Answer:
Speed of current: 5 miles per hour
Speed of the boat in still water: 17 miles per hour
Explanation:
Let us call sB the speed of the boat in still water and sC the speed of the current.
Now when the boat is with the current, its speed is 110 miles/hours = 22 miles per hour. When the boat is opposite the current, its speed is 110 / (9 + 1/6 ) = 12 miles per hour; therefore we have the equations
[tex]s_b+s_c=22\text{ (with the current )}[/tex]and
[tex]s_b-s_c=12\text{ (opposite the current)}[/tex]adding the two equations gives
[tex]\begin{gathered} s_b+s_c=22 \\ s_b-s_c=12 \\ ---------------- \\ 2s_b=34 \end{gathered}[/tex]dividing both sides by 2 gives
[tex]\begin{gathered} s_b=\frac{34}{2} \\ s_b=17 \end{gathered}[/tex]Hence, we find that the speed of the boat in still water is 17 miles per hour.
Now with the value of sB in hand, we now find sC.
[tex]\begin{gathered} s_b+s_c=22 \\ 17+s_c=22 \end{gathered}[/tex]subtracting 17 from both sides gives
[tex]s_c=5[/tex]Hence, the speed of the current is 5 miles per hour.
To conclude,
Speed of current: 5 miles per hour
Speed of the boat in still water: 17 miles per hour
.Write the answer in form ab
43 x 8²=
Answer:
2752
Step-by-step explanation:
[tex]43 \times 8^2 \\ \\ =43 \times 64 \\ \\ =(40+3)(60+4) \\ \\ =2400+160+180+12 \\ \\ =2752[/tex]
The inside of an ice cream cone is filled with cream and has height 12 cm Assuming that a half-scoop of ice cream is the shape of a hemisphere and that it fits perfectly on top of the cone (same radius) find the total volume of ice cream. Use 3.14 for pie and round your answer to the nearest tenth.
To obtain the total volume of ice cream, the following steps are necessary:
Step 1: Make a sketch of the shapes stated in the question, as below:
Step 2: Recall the formulas for the volume of a cone and that of a hemisphere, as follows:
The volume of a cone is:
[tex]V_{cone}=\frac{1}{3}\times\pi\times r^2\times h[/tex]And, the volume of a hemisphere is:
[tex]V_{hemisphere}=\frac{2}{3}\times\pi\times r^3[/tex]where, in both cases:
r = radius
h = perpendicular height
Step 3: Interpret the question to find clues, as follows:
"...that a half-scoop of ice cream is the shape of a hemisphere..." means that:
[tex]V_{hemisphere}=\frac{1}{2}\times V_{cone}[/tex]Thus, we have:
[tex]\begin{gathered} V_{hemisphere}=\frac{1}{2}\times V_{cone} \\ \Rightarrow\frac{2}{3}\times\pi\times r^3=\frac{1}{2}\times\frac{1}{3}\times\pi\times r^2\times h \end{gathered}[/tex]Since, the height of the cone is given to be 12 cm, we have:
[tex]\begin{gathered} \Rightarrow\frac{2}{3}\times\pi\times r^3=\frac{1}{2}\times\frac{1}{3}\times\pi\times r^2\times h \\ \Rightarrow\frac{2}{3}\times\pi\times r^3=\frac{1}{6}\times\pi\times r^2\times h \\ \text{Divide both sides by: }\frac{2}{3}\times\pi\times r^2 \\ \text{Thus:} \\ \Rightarrow\frac{\frac{2}{3}\times\pi\times r^3}{\text{ }\frac{2}{3}\times\pi\times r^2}=\frac{\frac{1}{6}\times\pi\times r^2\times h}{\text{ }\frac{2}{3}\times\pi\times r^2} \\ \Rightarrow r=\frac{1}{4}\times h \\ \sin ce\text{ h=12} \\ \Rightarrow r=\frac{1}{4}\times12=\frac{12}{4} \\ \Rightarrow r=3\operatorname{cm} \end{gathered}[/tex]Step 4: Now that we have used the clue to find the radius of the hemisphere (and cone), we can now proceed to find the total volume of the figure, as follows:
[tex]\text{Total volume of ice cream = }V_{hemisphere}+V_{cone}[/tex]Thus:
[tex]\begin{gathered} \text{Total volume of ice cream = }V_{hemisphere}+V_{cone} \\ \Rightarrow\text{Total volume of ice cream = }_{}\frac{2}{3}\times\pi\times r^3+\frac{1}{3}\times\pi\times r^2\times h \\ \Rightarrow\text{Total volume of ice cream = }_{}\frac{1}{3}\times\pi\times r^2(2r+h) \end{gathered}[/tex]Since:
h = 12 cm
r = 3cm
and pie = 3.14 (as given), we have that:
[tex]\begin{gathered} \Rightarrow\text{Total volume of ice cream = }_{}\frac{1}{3}\times\pi\times r^2(2r+h) \\ \Rightarrow\text{Total volume of ice cream = }_{}\frac{1}{3}\times3.14\times(3)^2(2(3)+12) \\ \Rightarrow\text{Total volume of ice cream = }_{}\frac{1}{3}\times3.14\times9(6+12) \\ \Rightarrow\text{Total volume of ice cream = }_{}\frac{1}{3}\times3.14\times9\times^{}(18) \\ \Rightarrow\text{Total volume of ice cream = }_{}\frac{508.68}{3}=169.56 \\ \Rightarrow\text{Total volume of ice cream = }_{}169.6\operatorname{cm}^3\text{ (to the nearest tenth)} \end{gathered}[/tex]Therefore, the total volume of ice cream is 169.6 cubic centimeter
Find the value of n if nP4=42nP2
Answer: n = 9.
Step-by-step explanation:
Recall that [tex]nPr = \frac{n!}{(n - r)!}.[/tex] Therefore, you have that [tex]\frac{n!}{(n - 4)!} = \frac{42n!}{(n - 2)!}.[/tex] Cancelling out the n! factor, you therefore, obtain (n - 2)! = 42(n - 4)!. But remember that (n - 2)! = (n - 2)(n - 3)(n - 4)!. In other words, cancelling out the (n - 4)! from both sides, we have that (n - 2)(n - 3) = 42, which is a quadratic in terms of n. This gives you n^2 - 5n + 6 = 42 or n^2 - 5n - 36 = 0. The solution to this is (n - 9)(n + 4) = 0. But we require that n >= 4 for nP4 to make sense, so n = 9 is our solution.
The value of n is 9.
Formula : ⁿPₓ = n! / (n-x)!
=> 42. ( ⁿP₂) = ⁿP₄
=> 42 = (n-2) * (n-3)
=> 42 = n² -5n + 6
=> n² - 5n - 36 = 0
=> (n-9) * (n+4) = 0
Therefore, n = 9
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i need help fast yes yes
can you be more clear? what is the question
2/3x-5=x-8 please show your work.
Given the expression 2/3x-5=x-8
we need to find the value of x from the expression as shown;
collect the like terms:
2/3x-5=x-8
2/3 x - x = -8+5
Find the LCM
(2x-3x)/3 = -3
-x/3 = -3
Cross multiply
-x = -3(3)
-x = -9
Multiply both sides by -1
-1(-x) = -1(-9)
x = 9
Hence the correct value of x is 9
What is the starter point increasing between What is the turtles starting point constant between seconds What is the turtles distant from his starting point decreasing between
A) The distance increases between starting and 6 seconds.
B) The distance is constant between seconds 6 and 8.
C) The distance decreases between seconds 8 and 12
Any point on the parabola can be labeled (x,y), as shown. What are the distances from the point (x,y) to the focus of the parabola and the directrix? Select two answers.distance to the focus: (squareroot over this whole problem)* (x+3)^2+(y-3)^2distance to the directix: |y-4|distance to the directix: |y+4|distance to the focus: *squareroot over again* (x+3)^2+(y-2)^2distance to the directix: |x-4|distance to the focus: *square root again* (x-2)^2+(y+3)^2
Given:
Vertex: (-3, 3)
Focus: (-3, 2)
Let's find the distance from the point (x, y) to the focus of the parabola and the directrix.
To find the distance, apply the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Thus, we have:
Distance from (x, y) to the focus:
Where:
(x1, y1) ==> (x, y)
(x2, y2) ==> (-3, 2)
Thus, we have:
[tex]\begin{gathered} d=\sqrt{(x-(-3))^2+(y-2)^2} \\ \\ d=\sqrt{(x+3)^2+(y-2)^2} \end{gathered}[/tex]Therefore, the distance from the point (x, y) to the focus is:
[tex]\sqrt{(x+3)^2+(y-2)^2}[/tex]• The distance from the point to the directrix.
From the graph, the directrix is:
y = 4
Now, to find the distance, subtract the y-coordinate of the point from y = 4.
The distance is the absolute value of the result.
Thus, we have:
[tex]|y-4|[/tex]ANSWER:
Distance from the point to the focus:
[tex]\sqrt{(x+3)^2+(y-2)^2}[/tex]Distance from the point to directrix:
[tex]|y-4|[/tex]If it takes Mattew an hour to get to his friends house, and 2 hours if he drives 25 mph slower, how far away does his friend live?
Matthew's friend is located roughly 50 miles away.
What does a number's distance mean?Counting each number in between them is a quick and easy approach to determine how far apart two numbers are on a number line. Finding the distance by taking the absolute value of the values' difference is a quicker method.
The entire journey that an object has taken can be used to define distance.
For instance : By combining the speed and the time, one may compute the distance between two points. Based on the information provided, the following can be inferred:
Time required= 2 hours
Speed = 25 mph.
Therefore, the distance will be:
= Speed × Time
= 25 × 2
= 50 miles
As a result, Matthew's friend is located roughly 50 miles away.
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convert 15 cm/s into m/hr
The converted unit of 15 cm/s to m/hr is 540 m/hr
How to convert the metric unit?From the question, we have the following parameters that can be used in our computation:
Unit = 15 cm/s
In metric units
1 cm equals 0.01 meters
This means that
1 cm = 0.01 m
Substitute 1 cm = 0.01 m in Unit = 15 cm/s
So, we have the following equation
Unit = 15 x 0.01 m/s
Evaluate the products
So, we have the following equation
Unit = 0.15 m/s
Also;
In metric units
1 seconds equals 1/3600 hours
This means that
1 s = 1/3600 hr
Substitute 1 s = 1/3600 hr in Unit = 0.15 m/s
So, we have the following equation
Unit = 0.15/(1/3600) m/hr
Evaluate the quotients
So, we have the following equation
Unit = 540 m/hr
Hence, the converted unit is 540 m/hr
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Alex read at most 41 pages of Frankenstein over the weekend. Write an inequality describing the number of pages she read using the variable p.
Answer: p ≤ 41 pages
Step-by-step explanation:
Alex read at most 41 pages this weekend. Since 41 is the most number of pages she read, p is going to be less than 41. If p is the number of pages she read;
p ≤ 41 pages
A compound of two chemicals is mixed in the ratio of 3:10. If there are 45 L of the compound, how much of each chemical is in the mixture?
It is 135/13 l of the first chemical and 450/13 l of the second one.
What is the number of possible options for each situation?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the method of getting possible options.
When asked to find the number of possible options, this is a permutation problem. Therefore, we use the permutation formula.
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]STEP 2: Solve the first question
[tex]\begin{gathered} ^nP_r=\frac{n!}{(n-r)!} \\ For\text{ the first question, n=}45,r=3 \\ ^{45}P_3=\frac{45!}{(45-3)!}=\frac{45!}{42!}=\frac{45\times44\times43\times42!}{42!} \\ \Rightarrow45\times44\times43=85140 \end{gathered}[/tex]There are 85140 possible options.
STEP 3: Solve the second question
[tex]\begin{gathered} ^nP_r=\frac{n!}{(n-r)!} \\ n=7,r=5 \\ ^7P_5=\frac{7!}{(7-5)!}=\frac{7!}{2!}=2520 \end{gathered}[/tex]There are 2520 possible options.
STEP 4: Solve the third question.
[tex]\begin{gathered} ^nP_r=\frac{n!}{(n-r)!} \\ n=11,r=9 \\ ^{11}P_9=\frac{11!}{(11-9)!}=\frac{11!}{2!}=19958400 \end{gathered}[/tex]There are 19958400 possible options.
STEP 5: Solve the fourth question
[tex]\begin{gathered} ^nP_r=\frac{n!}{(n-r)!} \\ n=20,r=4 \\ ^{20}P_4=\frac{20!}{(20-4)!}=\frac{20!}{16!}=\frac{20\times19\times18\times17\times16!}{16!}=20\times19\times18\times17=116280 \end{gathered}[/tex]There are 116280 possible options
Simplify by combining like terms: -5m + 9 + 2m - 4
Given data:
The given expression is -5m + 9 + 2m - 4.
The given expression can be written as,
[tex]\begin{gathered} -5m+9+2m-4=(-5m+2m)+9-4 \\ =-3m+5 \end{gathered}[/tex]Thus, the given expression can be written as -3m+5.
Find the total surface area of this triangular prism.
13 cm
12 cm
15 cm
20 cm
5 cm
9 cm
Evaluate
3^-2
???????
Answer:1/9
Step-by-step explanation:
Ok so you probably know 3^2 is 9
But since its negative you would reverse it so the answer is
1/9 or about 0.1 if you want it in decimal
54Find the exact value of x.
5/x = x/ 9
Cross-multiply
x² =45
Take the square root of both-side
x = 3√5 or 6.7082039325
Exercise #1: We would like to find the distance between points A and B if they have coordinates A(2,3) and B(14, 12).
This triangle is isosceles if:
[tex]AB=BC[/tex]Using the distance formula:
[tex]\begin{gathered} AB=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ (x1,y1)=(-3,8) \\ (x2,y2)=(-9,0) \\ AB=\sqrt[]{(-9-(-3))^2+(0-8)^2} \\ AB=\sqrt[]{60} \\ \end{gathered}[/tex][tex]\begin{gathered} BC=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ (x1,y1)=(-9,0) \\ (x2,y2)=(5,2) \\ BC=\sqrt[]{(5-(-9))^2+(2-0)^2} \\ BC=\sqrt[]{200} \end{gathered}[/tex]Since:
[tex]AB\ne BC[/tex]We can conclude that:
[tex]\Delta ABC[/tex]Is not an isosceles triangle
This figure has how many right angles?
The Solution.
The correct answer is 2 right angles.
Use the given information to prove that AABC-AEDC. E А CA CB Given: CD Prove: A ABC - AEDC
As given that:
[tex]\frac{CA}{CE}=\frac{CB}{CD}[/tex]Angle CAB and angle CED are right angles according to given diagram.
E bisects CA and D bisects CD.
E is perpendicular bisector of CA.
AS E and D are bisects CA and CD then they are midpoints of CA and CD respectively.
So according to all these statements ABC ~ EDC
Yes Angle CAB is a right angle.
Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the wire they need. Andy needs 21 feet of the wire. Emily needs 14 yards of the wire. How much will each of them spend for wire?
Cost of Wire
Length in Inches (x). cost in dollars.(y)
100 3.00
125 3.75
150 4.50
185 5.55
Andy will spend $ ? for his wire
Emily will spend $ ? for her wire
Using measurement conversions and mathematical operations, the costs for the two wire buyer are as follows:
Andy will spend $7.56 on his wireEmily will spend $15.12 for her wire.How are the costs determined?The first step in determining the costs spent by each buyer is to find the unit cost per inch.
Using the division operation, the unit cost for the given lengths remains at $0.03, respectively.
The second step involves converting the given measurements to inches, using the following measurement formulas:
1 yard = 36 inches
12 inches = 1 foot
1 yard = 3 feet
The last step is determining the product of inches of wire and the unit cost.
Cost of Wire
Length in Inches (x) Cost in dollars.(y) Cost per inch
100 3.00 $0.03 ($3.00/100)
125 3.75 $0.03 ($3.75/1125)
150 4.50 $0.03 ($4.50/150)
185 5.55 $0.03 ($5.55/185)
The length of wire Andy needs = 21 feet
21 feet = 252 inches (21 x 12)
252 inches of wire cost = $7.56 (252 x $0.03).
The length of wire Emily needs = 14 yards
14 yards = 504 inches (14 x 36)
504 inches of wire cost = $15.12 ($504 x $0.03).
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$20,000 is deposited into an account at an APR of 8%. What will be the new account balance after 9 months?
STEP - BY - STEP EXPLANATION
What to find?
The new the new account balance after 9 months.
Given:
Principal (p) = $20 000
Rate(R) = 8
Time(t) = 9 months = 9/12 year = 0.75 years.
We will solve the given problem using the steps below:
Step 1
State the formula that will be use to solve the problem.
[tex]I=\frac{P\times R\times T}{100}[/tex]Where I is the interest.
Step 2
Substitute the values into the formula.
[tex]I=\frac{20000\times8\times0.75}{100}[/tex][tex]=\frac{120000}{100}[/tex][tex]=1200[/tex]Hence, interest(I) = $1200
But;
Amount = principal + Interest
= 20 000 + 1200
=21200
Therefore, the account balance after 9 months is $21200
ANSWER
$21200
MHS Student Bookmarks Kami Export - How10.4 ReviewA group of 80 trees in a forest aren't growing properly. A botanist determines:• 68 of the trees have a disease or are being damaged by insects• 54 of the trees have a disease• 30 of the trees are being damaged by insectsWhat is the probability that a randomly selected tree has both a disease and is being damaged by insects?0꾧00 %0o1720ΟΟΟRE10123 9 5
Let the event that a tree has disease be D and the event that tree is being damaged by insects be I.
Therefore,
[tex]\begin{gathered} |D|=54 \\ |I|=30 \\ |D\cup I|=68 \\ \end{gathered}[/tex]Recall that:
[tex]\begin{gathered} |D\cup I|=|D|+|I|-|D\cap I| \\ 68=54+30-|D\cap I| \\ \text{ Therefore,} \\ |D\cap I|=84-68=16 \end{gathered}[/tex]The required probability is given by:
[tex]\frac{|D\cap I|}{80}=\frac{16}{80}=20\%[/tex]Hence, the required probability is 20%=0.2
A digital camera is on sale for 440$. This price is 18% off the original price. What was the original price? Round to the nearest cent.
Since the current price of $440 results from a discount of 18% on the original price, $440->100-18=82%. Thus,
[tex]\begin{gathered} 440\to82percent \\ x\to100\text{ percent} \\ \Rightarrow\frac{440}{82}=\frac{x}{100} \end{gathered}[/tex]Solving for x,
[tex]\begin{gathered} \Rightarrow x=100\cdot\frac{440}{82} \\ \Rightarrow x=\frac{44000}{82}=536.58536\ldots \\ \Rightarrow x\approx536.59 \end{gathered}[/tex]Once rounded, the answer is $536.59
Look at the triangles below.6BaiС4.321А-4-3-2-1 012.345B-1-2-3-419Point D will be added to the graph so thatAABC = AADC. What could be the coordinatesof point D?(1, -3)(2,-5)(3, -1)O (1, -2)
EXPLANATION
In order to get coordinates of D such that △ABC ≅ △ADC, the distance between the point A and the point D should be the same that the distance from the point A to the point B. Therefore, we just need to reflect the point B over the point A.
Reflecting the point B over the point A give us a point that is located 4 units right and 8 units down from the point B.
Thus, the coordinates of the point D are: (1,-3)
21. Five metal cubes with sides of 5 cm were melted and casted into a bigger cube. Find the volume of the new cube.A. 125 cu.cmB. 405 cu. cmC. 325 cu. cmD. 625 cu. cm
Answer:
[tex]625\text{ cu. cm}[/tex]Explanation:
Here, we want to get the volume of the combined cubes
Mathematically, that would be the sum of the volumes of the individual cubes
The volume of a cube can be obtained using the formula below:
[tex]V\text{ = l}^3[/tex]where l is the side length of a cube
The volume of one of the cubes is thus:
[tex]V\text{ = 5}^3\text{ = 125 cu cm}[/tex]Now, the total volume would be:
[tex]\begin{gathered} V_T\text{ = V}_1\text{ + V}_2\text{ + V}_3\text{ + V}_4\text{ + V}_5 \\ V_T\text{ = 125 + 125 + 125 + 125 + 125 = 625 cu. cm} \end{gathered}[/tex]Convert the polar equation r = 2 cos to a Cartesian equation.x + y = 2xx^2 + y^2 = 2yx^2 + y^2 = 2x
Step 1
Given r = 2cosθ
Draw the diagram
From the diagram,
[tex]\begin{gathered} y=\text{ rsin}\theta \\ x=r\cos \theta \\ \text{But given r = 2cos}\theta \\ r^2=2rcos\theta \end{gathered}[/tex][tex]\begin{gathered} r^2=\text{ 2}\times r\cos \theta=\text{ 2x} \\ \text{But} \\ x^2+y^2=r^2 \end{gathered}[/tex]Hence
[tex]x^2+y^2=2x[/tex]2. Heron's Formula (Fill-in from worksheet) A = a. With the sides a = 7, b = 14 C = 15 b. With the sides a = 11, b = 12 and c = 16
Heron's formula for the area of a triangle is;
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]Let's compute these areas;
i. a = 7 , b = 14 , c = 15 ;
[tex]\begin{gathered} s=\frac{7+14+15}{2} \\ s=18 \\ \text{thus} \\ A=\sqrt[\square]{18(18-7)(18-14)(18-15)} \\ A=\sqrt[\square]{18\times11\times4\times3} \\ A=\sqrt[\square]{2376} \\ A=48.7\text{ } \end{gathered}[/tex]Area = 48.7 square units.
ii. a = 11 , b = 12 , c = 16
[tex]\begin{gathered} s=\frac{11+12+16}{2} \\ s=19.5 \\ \text{thus} \\ A=\sqrt[]{19.5(19.5-11)(19.5-12)(19.5-16)} \\ A=\sqrt[]{19.5\times8.5\times7.5\times3.5} \\ A=65.96\approx66 \end{gathered}[/tex]Area = 66 square units
i’ve tried to do it but i’m confused and need someone to show me.
From the given question,
[tex]x^4+9x^2[/tex]Now,
Put x=-3 into the given expression
[tex]x^4+9x^2=(-3)^4+9(-3)^2[/tex][tex]\begin{gathered} x^4+9x^2=(-3)^4+9(-3)^2 \\ =81+9(9) \\ =81+81 \\ =162 \end{gathered}[/tex]Hence, the option D is correct.
Determine whether each ratio or rate is proportional. Explain your reasoning and write the proportion.#1) $18 for 3 bracelets; $30 for 5 bracelets#2) 120 calories in 2 servings; 360 calories in 6 servings
132÷1716 show your work
We will investigate the process of division and express a fraction in its simplest form.
We are given the following operation of division to be performed:
[tex]132\text{ / 1716}[/tex]We can express the above operation in a form of a fraction as follows:
[tex]\frac{132}{1716}[/tex]Whenever we are looking at the simplification process we try to determine the divisibility of both numerator an denominator with a common integer.
We see that both numerator and denominator are divisible by integer ( 3 ). Hence, we can go ahead and write down the divisibility of both numerator and denominator by 3 in the fraction form:
[tex]\begin{gathered} \frac{132}{1716}=\frac{44}{572}\ldots\text{ Divisibility of ( 3 )} \\ \\ \frac{44}{572} \end{gathered}[/tex]We see that both numerator and denominator are divisible by integer ( 11 ). Hence, we can go ahead and write down the divisibility of both numerator and denominator by 11 in the fraction form:
[tex]\begin{gathered} \frac{44}{572}\text{ = }\frac{4}{52}\ldots\text{ Divisibility of ( 11 )} \\ \\ \frac{4}{52} \end{gathered}[/tex]Next we see that we can further perform the divisibility operation by dividing both numerator and denominator by ( 4 ) and express in fraction in its simplest form:
[tex]\begin{gathered} \frac{4}{52}\text{ = }\frac{1}{13}\ldots\text{ Divisibility of ( 4 ) } \\ \\ \frac{1}{13} \end{gathered}[/tex]The above result is expressed in its most simplest form. This means the numerator and denominator can not be further divided or divisible by any common integer other than ( 1 ). Hence, we have arrived at the simplest answer to the division operation:
[tex]\frac{1}{13}\ldots Answer[/tex]