Brittany's kite is flying above a field at the end of 65 m of string. If the angle of elevation to the kite
measures 70°, how high is the kite above Brittany's head?
Answers
Answer:
61.1 m is the correct answer.
Step-by-step explanation:
Given that
Brittany's kite has a string length = 65 m
Angle of elevation of kite = [tex]70^\circ[/tex]
A right angled triangle can be constructed for the given situation.
Please refer to the attached figure.
[tex]\triangle BFK[/tex] in which B is the position of Brittany.
K is the position of kite and
F is the point of field above which the kite is flying.
Given that the side BK = 65m
[tex]\angle B = 70^\circ[/tex]
To find, side FK = ?
We can use sine trigonometric identity to find the value of FK.
We know that :
[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]\Rightarrow sinB = \dfrac{FK}{BK}\\\Rightarrow sin70 = \dfrac{FK}{65}\\\Rightarrow FK = 65 \times 0.94\\\Rightarrow FK = 61.1\ m[/tex]
Hence, the answer is 61.1 m.
Related Questions
which are exterior angles?
Answers
Please please please MARK BRAINLIEST
6. Yolanda's Purse
Yolanda finally cleaned her purse, and she found 40 coins at the bottom of her purse! All her
coins were dimes and pennies. Altogether she had $2.29. How many dimes and pennies did
she find? Make your own chart.
Answers
Answer:
She found 19 pennies and 21 dimes
Step-by-step explanation:
Let the number of dimes present be d and the number of pennies present be p
From the question, the total of both is 40
Mathematically;
p + d = 40 •••••••(i)
While a penny worths 1 cent, a dime is worth 10 cents
Total penny amount would be 1 * p = p cents
While total dime amount would be 10 * d = 10d cents
Before we add both to give the total amount, let’s convert this total amount to cents and that would be 2.29 * 100 = 229 cents
So mathematically;
p + 10d = 229 •••••••(ii)
So let’s solve both equations simultaneously
From i) p = 40 - d
let’s put this into equation ii
40 - d + 10d = 229
40 + 9d = 229
9d = 229-40
9d = 189
d = 189/9
d = 21
Recall;
P = 40-d
P = 40-21
P = 19
Graphing Exponential Functions: Which function is graphed below?
A) y=1/3(3)^x
B) y=3(1/3)^x
C) y=)1/2)^+2
D) y=(2)^x-1
Thank you!!
Answers
Answer:
B
Step-by-step explanation:
The y-intercept (or initial value) is 3 which means the coefficient of the exponential term is 3. The only answer choice that follows this is choice B.
The segments shown below could form a triangle
Answers
Answer:
yes it can form an isosceles triangle. when you join these lines AC will be the base and BC andAB will be two equal sides of an isosceles triangle.
Answer:
True i think
Step-by-step explanation:
tell me if you got it right. (btw switch to chrome its faster)
5. Three business partners Bela, Joan and Trinity contributed Ksh.112,000.Ksh.128,000 and Ksh.128,000
respectively to start a business. They agreed to share their profit as follows:
30% to be shared equally
30% to be shared in the ratio of their contributions
40% to be retained for the running of the business.
If at the end of the year the business realized a profit of ksh. 1,350,000
Calculate
(1mk)
a) The amount of money retained for the running of the business at the end of the year
Answers
40% is kept for the running of the business.
Multiply the profit by 40%
1,350,000 x 0.40 = 540,000
The amount kept for the business is 540,000
The length of a photo is 14 inches, which is 3 inches longer than its width. Write an equation that gives the photo's width (w) in inches. i need this asap!
Answers
Answer:
w+3=14
Step-by-step explanation:
The length is 3 more than the width, and more can be expressed as a plus sign, so w+3=14.
Mark noticed that the probability that a certain player hits a home run in a single game is 0.165. Mark is interested in the variability of the number of home runs if this player plays 150 games. If Mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the variance for a total of 150 games? Answer choices are rounded to the hundredths place.
Answers
Answer:
Variance for a total of 150 games is 20.67
Step-by-step explanation:
If x follows binomial distribution with parameters n and p then the probability distribution of [tex]\frac{x-np}{\sqrt{npq}}[/tex] tends to N (0.1)
As [tex]n\rightarrow \infty[/tex] where E(x)= np, var (x) = npq
[tex]\therefore[/tex] var (x) = 150[tex]\times[/tex]0.165 [tex]\times[/tex] (1-0.165)
(since, n= 150, p=0.165,
q = 1-p = 1-0.165)
= 20.66625
var (x) = 20.67
[tex]\therefore\\[/tex] variance for a total of 150 games is 20.67
Given to us:
Mark uses the normal approximation of the binomial distribution to model the number of home runs. Therefore,
Probability, p=0.165;
Number of samples, n=150;
Chances of failure, q = 1-p = 1-0.165 = 0.835;
According to binomial distribution,
Variance, var(x) = npq;
var (x) = npq
= 150 x 0.165 x 0.835
= 20.66625
Hence, the variance for a total of 150 games is 20.66625.
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Suppose you park your car at a trailhead in a national park and begin a 2-hr hike to a lake at 7 A.M. on a Friday morning. On Sunday morning, you leave the lake at 7A.M. and start the 2-hr hike back to your car. Assume the lake is 3 mi from your car. Let f(t) be your distance from the car r hours after 7 A.M. on Friday morning and let g(t) be your distance from the car t hours after 7 A.M. on Sunday morning.
a. Evaluate f(0), f(2), g(0), and g(2).
b. Let h(t) = f(t) - g(t). Find h(0) and h(2).
c. Use the Intermediate Value Theorem to show that there is some point along the trail that you will pass at exactly the same time of morning on both days.
Answers
Answer:
The answer is given below
Step-by-step explanation:
The distance from the lake to the car is 3 miles and it takes 2 hours. The velocity of the hiker is 3/2 mi/hr. Therefore f(t) which is the distance from the car t hours after 7 A.M is given by:
[tex]f(t)=\frac{3}{2}t[/tex]
When coming back on Sunday morning, the distance g(t) from the car at any point in time is given by:
[tex]g(t)=3-\frac{3}{2}t[/tex]
a)
[tex]f(t)=\frac{3}{2}t\\f(0)=\frac{3}{2}(0)=0\ mile\\f(2)=\frac{3}{2}(2)=3\ miles[/tex]
[tex]g(t)=3-\frac{3}{2}t\\g(0)=3-\frac{3}{2}(0)=3\ miles\\g(2)=3-\frac{3}{2}(2)=2-2=0\ mile\\[/tex]
b)
[tex]h(t)=f(t)-g(t)=\frac{3}{2}t -(3-\frac{3}{2}t)=\frac{3}{2}t -3+\frac{3}{2}t=3t-3\\h(t)=3t-3\\h(0)=3(0)-3=0-3=-3\\h(2)=3(2)-3=6-3=3[/tex]
c)
According to Intermediate Value Theorem, there exist a point b where f(b) = g(b). i.e. f(b) - g(b) = 0
[tex]h(b)=f(b)-g(b)=0\\h(0)=-3,h(2)=3[/tex]
This means there exist a point b within the interval [-3, 3] where f(b) - g(b) = 0
tim spends 25% of his time at the gym dooing leg exercises , 1/5 on shoulder exercises , 0.35 on biceps exercises , and warming up . what percentage of time does tim spend warming up
Answers
Answer:
20%
Step-by-step explanation:
25%+(35%)+(20%)=80%
100-80=20%
Factorise 8p^2-12/5p^2+6/25p-1/125
Answers
Answer:
[tex]8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125}=\frac{(p+\frac{11}{140})(p+\frac{1}{125})}{125}[/tex]
Step-by-step explanation:
You have the following polynomial:
[tex]8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125}[/tex] (1)
In order to obtain the factors of the previous polynomial, first you can multiply the polynomial for 125 to obtain only integer coefficients, but also you have to divide for 125, as follow:
[tex](8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125})\frac{125}{125}\\\\=\frac{1000p^2-300p^2+30p-1}{125}[/tex]
[tex]=\frac{700p^2+30p-1}{125}[/tex] (2)
Next, you use the quadratic formula to get the factors of the numerator of the previous expression:
[tex]p_{1,2}=\frac{-30\pm\sqrt{(30)^2-4(700)(-1)}}{2(700)}\\\\p_{1,2}=\frac{-30\pm 80}{1400}\\\\p_1=-\frac{11}{140}\\\\p_2=-\frac{1}{28}[/tex]
The factors are (p-p1) and (p-p2), then you have in the equation (2) the following factorization:
[tex]8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125}=\frac{(p+\frac{11}{140})(p+\frac{1}{125})}{125}[/tex]
factor by using the difference of two cubes
(2x)³- 8
Answers
Answer:
[tex](2x + 2)( {4x}^{2} - 4x + 4)[/tex]Solution,
[tex] {(2x)}^{3} - 8 \\ [/tex]
[tex]( {2x)}^{3} - {(2)}^{3} [/tex]
Use the formula:
[tex] {a}^{3} - {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )[/tex]
now,
[tex](2x + 2)( {(2x)}^{2} - 2x \times 2 + {(2)}^{2} )[/tex]
[tex](2x + 2)( {4x}^{2} - 4x + 4)[/tex]
Hope this helps...
Good luck on your assignment...
You invest $2500 in an account to save for college. Account 1 pays 6% annual interest compounded quarterly. Account 2 pays 4% annual interest compounded continuously. Which account should you choose to obtain the greater amount in 10 years and why.
Thank you!!
Answers
Answer: Account 2
Step-by-step explanation:
Account 1)
Formula for CI
Amount = p(1 + r/n)^nt
A = 2500 (1 + .06/4)^4x10
A = 2500 (1 + 0.015)^40
A = 2500 (1.015)^40
A = 4535.05
Account 2.
Formula for CI for interest compounded continously
A = Pe^rt
A = 2500 x e^0.06 x 10
A = 2500 x e^0.6
A = 2500e^3/5
A = 4555.297
Account 2 should you choose to obtain the greater amount in 10 years.
Important information:You invest $2500 in an account to save for college. Account 1 pays 6% annual interest compounded quarterly. Account 2 pays 4% annual interest compounded continuously.
Calculation of the amount in both the accounts:For Account 1
[tex]Amount = p(1 + r\div n)^{nt}\\\\A = 2500 (1 + .06\div 4)^4\times 10\\\\A = 2500 (1 + 0.015)^{40}\\\\A = 2500 (1.015)^{40}[/tex]
A = 4535.05
For Account 2:
A = Pe^rt
[tex]A = 2500 \times e^0.06 \times 10\\\\A = 2500 \times e^0.6\\\\A = 2500e^3/5[/tex]
A = 4555.297
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A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift. A cylinder has a height of 20 centimeters and a diameter of 8 centimeters. What is the approximate volume of the tube? Round to the nearest whole cubic centimeter. 1,005 cm3 1,340 cm3 3,351 cm3 4,021 cm3
Answers
Answer:
4021 cm^3
Step-by-step explanation:
The volume of a cylinder can be found using the following formula.
[tex]V=\pi r^2h[/tex]
where r is the radius and h is the height.
We know the cylinder has a height of 20 centimeters and a diameter of 8 centimeters.
h= 20 cm
d= 8 cm
Substitute these values into the formula.
[tex]V=\pi (8 cm^2) * 20 cm[/tex]
First, evaluate the exponent.
8 cm^2= 8 cm * 8 cm= 64 cm
[tex]V=\pi * 64 cm^2*20 cm[/tex]
Multiply 64 cm^2 and 20 cm
[tex]V=\pi *1280 cm^3[/tex]
Multiply 1280 cm^3 and pi
[tex]V=4021.2386 cm^3[/tex]
Round to the nearest cubic centimeter. The 2 in the tenth place tells us to leave the number as is.
[tex]V= 4,021 cm^3[/tex]
The volume is about 4,021 centimeters^3.
The approximate volume of the tube is 1005 cm³.
What is a cylinder?A cylinder is a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.
Given that a cardboard cylinder has a diameter of 8 centimeters and a height of 20 centimeters, we need to find the volume of the cylinder,
The volume of the cylinder = π × radius² × height
Radius = diameter / 2 = 8/2 = 4 cm
Therefore,
Volume = π × radius² × height
= 3.14 × 4² × 20
= 3.14 × 16 × 20
= 1004.8 ≈ 1005
Hence, the approximate volume of the tube is 1005 cm³.
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Please help me! Thx if you do
Answers
Answer:
3
Step-by-step explanation:
6(2x-3)=-(x-9)+4x (Distributive property)
12x-18=-x+9+4x
12x-4x+x=9+18 (Collecting like terms)
9x=27 (Division)
x=3
Hope I am correct :)
Answer:
3Option D is the correct option.
Step-by-step explanation:
6 ( 2x - 3 ) = - ( X - 9 ) + 4x
Distribute 6 through the parantheses
12x - 18 = - ( X - 9) + 4x
When there is a (-) in front of an expression in parantheses, change the sign of each term in the expression
12x - 18 = -x + 9 + 4x
Collect like terms
12x - 18 = 3x + 9
Move variable to Left hand side and change its sign
12x - 3x - 18 = 9
Move constant to Right hand side and change its sign
12x - 3x = 9 + 18
collect like term
9x = 9 + 18
Add the numbers
9x = 27
Divide both sides of the equation by 9
9x /9 = 27/ 9
Calculate
X = 3
Hope this helps....
Good luck on your assignment...
X/8 - 9 = 1 Solve for x
Answers
Answer:
x=80
Step-by-step explanation:
x/8-9=1x/8=9+1x/8=10x=80Help! Which choice is the most efficient first step to solve this set of equations?
Answers
Answer:
Substitute 3x - 5 for y in the second equation.
Step-by-step explanation:
Generally, to solve the system of linear equations of x and y, the first step would be trying to eliminate x (or y).
Then turn the system into the equation of only y (or x).
Next, try to solve for y (or x).
Then substitute the solved y (or x) into the original system to work out x (or y).
**********
3 options (1 addition, 2 subtractions) do not eliminate x or y (x and y still exist after manipulation).
=> Remaining option relating substitution would be a reasonable choice.
Given the proportion 3/4 = x/10 , the value of x is:
Answers
Answer:
7.5
Step-by-step explanation:
given:
3/4 = x/10 (multiply both sides by 10)
(3/4)(10) = x
x = 30/4
x = 7.5
The value of x is 7.5
Given:
The proportion 3/4 = x/10
3/4 = x/10
30 = 4x
30/4 = x
7.5 = x
Therefore, the final answer is 7.5.
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The height, h metres, of a flare as a function of the time, t seconds, since the flare was fired from a boat, can be modelled by the function h = -5t2 + 15t + 20 What was the maximum height of the flare?
Answers
Answer:
31.25 metres at t=1.5 seconds.
Step-by-step explanation:
The height, h metres, of a flare as a function of the time, t seconds, since the flare was fired from a boat, can be modeled by the function
[tex]h=-5t^2+15t+20[/tex]
We need to find the maximum height of the flare.
In the given quadratic function, the leading coefficient is negative it means the function represents the downward parabola.
Vertex of a downward parabola is the point of maxima.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then
[tex]Vertex=\left(-\dfrac{b}{2a}, f(-\dfrac{b}{2a})\right)[/tex]
In the given function, a=-5, b=15, c=20. So,
[tex]-\dfrac{b}{2a}=-\dfrac{15}{2(-5)}=\dfrac{15}{10}=1.5[/tex]
Put x=1.5 in the given function.
[tex]h=-5(1.5)^2+15(1.5)+20[/tex]
[tex]h=31.25[/tex]
Therefore, the maximum height of the flare is 31.25 metres and t=1.5 seconds.
Find side AB and round your answer to the nearest hundredth, help please.
Answers
Answer:
? = 5.12
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin B = opp/ hyp
sin 65= 5/ ?
? = 5/ sin 65
? =5.516889595
To the nearest hundredth
? = 5.12
What is the value of A when we rewrite... (PLZ HELP QUICK)
Answers
Answer:
[tex] \frac{133}{8} [/tex]Step-by-step explanation:
Given,
[tex] {( \frac{5}{2} )}^{x} + {( \frac{5}{2} )}^{x + 3} [/tex]
[tex] = {( \frac{5}{2}) }^{x} + {( \frac{5}{2}) }^{x} \times {( \frac{5}{2} )}^{3} [/tex]
[tex] = ( \frac{5}{2} ) ^{x} (1 + {( \frac{5}{2} )}^{3} [/tex]
[tex] = {( \frac{5}{2} )}^{x} (1 + \frac{125}{8} )[/tex]
[tex] = {( \frac{5}{2} )}^{x} ( \frac{1 \times 8 + 125}{8} )[/tex]
[tex] = {( \frac{5}{2}) }^{x} ( \frac{8 + 125}{8} )[/tex]
[tex] {( \frac{5}{2} )}^{x} ( \frac{133}{8} )[/tex]
Comparing with A • [tex] {( \frac{5}{2}) }^{x} [/tex]
A = [tex] \frac{133}{8} [/tex]
Hope this helps...
Good luck on your assignment...
59.6487 to 2 decimal places
Answers
Answer:
59.65
Step-by-step explanation:
2 decimal places is to the hundredths place.
Answer: 59.65
Step-by-step explanation: When rounding a number to a given place, look at the next place y o the right. If that digit is 5 or more, "round up" by adding one to the given place.
If the number to the right is 4 or less, leave the given place "as is"
In this example, the hundredths place is 4, the place to the right has an 8. So you round up the 4 to a 5. You end up with 59.65
PLEASE HELP FAST
answers:
a.) 4
b.) 10
c.) 6
d.) 1
Answers
Answer:
4
Step-by-step explanation:
There are 5 points. So there are 4 segments. The segments are the line between two points.
The number of text messages that Reza sent each day so far in this billing cycle is shown on the dot plot. A number line going from 1 to 13. 2 dots are above 2. 1 dot is above 3. 3 dots are above 6. 2 dots are above 7. 3 dots are above 8. 1 dot is above 11. 2 dots are above 12. Which statement must be true according to the dot plot? The data is symmetric and shows that he typically sent about 6 to 8 text messages per day. The data is symmetric and shows that he sent 11 or 12 texts with the same frequency that he sent 1 or 2 texts. The data is skewed and shows that he typically sent about 6 to 8 text messages per day. The data is skewed and shows that he sent 11 or 12 texts with the same frequency that he sent 1 or 2 texts.
Answers
Complete Question:
The number of text messages that Reza sent each day so far in this billing cycle is shown on the dot plot.
Which statement must be true according to the dot plot?
A) The data is symmetric and shows that he typically sent about 6 to 8 text messages per day.
B) The data is symmetric and shows that he sent 11 or 12 texts with the same frequency that he sent 1 or 2 texts.
C) The data is skewed and shows that he typically sent about 6 to 8 text messages per day.
D) The data is skewed and shows that he sent 11 or 12 texts with the same frequency that he sent 1 or 2 texts
*Check attachment for the dot plot referred to
Answer:
A. The data is symmetric and shows that he typically sent about 6 to 8 text messages per day
Step-by-step explanation:
Taking a look at the dot plot given in the attachment below, we can observe that most of the data set are concentrated in the middle of the dot plot than both ends of the dot plot. With this, we can infer that the distribution of the data is symmetric.
The dot plot also tells us that, 6 and 8 text messages have more frequency than any other data set on the dot plot. This also suggests that Reza usually sends 6 to 8 messages in a day.
Therefore, the statement that is true about the dot plot is:
"A. The data is symmetric and shows that he typically sent about 6 to 8 text messages per day"
Answer:
A
Step-by-step explanation:
Convert 25 km to feet
Answers
Answer: 82,020.997
Step-by-step explanation:
A student knows the height of a pyramid and the area of its base. What should the student do to find the volume of the pyramid
Answers
Answer:
Multiply the area of the base by the height and divide by 3.
Step-by-step explanation:
V = (1/3)Bh
where B = area of the base, and
h = height
Answer: Multiply the area of the base by the height and divide by 3.
Answer:
We khow that the volume of a pyramid is equal the product of the base and the height over 3
So he just needs to multiply them together then divide the result by 3
A grocery store sells a bag of 6 oranges for $2.76. How much would it cost for 5 oranges?
Answers
Answer:
$2.3
Step-by-step explanation:
6oranges=2.76$
5oranges=?
5×2.76/6.
=$2.3
Which rules could describe the rotation? Select two options. R0, 90° R0, 180° R0, 270° (x, y) → (–y, x) (x, y) → (–x, –y)
Answers
Answer:
R0,180(x,y)->(-x,-y)
Step-by-step explanation:
R0,180(x,y)->(-x,-y)
We note that
X(-2,2) has been transformed to X'(2,-2), and
Y(1,2) has been transformed to Y'(-1.-2)
[tex]\bold{R_0,\ 180^{\circ}}\ \ and \ \ \bold{(x,y)\longrightarrow (-x,-y)}[/tex] are the choice that's description can be defined as follows:
It implies we rotate the triangle 900 times clockwise.The point Z has been on the Positive Y-Axis, rotating this Figure by 1800 will place that on the Negative Y-Axis. In addition, Point Y results in the Fourth Quadrant.We can observe that the solution figure has been flipped twice along the vertical axis and once along the horizontal plane.Both X and Y values would be multiplied by -1 if we applied this change.Therefore, the final choice are "[tex]\bold{R_0,\ 180^{\circ}}\ \ and \ \ \bold{(x,y)\longrightarrow (-x,-y)}[/tex]".
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From a group of 8 women and 6 men, a committee consisting of 3 men and 3 womenis to be formed. How many different committees are possible if 2 of the men refuse toserve together? How many different committees are possible if 1 man and 1 womanrefuse to serve together?
Answers
Answer:
a) 896 ways
c) 910 ways
Step-by-step explanation:
The question is a combination problem since it has to do with selection. In combination, if r object is selected from a pool of n objects, this can be done in nCr ways.
nCr = n!/(n-r)!r!
If from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed, we need to first calculate the total committee formed without any condition.
8C3 × 6C3
= 8!/5!3! × 6!/3!3!
= 8×7×6×5!/5!×6 × 6×5×4×3!/3!×6
= 56×20
= 1120ways
Now if;
a) two of the men refuse to serve together.
Since two men refuse to serve together, we will select 1 man from remaining 4 men since two has already been selected then select 3 from 8 women as shown.
4C1×8C3
= 4×56
= 224ways
Number of ways this can be done will be 1120-224 = 896ways
b) 1 man and 1 woman refuse to serve together
We need to choose 2 men from remaining 5 and 2 women from the rest of the men which is 7 as shown:
= (8-1)C(3-1) × (6-1)C(3-1)
= 7C2 × 5C2
= 7!/5!2! × 5!/3!2!
= 7×6×5!/5!×2 × 5×4×3!/3!×2
= 21×10
= 210ways
The number of ways this can be done will be 1120-210 = 910ways
The isosceles triangle and the square shown here have the same area in square units. What is the height of the triangle, $h$, in terms of the side length of the square, $s$?
Answers
Answer:
h = 2s
Step-by-step explanation:
Area of square is equal to the area of triangle in this question.
the area of the square is s²
the area of the triangle is [tex]\frac{1}{2}[/tex] *h*s
s²= [tex]\frac{1}{2}[/tex] *h*s
s = [tex]\frac{1}{2}[/tex] *h
2s = h
hope that helps
Find the x- and y-intercept of the line.
5x – 4y = 40
A x-intercept is -4; y-intercept is 5.
B x-intercept is - 10; y-intercept is 8.
Cx-intercept is 5; y-intercept is -4.
D x-intercept is 8; y-intercept is -10.
Answers
Explanation:
x-intercept is 8; y-intercept is -10
Answer:
D
Step-by-step explanation:
you can put the function in your graphing calculator & the x-intercept is where the line crosses threw the line that goes left & right vise versa for the y-intercept.