The balloon's vertical distance above the ground is 430 feet.
What is the angle of depression?You look straight parallel to the ground. But when you have to watch something down, then you take your sight down by moving your head up.
The angle from horizontal to the point where you stopped your head is called the angle of depression.
From a hot-air balloon, Brody measures a 39° angle of depression to a landmark that's 532 feet away, measuring horizontally.
The angle of depression = 39°
The base = 532
We need to find the vertical distance consider perpendicular.
[tex]\rm Tan \theta = \dfrac{perpendicular}{base } \\\\\rm Tan 39 = \dfrac{perpendicular}{532} \\\\\rm Tan 39 \times 532 =perpendicular\\\\0.80 \times 532\\\\P = 430.80[/tex]
Therefore, the balloon's vertical distance above the ground is 430.80 feet.
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Answer:
430.81
Step-by-step explanation:
hard way
Let an denote the nth term of a geometric sequence. let a0=256 and an+1=0.5an .
part a
write an explicit formula for this sequence.
an=
part b
to the nearest whole number, what is the sum of the first 25 terms?
The explicit formula is [tex]a_{n-1} = 256 * 0.5^{n-1[/tex] and the sum of the first 25 terms is approximately 512
The explicit formulaThe given parameters are:
[tex]a_0 = 256[/tex]
[tex]a_{n +1} = 0.5a_n[/tex]
Set n = 0
[tex]a_1 = 0.5a_0[/tex]
Substitute 256 for a0
[tex]a_1 = 0.5 * 256[/tex]
[tex]a_1 = 128[/tex]
This means that the common ratio is 0.5.
The explicit formula is then represented as:
[tex]a_{n-1} = a_0 * r^{n-1[/tex]
This gives
[tex]a_{n-1} = 256 * 0.5^{n-1[/tex]
The sum of the first 25 termsThis is calculated using:
[tex]S_n = \frac{a_0(r^{n-1} -1)}{r - 1}[/tex]
This gives
[tex]S_{25} = \frac{256 * (0.5^{25-1} -1)}{0.5 - 1}[/tex]
Evaluate
[tex]S_{25} = 512[/tex]
Hence, the sum of the first 25 terms is approximately 512
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The graph of f(x) = 3.2x-3 is shown below. g(x) is a transformation of f(x).
How would you write the equation for the function g(x)?
Answer:
C. g(x) = 3·2^x +2
Step-by-step explanation:
The graph of g(x) appears to be a translation upward of the graph of f(x).
__
To find the equation of g(x), we can add 5 to f(x), since the translation appears to be 5 units. (The y-intercept of f(x) is 0; the y-intercept of g(x) is 5.)
g(x) = f(x) +5
g(x) = (3·2^x -3) +5
g(x) = 3·2^x +2
__
You can also determine the correct choice by looking at the value at x=0:
A. g(0) = 3 +6 = 9
B. g(0) = 1 +3 = 4
C. g(0) = 3 +2 = 5 . . . . matches g(0) on the given graph
D. g(0) = 3
Kat is painting the edge of a triangular stage prop with orange paint. The lengths of the edges of the triangle are (3x-4) feet, (x2-1) feet, and (2x-15) feet. What is the perimeter Of the triangle if x =4
The perimeter of the triangle is 16 feet
What is the perimeter of a triangle?The perimeter of a triangle refers to the calculation of the total distance bounded by the triangle or around the triangle.
Perimeter of a triangle = (3x - 4) + (x² - 1) + (2x - 15)
Perimeter of a triangle = 5x + x² - 20
If x = 4Perimeter of a triangle = 5(4) + (4)² - 20
Perimeter of a triangle = 16
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Roger works part-time as a waiter at a pizza joint. He earns $9 per hour. How much does he earn for 20 hours of work?
Answer:
180
Step-by-step explanation:
well 9×12=180 roger only works 20 hours he gets plaid $9 per hour he's working so yes the answer is 180
Answer:
180
Step-by-step explanation:
10×9=90, so 90+90= 180
40
A box contains
crayons.
Of these, 7 are red. 4 are blue. 8 are
green, and the rest are yellow. If a
crayon is chosen at random, not
replaced, then another is chosen.
what is the probability that
both crayons are yellow?
Answer:
51%
Step-by-step explanation:
What are the values of a and b? O a 14, b=6 O a=14, b = 8 O a=17, b = 6 O a = 17, b = 8
The value of a is 17 and the value of b is 6. The correct option is third option a = 17, b = 6
Calculating the length of the sides of a kiteFrom the question, we are to determine the values of a and b
From the given kite diagram, we can conclude that
/FG/ = /HG/
Thus,
30 = 2a - 4
∴ 2a - 4 = 30
2a = 30 + 4
2a = 34
a = 34 / 2
a = 17
Also,
/FJ/ = /HJ/
3b + 6 = 24
3b = 24 - 6
3b = 18
b = 18/3
b = 6
Hence, the value of a is 17 and the value of b is 6. The correct option is third option a = 17, b = 6
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Vera is looking for vegetables for dinner. She purchases 2 5/8 pounds of baby potatoes and 1 1/2 pounds of green beans. If she uses a $10 bill to pay, what will her change be?
Baby potatoes=$1.62 per pound and green beans=2.54 per pound
Answer:
6.5 $
Therefore she needs 6.5 $ is she doesn't rwk
Regress smoker on cubic polynomials of age, using a linear probability model. What is the p-value for testing the hypothesis that the probability model is linear in age? (two decimal places)
The statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
What is probit regression?A probit model is a type of regression in statistics where the dependant variable can only take two values.
We have:
Regress smoker on cubic polynomials of age
If we use linear probability model.
Here the data are missing, but we can say about the estimate that:
Only the estimate intercept is statistically significant at the 5% level is wrong,
Thus, the statement " only the estimate intercept is statistically significant at the 5% level is wrong" is wrong about the estimate.
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The graph of a linear function f passes through
the point (1,4) and has a slope of -2.
What is the zero of f?
Answer:
x = -1
Step-by-step explanation:
(x1,y1) = (1,4) and m = 2
(y-y1)/(x-x1) = m
derive the linear function first before finding the zero.
(y-4)/(x-1) = 2
cross multiply
y-4 = 2(x-1)
y-4= 2x - 2
y = 2x - 2+4
y. = 2x + 2 is the linear equation
at y = 0 gives the zero
2x + 2 = 0
2x = -2
x = -2/2
x = -1 is the zero
The expansion of (1 + px +qx2)8 is 1 + 8x + 52x² + kx³+... . Calculate the values of p, q and k.
Ans:
[p = 1, q=3, k = 224]
how do i do this question? It’s binomial theorem.
Answer:
i think you have to multiply
Step-by-step explanation:
true or false? The sum of the difference is not always zero for any distribution consisting of n observations
Answer:
i believe the answer is false !
Step-by-step explanation:
Given the parent function of f(x) = x³, what is the value of k in the translated graph of f(x - h) + k?
int)
k=-3
k=-2
k=2
k=3
The value of k in the translated graph of f(x - h) + k is; k = 2
How to carry out Translations on Graphs?We are given the parent function of f(x) = x³.
Now, the point (0, 0) in the graph of f(x) is the point (3, 2) in the translated graph. Thus;
The rule of translation is;
(x, y) → (x + 3, y + 2)
That means;
The translation is 3 units to the right and 2 units up
The equation of the translated graph is equal to;
f(x) = (x - 3)³ + 2
Thus;
The value of k is equal to 2.
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A. (x, y) = (x + 6, y)
B. (x', y') = (x − 6, y)
C. g(x) = f(x+6)
D. g(x) = f(x-6)
E. g(x) = f(x) + 6
F. g(x) = f(x) - 6
Answer:
i don't know, you need to tell us what we need to do
Step-by-step explanation:
What is the perimeter of the rectangle
30
108
96
54
15
Answer:
30
Step-by-step explanation:
The formula for the perimeter of a rectangle is, P = length + breadth + length + breadth.
so, P = 9+6+9+6
P = 30
pls answer quickly, thanks!!
At the equilibrium price p, we can solve for the quantity of goods x :
demand = supply
5200 - 0.0005x = 2800 + 0.0003x
2400 = 0.0008x
x = 3,000,000
With this quantity of goods, the equilibrium price is
p = 5200 - 0.0005 (3,000,000)
p = 5200 - 1500
p = 3700
Please help see picture
Answer:
688 cm²
Explanation:
Area of triangular prism = Base × Height + Length × (perimeter of base)
Here given:
Base: 6 cmHeight: 12 cmLength: 20 cmPerimeter of Base: (6 + 12.4 + 12.4) = 30.8 cm============================================
Surface Area = 6 × 12 + 20 × (30.8) = 688 cm²
please help me!!!!!!!! will mark brainliest
Answer:
i) 0.5
ii) 0.76
Step-by-step explanation:
i) 0.5
ii) 0.76
7/12 - 1/6 in simplest form
Answer:
5/12
Step-by-step explanation:
1/6 can be turned into 2/12
7/12-2/12=5/12
find the value of A , B and C from the following figure
Step-by-step explanation:
Here in the given figure the value of x will be 70° ( being alternative angle )
x = 70°
Now...
y = 60° ( being corresponding angle )
Now...
60° + 70° + z = 180° ( the sum of interior angle of triangle is 180°
z = 180° - 130°
z = 50° ..
[tex]...[/tex]
One evening, the candy counter at the Cineplex sold 532 buckets
of popcorn for $1,489.50. A large bucket sells for $2.25 and a
jumbo bucket sells for $3.75. How many jumbo buckets of
popcorn were sold?
Please help!!
Answer:
337 large buckets and 195 jumbo buckets were sold.
Step-by-step explanation:
x = the number of large buckets sold
y = the number of jumbo buckets sold
x + y = 532
(2.25x + 3.75y = 1489.50) x100 = 225x + 375y =148950
(x + y = 532) x -225 = -225x - 225y = -119700
+ 225x + 375y =148950
150y = 29250
y = 195
x + 195 = 532
x = 337
Bayangan segitiga ABC dengan A (2, 4), B(5,0), C(6,4)
karena refleksi terhadap sumbu Y adalah
Answer:
it is b.
Step-by-step explanation:
as if the slope of x is 5 then y,=,0
Find the slope of the line through the each pair of points
(16, 14), (-2, 0)
Answer:
[tex]\text{Slope} = \dfrac{7}9[/tex]
Step-by-step explanation:
[tex]\text{Given that,}~ (x_1,y_1) = (16,14)~ \text{and}~ (x_2,y_2) = (-2,0)\\\\\text{Slope,}~ m = \dfrac{y_2 - y_1}{x_2 -x_1}\\\\\\~~~~~~~~~~~~=\dfrac{0-14}{-2-16}\\\\\\~~~~~~~~~~~~=\dfrac{-14}{-18}\\\\\\~~~~~~~~~~~~=\dfrac{7}9[/tex]
Answer:
m = 7/9
m = 7/9m ≈ 0.80
Step-by-step explanation:
Given two points:
(16, 14), (-2, 0)
To find:
The slope
Solution:
We know that,
[tex] \rm Slope(m) = \cfrac{ y_2 - y_1}{x_2 - x_1} [/tex]
According to the question,
y_2 = 0y_1 = 14x_2 = -2x_1 = 16Note:[The underscore refers to that the numbers after the underscore is a subscript]
So Substitute them on the formulae:
[tex] \implies \rm \: m = \cfrac{0 - 14}{ - 2 - 16} [/tex]
Simplify it.
[tex] \implies \rm \: m = \cfrac{ \cancel{- 14} \: {}^{7} }{ \cancel{- 18} \: {}^{9} } [/tex]
[tex] \implies \boxed{ \rm \: m = \cfrac{7}{9} }[/tex]
[tex] \implies \rm \boxed{ \rm m \approx0.80}[/tex]
Thus,the slope is 7/9 in fraction and 0.80 (Nearest tenth) in decimal.
The perimeter of a semicircle is 81.212 yards. what is the semicircle's diameter?
[tex]\textit{circumference of a semicircle}\\\\ C=\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=81.212 \end{cases}\implies 81.212=\pi r\implies \cfrac{81.212}{\pi }=r \\\\\\ \stackrel{\textit{its diameter is}}{2r\implies 2\left( \cfrac{81.212}{\pi } \right)} ~~ \approx ~~ 51.7[/tex]
In the following diagram, BC is parallel to DE.
What is the measure of a?
Angles are not necessarily drawn to scale.
B
W
103
D
F
4* =
42°
E
Answer: 35
Step-by-step explanation:
Angles in a triangle add to 180 degrees, so in triangle ABC, [tex]m\angle C=180-103-42=35^{\circ}[/tex].
Sp, by the corresponding angles theorem, x=35
Write an equation for the line that is parallel to the given line that passes through the given point.
y = -6x + 2; (-1,2)
Answer:
The correct answer is y = -6x - 4
Step-by-step explanation:
The given equation of the line : y = -6x + 2
Now, the general equation of the line in the slope-intercept form is given by : y = mx + c
Now, comparing the given equation with the general form, We get slope, m = -6
We need to find the equation of the line which is parallel to the given line and since the slope of two parallel lines are equal so the slope of the required line will also be -6
And it passes through the point (-1, 2)
The required equation will be :
⇒ y - 2 = -6 × (x + 1)
⇒ y - 2 = -6x - 6
⇒ y = -6x - 4
Therefore, The required equation is y = -6x -4
Hence, The correct answer is. y = -6x - 4
Brainlist?????
Find the mean of the following set of numbers. 4,10,12,8,6
Answer:
Mean = 8
Step-by-step explanation:
The mean is another way of describing the average. To find the mean, you need to (1) add all of the numbers together and (2) divide by the amount of numbers added.
(Step 1)
4 + 10 + 12 + 8 + 6
= 40
(Step 2)
4, 10, 12, 8, 6 -----> There are 5 numbers
40 / 5
= 8
Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g. g(x) = f(x − 3) + 4 A. The graph of function f is shifted right 3 units and up 4 units. B. The graph of function f is shifted right 3 units and down 4 units. C. The graph of function f is shifted left 3 units and down 4 units. D. The graph of function f is shifted left 3 units and up 4 units. Reset Next
The option (A) "The graph of function f is shifted right 3 units and up 4 units. " is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a transformation function:
g(x) = f(x - 3) + 4
The parent function is f(x).
First transformation:
x → (x - 3)
The function will shift right by 3 units.
Second transformation:
Add 4 to the function:
g(x) = f(x - 3) + 4
The function will shift up by 4 units.
Thus, the option (A) "The graph of function f is shifted right 3 units and up 4 units. " is correct.
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A right square pyramid and its dimensions are shown below.
Answer:
C) 8 m²
Step-by-step explanation:
Volume of a square pyramid :
V = 1/3BhV = 1/3 x (2.5)² x 4V = 1/3 x 25V = 25/3V = 8.3 ≈ 8 m²Define a quadrilateral.
please explain and help me pls
Answer:
A Quadrilateral is a 4 sided figure. In other words any shape that has 4 sides is a quadrilateral for example square, rectangle, trapezium etc
Step-by-step explanation:
Jacob bought a deluxe computer system for his home business. The system cost
$2,395. The value of the computer system will depreciate at a rate of 12% a year.
What will be the cash value of the computer system in 3 years? Round your answer to
the nearest dollar.
O $287
O $2108
O $1632
O $2682
The cash value of the computer system in 3 years will be $1632. The correct option is the third option $1632
DepreciationFrom the question, we are to determine the cash value of the computer system in 3 years
From the given information,
The computer system cost $2,395 and it will depreciate at a rate of 12% a year
After the first year, the worth of the computer system will be
$2,395 - (12% of $2,395)
$2,395 - (0.12 × $2,395)
= $2,395 - $287.4
= $2107.6
After the second year, the worth of the computer system will be
$2107.6 - (12% of $2107.6)
$2107.6 - (0.12 × $2107.6)
= $2107.6 - $252.912
= $1854.688
After the third year, the worth of the computer system will be
$1854.688 - (12% of $1854.688)
$1854.688 - (0.12 × $1854.688)
= $1854.688 - $222.56256
= $1632.12544
≅ $1632
Hence, the cash value of the computer system in 3 years will be $1632. The correct option is the third option $1632
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