Answer:
The correct option is (d).
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired-samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
We use the paired t-test if we have 2 measurements on the same item, person or thing. We should also use this test if we have 2 items that are being measured with a unique condition.
For instance, an experimenter tests the effect of a medicine on a group of patients before and after giving the doses.
In this case, the same participants are selected for both the trials.
And the difference between the endurance before and after the usage of the new sports drink are noted.
Thus, the analysis that would be used on the data is the Dependent samples t-test.
7 less than the quotient of a number and 3 is 5. Find the number.
Answer:
The answer is 36
Step-by-step explanation:
Let the number be x
7 less than the quotient of a number and 3 is written as
[tex] \frac{x}{3} - 7[/tex]The result is 5
So we have
[tex] \frac{x}{3} - 7 = 5[/tex]Move - 7 to the right side of the equation
That's
[tex] \frac{x}{3} = 7 + 5[/tex][tex] \frac{x}{3} = 12[/tex]Multiply both sides by 3 to make x stand alone
We have
[tex]3 \times \frac{x}{3} = 12 \times 3[/tex]We have the final answer as
x = 36Hope this helps you
Mariah swam her leg of the race in 24.98 seconds and Janet swam her leg of the relay race in 25.874 seconds. What was their combined time for their part of the relay?
Answer:
50.854 seconds
Step-by-step explanation:
24.98 + 25.874 = 50.854 seconds
If Bobby drinks 5 waters in 10 hours how many does he drink in 1 hour ?
Water drunk by Bobby in 10 hours = 5 units
So, water drink by Bobby in 1 hour
= 5/10 units
= 1/2 units
= 0.5 units
Answer:
1/2 water
Step-by-step explanation:
We can use a ratio to solve
5 waters x waters
----------- = ------------
10 hours 1 hours
Using cross products
5*1 = 10 *x
5 = 10x
Divide by 10
5/10 = x
1/2 waters =x
Jennifer is saving money to buy a bike. The bike costs $227. She has $106 saved, and each week she adds
$11 to her savings.
How long will it take her to save enough money to buy tho hilo?
Answer:
11 weeks.
Step-by-step explanation:
227-106=121
121 divided by 11 = no. of weeks
Therefore it takes her 11 weeks.
Answer:
It will take 11 weeks
Step-by-step explanation:
11 times 11 is 121.
121 plus 106 is 227
which is the exact number the bike costs
Give a vector parametric equation for the line through the point (−2,−4,0) that is parallel to the line ⟨−2−3t,1−4t,−5t⟩:
The tangent vector for the given line is
T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩
On its own, this vector points to a single point in space, (-3, -4, -5).
Multiply this vector by some scalar t to get a whole set of vectors, essentially stretching or contracting the vector ⟨-3, -4, -5⟩. This set is a line through the origin.
Now translate this set of vectors by adding to it the vector ⟨-2, -4, 0⟩, which correspond to the given point.
Then the equation for this new line is simply
L(t) = ⟨-3, -4, -5⟩t + ⟨-2, -4, 0⟩ = ⟨-2 - 3t, -4 - 4t, -5t⟩
The vector parametric equation for the line through the point is [tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex].
GivenGive a vector parametric equation for the line through the point (−2,−4,0) that is parallel to the line ⟨−2−3t,1−4t,−5t⟩.
What is a parametric equation vector?Parametric equations of the line segment are defined by its endpoints.
To find the vector equation of the line segment, we’ll convert its endpoints to their vector equivalents.
Two lines are parallel if they have the same direction, and in the parametric form, the direction of a line is always the vector of constants that multiply t (or the parameter).
The vector equation of a line is given by:
[tex]\rm v = r_0+tv[/tex]
Where v is the direction vector and [tex]\rm r_0[/tex] is a point of the line.
The tangent vector for the given line is
T(t) = d/dt ⟨-2 - 3t, 1 - 4t, -5t⟩ = ⟨-3, -4, -5⟩
Here,
[tex]\rm r_0 = (-2,-4,0) \ and \ v=(-3, \ -4, \ -5)t\\\\[/tex]
Then,
[tex]r = (-2, \ -4, \ 0) +(-3, \ -4, \ -5)t\\\\[/tex]
x = -2-3t, y = -4-4t, and z = 0-5t
To know more about the Parametric equation click the link given below.
https://brainly.com/question/14701215
Question (2)
ASAP Please help.
Construct the "Square root spiral". Take a large sheet of paper and construct the "Square root spiral" in the following fashion.
Start with a point O and draw a line segment [tex]\rm{P_{1} P_{2}}[/tex] perpendicular to [tex]\rm{OP_{1}}[/tex] of unit length. Now draw a line segment [tex]\rm{P_{2} P_{3}}[/tex] perpendicular to [tex]\rm{OP_{2}}[/tex] . Then draw a line segment [tex]\rm{P_{3} P_{4}}[/tex] perpendicular to [tex]\rm{OP_{3}}[/tex]. Continuing in this matter, you get line segment of unit length perpendicular to [tex]\rm{OP_{n-1}}[/tex]. In this manner, you will have created the points [tex]\rm{P_{2}, P_{3},...... P_{n}....}[/tex], and joined them to create a beautiful spiral depicting [tex]\rm{\sqrt{2}, \sqrt{3}, \sqrt{4},...}[/tex]
Answer:
The "square root spiral," donned the "Spiral of Theodorus" was created by Theodorus to visualize a set of 17 isosceles triangles where [tex]n[/tex] is equal to a value between one and seventeen.
The central angle is attached to a central point, and the side opposite of the central angle is always equal to 1.The hypotenuse of the triangle is equivalent to [tex]\sqrt{n+1}[/tex]. The hypotenuse becomes a leg for the next triangle.I have attached an image of the Square Root spiral below.
1. Find the volume of the shipping box using the two methods and show your work plzzzzzzzz i neeeeeeeeeeeeeed help
Step-by-step explanation:
Measure the width, length and height of the shipping box in inches. Multiply the width, length and height of the box to calculate its volume in cubic inches. For example, if the box is 20 inches wide, 24 inches long and 16 inches high, then the volume is (20)(24)(16) = 7,680 cubic
Answer:
The volume of the shipping box would be 36 9/16
Step-by-step explanation:
One method to find the volume of the shipping box would be (l)(w)(h)
one we plug in our dimensions the equation would become 3 1/4 x 3 x 3 3/4
To simplify this we would first
Multiply
3 1/4 x 3 x 3 3/4 = 39/4 x 3 3/4
The bolded parts are the pieces we are working on
3 1/4 as an improper fraction is 13/4
13/4 x 3 = 13 x 3/4 = 39/4
- The second step would be to
Convert the mixed number to an improper fraction.
3 3/4 = ( 3 × 4 ) / 4 + 3/4 = 12 + 3 / 4 = 15/4
Now we have to Multiply
39/4 x 15/4 = 39 x 15 / 4 x 4 = 585/16
Lastly, we have to simplify
585/16 = 36 9/16
what decimal is equivalent to 0.85
Answer: 17/20
Step-by-step explanation:
0.85 = 85/100 = 17/20
The number 0.85 can be written using the fraction 85/100 which is equal to 17/20 when reduced to lowest terms.
What does 1.20 mean in this situation?
Answer:
hshsjzhzzoazuhsox9 hzbskznzjzbziznzkalajhzisjshaoianajs9zjgz
A^2 + 2AB +B^2
habsbsjabdhjsbfhjbsdjh
Find the area of'a triangle with legs that are: 12 m, 15 m, and 9 m.
M
O A. 25.5 m
OB. 38.2 m
OC. 42.4 m
OD. 54 m
Answer:
D. 54m
Step-by-step explanation:
by the side you can see that it is a right triangle with hypotenuse = 15
1/2(b)(h) = 1/2(9)(12) = 54
Answer:
D.) 54 m2
Step-by-step explanation:
I got it correct on founders edtell
What’s the distance between (4,-9) and (5,3)
Answer: Distance = √145
Concept:
Here, we need to know the concept of the distance formula.
The distance formula is the formula, which is used to find the distance between any two points.
If you are still confused, please refer to the attachment below for a clear version of the formula.
Solve:
Given information
(x₁, y₁) = (4, -9)
(x₂, y₂) = (5, 3)
Given formula
[tex]Distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute values into the formula
[tex]Distance = \sqrt{(5-4)^2+(3+9)^2}[/tex]
Simplify values in the parentheses
[tex]Distance = \sqrt{(1)^2+(12)^2}[/tex]
Simplify exponents
[tex]Distance = \sqrt{1+144}[/tex]
Simplify by addition
[tex]Distance = \sqrt{145}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
[tex]\boxed {\boxed {\sf \sqrt {145} \ or \ 12.04}}[/tex]
Step-by-step explanation:
The distance between 2 points is calculated using the following formula.
[tex]d= \sqrt {(x_2-x_1)^2+(y_2-y_1)^2)[/tex]
In this formula, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
We know the two points are (4, -9) and (5,3). If we match the values of the points and the coordinating variable, we see that:
x₁ = 4y₁= -9 x₂ = 5 y₂ = 3Substitute the values into the formula.
[tex]d= \sqrt { ( 5 -4)^2 + ( 3 --9)^2[/tex]
Solve inside the parentheses.
(5-4)= 1 (3 --9) = (3+9) = 12[tex]d= \sqrt {(1)^2 + (12)^2}[/tex]
Solve the exponents.
(1)² = 1 *1 = 1 (12)² = 12 * 12 = 144[tex]d= \sqrt{ 1+144}[/tex]
Add.
[tex]d= \sqrt{145[/tex]
Take the square root.
[tex]d=12.04159458[/tex]
Let's round to the nearest hundredth. The 1 in the thousandth place tells us to leave the 4 in the hundredth place.
[tex]d \approx 12.04[/tex]
The distance between the 2 points is √145 or approximately 12.04.
Look at photo and answer.
Answer:
h.
[tex] \frac{9 {x}^{10}(y. {x}^{3}) {}^{2} }{y.x(3 {x}^{3}) {}^{3} } \\ \\ = \frac{9 {x}^{10}(y {}^{2} )( {x}^{6} ) }{3y. {x}^{10} } \\ \\ = \frac{ {3}^{2} {x}^{16} {y}^{2} }{3y {x}^{10} } \\ \\ = 3y {x}^{6} [/tex]
j.
[tex] \frac{(3x. {y}^{7} ) {}^{2}. {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{3 {x}^{2} . {y}^{14} . {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{ {3x}^{7} {y}^{14} }{3 {x}^{7} {y}^{4} } \\ \\ = {y}^{10} [/tex]
SOMEONE PLEASEEEEEEEEEE HELP!!!!!!!!1
Answer: Angle LMN = 45
Step-by-step explanation:
The line MN will be parallel to the side Line JK
And LJ will be transversal
Therefore
Angle LMN = LJK (Corresponding angles)
ATQ
⇒3 + 6x = 101 - 8x
⇒6x + 8x = 101 -3
⇒14x = 98
⇒x = 98/14
⇒x = 7
Angle LMN = 3 + 6x
= 3 + 6(7)
= 3 + 42
= 45
Therefore Angle LMN will be 45°
Must click thanks and mark brainliest
In how many years will the population of a town be 26901 from 24400 at the growth rate of 5% per annum ?
Answer:
2 years
Step-by-step explanation:
population in 1 year= 24400*105%=25620
population in 2 year= 25620*105%=26901
The area of a square is 36cm2. What are the dimensions of the square? You must show your work. Pls tell me what the dimensions of the square are
Answer:
6 cm by 6 cm
Step-by-step explanation:
We know that the formula for area of a square is A = s² where A = area and s is the length of one side. We know that A = 36 so:
36 = s²
√36 = s
s = ±6
Note that s = -6 is an extraneous solution because you can't have a side length of -6, therefore the answer is s = 6 so the dimensions of the square are 6 cm by 6 cm.
The area of a square is found using the formula area = s^2, where s is the length of a side. ( a square has 4 equal sides).
Given the area you have:
36 = s^2
Find a by taking the square root of both sides:
S = sqrt(36)
S = 6
The square has a side length of 6 cm.
Which among the given schemes offers a monthly instalment of less than Rs 5000. ?
a) Scheme A
b) Scheme B
c) Scheme C
d) Both Scheme A and Scheme B
Please help. I’ll mark you as brainliest if correct!
Answer:
(DNE,DNE)
Step-by-step explanation:
-24x-12y = -16. Equation one
6x +3y = 4. Equation two
Multiplying equation two with +4 gives
4(6x +3y = 4)
24x +12y = 16...result of equation two
-24x -12y= -16...
A careful observation to the following equation will help us notice that the both equation are same thing.
Multiplying minus to equation one gives
-(-24x-12y=-16)
24x+12y = 16.
Since the both equation are same, there is no solution to it.
Reading a Tape Measure
Measure the green bar using the provided image of a tape measure
Answer:
3 inches
Step-by-step explanation:
The green bar reaches all the way to the 3 on the ruler, and each number represents an inch.
Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. 5x − 4 x(x2 + 7)2
Answer:
[tex]\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}[/tex]
Step-by-step explanation:
Given the expression [tex]\frac{5x-4}{x(x^2+7)^2}[/tex], we are to re-write the expression in form of a partial fraction.
Before we write in form of a partial fraction, we need to note the expression at the denominator. Since the expression in parenthesis is a quadratic equation, the equivalent numerator must be a linear expression.
Also the quadratic equation is a repeated form since it is squared. This means that we are to repeat the quadratic equation twice when writing as a partial fraction.
[tex]\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}[/tex]
From the above partial fraction, it can be seen that x² + 7 in parenthesis was repeated twice and their equivalent expressions at the numerator are both linear i.e Bx+E and Dx+ E where A, B, C, D and E are the unknown constant.
Write three fractions that are equivalent to 3 over 11 , but written in higher terms. One of them must
include one or more variables.
Answer:
Three fractions that are equivalent to [tex]\frac{3}{11}[/tex] are: [tex]\frac{6}{22}[/tex], [tex]\frac{24}{88}[/tex] and [tex]\frac{144}{528}[/tex].
Step-by-step explanation:
Equivalent fractions are set of fractions in which when simplified, they have the same answer.
Given: [tex]\frac{3}{11}[/tex]
i. multiply the numerator and denominator of [tex]\frac{3}{11}[/tex] by 2,
= [tex]\frac{3*2}{11*2}[/tex] = [tex]\frac{6}{22}[/tex]
i. multiply both the numerator and denominator of [tex]\frac{6}{22}[/tex] by 4,
= [tex]\frac{6*4}{22*4}[/tex]= [tex]\frac{24}{88}[/tex]
ii. multiply the numerator and denominator of [tex]\frac{24}{88}[/tex] by 6,
= [tex]\frac{24*6}{88*6}[/tex] = [tex]\frac{144}{528}[/tex]
So that;
[tex]\frac{3}{11}[/tex] = [tex]\frac{6}{22}[/tex] = [tex]\frac{24}{88}[/tex] = [tex]\frac{144}{528}[/tex].
Three fractions that are equivalent to [tex]\frac{3}{11}[/tex] are: [tex]\frac{6}{22}[/tex], [tex]\frac{24}{88}[/tex] and [tex]\frac{144}{528}[/tex].
A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of ounces and a standard deviation of ounce. You randomly select cans and carefully measure the contents. The sample mean of the cans is ounces. Does the machine need to be reset? Explain your reasoning. ▼ Yes No , it is ▼ very unlikely likely that you would have randomly sampled cans with a mean equal to ounces, because it ▼ lies does not lie within the range of a usual event, namely within ▼ 1 standard deviation 2 standard deviations 3 standard deviations of the mean of the sample means.
Complete question is;
A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.20 ounce. You randomly select 35 cans and carefully measure the contents. The sample mean of the cans is 127.9 ounces. Does the machine need to be? reset? Explain your reasoning.
(yes/no)?, it is (very unlikely/ likely) that you would have randomly sampled 35 cans with a mean equal to 127.9 ?ounces, because it (lies/ does not lie) within the range of a usual? event, namely within (1 standard deviation, 2 standard deviations 3 standard deviations) of the mean of the sample means.
Answer:
Yes, we should reset the machine because it is unusual to have a mean equal to 127.9 from a random sample of 35 as the mean of 127.9 doesn't fall within range of a usual event with 2 standard deviations of the mean of the sample means.
Step-by-step explanation:
We are given;
Mean: μ = 128
Standard deviation; σ = 0.2
n = 35
Now, formula for standard error of mean is given as;
se = σ/√n
se = 0.2/√35
se = 0.0338
Normally, the range of values should be within 2 standard deviations of mean. In this case, normal range of values will be;
μ ± 2se = 128 ± 0.0338
This gives; 127.9662, 128.0338
So, Yes, we should reset the machine because it is unusual to have a mean equal to 127.9 from a random sample of 35 as the mean of 127.9 doesn't fall within range of a usual event with 2 standard deviations of the mean of the sample means.
Hayley bought a bike that was on sale with a 15% discount from the original price of $142. If there is a 6% sales tax to include after the discount, how much did Hayley pay for the bike?
Answer:
$12,78
Step-by-step explanation:
$142 × 0,15 = $21,3
$21,3 × 0,6 = $12,78
While walking from the car into your dormitory you dropped your engagement ring somewhere in the snow. The path is 30 feet long. You are distraught because the density of its location seems to be constant along this 30-foot route. a) What is the probability that the ring is within 12 feet of your car
Answer:
0.4
Step-by-step explanation:
we are required to find the probability that the ring is within 12 meters from nthe car.
we start by defining a random variable x to be the distance from the car. the car is the starting point.
x follows a normal distribution (0,30)
[tex]f(x)=\frac{1}{30}[/tex]
[tex]0<x<30[/tex]
probabilty of x ≤ 12
= [tex]\int\limits^a_ b{\frac{1}{30} } \, dx[/tex]
a = 12
b = 0
[tex]\frac{1}{30} *(12-0)[/tex]
[tex]\frac{12}{30} = 0.4[/tex]
therefore 0.4 is the probability that the ring is within 12 feet of your car.
Transform the given parametric equations into rectangular form. Then identify the conic. x= 5cos(t) y= 2sin(t)
Answer:
Solution : Option D
Step-by-step explanation:
The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )
x = 5cos(t) ⇒ x / 5 = cos(t)
y = 2sin(t) ⇒ y / 2 = sin(t)
Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )
( x / 5 )² = cos²(t)
+ ( y / 2 )² = sin²(t)
_____________
x² / 25 + y² / 4 = 1
Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.
3x18 = 3 (10+8) is an example of the _________ property of multiplication.
Answer:
3x18 = 3 (10+8) is an example of the commutative property of multiplication
Step-by-step explanation:
Answer: commutative property of multiplication
Step-by-step explanation:
-36 = 6(2-8n) please
Answer:
n=1
Step-by-step explanation:
-36 = 6(2-8n)
-36=12-48n
-36-12=-48n
-48=-48n
n=1
Point M is the midpoint of CD. What is the value of a in the figure?
Answer:
a=3
Step-by-step explanation:
Given points (a, b) and (c,d), the midpoint of the points will be at
((a+c)/2, ((b+d)/2)
Therefore, given (9, 2) and (a,2a), our midpoint is at
((9+a)/2, (2+2a)/2) = (6,4)
Matching the x values to their corresponding x values and doing the same with the y values, we get
(9+a)/2 = 6
(2+2a)/2 = 4
First, we have
(9+a)/2 = 6
multiply both sides by 2 to remove the denominator
9+a = 12
subtract 9 from both sides to isolate a
a = 3
2a = 2 * a = 6
Confirming this, we have
(2+2a)/2 = 4
(2+6)/2 = 4
8/2=4
The value of a is 3 after using the bisection formula and the coordinate of the C is (3, 6).
What is an ordered double?It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
Point M is the midpoint of CD.
The coordinate of the C is (a, 2a)
The coordinate of the M is (6, 4)
The coordinate of the C is (9, 2)
Using bisection formula:
(a + 9)/2 = 6
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. I
a + 9 = 12
a = 12 - 9
a = 3
Or
(2a + 2)/2 = 4
a + 1 = 4
a = 3
Thus, the value of a is 3 after using the bisection formula and the coordinate of the C is (3, 6).
Learn more about the order double here:
brainly.com/question/10757890
#SPJ2
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 53.9 for a sample of size 24 and standard deviation 5.6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places.
_______ < μ < _________ please teach using calculator method
Answer:
The estimate is
[tex]52.02 < \mu < 55.78[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\ = x = 53.9[/tex]
The sample size is n = 24
The standard deviation is [tex]\sigma = 5.6[/tex]
Given that the confidence level is 90% the level of significance is mathematically represented as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table.The value is
[tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.10 }{2} } = 1.645[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because [tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval ( [tex]1 - \alpha[/tex] ) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{5.6 }{ \sqrt{24} }[/tex]
[tex]E = 1.880[/tex]
The estimate of how much the drug will lower a typical patient's systolic blood pressure(using a 90% confidence level) is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]53.9 - 1.880 < \mu < 53.9 + 1.880[/tex]
[tex]52.02 < \mu < 55.78[/tex]
QUE
The angle of depression of a banana from the monkey on the tree
25m high is 560. Calculate the distance of the banana from the
foot of the tree
and ton xamples of each
9514 1404 393
Answer:
16.9 m
Step-by-step explanation:
Angle BMT in the attached diagram is the complement of the angle of depression, so is 90° -56° = 34°. The distance BT is the side of the triangle opposite this angle, and the given tree height TM = 25 is the side of the triangle adjacent to the angle. Then the relevant trig relation is ...
Tan = Opposite/Adjacent
Opposite = Adjacent × Tan
BT = (25 m)·tan(34°) ≈ 16.863 m
The banana is about 16.9 meters from the tree.