*Help ASAP Please! Studying for finals and I'm stuck on this question!*
7. The two small triangles in the following are similar. Find the value of x to the nearest thousandth. (See attached image.)
A) x=32, y=25.6
B) x=12, y=15
C) x=9.6, y=12
D) x=15, y=12
E) None of the above.
Answers
So to find x you must first find y which can be done simply by using the pythagorean theorem. This theorem is defined as the sum of the squared legs is equal to the sum of the hypotenuse or x^2 + y^2 = z^2
If we substitute in the known values 16^2 + y^2 = 20^2 and solve for y we get that y = sqrt(20^2 - 16^2), this then simplifies to y = 12
Finding x is much more annoying, the easiest way I can immediately see is to find the upper angles by doing sin(16/20) and then 90 - sin(16/20) since the complementary angle is the one you want. I don't have a calculator or a trig table with me right now but I will tell you that x will be equal to 12 ÷ the inverse cosine of the angle (90degrees - sin(16/20)).
I am pretty sure the answer is D though because we know for sure y = 12 and x has to be greater than y because the hypotenuse must be larger than both legs. It could be E but you won't know unless you do the math for x. So it is either D or E but I would be surprised if a Professor made you do all of the work just to say it doesn't work...
Related Questions
Total cost of job = $147.51 Duration of job = 5 hours Price of parts = $32.50 Overhead rate = 55% Hourly labor rate = _____.
Answers
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
In a random sample of 97 women at a company, the mean salary is $45,902 with a standard deviation of $3865. In a random sample of 75 men at the company, the mean salary is $48,454 with a standard deviation of $6677. Which interval is the 95% confidence interval for the difference between the mean salaries of all women and men at the company?
A) ($1133.20, $3970.80)
B) ($856.36, $4247.64)
C) ($1686.88, $3417.12)
D) ($319.99, $4784.01)
Answers
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.
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 6 rows of the same length, he has 9 chairs left over. If he arranges the chairs in 4 rows of that same length, he has 13 left over. How many chairs does Liam have?
Answers
2x + 3 = 19
2x = 16
x = 8
So, x (8) is the number of chairs in each row with these setups.
9(8) + 3 = 75
There are 75 chairs total
The measure of angle θ is 7pi/6 so the measure of the reference angle is what?
Answers
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]
Given:
Triangle WXY, 1 an exterior .
Prove:
1 > 2
Answers
Answer:
<1 = <2+< 3.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.
A regulation soccer field has an area of 59,400 square feet. If the length is 330 feet, what is the width in feet
Answers
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
Helpppppppppppppppppp
Answers
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
What is the third quartile of this data set 21,24,25,28,29,35,37,43,44
Answers
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.
Lines AB and CD are graphed on this coordinate plane. Which point is the intersection of lines AB and CD?
Answers
What is 508 times 82 in math answer clear please and I really need help with math but thank you I will use this website more often (:
Answers
Answer:
508*82 is 41656
Step-by-step explanation:
A situation for which each member of a set, such as angles of a triangle, can be paired with one and only one member of another set. - ? Angles paired with one another in a one-to-one correspondence between geometric figures. - ? Sides paired with one another in a one-to-one correspondence between figures. - ? If 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 angle formed by two sides of a triangle. - ? The side of a triangle that is formed by the common side of two angles. - ?
Answers
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.
Explanation: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°.
Learn more about Geometry here:https://brainly.com/question/31408211
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A number to the 8th power divided by the same number to the 5th power is 64 what is the number?
Answers
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
You Havel 48.50 in the bank and your friend has $1.00 your allowance is 9.50 per week and your friend gets twice as much. After how many weeks do u have the same amount
Answers
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.
One copy of a new book by Amanda's favorite author cost $9.45. If a total of 2,740 copies of the book were sold on the first day of the book's real release, what were he total sales that day?
Answers
Answer:
25,893
Step-by-step explanation:
2.740 x 9.45=25,893
You have to complete a sales record to the nearest 10 drinks. A total of 776 drinks have been sold. What number do you write in the sales record? ... Drinks?
Answers
Answer:
780 drinks
Step-by-step explanation:
round 776 to nearest more and it is 780 drinks
Answer:
The answer is 780, you round the number to the nearest 10th if it was 774 drinks answer would be 770
Step-by-step explanation:
Find the first, fourth, and eighth terms of the sequence. A(n) = –5 • 2n–1
A. –5; –40; –640
B. –20; –160; –2,560
C. 1; –1,000; –10,000,000
D. –10; –80; –1,280
Answers
Answer:
-5; -40; -640
Step-by-step explanation:
Use this regular pentagon to answer the questions. What is the measure of one of the central angles in the regular pentagon?
Answers
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:
Solve the inequality 4x - 6 > 6x - 20
A.) x > 7
B.) x < 7
C.) x < 2
D.) x > 2
Answers
Steps:
4x - 6 > 6x - 20
-6+20>6x-4x
14>2x
14/2>x
7>x
x<7
Answer:
What the othe rguy said, also give him brainliest
Step-by-step explanation:
Use the slope formula to find the slope of the line passing through the given points.
(–4, 7) and (0, 8)
Answers
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.
12) Miranda wants to buy as many collectible dolls as possible, for $2.50 each. If she has $45.00 to spend, how many dolls can she buy? Which equation BEST represents this situation? A) 45x = 2.5 B) 2.5x = 45 C) x + 2.5 = 45 D) x + 45 = 2.5
Answers
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!
In your neighborhood, 7/25 of your neighbors have dogs. This is equivalent to what decimal?
Answers
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
At Pizza Pi 24% of the pizzas made last week had extra cheese. If 6 pizzas had extra cheese how many pizzas in all were made last week
Answers
Explanation
24%×6=1.44
Answer:
1.44
Step-by-step explanation:
Tia and her five friends are going to the ice skating rink. Each person $5 for admission and $5 for food. Write and evaluate a numerical expression to find the total cost for admission and food
Answers
Where C = Cost and P = People
C = 2(5p)
In the context of Tia and her five friends:
C = 2(5*6) = 2(30) = 60
C = 60
The cost for Tia and her five friends to be admitted to ice skate and eat is 60$, and the equation to calculate this is C = 2(5p).
A forest covers 41,000 acres. A survey finds that 0.4?% of the forest is? old-growth trees. How many acres of? old-growth trees are? there?
Answers
Answer: A forest covers 41,000 acres. A survey finds that 0.4?% of the forest is? old-growth trees. How many acres of? old-growth trees are? there?
Alrighty, let me help you out, make things easier! The ANSWER is going to be 24,600, by this process, just take 41,000 and multiply that by 0.4. that gives you 16400, and since you are trying to find a portion of the forest, you subtract 16400 from 41,000 total acres. Hope that helps!
A large chess tournament starts with 1024 players. How many players will be remaining after 6 rounds
Answers
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:
After Round 1: 1024 / 2 = 512 playersAfter Round 2: 512 / 2 = 256 playersAfter Round 3: 256 / 2 = 128 playersAfter Round 4: 128 / 2 = 64 playersAfter Round 5: 64 / 2 = 32 playersAfter Round 6: 32 / 2 = 16 playersTherefore, 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.
NEED HELP !!!!!!!! ASAP PLZ
In the process of proving that opposite sides of a parallelogram are congruent, Ross drew a diagonal of the parallelogram and determined that the two triangles formed are congruent. He then concluded that opposite sides must be congruent, because corresponding parts of congruent triangles are congruent.
Using his markings in the diagram, which postulate allowed him to determine that the two triangles formed are congruent?
A) AAS
B) ASA
C) SAS
D) SSS
Answers
Answer: Congruency criteria used by Ross to prove the opposite sides are congruent is B) ASA congruence postulate
How many solutions do these have?? PLEASE HELP!!
y=4x+3; 2y-8x=3
1
2
infinitely many
none
x-4y=12; 5x-20y=60
1
2
infinite
none
y-7x=-14; 7y-49x=-2
1
2
infinitely m
Answers
1 - NONE
2 - INFINITE SOLUTIONS
3 - NONE
Step-by-step explanation:
The leather depot buys a coat from a supplier for $90 wholesale and marks up the price by 40%. If the retail price is $134.82 , what is the sale tax?
Answers
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
Elton hiked 16 miles each day on a 12 day hiking trip.Lola hiked 14 miles each day on her 16 day hiling trip.In all, how many more miles did Lola hike than Elton hiked
Answers
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.
Find the distance between the two points shown in the coordinate plane below to the nearest hundredth.
Question 16 options:
61.0
7.23
7.81
8.02
Answers
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