Given:
The angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of the tree.
We need to determine the height of the tree.
Height of the tree:
Let the height of the tree be h.
The height of the tree can be determined using the trigonometric ratio.
Thus, we have;
[tex]tan \ \theta=\frac{opp}{adj}[/tex]
Substituting the values, we get;
[tex]tan \ 34^{\circ}=\frac{h}{25}[/tex]
Multiplying both sides by 25, we have;
[tex]tan \ 34^{\circ} \times 25=h[/tex]
[tex]0.6745 \times 25=h[/tex]
[tex]16.8625=h[/tex]
Rounding off to the nearest tenth of a foot, we get;
[tex]16.9=h[/tex]
Thus, the height of the tree is 16.9 feet.
Hence, Option B is the correct answer.
Correct option is B. The height of the tree can be found using the tangent of the angle of elevation, which is the ratio of the tree's height to the distance from the base. Applying the formula, the height is approximately 16.9 feet, matching option B.
To calculate the height of the tree given the angle of elevation and the distance from the point on the ground to the base of the tree, we can use trigonometric functions, specifically the tangent function in a right triangle. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the point on the ground to the tree).
Using the formula:
tangent(angle) = opposite / adjacent
Substitute the given values:
tangent(34°) = height of the tree / 25 ft
Now solve for the height:
height = 25 ft * tangent(34°)
Use a calculator to find:
height = 25 ft * 0.6745
height = 16.9 ft
Therefore, the height of the tree is approximately 16.9 feet (to the nearest tenth of a foot), making option B the correct answer.
John goel is to have more then -7 dollors in hisaccount by the end of this mounth. the varible d is the nuber of dollor in johns bank account at the end of the mounth. Whrite an lineqwalatiy in terms of d that is true only if john meets hif monthy goal
Answer:
d > - 7
Step-by-step explanation:
John is to have more then -7 dollars in his account by the end of this month.
Now, the variable d is the number of dollars in John's bank account at the end of the month.
Therefore, the inequality in terms of d that is true only if John meets his monthly goal will be
d > - 7 (Answer)
When ringing up a customer,a cashier needs 10seconds to process payment as well as 1second to scan each item being purchased .How long does it take to ring up a customer with 37 items ? Answer
Answer:
47 seconds
Step-by-step explanation:
It takes 37 seconds to scan 37 items at the rate of 1 second per item. It takes an additional 10 seconds to process the payment. Then the total time is ...
37 +10 = 47 . . . seconds
Keio and Taylor relapse after school to train for the baseball team the ratio of the number of laps Kyle ran to the number that Taylor 2 to 3 Kyle ran six slabs how many laps did Taylor
Answer: 9 miles
Step-by-step explanation: 6 divided by 2 is 3 and 3 times 3 is 9.
A circle has a radius of 32 inches. Find the circumference of the circle to the nearest tenth. Use 3.14 for PI.
The calculation of the circumference of a circle with a radius of 32 inches, using 3.14 for PI, gives a result of 201.0 inches.
Explanation:The subject of this question involves calculating the circumference of a circle. The formula used to find the circumference of a circle is 2πr, where r is the radius of the circle. Here, π is approximated to 3.14 as given in the question, and the radius r is given as 32 inches.
Substituting the given values into the formula, we get circumference = 2 * 3.14 * 32 = 200.96 inches. Thus, the circumference of the circle to the nearest tenth is "201.0 inches."
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please give answer ?
Answer:
M=(-8, -3.5)
Step-by-step explanation:
The midpoint formula for two points is [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]. Plugging in our numbers, you get [tex](\frac{-9-7}{2},\frac{-10+3}{2})=(-8, -3.5)[/tex]. Hope this helps!
Histidine has 3 nitrogens. arrange the indicated nitrogens in decreasing order of basicity (1 = most basic, 3 = least basic). if there are fewer than 3 nitrogens in the molecule, leave that answer space blank. if two nitrogens have the same basicity, give them the same number. histidine
Answer:
Nitrogen 7 = 1 ---- Most Basic
Nitrogen 1 = 2
Nitrogen 3 = 3 ------ Least Basic
Step-by-step explanation:
The basicity of amino acids is as a result f the unshared pair of electrons in the Nitrogen atoms.
Part of the rule of basicity of organic compounds(amino acids) posits that:
The more unstable an electron pair is, the more basic it is.
From the diagram attached below;
Nitrogen 7 posses and unstable electron due to the lone pair of electron in the NH₃⁺ which renders it most basic .
Nitrogen 1 and 3 are in ring form thereby they are less basic But nitrogen 1 is more basic compared to nitrogen 3 because lone pair on Nitrogen 1 is not involved in resonance unlike Nitrogen 3 that is resonance stabilized (i.e alternating by a resonance effect).
Another phenomenon to deduce the basicity of Histidine is the effect of hybridization.
Basicity of Organic Compounds increases with decreasing s character.
Therefore, the trend of basicity is as follows: sp³ > sp² > sp
Because in sp; the lone pairs are most stable, hence least basic
And in sp³; the lone pairs are least stable; hence most basic.
Therefore; From the diagram attached below:
Nitrogen 7 = 1 ---- Most Basic
Nitrogen 1 = 2
Nitrogen 3 = 3 ------ Least Basic
6.5% of people in the U.S. Have A- blood type. You randomly select 6 Americans and ask them if their blood type is A-. a) Find the probability that all 6 are type A-. b) Find the probability that at most 4 of them are type A-. c) Find the mean and standard deviation.
Answer:
a) 7.54189*10^-8
b) 0.99999999
c) E ( X ) = 0.39 , s ( X ) = 0.604
Step-by-step explanation:
Solution:-
- We will assume the proportion of people with A- blood group is independent and remains constant for a fairly small sample of n = 6 Americans selected at random.
- We will denote a random variable X = The number of americans out of 6 that have blood group type A-.
- The random variable is assumed to follow binomial distribution.
- The probability of success is the proportion of people in U.S that have blood group type A-, p = 0.065:
X ~ Bin ( 6 , 0.065 )
Where, r represents the number of americans out of selected 6 have blood group A-. The pmf of a binomial variate is given as:
P ( X = r ) = nCr * ( p ) ^r * ( 1 - p ) ^ ( n - r )
a) Find the probability that all 6 are type A-
- We will pmf given above and set r = 6. And evaluate the resulting probability:
P ( X = 6 ) = 6C6 * ( p )^6 * ( 1 - p ) ^ ( 0 )
= p^6
= ( 0.065 )^6
= 7.54189*10^-8
b) Find the probability that at most 4 of them are type A-
- We will pmf given above and evaluate the following expression:
P ( X ≤ 4 ) = 1 - P ( X = 5 ) - P ( X = 6 )
P ( X ≤ 4 ) = 1 - 6C5 * ( p )^5 * ( 1 - p ) ^ ( 1 ) - p^6
= 1 - 6*(0.065)^5 ( 0.935 ) - 0.065^6
= 1 - 6.50923*10^-8 - 7.54189*10^-8
= 0.99999999
c) Find the mean and standard deviation.
- The mean E ( X ) of the defined random variable distributed binomially is given by:
E ( X ) = n*p = 6*0.065 = 0.39 people
- The mean s( X ) of the defined random variable distributed binomially is given by:
s ( X ) = √n*p*q = √(6*0.065*0.935) = 0.604
Which set of three angles could represent the interior angles of a triangle? 26 degrees, 51 degrees, 103 degrees 29 degrees, 54 degrees, 107 degrees 35 degrees, 35 degrees, 20 degrees 10 degrees, 90 degrees, 90 degrees
Answer:
26 °, 51 °, 103 °
Step-by-step explanation:
-A triangle is a 3-sided regular polygon.
-The sum of it's interior angles add up to 180°.
-Only the 26 °, 51 °, 103 ° set add exactly up to 180° and therefore satisfies the triangle's interior angles condition.
Answer:
The answer A trust me
Step-by-step explanation:
SOLVE X/5+3=2
A)-5
B)25
C)5
D)-1/5
Answer:
b 25
Step-by-step explanation:
Answer:
A)-5 if its without parenthasis around 5+ 3
Step-by-step explanation
2 minus 3 is -1 and -1 times 5 is -5
What is the function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units?
Given:
The parent function is [tex]f(x)=x^2[/tex]
We need to determine the function g(x) created from the function f(x) by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units.
Shift left 9 units:
The rule to shift the graph c units to the left is given by
[tex]y=f(x+c)[/tex]
where c is the positive real number.
Hence, to shift the graph 9 units to the left is given by
[tex]f(x)=(x+9)^2[/tex]
Vertical stretch by a factor of 4:
The rule to stretch the graph vertically by a factor of c is given by
[tex]y=cf(x)[/tex]
where [tex]c>1[/tex]
Hence, to stretch the graph vertically by a factor of 4, we have;
[tex]f(x)=4(x+9)^2[/tex]
Shifting 5 units up:
The rule to shift the graph c units upward is given by
[tex]y=f(x)+c[/tex]
where c is the positive real number.
Hence, to shift the graph 5 units upward is given by
[tex]f(x)=4(x+9)^2+5[/tex]
Therefore, the function [tex]g(x)=4(x+9)^2+5[/tex] is created from the graph [tex]f(x)=x^2[/tex] by moving the graph left 9 units, vertically stretching it by a factor of 4 and shifting up 5 units.
Hence, the graph g(x) is [tex]g(x)=4(x+9)^2+5[/tex]
The function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units is g(x) = 4*(x+9)^2 + 5.
Explanation:To generate the function g(x) from f(x) = x^2, you will perform several transformations on it:
A horizontal shift of 9 units to the left. To do this, you change the x inside the function to (x+9). A vertical stretch by a factor of 4. To do this, you multiply the whole function by 4.A vertical shift of 5 units up. To do this, you add 5 to the entire function.So, after performing these transformations to f(x) = x^2, you get the function g(x) = 4*(x+9)^2 + 5.
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Advertisers often refer to CPM (Cost per thousand people reached) when quoting advertising rates. If a website
promises to reach 23,000 people for $1,540, what is the CPM? (Round to the nearest dollar.)
a) $67
b) $108
c) $150
d) $185
Answer:
$67
Step-by-step explanation:
There are 23 thousand clicks, so as it pays per thousand you need to divide $1 540 by 23, which results in 66.9.... reacurring which when rounded is (a) for $67.
What is the expression of 8 more than a number x
"more" means added to, or addition. So 8 more than 'x' is:
x + 8
line n passes through the points (-3 -7.5) and (2 -5) tahlia determined that the equation of line n is y = 0.5x. explain the error Tahlia made while determining her equation. Be sure to include the correct equation in your explanation
Answer:
She forgot to find the y intercept add it in the equation
y = .5x-6
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/(x2-x1)
= (-5 - -7.5)/ (2 - -3)
=(-5 +7.5)/( 2+3)
= 2.5/5
= 1/2
Substitute into the slope intercept form of the equation
y= mx+b
y= .5x +b
We need to determine b by substituting a point into the equation
-5 = .5(2) +b
-5 = 1+b
Subtract 1 from each side
-5-1 = 1-1+b
-6 = b
y = .5x-6
Answer:
She forgot the y-intercept
y = 0.5x - 6
Step-by-step explanation:
y = 0.5x + c
-5 = 0.5(2) + c
c = -6
Correct equation:
y = 0.5x - 6
You have a wire that is 74 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum
Answer:
32.55 cm
Step-by-step explanation:
Let x = the length of wire that becomes a circle.
Then 74 - x = the length of wire that becomes a square
Circumference of circle + perimeter of square = 74
1. Expression for the side of the square
P = 4s = 74 - x
s = ¼(74 - x)
2. Expression for the radius of the circle
C = 2πr = x
r = x/(2π)
3. Expression for the total area
[tex]\begin{array}{rcl}\text{Total area} & = &\text{area of circle+ area of square}\\A & = & \pi r^{2} + s^{2}\\& = &\pi \left(\dfrac{x}{2 \pi}\right)^{2} + \left (\dfrac{1}{4}(74 - x)\right)^{2}\\\\ & = & \dfrac{x^{2}}{4 \pi} + \dfrac{1}{16}(5476 - 148x + x^{2})\\\\ & = & 0.07958x^{2} + 342.25 - 9.25x + 0.0625x^{2}\\A & = & 0.1421x^{2} -9.25x + 342.25 \\ \end{array}[/tex]
This is the equation of a parabola.
In standard form,
ƒ(x) = 0.1421x² -9.25x + 342.24
a = 0.1421; b = -9.25; c = 342.24
The parabola opens upwards, because a > 0. Therefore, the vertex is a minimum.
The vertex of a parabola occurs at
x = -b/(2a) = 9.25/(2 × 0.1421) = 9.25/(0.2842) = 32.55
The circumference of the circle is 32.55 cm.
The graph below shows that the area of the circle is a minimum when x = 32.55 cm
Which name accurately describes the figure shown below and why?.
Answer:
the third answer is right
Step-by-step explanation:
its a rhombus because the 4 sides are of equal length and the opposite sides are parallel but there are no right angles.
I need another help again my bros
Answer:
a = 15.59 c= 31.18
27 tan 30 = a
c cos 30 = 27
c = 27/cos30
c = 31.18
The function () = 2 + 4 was replaced with ( + ) resulting in the function
() = 2 + 22. What is the value of ?
Let's evaluate explicitly [tex]f(x+k)[/tex]:
[tex]f(x)=2x+4\iff f(x+k)=2(x+k)+4=2x+2k+4[/tex]
If this must equal [tex]2x+22[/tex], we have
[tex]2x+2k+4=2x+22 \iff 2k+4=22 \iff 2k=18 \iff k=9[/tex]
Answer:
For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?
Step-by-step explanation:
For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?
What is twice a number minus 4 is less than three times the number?
Answer:
[tex]n > -4[/tex]
Step-by-step explanation:
Step 1: Convert into an expression
Twice a number minus 4 is less than three times the number
[tex]2n - 4 < 3n[/tex]
Step 2: Solve for the number
[tex]2n - 4 - 2n < 3n - 2n[/tex]
[tex]-4 < n[/tex]
Answer: [tex]n > -4[/tex]
A box contains 400 black pens and 50 red pens. Jose said the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1, P(not black) + P(not red) = 1. Do you agree with him? Complete the explanation to answer the question.
I (disagree/agree) with Jose that the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1.
Answer:
I agree with Jose that the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1.
Step-by-step explanation:
If we sum the probability of not black and probability of not red, we will get 1.
The probability of not black means probability of red i.e 50/450
The probability of not red means probability of black i.e 400/450.
When we add the probability, we get 1.
50/450 + 400/450 = 450/450 = 1
Invariably, the statement is same as finding probability of black and probability of red; just that the value are interchanged.
Two lines are perpendicular if they cross a 45° angle true or false
Answer: False
Step-by-step explanation:
what is the limit of the infinite series?
Answer:
Zero
Step-by-step explanation:
There is no solution to this.
urgent !! Convert the following equation to logarithmic or exponential form:
log subscript 49 left parenthesis 7 right parenthesis equals 1 half
Your answer:
49 to the power of 7 equals 1 half
7 to the power of 49 equals 1 half
open parentheses 1 half close parentheses to the power of 7 equals 49
49 to the power of 1 half end exponent equals 7
Answer:
The exponential form is 49 to the power of one-half equals 7 ⇒ 4th answer
Step-by-step explanation:
The exponential equation of [tex]log_{b}(m)=n[/tex] is [tex]b^{n}=m[/tex] , where b is the base, n is the exponent of b and m is the value of [tex]b^{n}[/tex]
Ex: If [tex]log_{3}(81)=4[/tex] , that means b = 3 , n = 4 and m = 81, then its exponential form is [tex]3^{4}=81[/tex]
Now let us solve the question
∵ The equation is [tex]log_{49}(7)=\frac{1}{2}[/tex]
∴ The base is 49
∴ The exponent is [tex]\frac{1}{2}[/tex]
∴ The answer is 7
- Substitute them in the form of the exponential form
∴ The exponential form is [tex](49)^{\frac{1}{2}}=7[/tex]
The exponential form is 49 to the power of one-half equals 7
The given equation is log49(7) = 1/2. To convert it to exponential form, we can write it as 49^(1/2) = 7.
Explanation:The given equation is:
log49(7) = 1/2
To convert this equation to exponential form, we need to remember that logarithms and exponentials are inverse functions. Therefore, we can write the equation as:
491/2 = 7
Hence, the exponential form of the given equation is 49 raised to the power of 1/2 equals 7.
Please help me idk this
Answer:
34.54 inches.
Step-by-step explanation:
The formula for the circumference of the circle is given as [tex]C=\pi d[/tex], where [tex]\pi[/tex] is rounded to 3.14 and d is the diameter of the circle, 11 inches. Simply plug these values into the equation for the circumference to get your answer:
[tex]C=\pi d\\C=(3.14)*(11)[/tex]
C = 34.54 inches
Answer:
34.54 inches
Step-by-step explanation:
C=πd
d=11
C = 11 * 3.14
C = 34.54 inches
How many minutes is it from 4:00 to 4:30
Answer:
30 minutes
Step-by-step explanation:
Just look at the minutes only. Since you need 4 o'clock to 4:30, its only 30 minutes.
Answer:
30 minutes
Step-by-step explanation:
All you have to do is subtract 4:30 and 4:00 and get 30 minutes.
Would having deadbolt locks on exterior doors affect a homeowner's insurance policy price? Why or why not? Answer in complete sentences.
Answer:
Having a deadbolt lock installed on the exteriors of a building would affect the price of Insurance.
The principles of insurance require that the Insurance Policy Holder or Insured should act as if uninsured. This means that even with an Insurance Policy in place, the owner of this house is required to ensure that all reasonable steps have been taken to secure the house.
This may include having a properly installed lock in place.
The price or insurance premium of a homeowner may go up very significantly if there is no lock installed, that is if the risk is accepted for coverage by the insurance company.
It (the premium that is) may or may not come down if there is a deadbolt lock in place. It all depends on the extent to which the deadbolt lock has reduced the exposure of the Insurance company. Where the deadbolt lock has very significantly reduced the risk, the policyholder may press for a reduction in insurance premium.
In most Homeowners Insurance policy, for a claim concerning theft of insured home items, the policyholder has to provide evidence of forceful entry or exit, showing that the house was reasonably secured to warrant a breaking in or breakout.
Cheers!
Which measure of center would you use to compare the populations represented by the box plots?
Which measure of variability would you use to compare the populations represented by the box plots?
Answer:
Median and Interquartile range (IQR)
Step-by-step explanation:
I did it :)
What is the greatest common factor
of 48 and 120?
Answer:
24
Step-by-step explanation:
A growth medium is inoculated with 1,000 bacteria, witch grow at rate of 15% each day. What is the population of the culture 6 days after inoculation?
Answer: the population of the culture 6 days after inoculation is 2313.
Step-by-step explanation:
The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
y = b(1 + r)^ t
Where
y represents the population after t days.
t represents the number of days.
b represents the initial population.
r represents rate of growth.
From the information given,
b = 1000
r = 15% = 15/100 = 0.15
t = 6 days
Therefore
y = 1000(1 + 0.15)^6
y = 1000(1.15)^6
y = 2313
Which equations are equivalent to y = two-thirds x minus 4 when written in slope-intercept form? Check all that apply.
3 x minus 2 y = 4
2 x minus 3 y = 12
Negative 4 (2 x minus 3 y) = negative 4 (12)
2 (x + 6) = 3 y
2 x minus 3 y = 4
Answer:
2 x minus 3 y = 12
Negative 4 (2 x minus 3 y) = negative 4 (12)
Step-by-step explanation:
y = two-thirds x minus 4
y = (⅔)x - 4
Multiply the entire equation by 3
3y = 2x - 12
2x - 3y = 12
Multiply both sides by -4
-4(2x - 3y) = -4(12)
Answer:
b
Step-by-step explanation:
Please someone help me answer this! Rico is making 6 batches of salsa. Each batch needs 3/4 cup of corn. He only has 1/4 cup measure. How many times must Rico measure 1/4 cup of corn to have enough for all the salsa?
Answer:
18
Step-by-step explanation:
3/4 divided by 1/4 equals 3
3 times 6 equals 18