Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º. Scarlett's height is 1.65 meters, so the height of the dam is meters. NextReset
Answers
h = x + 1.65 m,
where:
x = 90 m · tan 26°
x = 90 · 0.4877
x = 43.90
h = 43.90 m + 1.65 m = 45.55 m
Answer:
The height of the dam is 45.5 m.
Answer:
The height of dam =45.5 m.
Step-by-step explanation:
We are given that Scarlett stands 90 m away from the dam and records the angle of elevation to the top of the dam to be [tex]26^{\circ}p[/tex]
Scarelett's height is 1.65 meters.
We have to find the height of the dam.
Let h be the height of dam
AC=AB+BC
BC=x
h=1.65+x
CD=EB=90 m
In triangle ABE
[tex]\theta=26^{\circ}[/tex]
[tex]tan\theta=\frac{perpendicular\;side}{Base}[/tex]
[tex]tan26^{\circ}=\frac{AB}{90}[/tex]
[tex]0.4877=\frac{x}{90}[/tex]
[tex]x=0.4877\times 90[/tex]
[tex]x=43.893 m[/tex]
Therefore, the height of dam=1.65+43.893=45.543 m
Answer: The height of dam =45.5 m
Related Questions
Batteries of each type have lifetimes before recharge that can be assumed independent and Normally distributed. The mean and standard deviation of the lifetimes of the Duxcell batteries are 10 and 2 minutes respectively, the mean and standard deviation for the Infinitycell batteries are 14 and 3 minutes respectively.
Part a) What is the probability that a Duxcell battery will last longer than an Infinitycell battery?,
Answers
X = N(10, 2^2)
This means that:
mean is 10
variance is 2^2
Y = N(14, 3^2).
Asked:P(X > Y)
= P(X - Y > 0).
mean of Z = X - Y
= 10 - 14
variance = 2^2 + 3^2
Z = N(-4, 2^2 + 3^2).
Answer:
0.1562
Step-by-step explanation:
Step 1
In this tep we define the normal distributions in this problem. . The lifetime of the Duracell battery is a normal random variable X with parameters (10,4). The lifetime of the Infinitycell battery is a normal random variable with parameters (14.9).
Step 2
Define the new normal distribution formed by the combination of these two distributions. We define a random variable Z such that
,[tex]Z=X-Y.[/tex]
This will be a random variable with mean of [tex]\mu_x-\mu_y=10-14=-4[/tex]. This random variable will have a variance of [tex]\mu_z^2 =\mu_x^2+\mu_y^2=2^2+3^2=13[/tex]. The mean for this distribution is [tex]\mu_z=\sqrt{13}[/tex] . The random variable Z is normally distributed with parameters (-4,13)
Step 3
The next step is to calculate the probability that [tex]Z=X-Y>0[/tex]. For that we perform the calculation shown below. Along the way , we will use the method of transforming any normal distribution to the standard normal distribution.This transformation is [tex]z=\frac{x-u}{\sigma}[/tex].
[tex]P(Z>0)=P(X-Y>0)=P(Z>0)\\P(Z>0)=1-P(Z<0)\\P(Z>0)=1-P(\tfrac{0-(-4)}{\sqrt{13}})=1-P(\tfrac{4}{\sqrt{13}})\\P(Z>0)=1-0.8438\\P(Z>0)=0.1562[/tex]
A regular hexagon has a perimeter of 120 m. Find its area. Leave your answer in simplest radical form.
Answers
(1/2) • a • p
Where a is the apothem (a line from the center of a side to the center of the shape) and p is the perimeter.
We have the perimeter: 120
Now to find the apothem. To find it, we’re going to cut any sidelength in half, and the line from that half to the center of the hexagon will form a right triangle. We know the bottom leg (where the shape is) is 10 (since 120/6 = 20, and we cut that in half). All we need is angles. To find the interior angle of any regular shape, we use
(180(n - 2))/n
Plugging in, we get 120 degrees for every side. Since we cut it in half, then the top angle of our right triangle is 60. You know what that means? We’ve just found a 30, 60, 90 triangle.
Using the laws of this special triangle, the length of the apothem is the shortest leg times sqrt(3)
So, 10sqrt(3) is your apothem.
Plug everything in!
(1/2) • a • P
(1/2) • 10sqrt(3) • 120
Your area is 600sqrt(3)
Mickey’s beagle has a mass of 15 kilograms. His dachshund has a mass of 13 kilograms. What is the combination of both?
Answers
Which object would be best measured in ounces?
A.
strawberry
B.
bed
C.
car
D.
horse
Answers
A small software company has two customer service representatives.The supervisor of he customer service department determines that there is an 85% probabiiy that a customer sevice representative will e on the phone with a customer at any given time. what is the probability o both representatives being on the the phone at the same time?,
Answers
Answer:
The probability that both customer representatives are on the phone at the same time is 72.25%.
Step-by-step explanation:
Consider the provided information.
There is an 85% probability that a customer service representative will be on the phone with a customer at any given time.
There are 2 customer service representatives.
To find the probability that both customer representatives are on the phone at the same time, we multiply the independent probabilities together.
0.85×0.85=0.7225
Hence, the probability that both customer representatives are on the phone at the same time is 72.25%.
In the wrong hands, which of the following pieces of personal information would present the greatest risk for identity theft?
a.
address
b.
date of birth
c.
mother’s maiden name
d.
social security number
Answers
Answer:
D. social security number
Step-by-step explanation:
If a thief uses your your Social Security number for financial gain, you’re a victim of financial identity theft, criminal identity theft and also utility fraud.
Hope this will helpful.
Thank you.
Answer:
The correct option is D. social security number
Step-by-step explanation:
Address : Address cannot do much harm in the case of identity theft because other identity related information cannot be stolen by using the address.
So, this option is rejected.
Date of Birth : By using date of birth, no information about anyone's personal identity can be found. So this also cannot be related to identity theft.
So, this option is also rejected.
Mother's maiden name : This option is also not helpful in case of identity theft as this will not give any valuable information about someone's identity.
So, this option is also rejected.
Social security number : This number holds every personal information about a person so by using this complete identity of a person can be accessed and will present the greatest risk for identity theft.
Hence, The correct option is D. social security number
Choose the equation of the vertical line passing through the point (-2, 3).
y = 3
x = 3
y = -2
x = -2
Question 10 (Multiple Choice Worth 5 points)
[4_05]Choose the equation of the horizontal line that passes through the point (-5, 1).
y = -5
x = 1
y = 1
x = -5,
Answers
a) = -2
b) = 1
What is the value of tan D?
Answers
As according to the mathematical acronym SOH CAH TOA (Sin Opposite Hypotenuse, Cos Adjacent Hypotenuse, Tan Opposite Adjacent), the correct answer would be the first choice, [tex] \frac{12}{5} [/tex].
The reason behind this is because the tangent value of an angle is always the length value opposite of given angle over the value adjacent (or right next to) the given angle.
In this case, the question is asking for Tan D. The side value opposite of angle D would be 12, and the length value that is adjacent to angle D is 5.
Therefore, the value of tan D would be [tex] \frac{12}{5} [/tex].
Hope this helps and I hope you have a marvelous day! :)
The value of tan D would be as follows:
[tex]\frac{12}{5}[/tex]Find the value of TanGiven that,
A right-angled triangle EFD,
As we know,
Tan = Opposite sides' length/adjacent sides' length
So,
it is given that,
The length of the opposite side = 12
Adjacent Side's length = 5
∵ The value of Tan D [tex]= 12/5[/tex]
Thus, the above-mentioned answer is correct.
Learn more about "Trigonometry" here:
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How do I solve #21???? Please don't just give me the answer.... tell me how u got it... thanks!
Answers
_______________________________________________
XY = 3 units (obtained from counting on the graph provided).
YZ = 5 units (obtained from counting on graph provided).
_______________________________________________
To find ZX (the hypotenuse); use the Pythogorean Theorem:
→ 3² + 5² = c² ; in which "c" = ZX ;
→ c² = 3² + 5² = 9 + 25 = 34 ;
→ c² = 34 ;
To find "c" ; take the positive square root of each side of the equation;
to isolate "c" on one side of the equation; & to solve for "c" ;
→ √(c²) = √34 ;
→ c = 5.8309518948453005 ;
→ round to: "5.831 "
_______________________________________________________
Wich fraction is equivalent to negative 7 over 8
Answers
: Below are two expressions. Simplify each and then choose the statement that is true.
Expression #1
Expression #2
Expression 1: (3x2)3x^2
Expression 2: (3x^3)^2(x^2)
The exponents in Expression #1 are greater than the exponents of Expression #2.
The exponents on Expression #2 are greater than the exponents of Expression #1.
The exponents of Expression #1 are the same as the exponents of Expression #2.
The relationship cannot be determined with the given information.
The answer I got was A
Answers
We have then:
Expression 1:
(3x2) 3x ^ 2
(9x ^ (2 + 2))
9x ^ 4
Expression 2:
(3x ^ 3) ^ 2 (x ^ 2)
(9x ^ 6) (x ^ 2)
(9x ^ (6 + 2))
9x ^ 8
Answer:
The exponents on Expression # 2 are greater than the exponents of Expression # 1.
(8> 4)
What is the locus of all points equidistant from lines X and Y in the figure?
Answers
More details about X and Y in this question would be really helpful!
Which is the most appropriate unit to measure the length of a slice of pizza?
Answers
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Enter your answer in the box.
Answers
For the quadrilateral ABCD and the inscribed circle, the measure of angle c will be 62⁰.
We already know that the opposite angles of an inscribed quadrilateral are supplementary in nature.
Therefore, In this problem
m<D+m<B=180⁰
m<C+m<A=180⁰
First, we have to find the value of x
m<D+m<B=180⁰
then substitute the values to solve for x, we get
(x+20)⁰ + (3x)⁰ = 180⁰
4x = 180⁰ - 20⁰
x = 160/4
x = 40⁰
second, to find the measure of angle A
m<A = (2x+38)⁰
put the value of x from first step,
angle A = 2(40)⁰+38⁰=118⁰
third, to find the measure of angle C
m<C+118⁰=180⁰
m<C = 180⁰-118⁰
angle C = 62⁰
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y=2x-7
3x-4y=8 can someone solve for x and y ? What method is used ? elimination or subtraction ?
Answers
What is 2 ¾% in decimal form?
Answers
2 3/4 = 2 + 3/4
2 + ( 3 ÷ 4 )
2 + 0.75 = 2.75
Hope this helped!
Maria wants to solve the following system using the elimination method:
4x + 9y = 59
x + y = 17
What number should the equation x + y = 17 be multiplied by to eliminate y?
4
−4
9
−9
Answers
The first equation has 9y.
To eliminate y, you need to add to it -9y.
The second equation has y. In order for the second equation to have -9y, you must multiply both sides of the second equation by -9.
Answer: D -9
Answer:
d
Step-by-step explanation:
i took the test
Trey wants to plant grass in his backyard. His backyard is in the shape of a rectangle. Its length is 31
feet and its width is 24
feet. Suppose each pack of seed covers 12
square feet. How many packs of seed will he need to cover the backyard?
Answers
Area of a rectangle is length x width.
31 x 24 = 744
Divide the total area of the yard by the coverage of the seeds.
744/12 = 62
He will need 62 packs of seed.
To find out how many packs of seeds Trey needs, we need to first determine the area of his backyard which is 744 square feet. Each pack of seed cover 12 square feet. Therefore, dividing the total area by the area a pack of seed covers, we find that he needs 62 packs of seeds.
Explanation:The subject of this question is Mathematics. Specifically, it involves the concept of area and multiplication, commonly taught in middle school. Trey's backyard is in the shape of a rectangle, and we know that the area of a rectangle is calculated by multiplying its length by its width. In this case, the length is 31 feet and the width is 24 feet. Multiplying these numbers gives us a total area of 744 square feet.
Each pack of seed covers 12 square feet. So, to figure out how many packs Trey needs, we would divide the total area by the area each pack covers. Dividing 744 by 12 gives us 62, which means Trey will need to buy 62 packs of seeds.
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Which unit would you use to measure the weight of a flea?
mg
g
ounces
kg
Answers
There are 250 degrees in the sum of the interior angles of a polygon. Always, sometimes, never
Answers
Use the table to determine the location with the greatest amount of rainfall and the location with the least amount of rainfall.
a.Using complete sentences, identify the location with the greatest amount of rainfall and the location with the least amount of rainfall, and express the ratio of their respective rainfalls as a whole number.
b. Describe what this ratio tells you.
Needles, California 0.1173 m
Mt. Waialeale, Hawai'i 11.4 m
Puako, Hawai’i 25.6 cm
Death Valley, California 57 mm
Mojave, California 160 mm
Hilo, Hawai'i 480 cm,
Answers
The other person answered Part A, so I'll answer Part B (at least I'll try my best to)
"With every 200 millimeters of rain in Waialeale, there will be 1 millimeter of rain in Death Valley." <- This is what I put for B
Sorry I'm late and if I'm wrong, good luck to everyone who sees this
A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, then its volume is:
A) 36
B) 12sqrt3
C)18sqrt3
D)24sqrt3
E)36sqrt3
The correct answer was E. Hoping someone could explain how that is.
Answers
Area of equilateral trianlge= (1/2) tiime a^2 square root 3
Equation for the base is = x^2+y^2 =9
at x ,
y= square root (9-x^2)
Side of triangle a= 2y
d times Volume = (1/2)a^2 square root 3 dx
d times V= (square root 3) (9-x^2) dx
V= square root 3 INT (9-x^2) dx
-3V= 2square root INT (9-x^2) dx
0
V= 2 square root 3 ( 9x-x^3/3)
V=2 square root 3 ( 27-9)
V= 36 square root 3
The answer is E.
Final answer:
The correct answer is E) 36sqrt(3), which is the volume of the described solid.
Explanation:
The student's question relates to finding the volume of a solid with unusual properties: it has a circular base and each plane cross-section perpendicular to the x-axis is an equilateral triangle. We will solve this problem using calculus, specifically by integrating the cross-sectional area along the x-axis.
The circular base of the solid defines the limits of integration, as it gives the diameter of the solid which, in turn, represents its height because the triangle is equilateral.
The radius given is 3, so the diameter (and hence the height of the solid) is 6.
The area of an equilateral triangle with side length s is (sqrt(3)/4) * s².
Since the side length of the triangles is equal to the diameter of the base, s is 6.
Therefore, the area of each cross-section is (sqrt(3)/4) * 6².
Now, to find the volume, we integrate the area of each cross-section along the height of the solid. Doing this gives us:
Volume = [tex]int_0^6 ((sqrt(3)/4) * 6^2) dx[/tex]= (sqrt(3)/4) * 36 * 6
= 6*6*6*sqrt(3) / 4
= 36sqrt(3)
Thus, the correct answer is E) 36sqrt(3), which is the volume of the described solid.
60 PTS, Will Mark Brainliest
Listed in the Item Bank are key terms and expressions, each of which is associated with one of the columns. Some terms may display additional information when you click on them. Drag and drop each item into the correct column. The order does not matter.
Answers
1 and 5 are corresponding angles
2 and 6 are corresponding angles
2 and 7 are alternate exterior
3 and 5 are alternate interior
3 and 6 are consecutive interior
3 and 8 are corresponding
4 and 5 are consecutive interior
4 and 6 are alternate interior
4 and 7 are corresponding
John has opened 8 gifts and 6 of them have been toys. What is the probability that the next Gift ?he opens will be a toy
Answers
6:8=3/4.
John has a 3/4 probability of opening another toy.
Hope this helps!
The measure of an angle is 45°. what is the measure of a supplementary angle?
Answers
45 + x = 180
x = 135
so the answer is 135°.
use the graph for all 3 question
1) Henry, a 41-year-old male, bought a $100,000, 10-year life insurance policy through his employer. Henry is paid biweekly. what is his annual life insurance premium?
A)$455
B)$578
C)$1033
D)$1368
2) Karen, a 52-year-old female, bought a $75,000, 20-year life insurance policy though her employer. Karen is paid weekly. How much is deducted from her paycheck for life insurance?
A)$10.86
B)$25.33
C)$35.12
D)$50.65
3) Nikos, a 39-year-old male, bought a $300,000, 20-year life insurance policy.
What is the total amount he will pay for 20 year of coverage?
A)$13,650
B)$27,300
C)$30,990
D)$61,980
Answers
1.) Henry- $578
2.) Karen- $25.33
3.) Nikos- $61,980
Hope it helps!(:
Answer:
1: B) $578
2: B) $25.33
3: D) $61,980
Step-by-step explanation:
1) Henry's premium = ($100,000 / $1,000) x $5.78 = $578
2) Karen's total premium = ($75,000 / $1,000) x $17.56 = $1,317
if she is paid weekly, then the premium must be divided by 52 weeks = $1,317 / 52 weeks = $25.33 deducted per week
3) Nikos's premium per year = ($300,000 / $1,000) x $10.33 = $3,099
times 20 years = $3,099 x 20 = $61,980
what’s the answer to
2(x+6) + 3x +4
Answers
2x + 12 + 3x + 4
Next, combine all like terms (terms with x, and terms without x).
5x + 16
That is the final answer, because it cannot be simplified any further. Hope this helps!
Part 1.] Does the graph have even symmetry, odd symmetry, or neither?
Part 2.] Does the graph of y = sin x have even symmetry, odd symmetry, or neither?
Part 3.] Identify the transformations that describe the graph of an even function. Select all that apply.
reflection over the x-axis; reflection over the y-axis; reflection over the line y=x; 90° rotation around the origin; 180° rotation around the originAnswers
The graph has even symmetry. You can see that because it is symmetric with respect to the y-axis.
Functions that have even symmetry have the following property:
[tex]f(x)=f(-x)[/tex]
Part 2
To answer this we can simply check if the property we mentioned earlier holds for this function.
[tex]sin(\frac{\pi}{2})\ne sin(-\frac{\pi}{2})[/tex]
We can see that sine does not have even symmetry.
In fact, sine function has the following property:
[tex]sin(x)=-sin(x)[/tex]
This is called odd symetry.
Part 3
Take a look at the function that you attached in the picture. We know that function has even symmetry.
Reflection over x-axis and 180° rotation around the origin would give us -f(x). We would not end up with the same function, so these two are out.
90° rotation around the origin would mean we swapped x and y so that one is out too. Reflection over the line y=x is a property of functions that have an odd symmetry.
We are left with reflection around y-axis and, as mentioned before, this is the property of evenly symmetric functions.
help please.
1. Oatmeal costs $1.73/lb.
How much would 2.6 lb of oatmeal cost?
(Points : 1)
$1.50
$4.48
$4.50
$4.58
Question 2. 2. What percent of $520 is $494?
(Points : 1)
5%
11%
26%
95%
Answers
1.73/lb * 2.6 pounds= $4.498= $4.50
ANSWER: C) $4.50
2) set up a proportion. 494 is what % out of 520 as x is what out of 100.
$494/$520= x/100
cross multiply
(494*100)= (520*x)
49400= 520x
divide both sides by 520
95%= x
ANSWER: D) 95%
Hope this helps! :)
1. Cost of oatmeal:
Cost of oatmeal=1.73/lb× 2.6 pounds
Cost of oatmeal= $4.498
Cost of oatmeal= $4.50 (Approximately)
2. Percentage:
Percentage=494/520×100
Percentage=95%
Inconclusion the amount that 2.6 lb of oatmeal cost is $4.50 and the percent of $520 that is $494 is 95%.
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Answer ASAP
Find the area for this shape
Answers
so...
A = 1/2(4.9 + 1.5)(4)
A = 1/2(6.4)(4) = [tex]12.8 km^{2}[/tex]
A = [tex] \frac{a+b}{2} (h)[/tex]
A = [tex] \frac{1.5+4.9}{2} (4) [/tex]
A = 12.8
The area is 12.8 km²