + 360k) = 1 for all integers k

cos(arcsin(15/17) + 180 + 360k) = -1 for all integers k

Therefore, the exact value of the expression cos(arcsin(15/17)) is 1.

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Albert's total earnings for the last two weeks is $320.82.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Albert got a regular salary of $312 every two weeks.

Also given, he makes 9% of the commission on sales and he sold worth $98.

So, His total earnings of Albert is the sum of his fixed earnings and the percentage of commission he made which is,

= $[312 + (9/100)×98].

= $[312 + 8.82].

= $320.82.

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Answer:

[tex] \sf \: 4 \frac{4}{8} [/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: 2 \frac{3}{8} + 2 \frac{1}{8} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: 2 \frac{3}{8} + 2\frac{1}{8} [/tex]

[tex] \sf \rightarrow \: \frac{19}{8} + \frac{17}{8} [/tex]

[tex] \sf \rightarrow \: \frac{(19 + 17)}{8} [/tex]

[tex] \sf \rightarrow \: \frac{36}{8} [/tex]

[tex] \sf \rightarrow \: 4 \frac{4}{8} [/tex]

Hence, the answer is 4 4/8.

Step-by-step explanation:

0.05 = 2a + 5b

0.2 = 8a + 2b

the trick is to multiply the equations with contacts, so that an addition or subtraction of the equating can be made, and one variable is eliminated in that result, which allows us then to solve for the second variable.

and then we use one of the original equations to solve for the first variable.

in our case, multiplying the first one by 4 and then subtracting the second one sends to be the simplest approach :

0.2 = 8a + 20b

- 0.2 = 8a + 2b

-------------------------

0 = 0 + 18b

b = 0/18 = 0

0.05 = 2a + 5b = 2a + 5×0 = 2a

a = 0.05 / 2 = 0.025

a = 0.025

b = 0

Step-by-step explanation:

To find out how much you need to deposit in an account now to have a certain amount after a certain number of days, you can use the formula:

P = F / (1 + r * t)

where:

P is the present value or the amount you need to deposit now.

F is the future value or the amount you want to have in the account after a certain number of days.

r is the annual interest rate, expressed as a decimal.

t is the number of years for which the money will be invested.

In this case, you want to have $5,000 in the account in 697 days, which is equivalent to 697 / 365 = 1.91 years. The annual interest rate is 0.0375. Plugging these values into the formula, we get:

P = 5000 / (1 + 0.0375 * 1.91)

Solving this equation, we find that you would need to deposit $4,921.15 in your account now to have $5,000 in the account in 697 days.

The slope of the equation is 0.50 and its interpretation in the context of the problem is that Emily will spend 0.50 dollars, or 50 cents, for each minute of use.

The slope-intercept form of a straight line is used to get the equation of a line. To utilize the slope-intercept formula, we need to know the line's slope and the point at which it crosses the y-axis, or intercept. For a straight line with slope "m" and y-intercept "b," the slope-intercept form equation is: y = mx + b.

Given equation,

C = 9 + 0.50t

Here, c = 0.50

Hence, the slope is 0.50.

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The value of the missing side QT using the similar triangles concept is;

QT = 6

We are given;

TU is parallel to QR.

TS = 12

QR = 18

Now, TU is 6 more than QT, Thus;

TU = QT + 6

From the concept of similar triangles, we can say that;

QS/TS = QR/TU

Plugging in the relevant values gives us;

(12 + QT)/12 = 18/(QT + 6)

(12 + QT)(QT + 6) = 18*12

QT² + 18QT + 72 - 216 = 0

QT² + 18QT - 144 = 0

Solving this using online quadratic equation calculator gives;

QT = 6

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The length of the larger filter is 6 inches.

What is area of rectangle ?

The area of a rectangle is the product of its length and width. That is, A = l x w where l is the length and w is the width

Given:

Small heater :  Length = 20 inches , width = 16 inches

larger heater :  Length = ?, width = 56 inches

Since, larger heater requires a similar filter

∴Area of  small heater = Area of  larger heater

(length * width) of smaller heater = (length * width) of larger heater

20 * 16 = length * 56

length = 20*16/56 = 320/56

length = 5.714

0r , length = 6 inches

Hence , the length of the larger filter is 6 inches.

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The interest rate should be 6.4116% to achieve the required goal.

What is simple interest?

The daily interest rate, the principal, and the number of days between payments are multiplied to determine simple interest. Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest. Simple-interest loans are frequently used for auto loans and short-term personal loans.

Given data:

A = 4176 + 1071 = $5247

t = 4 years

P = $4176

r = ?

By using the formula,

  A = P(1 + rt)

  r = (1/4)((5247/4176) - 1)

    = 0.06411638

   r = 0.06411638

Converting r decimal to R a percentage

R = 0.06411638 * 100

  = 6.4116% per year

Hence, the interest rate should be 6.4116% to achieve the required goal.

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Answer: 6y = 7x - 40

Step-by-step explanation: