PLEASE HELP WILL GIVE LOTS OF POINTS!!!

Answer:

Utility's percent Change from 2010 to 2020 = 7%

Step-by-step explanation:

Jobs available at the utility industry in 2010= 428.5 thousand

Average rate of decline = 3 thousand

Years between 2010 and 2020

Utility's percent Change from 2010 to 2020 = Total change in jobs / jobs in 2010 × 100

Total change in jobs:

There are 10 years between 2010 and 2020

Jobs decline at an average of 3 thousand per year

Total change in jobs= 10 years × 3 thousand

= 30 thousand

Utility's percent Change from 2010 to 2020 = Total change in jobs / jobs in 2010 × 100

= 30 thousand / 428.5 thousand × 100

= 0.07 × 100

= 7%

Utility's percent Change from 2010 to 2020 = 7%

Answer:

11

Step-by-step explanation:

30-2(7+2)-1

30-2(9)-1

Then multiplication

30-18-1

Then left to right

12-1

Then again

So your answer is 11

Hope that helps!

Answer:

31.41592...

Step-by-step explanation:

If the radius of the circle is 10 inches, the circle's circumference is 31.4 because you calculate circumference as follows:

x = r * pi (3.1415926535)

Using Substitution method ,

the solution of expression is either

x =( -5 +√21 )/2 or x = ( -5-√21 )/2.

Substitution method : In mathematics, the substitution method is generally used to solve a system of equations.

In this method, first solve the equation for one variable and substitute the value of the variable into the second equation.

Finally, solve the equation to find the value of the second variable.

We have given expression,

(x + 4)² – 3(x + 4) – 3 = 0

use substituion, a = (x+4)

then we get , a² - 3a - 3 = 0

the above equation is quadrtic equation.

we solve it by using the formula of finding roots of a quadratic equation.

formula for px² + qx + c = 0 quadratic equation is x =( -q +- √q²- 4qc )/2p

so, we have p= 1 , q = - 3 , c = -3

putting the values in above formula we get,

a ={ -(-3) +- √9 - 4×1(-3)}/2×1

=> a = { 3 +/- √21}/2

substitute, a= x+ 4 => x = a-4

=> x = (3 +- √21)/2 - 4 = 1/2 ( 3 +- √21 - 8)

=> x = 1/2( -5 +- √21)

either x = 1/2( -5+√21) or। x = 1/2(-5 -√21)

Hence, the solution for given equation are

x = (-5+√21)/2 or (-5-√21)/2

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Answer:

None of the first 4 do. so I guess the answers E.

Step-by-step explanation:

Answer: x= 114/5

Step-by-step explanation:

Opposite angles in between parallel lines are equal. Just solve for x. (5x-3)=117  

Answer:

smaller = 25, bigger = 65

Step-by-step explanation:

x = smaller

y = bigger

2x + 15 + x = 90

3x + 15 = 90

3x = 75

x = 25

y + x = 90

y + 25 = 90

y = 65

Answer:

StartFraction x over 7.5 EndFraction = StartFraction 12 over 1 EndFraction

Step-by-step explanation:

Here, in this question, given that Rosa earns $12 in an hour, she earns x dollars in 7.5 hours. So we are interested in finding the value of x.

Let’s write this in terms of proportion;

$12 = 1 hour

$x = 7.5 hours

$12 * 7.5 hours = $x * 1 hour

So this can be rewritten as;

$x/7.5 = $12/1 hour

Answer: Start Fraction x over 7.5 End Fraction Start Fraction 12 over 1

explanation:

Answer:

580 cm

Step-by-step explanation:

To find the surface area you just need to find the area of every side of the box and add them together.

SO- the equation for this would be

SA (Surface Area) = 2(20 x 10) + 2(20 x 3) + 2(10 x 3)

SA = 2(200) + 2(60) + 2(30)

SA = 400 + 120 + 60

SA = 520 + 60

SA = 580

Answer: if the formula for this question is f=52/d, then

D’s equation is (πd^2)/4.

E’s equation is (676 π)/f^2

Step-by-step explanation:

MML

Parabola equation , characteristic points

Vertex is the point of minimum-max value

A Directrix is a line outside parabola

Vertex is at (x,y) = (4,-5)

Parabola equation in general is

(x-h)^2 = 4•c•(y-k)

here c = -9

and (h,k) = (4,-5)

Then

(x-4)^2 = 4•(-9) •(y+5) = (-36)•(y+5)

(x-4)^2 = (-36)•(y+5)

Now divide by (-36)

-0.06((x-4)^2 = y + 5

-0.06(x-4)^2 - 5 = y

Looking at options, right answer comes to be D) , last option

Answer:

The length of the hypotenuse = 25 inches

Step-by-step explanation:

A right triangle has leg lengths of 7 inches and 24 inches.

Given

Pythagorean Theorem

For a right-angled triangle with sides 'a' and 'b', the hypotenuse 'c' is

defined as:

\(c=\sqrt{a^2+b^2}\)

so substituting the values

\(c=\sqrt{7^2+24^2}\)

\(c=25\) inches

Thus, the length of the hypotenuse = 25 inches

Answer:

C

Step-by-step explanation:

The equation of the line in the slope-intercept form is: \(y = 4 - \frac{3x}{2}\).

The slope of the parallel line is the same: \(m = - \frac{3}{2}\).

So, the equation of the parallel line is: \(m = - \frac{3x}{2} + a\).

To find a, we use the fact that the line should pass through the given point: \(-3 = (-\frac{3}{2})*(4)+a\).

Thus, \(a=3\).

Therefore, the equation of the line is: \(y = 3 -\frac{3x}{2}\).

The blanks are shown below for the area of hexagon with sides equal to 12cm.

In geometry, a hexagon is defined as a six-sided polygon. The two-dimensional form contains six sides, six vertices, and six angles.

All of the fill in the blanks are answered below:

(1) The number of  equilateral triangles are 6

(2) The measure of each of the three angles in the equilateral triangle 60°

(3) If we cut an equilateral triangle down the middle the special right triangle we create is 30-60-90

(4)  The vocabulary word for the green line is perpendicular bisector.

(5) The length of the short side of one 30-60-90 triangle is 4cm

(6) What is the length of the hypotenuse of one 30-60-90 triangle is 8cm

(7) Using the properties of 30-60-90 triangles,  the length of the long leg. is 4√3cm

(8) The height of the equilateral triangle is 4√3cm

(9) The area of one equilateral triangle is ½(8)(4√3) = 16√3 cm²

(10) The area of one equilateral triangle by the number of triangles. is 8(16√3) = 128√3 cm²

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Using properties of right angle, The value of a will be 32 units.

Particular Right Triangle Formula

The right triangle formula, which states that the square of a right-angled triangle's right triangle is equal to the product of its other two squares, is the fundamental Pythagoras theorem formula.

How long are the other two legs if a hypotenuse of a triangle with a 45°, 45°, and 90° angle is 32 units.

We are aware that Leg: Ankle: Length x = x: x: x2 is the formula for a triangle with a 45°, 45°, and 90° angle.

We can state that x2 = 32 because it is a known that the hypotenuse equals 32. As a result, x = 3 is determined.

After replacing this number of x = 3, the lengths of the empty sides may now be determined.

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Complete question -

Find values of a and b -

$10.50

10 Tickets would be $105.00

$105.00 - $10.50 = $94.50 so 9 Tickets would be $94.50

$105.00 + $94.50 = $199.50

$205.00 - $199.50 = $5.50 which isn't enough for another ticket.

10 Tickets + 9 Tickets = 19 Tickets.

The simplified expression is \(X = A \cdot \overline{B}\).

41. De Morgan's Theorems state the following:

a) De Morgan's First Theorem: The complement of the union of two sets is equal to the intersection of their complements. In terms of Boolean algebra, it can be expressed as:

\(\overline{A \cup B} = \overline{A} \cap \overline{B}\)

b) De Morgan's Second Theorem: The complement of the intersection of two sets is equal to the union of their complements. In terms of Boolean algebra, it can be expressed as:

\(\overline{A \cap B} = \overline{A} \cup \overline{B}\)

42. Now, let's use the two De Morgan's theorems to simplify the given expression:

\(X = \overline{\overline{A(B + \bar{A})}}\)

Using De Morgan's Second Theorem, we can distribute the complement over the sum:

\(X = \overline{\overline{A} \cdot \overline{(B + \bar{A})}}\)

Now, applying De Morgan's First Theorem, we can distribute the complement over the sum inside the brackets:

\(X = \overline{\overline{A} \cdot (\overline{B} \cap \overline{\bar{A}})}\)

Since \(\overline{\bar{A}}\) is equal to \(A\), we can simplify further:

\(X = \overline{\overline{A} \cdot (\overline{B} \cap A)}\)

Applying De Morgan's First Theorem again, we can distribute the complement over the intersection:

\(X = \overline{\overline{A} \cdot \overline{B} \cup \overline{A} \cdot A}\)

Since \(A \cdot \overline{A}\) is always equal to 0, we can simplify further:

\(X = \overline{\overline{A} \cdot \overline{B} \cup 0}\)

The union of any set with 0 is equal to the set itself:

\(X = \overline{\overline{A} \cdot \overline{B}}\)

Finally, applying the double complement law (\(\overline{\overline{X}} = X\)), we get:

\(X = A \cdot \overline{B}\)

Therefore, the simplified expression is \(X = A \cdot \overline{B}\).

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Q1 . The lower quartile (Q1) is the median of the lower half of the data set. It is the 25th percentile.

Q3 . The upper quartile (Q3) is the median of the upper half of the data set. It is the 75th percentile.

The Tukey method of calculating quartiles involves sorting the data set from lowest to highest, then determining the median of each half of the data.

The lower half’s median is Q1 and the upper half’s median is Q3. For data sets with an even number of data points, the quartiles are calculated as the average of the two data points that define the middle.

For example, if there are 10 data points and the 5th and 6th data points are the median, then Q1 is the average of the 4th and 5th data points, and Q3 is the average of the 6th and 7th data points.

If there are an odd number of data points, the quartiles are calculated as the median of the lower and upper halves, respectively. For example, if there are 11 data points and the 6th data point is the median, then Q1 is the median of the lower 5 data points and Q3 is the median of the upper 5 data points.

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Answer:

1. 23.6

2. 3.8

3. 5

4. 0.346

Step-by-step explanation:

You round the number down if its lower than 4 but if its 5 or higher you round up.

The solution to the inequality is x ≥ 1500

What is inequality?

An inequality is a mathematical statement that shows the relationship between two values or expressions. It consists of two expressions separated by one of the following inequality symbols:

Greater than: >

Less than: <

Greater than or equal to: ≥

Less than or equal to: ≤

Let's say that the salesperson sells x dollars worth of products in a week. The income from the commission on these sales would be 0.15 * x dollars.

The total income for the week would be the base salary plus the income from the commission. This can be represented as 275 + 0.15x dollars.

The salesperson wants to earn at least $500 per week. We can represent this as an inequality as follows:

275 + 0.15x ≥ 500

Subtracting 275 from both sides of the inequality gives us:

0.15x ≥ 225

Dividing both sides of the inequality by 0.15 gives us:

x ≥ 1500

Hence, The solution to the inequality is x ≥ 1500, which means that the salesperson must sell at least $1500 worth of products per week in order to earn at least $500 per week.

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To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.

In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.

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The two triangles are similar If they have the same shape, but their sizes are different.

Similar triangles are triangles that have the same shape, but their sizes may be same or different. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. The similarity of triangles are denoted by ‘~’ symbol

AA (or AAA) or Angle-Angle Similarity

If any two angles of a triangle are equal to any two angles of another triangle, then those two triangles are similar to each other.

SAS or Side-Angle-Side Similarity

If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed between those two sides in both the triangle are equal, then two triangles are said to be similar.

SSS or Side-Side-Side Similarity

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

Therefore, two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

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The rotation of the quadrilateral about the origin gives;

1. The location of the image following a 270° rotation is in the fourth quadrant.

2. The image will be returned back to location of the pre-image

1. The location of the point (x, y), following a rotation of 270° about the origin is given by the formula;

The vertices of the quadrilateral are;

(0, 2), (1, 4), (4, 2), and (3, 1)

The vertices following a rotation are therefore;

Given that three y-values negative and the fourth is 0, and all the x-values are all positive, we have that the image is in;

2. If the image is rotated a further 90°, the sum of the rotation will therefore be 270° + 90° = 360°

A rotation of the figure, 360° about the origin will generate an image at the pre-image location, such that the quadrilateral will appear to remain in position.

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Answer: D

Step-by-step explanation: To solve the inequality, subtract 8 from 19 to get h \(\less\)is less than 11. The only answer that is less than 11 is D.

Answer:

A

Step-by-step explanation:

not sure if it is correct

The -1 part is not inside the natural log.

==============================================

Work Shown:

1 + 2*e^(x+1) = 9

2*e^(x+1) = 9-1

2*e^(x+1) = 8

e^(x+1) = 8/2

e^(x+1) = 4

x+1 = Ln(4)

x = Ln(4) - 1