say a certain manufacturing industry has 63.1 thosand jobs in 2008,but is

Answer:

D

Step-by-step explanation:

if x = 0 or x = 3 the function doesn’t exist

If x = 1  Y = 0

Answer:

y ≤ 5

Step-by-step explanation:

7y ≤ 20 + 3y

-3y         -3y

4y ≤ 20

y ≤ 5

\(7y\leq 20+3y\)

Simplify:

\(7y\leq 3y+20\)

Subtract 3y from both sides:

\(7y-3y\leq 3y-3y+20\)

\(4y\leq 20\)

Divide both sides by 4:

\(\dfrac{4y}{4} \leq \dfrac{20}{4}\)

\(\boxed{y\leq 5}\)

There is enough evidence to support the claim that the mean GPA of night students is less than the mean GPA of day students at the 5% level of significance.

To compare the mean GPA of night students and day students, we need to conduct a hypothesis test. We set the null hypothesis (H0) as the mean GPA of night students being equal to the mean GPA of day students (μN = μD), while the alternative hypothesis (H1) is that the mean GPA of night students is less than the mean GPA of day students (μN < μD).

The level of significance (α) is typically predetermined, but in this case, it is not given. We assume a significance level of α = 0.05.

Since the sample sizes of both groups are small, the t-distribution is appropriate for our analysis.

To calculate the test statistic (t), we use the formula: t = (X1 - X2) / √(S12/n1 + S22/n2). Here, X1 and X2 represent the sample means, S1 and S2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Given the values:

X1 = 2.45 (mean GPA of night students)

X2 = 2.03 (mean GPA of day students)

S1 = 0.72 (sample standard deviation of night students)

S2 = 0.65 (sample standard deviation of day students)

n1 = 25 (sample size of night students)

n2 = 60 (sample size of day students)

By plugging in these values into the formula, we find that the test statistic (t) is approximately 3.08 (rounded to 2 decimal places).

Next, we determine the p-value associated with the calculated test statistic. We can refer to the t-distribution table with the appropriate degrees of freedom (df = n1 + n2 - 2) and the chosen significance level (α). In our case, df is calculated as 83 (25 + 60 - 2). Consulting the table for α = 0.05, we find that the p-value is approximately 0.0018.

Finally, based on the p-value, we can make a decision. Since the calculated p-value (0.0018) is smaller than the chosen significance level (0.05), we reject the null hypothesis.

in summary there is enough evidence to support the claim that the mean GPA of night students is less than the mean GPA of day students at the 5% level of significance.

To know more about hypothesis, click here

https://brainly.com/question/29576929

#SPJ11

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

To know more about satisfies visit-

brainly.com/question/16993710

#SPJ11

Answer:

14/27

Step-by-step explanation:

7/3 ÷ 9/2

7/3 x 2/9 = 14/27

Answer:

3,125

Step-by-step explanation:

1. This sequence is similar to the Fibonacci sequence, where you add the two terms to get the next term and so on. (e.g. 1, 1, 2, 3, 5, 8, 13)

2. However, this differs from the Fibonacci sequence because instead of adding, we're multiplying. 1 x 5 = 5, 5 x 5 = 25, 5 x 25 = 125. Given this sequence, we have to multiply 25 by 125 next, and the product of that expression is 3,125!

There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

Let's start by representing the two consecutive even numbers as x and x+2. Then, the difference between their squares can be expressed as:

(x+2)^2 - x^2

Expanding the squares and simplifying, we get:

(x^2 + 4x + 4) - x^2

Which simplifies further to:

4x + 4

Factoring out 4, we get:

4(x + 1)                

This shows that the difference between the squares of consecutive even numbers is always a multiple of 4. Therefore, we have proven algebraically that the statement is true for all even numbers.          

Answer:

See below for proof.

Step-by-step explanation:

An even number is an integer (a whole number that can be either positive, negative, or zero) that is divisible by 2 without leaving a remainder. Therefore:

Consecutive even numbers are a sequence of even numbers that increase by 2 with each successive number. Therefore:

The difference between the squares of consecutive even numbers can be written algebraically as:

\((2n + 2)^2 - (2n)^2\)

Use algebraic manipulation to rewrite the expression:

\(\begin{aligned}(2n + 2)^2 - (2n)^2&=(2n+2)(2n+2)-(2n)(2n)\\&=4n^2+4n+4n+4-4n^2\\&=4n^2-4n^2+4n+4n+4\\&=8n+4\\&=4(2n+1)\end{aligned}\)

As the common factor of 4 can be factored out of the expression, this proves that the difference between the squares of consecutive even numbers is always a multiple of 4.

Answer:

All real numbers are solutions

Step-by-step explanation:

4(x+3)−7>x+3(x+1)

Step 1: Simplify both sides of the inequality.

4x+5>4x+3

Step 2: Subtract 4x from both sides.

4x+5−4x>4x+3−4x

5>3

Step 3: Subtract 5 from both sides.

5−5>3−5

0>−2

Explanation

Step 1: Simplify both sides of the inequality.

4x+5-4x>4x + 3, - 4x

Step 2: Subtract 4x from both sides.

4x+5-4x>4x+3-4x

5>3

Step 3: Subtract 5 from both sides.

5 - 5 > 3 - 5

0> -2

Answer:

All real numbers are solutions.

Answer:

3a+b

3(4)+3

12+3

15

Step-by-step explanation:

You substitute the variables with the given numbers. I think this is correct.

Answer:

8) a and c

9) b and c

Step-by-step explanation:

Explanation and work are in the picture :)

Answer:

A

Step-by-step explanation:

Hold on servers are swamped please wait.

So the expression is:

if we operate that:

a) after 30 minutes, they will 12.5 m apart

b)  25  is the distance between the boats changing 30 minutes after they leave port

The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.

Let x represent the length the shorter leg(west) of the right angle triangle.

Let y represent the length the longer leg(south) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

 = 20^2+15^2

 z = 25

but after 30 minutes one travels 10mph

and another 7.5mph

then

z= 12.5

learn more about of speed here

https://brainly.com/question/16955861

#SPJ4

Answer:

14

Step-by-step explanation:

Answer:

Y'(-5, 5)

Step-by-step explanation:

To find the coordinates of Y' after the translation, we apply the given rule to the coordinates of point Y(-3, 4).

Using the translation rule (x, y) → (x - 2, y + 1), we can substitute the coordinates of Y(-3, 4) into the rule:

x' = x - 2 = -3 - 2 = -5

y' = y + 1 = 4 + 1 = 5

Therefore, the coordinates of Y' are (-5, 5).

In a 30°-60°-90° triangle, the sides occur in a ratio of 1 to √3 to 2. In this case, x is half the length of the hypotenuse, so x = 4.

Or, using trig,

cos(30°) = x/8

x = 8 cos(30°) = 8 (1/2) = 4

Answer:

GH = 62°

Step-by-step explanation:

the chord- chord angle 45° is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , that is

45° = \(\frac{1}{2}\) (FE + GH) ← multiply both sides by 2 to clear the fraction

90° = FE + GH = 28° + GH ( subtract 28° from both sides )

62° = GH

Answer:

Paul squash with 9/20 part of squash and 11/20 parts of waterStep-by-step explanation:

3/7 part of squash :- Henry

9/20 parts of squash:-Paul

When we compare the 2 quantities we first find there LCM.

So LCM of 7 and 20 is 140

Now will convert them to equal unit and then compare

So ,

60/140 and 63/140

60 is less than 63

So the one with 63 amount of squash should be tastier than that of 60 amount of squash...

The statement "double *num2;" declares a pointer variable named num2. Option D) "Declares a pointer variable named num2" is the correct answer.

The asterisk (*) before the variable name indicates that num2 is a pointer variable. Pointers are variables that store memory addresses rather than values directly. In this case, the pointer variable num2 is expected to hold the memory address of a double type variable. However, the statement does not initialize the pointer or assign any specific memory address to it.

Therefore, The statement "double *num2;" declares a pointer variable named num2. Option D) "Declares a pointer variable named num2" is the correct answer.

Learn more about pointer variable here

https://brainly.com/question/32414194

#SPJ4

The statement 'double *num2;' declares a pointer variable named num2.

The statement 'double *num2;' is used to declare a pointer variable named num2. In programming, a pointer is a variable that stores the memory address of another variable. The asterisk (*) is used to indicate that num2 is a pointer variable. The 'double' keyword is used to specify the type of variable that num2 can point to, in this case, a double variable.

About statement here:

https://brainly.com/question/17238106

#SPJ11

The simplified expression is \((-2x^2 - 2 + 1)/(2x).\)

To simplify the expression (3/2x - 4) + (2/6 - 3x), we can first combine like terms. Let's work on each fraction separately:

For the first fraction, 3/2x - 4, we cannot directly combine the terms since the denominators are different. To add or subtract fractions, we need a common denominator. In this case, the least common denominator (LCD) is 2x. So, we multiply the numerator and denominator of the first fraction by x to obtain:

(3x)/(2x^2) - 4

Now, for the second fraction, 2/6 - 3x, the denominator is 6. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:

1/3 - 3x

Now, we can combine the two simplified fractions by finding a common denominator, which is 2x^2:

(3x)/(2x^2) - 4 + 1/3 - 3x

To add these fractions, we need to have the same denominator, so we multiply the second fraction by (2x^2)/(2x^2):

(3x)/(2x^2) - 4 + (2x^2)/(6x^2) - (6x^3)/(2x^2)

Combining the like terms:

(3x - 6x^3 + 2x^2 - 8x^2)/(6x^2)

Simplifying further:

(-6x^3 - 6x^2 + 3x)/(6x^2)

Finally, we can divide every term by the greatest common factor, which is 3x:

(-2x^2 - 2 + 1)/(2x)

The simplified expression is \((-2x^2 - 2 + 1)/(2x).\)

For more such questions on  simplified expression

https://brainly.com/question/723406

#SPJ8

The ordered pairs which correctly lists all of the x-intercepts of the graphed function include the following: C. (1, 0), (2, 0), and (–3, 0).

In Mathematics, the x-intercept can be defined as the point at which the graph of a particular function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).

By critically observing the given graphed function (see attachment), the x-intercept is given by the following ordered pairs:

This ultimately implies that, this function would cross the x-coordinate (x-axis) at points (1, 0), (2, 0), and (-3, 0).

Read more on function here: https://brainly.com/question/9795474

#SPJ1

The volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L, calculated using the ideal gas law equation.

To compute this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the initial temperature of 25 °C to Kelvin:

T1 = 25 + 273.15 = 298.15 K

Next, we can rearrange the ideal gas law equation to solve for V2:

V2 = (P1 * V1 * T2) / (P2 * T1)

We have:

P1 = 1.08 atm (initial pressure)

V1 = 50.0 L (initial volume)

P2 = 0.855 atm (final pressure)

T2 = 10.0 °C (final temperature)

Converting the final temperature to Kelvin:

T2 = 10 + 273.15 = 283.15 K

Substituting the values into the equation:

V2 = (1.08 * 50.0 * 283.15) / (0.855 * 298.15)

V2 ≈ 42.81 L

Therefore, the volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L.

To know more about ideal gas law refer here:

https://brainly.com/question/30458409#

#SPJ11

Answer:

88 trucks

Step-by-step explanation:

Ratio of cars : vehicles = 5:13

Hence, the ratio of trucks : vehicles = 8:13

143/13 = 11

If the number of vehicles is 143,

we have to multiply both sides of the ratio by 11:

8*11 : 13* 11

88 : 143

Hence, there are 88 trucks for every 143 vehicles.

Hope this answers your question... Have a wonderful time ahead at Brainly!

The series on the right-hand side is a convergent p-series with p = 2. Therefore, by the comparison test, the original series converges as well.

To prove that if lim an/bn = 0 and bn is convergent, then an is also convergent, we can use the limit comparison test. Since bn is convergent, we know that its terms approach 0. Therefore, we can choose a positive number ε such that 0 < ε < bn for all n. Then, we have:

lim (an/bn) = 0
=> for any ε > 0, there exists N such that for all n > N, |an/bn| < ε
=> for all n > N, an < εbn

Since ε is a positive constant and bn is convergent, we know that εbn is also convergent. Therefore, by the comparison test, an is convergent as well.

To show that the series ∑(ln n)/(n^3 ln n^1/2 e^n) converges, we can use the comparison test again. Note that:

ln n^1/2 = (1/2)ln n
ln n^3 = 3ln n

Therefore, we can rewrite the series as:

∑[(1/2)/(n^2 e^(ln n))] = (1/2)∑(1/(n^2 n^ln(e)))

Since n^ln(e) > 1 for all n, we have:

(1/2)∑(1/(n^2 n^ln(e))) < (1/2)∑(1/n^2)

The series on the right-hand side is a convergent p-series with p = 2. Therefore, by the comparison test, the original series converges as well.

To know more about Convergent visit :

https://brainly.com/question/31756849

#SPJ11

Answer:

Complementary angles are those that sum up to 90o.Vertical angles have equal measures. Therefore, if vertical angles measure 45o each, they are complementary.

Explanation: Here how it might look if angles ∠1 and ∠3 are measured at 45o.

The range in which 95% of the scores lie is between 75 and 95.

According to the Empirical Rule: For a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, approximately 95% of the data falls within 2 standard deviations of the mean, and approximately 99.7% of the data falls within 3 standard deviations of the mean.

So, about 95% of the scores lie between 75 and 95. T

This is because the mean score is 85 and one standard deviation is 5, so one standard deviation below the mean is 80 (85-5) and one standard deviation above the mean is 90 (85+5).

Two standard deviations below the mean are 75 (85-2*5) and two standard deviations above the mean is 95 (85+2*5).

Therefore, the range in which 95% of the scores lie is between 75 and 95.

Know more about range here:

https://brainly.com/question/2264373

#SPJ11

Answer:

Let's start by using a proportion to find the total number of questions on the test. We know that Charles answered 23 questions correctly and received a grade of 92%, which means he missed 8% of the questions.

Let x be the total number of questions on the test. Then 8% of the questions that Charles missed can be expressed as 0.08x.

The number of questions that Charles answered correctly plus the number of questions he missed must add up to the total number of questions on the test:

23 + 0.08x = x

Simplifying and solving for x, we get:

0.92x = 23

x = 23 / 0.92

x ≈ 25

Therefore, the total number of questions on the test was approximately 25.