The horizontal distance from the base of the skyscraper out to the ship is 349.8feet
Angle of elevation and depressionThe angle situated above the hill is known as the angle of depression
Given the following parameters
Height of the harbor = 824 feet
Angle of depression = 67degrees
According to SOH CAH TOA identity:
tan 67 = opp/adj
tan 67 = 824/d
d = 824/tan67
d = 349.8 feet
Hence the horizontal distance from the base of the skyscraper out to the ship is 349.8feet
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Help me please and thank you
Step-by-step explanation:
jlejej
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1. In the past, Sam cashed his paycheck each month at Ready Cash, a check cashing service that
charges a 5% fee. He recently opened a checking account at Bank of America so he can now
deposit and/or cash his paycheck without a fee. If Sam is making $28,500 per year, how much will
he save by not going to Ready Cash anymore?
Step-by-step explanation:
28000 ÷ 100
=280
280 × 5
=1400
Please Answer This!!! I NEEEDDD TOOO KNOWWWWW ANSWER!!!
Answer:
77.5
Step-by-step explanation:
Its rising at a constant rate between +10-15 each hour, so we if we were to add 25 or so to the 50, it would be close to 77.5, so I would assume the answer was B
Surface Area of cones
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
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Answer:
64.1 ft²
Step-by-step explanation:
The area of the cone is given by ...
A = πr(r +h) . . . . for radius r and slant height h
A = π(2 ft)(2 ft +8.2 ft) ≈ 64.1 ft²
I need to know the answer please
Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.
g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]
Option C
Hope this helps!
Triangle DEF has sides of length x, x+3, and x−1. What are all the possible types of DEF?
Triangle DEF is scalene
Must click thanks and mark brainliest
The triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
What is a scalene triangle?A scalene triangle is a type of triangle which have all the sides to be unequal and similarly, all the angles will also be unequal to each other.
Given that:-
Triangle DEF has sides of length x, x+3, and x−1it is given that all the sides of the triangle are x, x+3, and x−1 we can clearly see that for any value of x all the three sides will have different values. we can conclude from this that the triangle DEF is a scalene triangle.
Therefore triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.
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4. Lynn can walk two miles intenta
24 minutes. At this rate, how long will
it take her to walk 6 miles?
Help please!??!!?!?
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Answer:
a) CP = SP/1.1
b) CP = $59.50
c) GST = $5.95
Step-by-step explanation:
a) Divide by the coefficient of CP.
SP = 1.1×CP
CP = SP/1.1
__
b) Use the formula with the given value.
CP = $65.45/1.1 = $59.50
__
c) You can do this two ways: subtract CP from SP, or multiply CP by 0.1.
GST = SP -CP = $65.45 -59.50 = $5.95
GST = CP×0.10 = $59.50 × 0.10 = $5.95
The least-squares regression equation
y = 8.5 + 69.5x can be used to predict the monthly cost for cell phone service with x phone lines. The list below shows the number of phone lines and the actual cost.
(1, $90)
(2, $150)
(3, $200)
(4, $295)
(5, $350)
Calculate the residuals for 2 and 5 phone lines, to the nearest cent.
The residual for 2 phone lines is $___
The residual for 5 phone lines is $___
Answer:
First one: 2.5
Second: -6
8.5+69.5(5) = 147.5
150 - 147.5 = 2.5
8.5 + 69.5(5) = 356
350 - 356 = -6
ED2021
The residual for 2 phone lines is $2.5.
The residual for 5 phone lines is -$6.
What is the residual in a least-square regression equation?
The residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.
How to solve the question?In the question, we are asked to find the residual for 2 and 5 lines using the least-squares regression equation y = 8.5 + 69.5x and the actual costs given to us.
We know that the residual is the vertical distance separating the observed point from your expected y-value, or more simply put, it is the difference between the actual y and the predicted y.
Thus for 2 phone lines:-
Actual Cost = $150.
Predicted Cost, y = 8.5 + 69.5*2 = 147.5.
Residual = Actual Cost - Predicted Cost = 150 - 147.5 = $2.5.
Thus, the residual for 2 phone lines is $2.5.
Thus for 5 phone lines:-
Actual Cost = $350.
Predicted Cost, y = 8.5 + 69.5*2 = 356.
Residual = Actual Cost - Predicted Cost = 350 - 356 = -$6.
Thus, the residual for 2 phone lines is -$6.
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What is the remainder when () = 3 − 11 − 10 is divided by x+3
Answer:
-18/x+3
Step-by-step explanation:
Given the following matrices, what 3 elements make up the first column of the product matrix DA?
We have to figure out what the product of DA is,
[tex]\begin{bmatrix}-1&2&3\\8&-4&0\\6&7&1\\ \end{bmatrix}\begin{bmatrix}1\\3\\5\\ \end{bmatrix}=\begin{bmatrix}a\\b\\c\\ \end{bmatrix}[/tex]
We know that,
[tex]\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\\\end{bmatrix}\begin{bmatrix}x\\y\\z\\\end{bmatrix}=\begin{bmatrix}ax+by+cz\\dx+ey+fz\\gx+hy+iz\\\end{bmatrix}[/tex]
So,
[tex]a=-1\cdot1+2\cdot3+3\cdot5=-1+6+15=20[/tex]
[tex]b=8\cdot1+(-4)\cdot3+0\cdot5=8-12=-4[/tex]
[tex]c=6\cdot1+7\cdot3+1\cdot5=6+21+5=32[/tex]
So the solution is,
[tex]a,b,c=\boxed{20,-4,32}[/tex]
Hope this helps :)
Please help explanation if possible
Answer:
N=18
Step-by-step explanation:
Hope it will help you
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Have a nice day
Answer:
18
Step-by-step explanation:
use the concept of similarity and enlargement.
[tex] \frac{15}{n} = \frac{5}{6 } [/tex]
[tex]n = \frac{15 \times 6}{5} [/tex]
[tex]n = 18[/tex]
PLEASE HELP!!!
Evaluate each expression.
(252) =
Answer:
1/5
Step-by-step explanation:
find lub and glb of the following set E={0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,.....}
The lub is 0.23[tex]\mathbf{\overline{43}}[/tex], while the glb is 0.2
The given set is presented as follows;
E = {0.2, 0.23, 0.234, 0.2343, 0.23434, 0.234343,...}
The least upper bound, lub, of a set, E, is known as the supremum of the set which is the number B such that all x ∈ E are of the value x ≤ B, while there all y ∈ E has a x ∈ E such that t < x
Therefore;
The supremum, lub of the given set is 0.23[tex]\overline{43}[/tex]
The greatest lower bound, glb, b, also known as the infimum, is defined as follows;
b is the greatest lower bound if for all x ∈ E then x ≥ b
Given that b < t, then where x ∈ E, there exist a x < t
The glb of the given set is 0.2
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if a stone is dropped from a cliff that is 122.5m high then its height in meters after t seconds is h=122.5-4.9t^2. find its velocity after 2s
Answer:
Step-by-step explanation:
Let t = 2
h = 122.5 - 4.9·2² = 122.5-19.6 = 102.9
If ‘BOXES’ is OBXSE, then BOARD is
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Answer:
OBADR
Step-by-step explanation:
The first two letters are swapped, and the last two letters are swapped.
BOARD . . . becomes
OBADR
What is the x-coordinate of the point of intersection for the two lines below?
-6 + 8y = -6
7x -10y = 9
Answer choices
1.) -6
2.) -3
3.) 3
4.) 7
Answer:
c.
Step-by-step explanation:
Five subtracted from seven times a number is 9. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is _____________
B) Solve your equation in part [A] for
Answer:
x=
Answer:
18
Step-by-step explanation:
7-5=2
2x9=18
A normal distribution has a mean of 20 and a standard deviation of 4. Determine the z-score for the data value of 42.
Answer:
Z = (42-20)/4 = 5.5
Z = X-μ / σ
Step-by-step explanation:
The z-score for the data value of 42 is 5.5.
What is a z-score?A z-score is defined as the fractional representation of data point to the mean using standard deviations.
Formula of z-score = (X - μ) / σ
Given,
μ = 20
σ = 4
X = 42
z-score = (X - μ) / σ
Substitute the values,
z-score = (42-20)/4
z-score = 22/4
z-score = 5.5
Hence, the z-score for the data value of 42 is 5.5.
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The probability distribution of a random variable X is given. x 1 2 3 4 P(X = x) 0.4 0.1 0.3 0.2 Compute the mean, variance, and standard deviation of X. (Round your answers to two decimal places.) mean variance standard deviation
Mean:
[tex]E(X) = \displaystyle \sum_{x\in\{1,2,3,4\}}x\,P(X=x) = 1\times0.4 + 2\times0.1 + 3\times0.3 + 4\times0.2 = \boxed{2.3}[/tex]
Variance:
[tex]\displaystyle V(X) = E\left((X-E(X))^2\right) = E(X^2) - E(X)^2 \\\\ E(X^2) = \sum_{x\in\{1,2,3,4\}}x^2\,P(X=x) = 1^2\times0.4 + 2^2\times0.1 + 3^2\times0.3 + 4^2\times0.2 = 6.7 \\\\ \implies V(X) = 6.7 - 2.3^2 = \boxed{1.41}[/tex]
Standard deviation:
[tex]\sigma_X = \sqrt{V(X)} = \sqrt{1.41} \approx \boxed{1.19}[/tex]
–21:(–2 – 5) + ( –14) + 6.(8 – 4.3)
1. Ewa has 20 balls of four colors: yellow, green, blue, and black. 17 of them are not green, 5 are black, and 12 are not yellow. How many blue balls does Ewa have? (Use Gaussian elimination method).
Answer:
In a bag of balls, 1/4th are green, 1/8th are blue, 1/12th are yellow and the remaining 26 are white. How many balls are blue?
There are 4 colours of balls - green, blue, yellow and white.
Add (1/4)+(1/8)+(1/12) = (6/24)+(3/24)+(2/24) = 11/24 so the balance or (24–11)/24 = 13/24 = 26 white. Hence the total number of balls are 2*24 = 48.
Of the 48 balls, green are (1/4)*48 = 12, blue are (1/8)*48 = 6, yellow are (1/12)*48 = 4 and the rest, white are 26.
Check: Total number of balls = 12+6+4+26 = 48
Answer: 6 balls are blue....
please help! thanks!
find y.
Answer:
y = 4
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
1 : √3 : 2
The sides in this triangle are in the order:
y : 4√3 : x
y/1 = 4√3/√3
y = 4
Find the length of FT
Step-by-step explanation:
Hey there!
From the given figure;
Angle FVT = 43°
VT = 53
Taking Angle FVT as reference angle we get;
Perpendicular (p) = FT = ?
Base (b) = VT = 53
Taking the of tan;
[tex] \tan( \alpha ) = \frac{p}{b} [/tex]
Keep all values and simplify it;
[tex] \tan(43) = \frac{ft}{53} [/tex]
0.932515*53 = FT
Therefore, FT= 49.423.
Hope it helps!
Answer:
A. 49.42
Step-by-step explanation:
tan 43 = FT ÷ VT
0.932515086 = FT ÷ 53
49.42 = FT
3. Solve the system of equations using the elimination method.
5x + 2y = 9
-5x + 4y = 3
please give detailed steps!!
Answer:
x = 1
y = 2
Step-by-step explanation:
5x + 2y = 9
-5x + 4y = 3
==> 6y = 12 ==> y = 12/6 ==> y = 2.
we replace y by its value in the first or the second equation, so will have:
5x + 2×2 = 9
5x + 4 = 9
5x = 5
x = 1
In a high school graduating class of 300, 200 students are going to college, 40 are planning to work full-time, and 80 are taking a gap year.
a. These are mutually exclusive events.
b. These are not mutually exclusive events.
c. You should add their individual probabilities.
d. None of the above are true.
Find the quotient of 90 over -10
90/-10
= 9/-1
= -9
So, -9 is the quotient.
If the white rod is 1/3, what color is the whole??
Answer:
brown
Step-by-step explanation:
it might be brown because it compelled
If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields
consecutive terms of a geometric sequence. What are the first three terms in the
geometric sequence?
You're looking for a number w such that the numbers
{1 + w, 7 + w, 15 + w}
form a geometric sequence, which in turn means there is a constant r for which
7 + w = r (1 + w)
15 + w = r (7 + w)
Solving for r, we get
r = (7 + w) / (1 + w) = (15 + w) / (7 + w)
Solve this for w :
(7 + w)² = (15 + w) (1 + w)
49 + 14w + w ² = 15 + 16w + w ²
2w = 34
w = 17
Then the three terms in the sequence are
{18, 24, 32}
and indeed we have 24/18 = 4/3 and 32/24 = 4/3.
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis.
Using the shell method, the volume integral would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]
That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].
The volume itself would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]
Using the disk method, the integral for volume would be
[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]
where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.
The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have a function:
[tex]\rm y = x^8[/tex] or
[tex]x = \sqrt[8]{y}[/tex]
And y = 256
By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.
[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]
Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]
[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]
After solving definite integration, we will get:
[tex]\rm V = \pi(\frac{4096}{5} )[/tex] or
[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit
Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
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