What does the fundamental theorem of algebra state about the equation 2x^2−4x+16=0 ?

Answer:

Hourly labor rate = $14.84

Step-by-step explanation:

Total cost of job = $147.51

Price of parts = $32.50

Labor cost + overhead = Total cost - parts = 147.51 - 32.5

=115.01

Overhead rate = 55%

Labor cost = 115.01/(1+55%) = 115.01/1.55

=74.2

Duration of job = 5 hours

Hourly labor rate = 74.2/5

= $14.84

Answer:

$14.84

Step-by-step explanation:

Total cost of job = $147.51=labor+overhead+parts

Price of parts = $32.50

labor+overhead =147.51-32.5=115.01

Overhead rate = 55%

labor+0.55labor= 115.01

labor=115.01/(1.55)=74.2

Duration of job = 5 hours

hourly labor=74.2/5=$14.84

Answer:

4 weeks

Step-by-step explanation:

Final answer:

After 5 weeks, you and your friend will have the same amount.

Explanation:

To find out after how many weeks you and your friend will have the same amount, we need to set up an equation and solve for the number of weeks. Let's assume the number of weeks is represented by 'w'.

Your balance in the bank after 'w' weeks can be represented by the expression: 48.50 + 9.50w. Your friend's balance after 'w' weeks can be represented by the expression: 1 + 2(9.50w). We want to find out when these two balances are equal, so we set up the equation: 48.50 + 9.50w = 1 + 19w.

Solving this equation, we get:

48.50 + 9.50w = 1 + 19w

48.50 - 1 = 19w - 9.50w

47.50 = 9.50w

w = 47.50/9.50

w = 5

After 5 weeks, you and your friend will have the same amount.

Let the number = X

You have X^8 / X^5

When dividing two numbers with powers, Simplify the expression by subtracting the powers.

8-5=3

so X^8 / X^5 becomes x^3

Now you have x^3 = 64

To find x take the cubic root of 64:

X = ∛64

X = 4

The number is 4

Answer: A one-to-one correspondence between the parts of two figures is such that the corresponding parts are equal, then the figures are congruent.

The question pertains to geometric concepts of congruence, one-to-one correspondence, included side, included angle, and vector concepts in mathematics, such as orthogonal and parallel vectors, which are key concepts in solving geometry and trigonometry problems.

The question refers to several key concepts in geometry. When each member of a set, such as angles of a triangle, can be paired with one and only one member of another set, we have a one-to-one correspondence. This correspondence can be applied to situations such as pairing angles or sides of one geometric figure with another.

For example, let's consider two triangles. If each angle of the first triangle corresponds to an angle of the second triangle, and all pairs of corresponding elements (angles or sides) are equal, then those two triangles are congruent. This is the basic principle of congruence in geometry.

The angle formed by two sides of a triangle is called an included angle. The side of a triangle that is formed by the common side of two angles is an included side. In a right triangle, like in Figure 5.17, we see the terms adjacent side, opposite side, and hypotenuse, which are used for trigonometric calculations such as sine, cosine, and tangent.

The Pythagorean Theorem plays a crucial role for right-angled triangles, stating that the square on the hypotenuse is equal to the sum of squares on the other two sides. Also, the question talks about parallel and orthogonal vectors. Two vectors are said to be parallel if they have identical directions, while orthogonal vectors are perpendicular to each other, with directions differing by exactly 90°.

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Answer:

2.4 hours Electrician works.

Step-by-step explanation:

Let us assume that the number of hours  Electrician works be x.

As given

An Electrician charges $30 for a service call plus $75 per hour of service.

If Electrician  charged $210.

Than the equation becomes

30 + 75x = 210

75x = 210 - 30

75x = 180

[tex]x =\frac{180}{75}[/tex]

x =2.4 hours

Therefore 2.4 hours Electrician works.

Answer:

7.81

Step-by-step explanation:

= √(5^2 + 6^2)

= √(25 + 36)

= √61

= 7.81

Answer:

7.81

Step-by-step explanation:

we have the points: (-2, -2) and (3, 4)

where i will call [tex]x_{1}=-2, y_{1}=-2,x_{2}=3,y_{2}=4[/tex]

We can find the distance using the Pythagorean theorem, considering that the distance in x between the points is: [tex]d_{x}=[/tex] [tex]x_{2}-x_{1}=3-(-2)=3+2=5[/tex]

and the distance in y  between the points is: [tex]d_{y}=[/tex][tex]y_{2}-y_{1}=4-(-2)=4+2=6[/tex]

and using the Pythagorean theorem

[tex]d=\sqrt{d_{x}^2 +d_{y}^2}[/tex]

[tex]d=\sqrt{5^2+6^2}=\sqrt{25+36}=\sqrt{61} =7.81[/tex]

the distance between the two points ia 7.81

Answer:

13,000 meters.

Step-by-step explanation:

We have been given that Lisa went on a 52 km hike. She divided the distance traveled evenly over 4 days.

Let us convert our given distance in meters.

1 km = 1,000 meters.

52 km= 52*1,000 meters = 52,000 meters.

Let us divide total distance traveled by total number of days to find the distance traveled per day.

[tex]\text{Lisa walked each day}=\frac{52000\text{ meters}}{\text{ 4 days}}[/tex]

[tex]\text{Lisa walked each day}=13,000\frac{\text{ meters}}{\text{ day}}[/tex]

Therefore, Lisa walked 13,000 meters each day.

Lisa hiked 52 km in 4 days, equaling to 13 km per day. However, this must be converted to meters, so Lisa hiked 13,000 meters each day.

This problem is an exercise in unit conversion and division. Since Lisa divided the total distance of 52 kilometers evenly over 4 days, she hiked 13 kilometers each day (52 km / 4 = 13 km/day). However, the question asks for the answer in meters, not kilometers. Therefore, we must convert kilometers to meters. We know that 1 kilometer is equivalent to 1000 meters, so Lisa hiked 13,000 meters each day (13 km * 1000 = 13,000 m/day).

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The 95% confidence interval for the difference between the mean salaries of all women and men at the company is (−3570.8,−1533.2), which is option C.

Identify the relevant parameters:

Sample size for women (n_w) = 97

Mean salary for women (μ_w) = $45,902

Standard deviation for women (σ_w) = $3865

Sample size for men (n_m) = 75

Mean salary for men (μ_m) = $48,454

Standard deviation for men (σ_m) = $6677

Confidence level = 95%

Calculate the pooled standard error (s_p):

s_p = √[(n_w * σ_w^2 + n_m * σ_m^2) / (n_w + n_m - 2)]

s_p = √[ (97 * 3865^2 + 75 * 6677^2) / (97 + 75 - 2)]

s_p ≈ $4973.49

Calculate the margin of error (z):

Since the sample size is large for both groups (n_w > 30 and n_m > 30), we can use the standard normal distribution (z-score) with a confidence level of 95%.

z = 1.96 (for 95% confidence level)

Calculate the confidence interval:

Lower bound = (μ_w - μ_m) - z * s_p

Lower bound = ($45,902 - $48,454) - 1.96 * $4973.49

Lower bound ≈ -$3570.80

Upper bound = (μ_w - μ_m) + z * s_p

Upper bound = ($45,902 - $48,454) + 1.96 * $4973.49

Upper bound ≈ -$1533.20

Therefore, the 95% confidence interval for the difference between the mean salaries of all women and men at the company is (-$3570.80, -$1533.20), which confirms your answer of option C.

Answer:

The answer is 6.

Step-by-step explanation:

You need to have side x + 4 equal side 3x - 8. If you plug 6 into both equations, then you get x + 4 = 910and 3x - 8 = 10. The last side of the triangle equals 6. You then add all three sides together to get 25. 10 + 10 + 5 = 25.

This is an isosceles triangle (a triangle with 2 congruent/equal sides and 2 congruent angles)

If you look at the triangle, most likely side AB and BC are congruent.

Since the sides are suppose to be the same/equal to each other, you can do this:

AB = BC

x + 4 = 3x - 8       Subtract x on both sides

4 = 2x - 8    Add 8 on both sides

12 = 2x      Divide 2 on both sides

x = 6

You need to find AC.

AC = x, since you know x = 6, side AC is 6 units

Answer:

Option a. Greece.

Step-by-step explanation:

According to the table listing average daily expenses for a tourist by country based on high and medium categories,

Brazil has a range from = $12.25 to $18.33

Greece has a range from = $9.48 to $16.55

To find out the difference in range, first we get range of both the countries.

by subtracting lowest from highest

Brazil = $18.33 - $12.25 = 6.08

Greece = $16.55 - $9.48 = 7.07

= 7.07 > 6.08

Therefore, Greece has the larger difference between categories.

Option a. Greece is the correct answer.

Answer:

Step-by-step explanation:

Given triangle WXY and <1 is an exterior angle.

We need to prove <1 is greater than <2.

First statement is:

Triangle WXY and <1 is an exterior angle.

Reason : Given

Note: An exterior angle of a triangle is the sum of two angles side the triangle those don't makes the linear pair with exterior angle.

We can see that <2 and < 3 are the angles of triangle those are not making a linear pair.

Therefore, <1 = <2+< 3.

So, the second statement should be first option <1 = <2+< 3.

Answer:

[tex]\frac{\pi }{6}[/tex]

Step-by-step explanation:

Since [tex]\frac{7\pi }{6}[/tex] is in the third quadrant then

reference angle = [tex]\frac{7\pi }{6}[/tex] - π = [tex]\frac{\pi }{6}[/tex]

Answer:

-5; -40; -640

Step-by-step explanation:

Answer: Congruency criteria used by Ross to prove the opposite sides are congruent is B) ASA congruence postulate

Answer:

25,893

Step-by-step explanation:

2.740 x 9.45=25,893

Answer:

40

Step-by-step explanation:

The data is

21,24,25,28,29,35,37,43,44

To find the third quartile we have to arrange the data in increasing order

so the data in increasing order is

21,24,25,28,29,35,37,43,44

total number of values = 9

Median value = (n + 1 )/ 2

                       =(9+1)/2

                       =5th value

so the median is  29

Lower half of the data is the values before the median and upper half of the data is values after the median

so lower half = {21,24,25,28}

Upper half = {35,37,43,44}

so to find the third quartile we will use the upper half of the values

Third quartile means that the median of the values of upper half of the data

As the total No of value in upper half is 4 which is an even no

we will take the middle values of the upper half and take their mean

so

Third Quartile = [tex]\frac{37+43}{2}[/tex]

                        =[tex]\frac{80}{2}[/tex]

                        =40

so the value of third quartile is 40

Final answer:

The third quartile (Q3) of the data set is 40, calculated by finding the average of the two middle numbers of the upper half of the data after excluding the median.

Explanation:

To find the third quartile of a data set, which is also referred to as Q3 or the 75th percentile, one must identify the median of the upper half of the data. For the provided data set (21, 24, 25, 28, 29, 35, 37, 43, 44), with nine values, the median is 29, which is the fifth value. To calculate Q3, we take the upper half of the data set which does not include the median itself. The upper half includes (35, 37, 43, 44), and the median of this half is the third quartile. Since we have an even number of data points in the upper half, we must find the average of the two middle numbers, 37 and 43, which is (37+43)/2 or 40. Therefore, the third quartile of the provided data set is 40.

Final answer:

To eliminate the fractions in the equation x/2 + x/3 = 25/3, we need to multiply the entire equation by 6.

Explanation:

To eliminate the fractions in the equation x/2 + x/3 = 25/3, we need to find a common denominator for both fractions. The common denominator for 2 and 3 is 6. Therefore, we need to multiply the entire equation by 6 to eliminate the fractions.

Multiplying the equation by 6 gives us: 6(x/2) + 6(x/3) = 6(25/3)

Simplifying further, we get: 3x + 2x = 50

Combining like terms, we have: 5x = 50

Finally, dividing both sides of the equation by 5 gives us:  x = 10

Final answer:

To eliminate the fractions in the equation x/2 + x/3 = 25/3, one must multiply each term by 6, which is the least common multiple of the denominators 2 and 3, making option D correct.

Explanation:

The equation x/2 + x/3 = 25/3 should be multiplied by a number that is a common multiple of the denominators 2 and 3 to eliminate the fractions. To find the least common multiple (LCM) of 2 and 3, we can list out the multiples of these numbers (2,4,6,8,... for 2 and 3,6,9,12,... for 3) and identify the smallest multiple they have in common, which is 6. Therefore, multiplying the entire equation by 6 will eliminate the fractions and give us an equation with whole numbers.

Multiplying each term of the equation by 6 gives us: 6(x/2) + 6(x/3) = 6(25/3). Simplifying each term results in: 3x + 2x = 50 which is an equation without fractions.

The correct answer to the question is D. 6.

Where C = Cost and P = People

C = 2(5p)

In the context of Tia and her five friends:

C = 2(5*6) = 2(30) = 60

C = 60

The cost for Tia and her five friends to be admitted to ice skate and eat is 60$, and the equation to calculate this is C = 2(5p).

Final answer:

After 6 rounds of the chess tournament starting with 1024 players, 16 players will remain. In the story of the king and chessboard with exponential doubling of rice, the total would be [tex]2^{64[/tex] - 1 grains.

Explanation:

To determine how many players will remain after 6 rounds in a chess tournament that starts with 1024 players, we recognize this as a process of successive halving. If each round eliminates half the players, then after each round, the number of players will be:

Therefore, 16 players will remain after 6 rounds in the tournament. Referring to the classic story of the king and the chessboard, when grains of rice are doubled on each square, the final total is one less than [tex]2^{64[/tex] grains. Without adding it all up, we can say this final number is [tex]2^{64[/tex] - 1 grains of rice.

Answer:

The arcs are not congruent which makes the statement false.

Step-by-step explanation: Congruent means equal to my understanding.

Answer:

The answer would be B

2.5x = 45

(x) would be the number of dolls, multiplied by how much each doll costs ($2.50) and the product would be how much she has to spend. Hope this helps!

Answer:

Measure of one of the central angles in the regular pentagon is 72 degree.

Step-by-step explanation:

A Central angle states that the angle made at the center of the polygon by any two adjacent vertices of the polygon.

If you draw a line from any two adjacent vertices to the center, then they would make the central angle.

Since, it is given that the polygon we use here is regular pentagon.

⇒ All the central angles are equal.

The formula to find the central angle is:

Central Angle = [tex]\frac{360^{\circ}}{n}[/tex] where n is the number of sides.

Since, the measure of the central angle thus depends only on the number of sides.

Here, side(n) = 5 (Polygon is regular pentagon)

then;

Central angle = [tex]\frac{360^{\circ}}{5} =72^{\circ}[/tex]

Therefore, the measure of one of the central angle in the regular pentagon is, [tex]72^{\circ}[/tex]

Answer:

72 and 54 are your answers

Step-by-step explanation:

Hi there! :)

Answer:

7/25 is equivalent to 0.28

Step-by-step explanation:

In order to go from a fraction to a decimal, you need to divide the numerator (top number) by the denominator (bottom number):

7/25 = 7 ÷ 25

7 ÷ 25 = 0.28

There you go! I really hope this helped, if there's anything just let me know! :)

Answer:0.28

Step-by-step explanation:

so you divided 7 and 25 and it gives 0.28

Answer:

32 miles.

Step-by-step explanation:  

We have been given that Elton hiked 16 miles each day on a 12 day hiking trip.

So, the number of miles hiked by Elton in 12 days will be: [tex]16\times 12=192[/tex] miles.

Lola hiked 14 miles each day on her 16 day hiking trip.

So, the number of miles hiked by Lola in 16 days will be: [tex]14\times 16=224[/tex] miles.  

Let us subtract number of miles hiked by Elton from Number of miles hiked by Lola.

[tex]\text{Number of miles that Lola hiked more than Elton}=224-192[/tex]

[tex]\text{Number of miles that Lola hiked more than Elton}=32[/tex]

Therefore, Lola hiked 32 miles more than Elton in all.  

Answer:

x = 1 11/15

Step-by-step explanation:

Using ratios of similar triangles

3            5.2

-------- = ----------

4            (5.2 + x)

Using cross products

3 * (5.2 + x) = 5.2 * 4

Distribute

15.6 + 3x = 20.8

Subtract 15.6 from each side

15.6-15.6 + 3x = 20.8 -15.6

3x =5.2

Divide each side by 3

3x/3 = 5.2/3

x = 5.2/3

x=52/30

x = 26/15

x = 1 11/15

Answer:

$8.82 is the amount of sales tax

Step-by-step explanation:

$90 x .40 = $36.00

$90 + $36 = $126

$134.82 - $126 = $8.82 in taxes

Answer:

Slope of the line passing through the given points are: [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Slope of a line : For any two point [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]

the formula of slope is given by:

Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Given the points ( -4, 7) and (0, 8)

then, by using slope formula;

[tex]m = \frac{8-7}{0-(-4)} = \frac{1}{0+4} = \frac{1}{4}[/tex]

Therefore, the slope of the line passing through the given points are: [tex]\frac{1}{4}[/tex]

Answer:

1 / 4

Step-by-step explanation:

We are to find the slope of a line which passes through the two given points: (–4, 7) and (0, 8).

We know the formula of the slope (m):

[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

So putting in the values of the coordinates of the given points in the formula to get:

Slope = [tex]\frac{8-7}{0--4} = \frac{1}{4}[/tex]

Therefore, the slope slope of a line which passes through the two given points: (–4, 7) and (0, 8) is 1 / 4.

To find the width of a rectangle when given the area and length, divide the area by the length:

Width = 59,400 / 330 = 180 feet