To indirectly measure the distance across a river, Khalil stands on one side of the river
and uses sight-lines to a landmark on the opposite bank. Khalil draws the diagram
below to show the lengths and angles that he measured. Find PR, the distance across
the river. Round your answer to the nearest foot.
N
RI
185 ft
150 ft
0
275 ft
(Diagram is not to scale.)
ft
Submit Answer
Answer:
Answers
Khalil uses the method of similar triangles to find the distance across the river, [tex]\overline{PR}[/tex]
The distance across the river is [tex]\underline{308.\overline 3 \ feet}[/tex]Reasons:
The distances between the formed the sight-lines are;
[tex]\overline{RB}[/tex] = 185 feet
[tex]\overline{OC}[/tex] = 275 feet
The distance between the point close to the river and the next point further from the river [tex]\overline{RO}[/tex] = 150 feet
In triangles ΔPRB and ΔPOC, we have;
∠PRE = ∠POC = 90° Given
∠PER ≅ ∠PCO By corresponding angle formed between two parallel lines and a common transversal.
∴ ΔPRE is similar to ΔPOC by Angle-Angle, AA, similarity theorem
Which gives;
[tex]\displaystyle \frac{\overline {PR}}{\overline {PO}} = \mathbf{\frac{\overline {RE}}{\overline {OC}}}[/tex]
Let x represent the distance across the river, we have;
[tex]\overline{PR}[/tex] = x
[tex]\overline{PO}[/tex] = 150 + x
Which gives;
[tex]\displaystyle \frac{x}{150 + x} = \frac{185}{275}[/tex]
275·x = 185 × (150 + x) = 27,750 + 185·x
275·x - 185·x = 27,750
90·x = 27,750
[tex]\displaystyle x = \frac{27,750}{90} = \mathbf{308.\overline 3}[/tex]
Therefore, the distance across the river, x = [tex]\mathbf{\overline{PR}}[/tex] = [tex]\underline{308.\overline 3 \ feet}[/tex]
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Answer:
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Step-by-step explanation:
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Answer:
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Answer:
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Step-by-step explanation:
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The probability that 2 men are selected is 49/144
Probability is the likelihood or chance that an event will occur.
If 7 men and 5 women have applied for job, the total number of people that applied will be 12 people
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Step-by-step explanation:
the slope is the ratio of "y coordinate change / x coordinate change".
so, in our case here
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Answer:
The answer is 6.79 dollars
Step-by-step explanation:
The answer is 6.79 dollars because 5 times 1 (she bought 5 eggs for 1 dollar each) + the added basket 1.79 equals $6.79
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Answer:
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Answer:
Step-by-step explanation:
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Sam earns $12 per hour. The store offers him a raise--a 6% increase per hour. After the raise,
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Answers
Answer:
Solution here
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Answer:C TRUST MEEE
Step-by-step explanation:
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Admission to the state fair is $12, and each ride ticket costs $3.50. Write an
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Answers
Answer : 3.50t + 12
Step - by - step explanation :
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Answers
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Step-by-step explanation:
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Answer:
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Hope it helps
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Netan surveyed 460 teenagers to find out their favorite type of movie. He found that 45% of the teenagers surveyed like comedies.
Part A: How many teenagers surveyed like comedies? Show your work. (4 points)
Part B: In another survey, Hannah found that 50% of the total number of teenagers surveyed like thrillers. If 40 teenagers like thrillers, what is the total number of teenagers that Hannah surveyed? Show your work. (4 points)
Part C: Give an example of a situation in which a percentage is greater than 100%. (2 points)
Question 3 options:
Answers
Answer with step-by-step explanation:
A: 207
We know that percentage is out of 100, so we can divide 460 by 100 to find 1%, which is 4.6. We also know 45% percent of teenagers like comedies, so we multiply 4.6 by 45, or 207. 207 teenagers like comedies.
B. 80 teenagers
We know that 50% of teens Hannah surveyed like thrillers. We also know that 40 teenagers like thrillers. Using multiplication, we can multiply 40 by 2, since 50% is half, we need to multiply by 2 to get the total number of teenagers. Hannah surveyed 80 teenagers.
C. Jamie went to the candy store and spent his entire allowance of $20 on candy. His friends gave him $5 more dollars, so he bought candy with that too. He spent 125% of his allowance on candy.
The number of teenagers who like comedy is 207, and The total number of teenagers Hannah surveyed is 100.
What is percentage?A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
Given:
Netan surveyed 460 teenagers, He found that 45% of the teenagers surveyed like comedies,
(a) Calculate the number of teenagers who like comedy as shown below,
The number of teenagers who like comedy = 45 × 460 / 100
The number of teenagers who like comedy = 207
(b) Calculate the total number of teenagers as shown below,
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The total number of teenagers = 40 × 100 / 40
The total number of teenagers = 100
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Triangle in space with vertices P= (1, 0, 0), Q = (0,1,0), R=(0, 0, 2), find angle at P P=
Answers
Answer:
71.6°
Step-by-step explanation:
The angle can be found from the dot product of PQ and PR.
PQ·PR = |PQ|×|PR|×cos(α)
where α is the angle between the two segments.
cos(α) = (Q -P)·(R -P)/(|Q -P|×|R -P|)
= ((0, 1, 0) -(1, 0, 0))·((0, 0, 2) -(1, 0, 0))/(|Q -P|×|R -P|)
= (-1, 1, 0)·(-1, 0, 2)/(√(((-1)² +1²)((-1²) +2²)) = (1+0+0)/√10
α = arccos(1/√10) ≈ 71.6°
The angle at P is about 71.6°.
_____
Additional comment
The side lengths of the triangle are √2, √5, √5. As we have seen, the angle at P is bounded by the sides of length √2 and √5. The law of cosines can also be used to arrive at the angle between these sides.
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two stores opened on the same day. Both stores have 75 customers by the end of the first week, Store A'S customers doubled each week for six weeks, Store B's customers increased by 200 each week for six weeks. Which store had more customers at the end of week 5 ?
A Store A
B Store B
C They have the same number of customers
D Not enough information
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Answers
Answer: store b
Step-by-step explanation:
Step by step explanation
in the given figure ,o is the centr of the circle, ab is the diameter and do is perpendicular to ab. prove that angle AEC= ANGLE ODA
Answers
The given triangles ΔDOA and ΔABC are right triangles that have a
common vertex at point A.
ΔDOA is similar to ΔABC, and ∠AEC is equal to ∠ABC, therefore, ∠AEC = ∠ODAReasons:
The given parameters are;
The diameter of the circle with center O = AB
DO ⊥ AB (DO is perpendicular to AB)
Required:
Prove that ∠AEC = ∠ODA
A two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. AB is the diameter of circle [tex]{}[/tex] 1. Given
2. DO is perpendicular to AB [tex]{}[/tex] 2. Given
3. ∠DOA = 90° [tex]{}[/tex] 3. Definition of DO ⊥ AB
4. ∠BCA = 90° [tex]{}[/tex] 4. Thales theorem
5. ∠BCA ≅ ∠BCA [tex]{}[/tex] 5. Reflexive property
6. ΔDOA ~ ΔABC [tex]{}[/tex] 6. AA similarity postulate
7. ∠ABC ≅ ∠ODA [tex]{}[/tex] 7. CASTC
8. ∠ABC = ∠ODA [tex]{}[/tex] 8. Definition of congruency
9. ∠AEC ≅ ∠ABC [tex]{}[/tex] 9. Angles in the same segment
10. ∠AEC = ∠ABC [tex]{}[/tex] 10. Definition of congruency
11. ∠AEC = ∠ODA [tex]{}[/tex] 11. Transitive property of equality
In statement 6, ΔDOA is similar to ΔABC by Angle-Angle, AA, similarity
postulate, therefore, the three angles of ΔDOA are congruent to the three
angles of ΔABC.
Therefore ∠ABC ≅ ∠ODA by Corresponding Angles of Similar Triangles
are Congruent, CASTC.
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Principal = $ 15000, rate = 10% p.a. and time
21/5 years
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Answers
Answer:
Simple Interest: A=P(1+rt)
A=15000(1+(0.1*4.2))
A=$21,300
Compound Interest:A=P(1+r/n)^nt
A=15000(1+0.1/4.2)^1*4.2
A=$64,500
Step-by-step explanation:
a simplifie 6 × ( - 24 ) ÷ ( -4 )
Answers
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{6\times(-24)\div (-4)}}\\\huge\boxed{= \mathsf{\dfrac{6(-24)}{-4}}}\\\huge\boxed{\mathsf{= \dfrac{\bold{-144}}{-4}}}\\\huge\boxed{\mathsf{\dfrac{-144\div-4}{-4\div-4}}}\\\huge\boxed{= \mathsf{\dfrac{\bold{36}}{1}}}\\\huge\boxed{\mathsf{= 36\div1}}\\\huge\boxed{\mathsf{= 36}}\\\\\\\huge\text{\bf Therefore, your answer is: \boxed{\mathsf{36}}}\huge\checkmark[/tex]
[tex]\huge\text{\bf Good luck on your assignment and enjoy}\\\huge\text{\bf your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
How do u do these percentages questions
Answers
Answer:
Step-by-step explanation:Determine the initial format of the number to be converted to a percentage. ...
Carry out a mathematical process on the number to be converted to a percentage. ...
Multiply the result of the mathematical process by 100. ...
Find the percentage of the original or real number. ...
Multiply the final number by 100.
heyyy can have halppppp
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Answer:
ang hirap naman plss answee
Income You are starting your first job as an assistant manager at a
sporting goods store. You receive a base salary of $14.75 per hour with
time-and-a-half for hours in excess of 40 hours per week. You are paid
every two weeks. Social Security and Medicare are deducted from your
pay. Social Security tax is 6.2% of the gross pay. Medicare tax is 1.45% of
the gross pay. What is the bi-weekly (every two weeks) deduction for
Social Security and Medicare? *
O $118.00
O $76.50
$89.90
$90.27
Answers
The bi-weekly deduction for Social Security and Medicare is $90.27.
Since you receive a base salary of $ 14.75 per hour with time-and-a-half for hours in excess of 40 hours per week, and you are paid every two weeks, and Social Security and Medicare are deducted from your pay, and Social Security tax is 6.2% of the gross pay, and Medicare tax is 1.45% of the gross pay, to determine what is the bi-weekly (every two weeks) deduction for Social Security and Medicare, the following calculation must be performed:
(14.75 x 40 x 2) x ((1.45 + 6.2) / 100) = X 1180 x 0.0765 = X 90.27 = X
Therefore, the bi-weekly deduction for Social Security and Medicare is $90.27.
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can anyone slove this
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Δ PQR has: PM is a median
so: MR = QM = 3 cm
ANSWER: MR = 3 cm
Ok done. Thank to me :>
Margit works in a factory. She receives a salary of $12 per hour and piecework pay of 12 cents per unit produced. Last week she worked 38 hours and produced 755 units. What was her piecework pay?
Answers
Based on the way the piecework pay is calculated, Margit's piecework pay will be $90.60
The piecework pay is 12 cents for every unit that is produced.
Margit was able to produce 755 units in that week so her piecework pay will be:
= Number of units produced x Pay per unit
= 755 x 0.12
= $90.60
In conclusion, Margit should get a piecework pay of $90.60
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