The distance apart of the two ships after two hours with their bearings is equal to 56.7 miles using cosine rules.
What is bearing?Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.
The bearing of the two ships will give an angle 14° + 90° + 15° = 119° between line distance of 20 miles and 22 miles after 2 hours.
Let ∆ABC be the triangle formed with bearings so that:
angle A = 119°
b = 20
c = 22
a = distance of the ships apart
a² = b² + c² - 2(b)(c)cosA {cosine rule}
a² = 20² + 22² - 2(20)(22)cos119°
a² = 400 + 484 - 4800cos119°
a² = 884 - 4800(-0.4848)
a² = 3211.0862
a = √3211.0862 {take square root of both sides}
a = 56.6664.
Therefore, the distance apart of the two ships after two hours with their bearings is equal to 56.7 miles using cosine rules.
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What is the volume of a cylinder with a height of 2 feet and a radius of 6 feet?
Use 3.14 for pi.
please help me use this for a study guide i have a test tomorrow!!
The volume of a cylinder is πr²h.
Given, that H = 2 ft and R = 6 Feet.
So V = πr²h = 3.14 x 6 x 6 x 2
= 3.14 * 72
= 226.08 ft³
Answer:
The volume of the cylinder is 226.08 feet^3
Step-by-step explanation:
The volume of a 3-d shape with sides straight up is
BaseArea × height.
For a cylinder the base is a circle. Area of a circle is pi•r^2
So the Volume of your cylinder is:
V = pi•r^2 • h
Fill in the info given.
V = 3.14 • 6^2 • 2
= 226.08
The units for volume are cubed, that is, 3rd power.
So 226.08 cubed ft
or 226.08 ft^3
Hope this helps!
A child's bank contains 143 coins consisting of nickels and quarters. If the total amount of money is $18.35, find the number of nickels and quarters in the bank.
Answer:
The number of nickels and quarters in the bank are 87 and 56, respectively.
Step-by-step explanation:
Let's denote the number of nickels in the bank as "n" and the number of quarters as "q". Then we can set up a system of two equations based on the given information:
n + q = 143 (equation 1, representing the total number of coins)
0.05n + 0.25q = 18.35 (equation 2, representing the total value of the coins)
To solve this system, we can use substitution or elimination method. Let's use elimination method here:
Multiplying equation 1 by 0.05, we get:
0.05n + 0.05q = 7.15 (equation 3, obtained by multiplying equation 1 by 0.05)
Subtracting equation 3 from equation 2, we get:
0.2q = 11.2
Dividing both sides by 0.2, we get:
q = 56
Substituting this value of q into equation 1, we get:
n + 56 = 143
n = 87
Therefore, there are 87 nickels and 56 quarters in the bank.
Hopefully this helped you! If not, I'm sorry! If you need more help, ask me! :]
What is the domain of H(t)?
The domain of the given function H (t) is 0 ≤ t ≤ 40.
What is the domain of a function?
The collection of all the values for which a function is defined is known as the domain of that function.
We are given that the height of a model rocket, H (t) is a function of time since it was launched, t.
From the graph, we can see that the value of t is represented on the x- axis is ranging from 0 to 40.
Hence, the domain of the given function H (t) is 0 ≤ t ≤ 40.
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For circle B, if BG=BE, what conclusion can be made
If BG=BE, we can conclude that triangle BGE is an isosceles triangle.
In a circle, the radius is a line segment that connects the center of the circle to any point on the circle. Therefore, BG and BE are both radii of the circle. In an isosceles triangle, two sides have the same length, and the third side is a different length. In this case, the two sides with the same length are BG and BE, and the third side is GE. Since BG and BE are radii of the circle and therefore have the same length, we can conclude that triangle BGE is isosceles, and the angles opposite BG and BE are congruent.
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Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. \[ \log \left[\frac{10 x^{2} \sqrt[3
The evaluated logarithmic expression is: [tex]\[ \log \left[\frac{10 x^{2}}{\sqrt[3]{y}}\right] = 2\log[10] + 2\log[x] + \frac{1}{3}\log[y] \][/tex]
Expression mentioned in the question :[tex]\[ \log \left[\frac{10 x^{2}}{\sqrt[3]{y}}\right][/tex]. . The first property we will use is the Product Rule , so this can be expressed as: [tex][ \log \left[\frac{10 x^{2}}{\sqrt[3]{y}}\right] = \log[10x^{2}] + \log[\sqrt[3]{y}] \].[/tex] We can now apply the Power Rule to the first term, which states that the logarithm of a power is equal to the exponent times the logarithm of the base. This can be expressed as: \[ \log[10x^{2}] = 2\log[10x] \]
We can now apply the Quotient Rule to the second term, which states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. This can be expressed as: [tex]\[ \log[\sqrt[3]{y}] = \frac{1}{3} \log[y] \].[/tex] Substituting this back into the original equation gives us:[tex]\[ \log \left[\frac{10 x^{2}}{\sqrt[3]{y}}\right] = 2\log[10x] + \frac{1}{3}\log[y] \][/tex]
We can now evaluate this expression without using a calculator. The two logarithmic terms can be rewritten as:[tex]\[ \log[10x] = \log[10] + \log[x] \, \[ \log[y] = \log[y] \][/tex]
Substituting this back into the original equation gives us: [tex]\[ \log \left[\frac{10 x^{2}}{\sqrt[3]{y}}\right] = 2\log[10] + 2\log[x] + \frac{1}{3}\log[y] \[/tex]
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Which of these could be the area of Circle B? b. About 300 in2
c. About 900 in2
d. About 2,700 in2
The area of Circle B could be about 300 in², about 900 in², or about 2,700 in² depending on its radius.
To determine which one is correct, you would need to know the radius or diameter of the circle.
Use the formula for the area of a circle, which is
A = πr²,
where A is the area and
r is the radius.
If you have the radius, plug it into the formula and calculate the area.
Compare the calculated area to the options provided (300 in², 900 in², or 2,700 in²)
to determine which one is closest to the area of Circle B.
Without more information about Circle B's radius or diameter, it is impossible to determine the exact area from the
options given.
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Find the area of the figure. Round to the nearest tenth.
A 23.4 ft^2
B 28.3 ft^2
C 29.7 ft^2
D 36.0 ft^2
Answer:
C
Step-by-step explanation:
What is the area?The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
What is diameter?Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.
To solve for the area of a rectangle we use the expression:
A = length × widthInserting the dimensions of the rectangle:
4 × 4 = 36So, the area of the rectangle is 36 square feet.
Because the rectangle has a gap on the left side in the shape of a semicircle, we can first solve for the area of that semicircle.
How do we solve for the area of a semicircle?if you know the radius of a semicircle, you can use the formula:
[tex]A = \frac{\pi r^{2} }{2}[/tex]
But first, we need to solve for the radius.
Because the diameter is twice the size of the radius, we can use this expression:
4 ÷ 2 = 2So, the radius of the semicircle is 2ft.
Inserting 2 into the formula for r:
[tex]A = \frac{\pi 2^{2} }{2}[/tex]First, we need to evaluate the exponent:
[tex]A = \frac{\pi 2^{2} }{2} = \frac{\pi4}{2}[/tex]Dividing 4 by 2 gives:
[tex]\pi2[/tex]This simplifies to:
6.28319Subtracting that from the area of the rectangle:
36 - 6.28319 = 29.71681 = [tex]29.7ft^{2}[/tex] (Rounded to the nearest tenth)
Therefore, the answer is C.
PLEASE HELP ME WITH GEOMETRY 4 QUESTIONS FOR 20 POINTS
Please help i dont understand your help helps me alot
Thank you so so much <3
Answer:
14
Step-by-step explanation:
6/9 = x+2/24
Cross multiply to expand
9( x + 2) = 24x 6
9x + 18 = 144
Subract 18 from both sides
9x = 126 Divide both sides by 9
X = 14
10/ 2x-9 = 20/9
Cross multiply
20( 2x - 9) = 10 x 9
40x - 180 = 90
Add 180 to both sides
40x = 270
Divide both sides by 40
X = 6.75
Scale question
Convert 240miles to inches
240 x 63, 660 = 15,206,400
Ratio is 3:15,206,400
Reduce to lowest term by divide both sides by 3
Scale is 1: 5068800
A bicycle wheel make five rotations. The bicycle travel 30.09 find the diameter
Show that the probability density function for a normally distributed random variable has inflection points at x = μ ± σ.
At the inflection points, f''(x) = 0, which implies that x = μ ± σ. Therefore the probability density function has inflection points at x = μ ± σ.
The probability density function (PDF) of a normally distributed random variable is defined as:
f(x) = 1/(σ√2π) e-(x - μ)²/2σ²
where μ is the mean,
σ is the standard deviation.
This equation has two inflection points at x = μ ± σ. To show this, we differentiate the equation twice with respect to x.
f'(x) = -(x - μ) / σ² e-(x - μ)²/2σ²
f''(x) = [-(x - μ)² / σ³ - 1] e-(x - μ)²/2σ²
At the inflection points, f''(x) = 0, which implies that x = μ ± σ. Thus, we have proved that the PDF of a normally distributed random variable has inflection points at x = μ ± σ.
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Please help I have a lot of trouble with math and i don't really understand how to do this
Find figure B
So, the volume of big cone is 226.08 cu ft for this we have to know about volume.
What do you meant by volume?The area occupied within any three-dimensional solid's borders is known as its volume.
Given, radius of small cone, r = 2 ft
Volume of small cone 25.12 cu ft
[tex]So\ Volume\ of\ small\ cone = \pi rl[/tex]
[tex]25.12 = 3.14 * 2*l[/tex]
[tex]l=\frac{25.12}{3.14\ *\ 2}[/tex]
[tex]l = 4ft[/tex]
Since, cones are similar and bai cone radius is 3 times of small cones then ,
Slant height of big cone = 3 * Slant height of small cone
= 3*4 ft
= 12 ft.
[tex]Volume\ of\ big\ cone = \pi rl[/tex]
[tex]= 3.14*6*12[/tex]
[tex]= 226.08\ cu ft[/tex]
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the alvin secretarial service procures temporary office personnel for major corporations. they have found that 50% of their invoices are paid within ten working days. a random sample of 12 invoices is checked. what is the probability that exactly 5 of the invoices will be paid within ten working days? round your answer to four decimal places.
The probability that exactly 5 of the invoices will be paid within ten working days is 19.34% or 0.1934.
This is a binomial distribution problem, with n = 12 (the sample size) and p = 0.5 (the probability of success, which is an invoice being paid within ten working days). We want to find the probability that exactly 5 of the invoices will be paid within ten working days.
Using the binomial probability formula, the probability of exactly 5 invoices being paid within ten working days is:
P(X = 5) = (12 choose 5) * (0.5)^5 * (1-0.5)^(12-5) = 0.1934
Where (12 choose 5) is the binomial coefficient, which represents the number of ways to choose 5 invoices from a sample of 12.
Therefore, the correct answer is 0.1934 rounded to four decimal places.
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Find the length of MN. Round to the nearest tenth of a foot.
The length of MN is equal to: 32.2 ft.
What is Pythagorean theorem?In Mathematics, Pythagorean's theorem is modeled by the following mathematical expression:
a² + b² = c²
Where:
a, b, and c represents the length of sides of a right-angled triangle.
In order to determine the length of MN in right-angled triangle LNM, we would have to apply Pythagorean's theorem.
LN² + MN² = LM²
16² + MN² = 36²
256 + MN² = 1,296
MN² = 1,296 - 256
MN² = 1,040
MN = √1,040
MN = 32.2 ft.
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An investor buys stock in a company and in the 12 months after she invests the value of the stock decreases by 30%. By what amount will the value of the stock need to go up from there in order that the price of the stock will be equal to what investor first paid for it?
The value of the stock needs to go up by 42.86% to be equal to what the investor first paid for it.
Let's say the investor initially paid $100 for the stock. A 30% decrease in the value of the stock would mean it is now worth $70. To bring the value of the stock back up to $100, it needs to increase by $30, which is 42.86% of the current value ($30/$70).
Therefore, the value of the stock needs to go up by 42.86% from its current value for the investor to break even.
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A grounds committee of a housing community plans to build a basketball court in an empty rectangular field
The mathematical equation f(w) = w² - 6w provides a representation of the remaining surface area, measured in square meters, of the field following the construction of the basketball court.
The rectangular field has an area of length x width, which can be expressed as (2w)(w) = 2w² square meters.
The basketball court has an area of length x width, which can be expressed as (w)(w+6) = w² + 6w square meters.
To find the remaining area of the field after the basketball court is built, we need to subtract the area of the basketball court from the area of the rectangular field.
So the function f(w) representing the remaining area, in square meters, is:
f(w) = 2w² - (w² + 6w)
f(w) = 2w² - w² - 6w
f(w) = w² - 6w
Therefore, the function f(w) = w² - 6w represents the area, in square meters, remaining of the field once the basketball court is built.
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Complete question:
A grounds committee of a housing community plans to build a basketball court in an empty rectangular field.
1. The rectangular field-has a width of 2w meters and a length that is 13 meters longer than its width.
2. The basketball court has a width of w meters and a length that is 6 meters longer than its width.
Which function, f(w), represents the area, in square meters, remaining of the field once the basketball court is built?
Anthony and Jacob have some circles. All the circles are the same size. Anthony and Jacob want to completely color twelve circles to make a border for their math project.
Anthony colors six and one-fourth circles before having to go to lunch. Jacob colors five and three-fourths circles before having to go to lunch. Anthony says if he had colored one-fourth of Jacob's last circle instead of one-fourth of his last circle, they would have twelve whole sircles colored. Is Anthony correct?
please show work : - )
50 points!
6 min due..
Anthοny is accurate, and had he cοlοred a quarter οf Jacοb's final circle rather than a quarter οf his οwn, they wοuld have cοlοred 12 cοmplete circles.
In math, what is a circle?A circle is a spherical shape that lacks bοrders and edges. In geοmetry, a circle is indeed a clοsed, curved shape having twο dimensiοns.
Tο start, let's cοunt the tοtal number οf circles Anthοny οr Jacοb cοlοred befοre tο lunch:
Anthοny cοlοred 6.25 circles, οr 6 and 1/4 circles.
Jacοb cοlοred 5.75 circles, οr 5 and 3/4 circles.
They cοmbined tο cοlοr a tοtal οf 12 circles (6.25 + 5.75).
Let's nοw imagine that Anthοny cοlοred a quarter οf Jacοb's final circle rather than a quarter οf his οwn. Jacοb cοlοred 5 and 3/4 + 1/4 = 6 circles, while Anthοny cοlοred 6 with 1/4 - 1/4 = 6 circles.
Tοgether, we wοuld have cοlοured 12 circles since 6 + 6 = 12. This is what they desired. Anthοny is therefοre right!
By calculating the tοtal number οf circles that each persοn cοlοured while accοunting fοr the fact that they all cοlοred the very same number οf circles, we can further cοnfirm οur cοnclusiοn:
Anthοny drew 6 circles.
Jacοb filled in 6 circles.
Tοgether, they cοlοred 6 + 6 = 12 circles.
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Evaluate. Write your answer as a fraction or whole number without exponents. 3^-1
Answer:
1/3
Step-by-step explanation:
The exponent -1 indicates that we need to take the reciprocal of the base 3.
So, 3^(-1) = 1/3
Therefore, the answer is 1/3.
Answer:
1/3
Step-by-step explanation:
Rewrite the expression using the negative exponent rule [tex]b^{-n}[/tex] = [tex]\frac{1}{b^{n} }[/tex]
The answer is 1/3
Pls answerrrrr
with simple working
Answer:
-137
Step-by-step explanation:
23, 15, 7, -1, -9,-17...........
-8 -8 -8 -8.....
∴ -8n+23
if n = 20
-8(20)+23=-137
Answer:
-137
Step-by-step explanation:
The pattern is -8 every term so
15 + (-8(20-1)) = -137
its pretty much multiplying the rate by what term you want. you subtract the 1 because you started with the first term.
7. Find the x-intercept of the line having
the equation 2x - 5y = 8.
A. -5/2
B. 4
C. -4
D. -2/5
E. 2/5
Answer:
E
Step-by-step explanation:
My answer
[tex] \frac{2}{5} [/tex]
The length of a
rectangular poster is 5 more inches than two
times its width. The area of the poster is 33 square inches. Solve
for the dimensions (length and width) of the poster.
Answer:
width is 3 inches, length is 11 inches.
Step-by-step explanation:
Let l be the length and w be the width.
We have:
[tex]l = 2w + 5[/tex]
[tex](2w + 5)(w) = 33[/tex]
[tex]2 {w}^{2} + 5w = 33[/tex]
[tex]2 {w}^{2} + 5w - 33 = 0[/tex]
[tex](w - 3)(2w + 11) = 0[/tex]
[tex]w = 3[/tex]
[tex]l = 2(3) + 5 = 11[/tex]
Find the value of x if ABCD is a square ( given in picture)
The diagonal of the square bisect the angles. Therefore, the angle x in the square is 60 degrees.
How to find the angle of a square?A square is a quadrilateral with each angles equal to 90 degrees. The sum of angles in a square is 360 degrees.
The diagonal of a square is perpendicular to each other. It divided the square into two congruent isosceles triangle.
The diagonal of a square bisects the angles of a square. Therefore, the angles are 45 degrees each after bisection.
Hence, let's find the angle x in the square.
Therefore,
180 - 105 + x + 45 = 180
75 + x + 45 = 180
x + 120 = 180
subtract 120 from both sides of the equation
x + 120 - 120 = 180 - 120
x = 60 degrees
Therefore,
x = 60 degrees
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You run a trail at 7 mph and walk back at 3 mph. If your total time is 2 hours, your round-trip distance is how many miles?
Point P divides the directed line segment from point A(-4,-1) to point B(6,4) in the ratio 2:3. The coordinates of point P are
The coordinates of point P are(0,1)
Line segment:A part of line which has 2 end points and it is also can be measured
example:
the objects which has starting and the ending point can be taken for consideration
pencil: which is straight and has a fixed length of about 16-22 cm
coordinates:The intersection of points in a grid system
example the points(25,10) is 25 units long and 10 units up
A(-4,-1) B(6,4) in the ratio 2:3
x1=-4, x2=6,y1=-1,y2=4,m=2,n=3
x=(mx2+nx1)/m+n
=2*6+3*(-4)/2+3
=12-12/5
=0/5
=0
y=my2=ny1/m+n
=2*4+3(-1)/2+3
=8-3/5
=5/5
=1
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What is 5 to the fourth power?
The correct response, based on the facts provided, is 625.
What does a math power mean?
When a base number is raised to an exponent in mathematics, the exponent represents how many times the base number has been multiplied, and the base amount is the factor that is multiplied by itself.
What do you call 5 to the power of?
In mathematics and mathematics, the fifth power, or subsolid, of a number, n, is obtained by multiplying five occurrences of n around each other:[tex]n⁵ = n × n × n × n × n.[/tex]The fourth power of a number or the squares of a number of times its cube can also be used to create fifth powers.
5 to the fourth power (also written as 5⁴) is:
[tex]5 × 5 × 5 × 5 = 625[/tex]
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Which equation represents exponential growth?
Answer:
Option C) is the correct answer.
Use the factor theorem to determine if the given binomial is a factor of f f(x)=x^(4)-9x^(3)+5x^(2)+5x-2 (a) x-1 (b) x+1
Answer: f(-2)=0; yes, the binomial is a factor of the polynomial.
f(-2)≠0; the binomial is not a factor of the polynomi f(2)=0; yes, the binomial is a factor of the polynomial.
f(2)≠0; the binomial is not a factor of the polynomial.
Step-by-step explanation:
If you only have $14 to spend, which park would you attend (assume the rides are the same quality)? Explain.
If you only have $14 to spend, the park you would attend would depend on the cost of admission and the price of the rides. Assuming that the rides are the same quality at both parks, the decision would come down to which park offers the most affordable pricing.
If Park A charges a $10 admission fee and $2 per ride, you would be able to afford 2 rides with your $14 budget.
If Park B charges a $5 admission fee and $3 per ride, you would be able to afford 3 rides with your $14 budget.
Therefore, if the pricing is as described above, it would be more cost-effective to attend Park B as you would be able to enjoy an additional ride with your budget. However, if the pricing is different or if there are other factors to consider such as distance, location, or amenities, then the decision might change.
Answer:
It's difficult to provide a definitive answer without knowing the specific parks you are considering, but I can offer some general advice on how to choose which park to attend.
First, consider the admission price for each park. If one park has a significantly higher admission price than the other, it may not be worth attending if you only have $14 to spend.
Next, consider the cost of the rides and other attractions at each park. If one park has more expensive rides or requires you to purchase tickets for each ride separately, you may not be able to enjoy as many attractions with your $14 budget.
Finally, consider any other expenses you may incur, such as food, parking, or souvenirs. If one park has significantly higher prices for these items, it may not be the best choice if you are on a tight budget.
Based on these factors, you may want to choose the park that offers the best value for your $14 budget. This could mean choosing a park with lower admission prices and more affordable rides, or a park that offers special deals or discounts that allow you to stretch your budget further. Ultimately, the park you choose will depend on your personal preferences and priorities, as well as the options available in your area.
Step-by-step explanation:
An item is regularly priced at $70. Shen bought it on sale for 20% off the regular price. How much did Shen pay?
An item is regularly priced at 70. Shen bought it on sale for 20% off the regular price. Shen paid 56 for the item on sale.
To determine how much Shen paid for the item on sale, follow these steps:
Find the discount amount
Subtract the discount amount from the regular price.
Calculate the discount amount.
Discount amount = Regular price × Discount percentage
Discount amount = 70 × 20%
Discount amount = 70 × 0.20
Discount amount = 14
Calculate the sale price.
Sale price = Regular price - Discount amount
Sale price = 70 - 14
Sale price = 56
Shen paid 56 for the item on sale.
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PLEASE HELLP MY WITH THIS An experiment consists of randomly drawing a card and recording its suit, then rolling a die and recording whether it is even or odd. The following tree diagram represents some of the possible outcomes. A 2-column tree diagram: Card & Die. The card column shows Heart, Diamond, & Club, each of which branches to even & odd in the Die column.What needs to be done to complete the tree diagram?
Add "Spade" to the Card column, with branches to "Even" and "Odd" in the Die column. Thus, option 3 is correct.
What is the probability?Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.
Tο cοmplete the tree diagram, we need tο add the missing branch fοr the spades suit in the card cοlumn.
Here is the cοmpleted tree diagram:
We have added the missing branch fοr the spades suit, which alsο branches intο even and οdd fοr the die rοll. We have alsο filled in the οutcοmes fοr each branch οf the tree, which include the pοssible values fοr the card (2, 3, 4, 5, 6, οr 1 fοr Ace) and the die rοll (even οr οdd).
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I need help with this question
The value of cos C is 3/5
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
In a right angle triangle, the longest side is called the hypotenuse and the other two sides are called opposite and adjacent. The line facing the acute angle( tetha) is the opposite. The ratio of the sides with the acute angle are called trigonometric ratio.
sin(tetha) = opp/ hyp
cos( tetha) = adj/ hyp
tan(tetha) = opp/adj
In the triangle, using angle C,
opposite = 4
adjascent = 3 and hypotenuse = 5
cos (C) = 3/5
therefore the value of cos (C) = 3/5
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