Given:
Time it takes Tom = 4 hours
Time it takes Huck = 5 hours
Tom then whitewashes with Huck for 1 hour and then leaves.
Let's find how long it will take Huck to finish whitewashing the fence.
We have:
Tom's rate = 1/4
Huck's rate = 1/5
Total rate:
[tex]\frac{1}{4}+\frac{1}{5}=x[/tex]Now, let's find the time it will take them to whitewash together.
[tex]\begin{gathered} \frac{1}{T}=\frac{5+4}{20} \\ \\ \frac{1}{T}=\frac{9}{20} \\ \\ T=\frac{20}{9} \\ \\ T=2.22 \end{gathered}[/tex]It will take them 2.22 hours to whitewash together.
Now they both whitewash together for 1 hour before Huck leaves.
We have:
[tex]2.22-1=1.22[/tex]When Huck leaves after one hour, the time left for both of them to finish together is 1.22 hours.
Since only Huck will finish whitewashing the fence, the time it will take him will be:
[tex]5(1-\frac{1.22}{2.22})=2.25[/tex]Therefore, it will take Huck to finish whitewashing the fence is 2.25 hours.
ANSWER:
2.25 hours
A tank in the shape of a hemisphere has a diameter of 10 feet. If the liquid that fills the tank has a density of 74.4 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Step 1
State the volume of a hemisphere.
[tex]v=\frac{2}{3}\pi r^3[/tex]Where;
[tex]\begin{gathered} r=\frac{diameter}{2}=\frac{10}{2}=5ft \\ \end{gathered}[/tex]Step 2
Find the volume of the hemisphere
[tex]v=\frac{2}{3}\times\pi\times5^3=\frac{250\pi}{3}ft^3[/tex]Step 3
Find the total weight of the liquid in the tank
[tex]\begin{gathered} \text{Density}=\frac{mass}{\text{volume}} \\ 74.4=\frac{mass}{\frac{250\pi}{3}} \\ \text{mass}=19477.87445lb \\ \text{mass}\approx19478lb \end{gathered}[/tex]Hence the total weight of the liquid in the tank to the nearest full pound = 19478lb
Two segments of Parallelogram ABCD are shown below.  Which coordinate pair BEST represents the location of Point D, the fourth vertex of Parallelogram ABCD? A. (6, 1) B. (7, 0) C. (8,2) D. (7,1)
Given coordinates of A(2,-1), B(1,3), C(6,5)
Let the coordinates of D(x,y)
Let join AC and BD:
SO by mid point rule:
Coordinates of midpoint by AC are:
[tex](\frac{2+6}{2},\text{ }\frac{-1+5}{2})\rightarrow(4,2)[/tex]And the midpoint of BD are same as AC:
[tex]\begin{gathered} \frac{1+x}{2}=4 \\ 1+x=8 \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} \frac{3+y}{2}=2 \\ 3+y=4 \\ y=4-3 \\ y=1 \end{gathered}[/tex]hence the coordinates of D are (7,1)
Option D is correct.
Which fraction is less than 3/5 is it 5/7, 9/15, 4/6, 7/12
Answer: 7/12
Step-by-step explanation:
3/5=0.6
5/7=0.71428571428
9/15=0.6
4/6=0.66666
7/12=0.583333
Answer: 7/12
Step-by-step explanation:
I have attached my work.
figure0123456vehicles4122028364452linear ?pattern ?constant?
Problem
Solution
For this case we need to verify if the pattern is linear so we cna check this doing the following operations:
(12-4)/(1-0) =8
(20-12)/(2-1) =8
(28-20)/(3-2) =8
(36-28)/(4-3) =8
(44-36)/(5-4) =8
(52-44)/(6-5) =8
And as we can see we have the same constant so we can conclude that we have a linear pattern with a constant value of k=8
That means for every increase in the figure the vehicles increase by 8
We can also find the formula for the linear pattern and we have:
4 =8 (0)+b
And solving for b we got
b= 4
And the equation y=mx+b is:
y= 8x +4
Angles A and B are adjacent on a straight line. Angle A has a measure of (2r +20) and angle B has a measure of 130.. What is the measure of r?
When two angles are adjacent on a straight line, then the sum of the two angles equals 180 (that is sum of angles on a straight line). Therefore;
[tex]\begin{gathered} (2r+20)+130=180 \\ \text{Subtract 130 from both sides and you'll have} \\ 2r+20=50 \\ \text{Subtract 20 from both sides and you'll have} \\ 2r=30 \\ \text{Divide both sides by 2 and you'll have} \\ r=15 \end{gathered}[/tex]The measure of r is 15
answer this question that stumbles tons of people around the world!!
The values of x and y in the angles formed by the straight lines are:
x = 18.5
y = 37
What are Angles on a Straight Line?If two or more angles lie on a straight line, they will have a sum of 180 degrees when added together. Therefore, all angles on a straight line have a sum of 180 degree.
Therefore:
16 + 90 + 2y = 180 [straight line angle]
Combine like terms
106 + 2y = 180
Subtract both sides by 106
106 - 106 + 2y = 180 - 106 [subtraction property of equality]
2y = 74
2y/2 = 74/2
y = 37
Also,
16 + 90 + 4x = 180
106 + 4x = 180
4x = 180 - 106 [subtraction property of equality]
4x = 74
4x/4 = 74/4
x = 18.5
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simplifying with like terms; 2(m+10)
In order to simplify the expression, we would multiply the terms inside the bracket by the term outside. It becomes
2 * m + 2 * 10
= 2m + 20
1.- (picture) 2.-Assuming that the global population is seven billion and that no person receives the letter more than once, the maximum number of mailings is fourteen. Suppose that you are one of the recipients of mailing number 8 and there are ten names on the list (so your five outgoing letters will be in mailing number 9 and there will be nine names above yours on the list). If everyone who receives the letter participates, how much money will you receive?$
Kindly check below
Question 1) We can see that in the column "number of recipients" there is a Geometric Sequence whose common ratio is 5.
2) Therefore, we can fill in those gaps with the following:
[tex]\begin{gathered} Number\:of\:mailings|\:Number\:of\:recipients \\ 1\:|\:5 \\ 2\:|\:25 \\ 3\:|\:125 \\ 4\:|\:625 \\ 5\:|\:3125 \\ 6\:|\:15625 \\ 7\:|\:78125 \\ 8\:|\:390625 \\ 9\:|\:1953125 \\ 10\:|\:9765625 \\ 11\:|\:48828125 \\ 12\:|\:244140625 \\ 13\:|\:1220703125 \\ 14\:|\:6103515625 \\ \\ % \end{gathered}[/tex]3) Thus is the table.
Margo borrows $1200, agreeing to pay it back with 4% annual interest after 17 months. How much interest will she pay?
Answer:
$68
Step-by-step explanation:
P = $1200
R = 4%
T = 17months (Convert to years; 17 months ÷ 12 months)
Formular for Interest; I = PRT
100
I = $1200 × 4 × 17
100 × 12
I = $68
sketch the graph of and identify the axis of symmetry
Given the following equation:
[tex]y=(x-1)^2+2[/tex]We will sketch the graph and identify the axis of symmetry.
the given function is a quadratic function with a vertex at (1, 2)
the graph of the function will be as follows:
As shown, the graph of the function has an axis of symmetry at x = 1
So, the answer will be option 3) x = 1
Can someone help me out??
The correct option for the missing sides of given triangles is-
Part 1: x = 30Part 2: x = 21Part 3: x = 49Part 4: x = 22What is termed as the similar triangles?If two triangles' corresponding angles seem to be congruent and their corresponding sides are proportional, they are said to be similar. In other phrases, similar triangles have the same shape but may or may not be the same size.For the given question,
The dimension of the two triangles are given with the missing sides.
Part 1: In the given rectangles;
5/3 = x/18
x = 30
Part 2: In the given rectangles;
9/x = 3/7
x = 21
Part 3: In the given triangles;
x/63 = 7/9
x = 49
Part 4: In the given triangles;
16/x = 8/11
x = 22
Thus, the missing sides of the given shapes are found.
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27. If figure A and figure B are similar with a ratio of similarity of 2, and the perimeter of figure A is 28 units,what is the perimeter of figure B?
SOLUTION
Since the two shapes are similar, that is A and B similar with a ratio of 2, then we have that
[tex]\begin{gathered} \frac{length\text{ A}}{lemgth\text{ B}}=\frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{perimeter\text{ A}}{perimeter\text{ B}} \\ \frac{2}{1}=\frac{28}{perimeter\text{ B}} \end{gathered}[/tex]Cross multiplying we have
[tex]\begin{gathered} 2Perimeter\text{ B = 28} \\ Perimeter\text{ B = }\frac{28}{2} \\ =14\text{ units } \end{gathered}[/tex]hence the answer is 14 units
use the quadratic formula to find both solitions to the quadratic equation given below x^2+6×=16
Answer:
x1=4
x2=-8
Step-by-step explanation:
x^2+6x-16=0
a=1 b=6 c=-16
D=b^2 - 4ab= 36+64=100
D>0, 2 sqrt
x1= -b+sqrt{D} /2= -6+10/2= 4
x2= -b-sqrt{D} /2= -6-10/2= -8
(That's what we were taught!)
Find m∠1 I need help please
Answer: 70
Step-by-step explanation: 180-110=70
because of isosceles, so ∠1=70
In 2019, the USDA reported that acreage for wheat was approximately 45.6 million acres;this is down 5% from 2018. Which of the following can you conclude?a) The 2018 wheat acreage was 47.88 million acres.b) The 2018 wheat acreage was 48.0 million acres.c) The 2019 wheat acreage was 43.43 million acres.d) The 2019 wheat acreage was 43.32 million acres.
Given that the USDA reported the acreage for wheat in 2019 was approximately 45.6 million acres; and was down 5% from 2018. We were asked to pick an option that would represent the right conclusion to the given statement.
To do this, we would assume that the acreage for wheat in 20 18 is x. Since 2018 differs from 2019 by 5%
This implies that the representation of 2019 acreage would be;
[tex]100\text{\%-5\%=95\%}[/tex]Therefore, we can have
[tex]\begin{gathered} \frac{95}{100}\times x=45.6 \\ \text{Cross multiply} \\ 95x=45.6\times100 \\ \text{Divide both sides by 95} \\ \frac{95x}{95}=\frac{45.6\times100}{95} \\ x=48 \end{gathered}[/tex]Therefore the 2018 acreage was;
Answer: Option B
URGENT TWO WAY TABLES
Answer: A) 6 B) 19.5
Step-by-step explanation:
A) 2,4,6,8,10
B) 8+16+30+24=78
78/4=19.5
Let me known if question b was right
Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set.
Answer:
(D) {xIx ≥ 5} or [5, ∞)
Explanation:
Given inequality: 5x - 11 ≥ 9 + x
By collecting the like terms, we have
5x - x ≥ 9 + 11
4x ≥ 20
Divide bothsides by 4
4x/4 ≥ 20/4
x ≥ 5
In set notation, we have {5, ∞}
The graph of the solution set is
Christian buys a $3500 computer using an installment plan that requires 17% down and a 3.7% interest rate. How much is the down payment?
1) Gathering the data
$3500 computer
17% down
3.7% interest rate.
2) Since we want to know how much is that down payment, we must turn that 17% into decimal form, then multiply it by the computer value:
17%=0.17
3500 x 0.17 = $595
3) So Christian must pay $595 as the down payment
X-1 what is the answer
Answer:
x - 1 = x - 1
Step-by-step explanation:
If you were expecting a singular solution, you won’t get it. You’ll likely instead get a lot of smart alecks snidely answer your question. Looks like you already have actually.
But they speak true. x – 1 on its own like that wont really get you anything. Now if you asked something along the lines of “What is x – 1 equal to if x is equal to 5?” then you’d get one solid definitive solution: 4.
Answer:
YES!!!!!
Step-by-step explanation:
LOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLOLLOLOLOLOLOLOLOLOL
It goes from -1 to 1 on the x axis.
ANSWER :
EXPLANATION :
What is the amplitude of the graph g(x)=f(x)+2 Where f(x)=cos x
In the cosine equation
[tex]y=AcosB(x-C)+D[/tex]A is the amplitude
B is using it to find the period
C is the phase shift
D is the vertical shift
Since the given function is
[tex]g(x)=cos(x)+2[/tex]A = 1
B = 1
C = 0
D = 2
The amplitude is 1
The answer is 1
Find to the nearest degree the measure of the angle of elevation of the sun when a woman 150 cm tall casts a shadow 40 cm long.
The triangle formed is shown in the diagram below
The angle of elevation of the sun is represented by x. To determine x, we would apply the tangent trigonometric ratio which is expressed as
Tan# = opposite side/adjacent side
opposite side = 150
adjacent side = 40
Tan x = 150/40 = 3.75
x = Tan^-1(3.75)
x = 75.069
To the nearest degree, the measure of the angle of elevation of the sun is 75 degrees
Dave and his brother. Theo, are selling cookies by the pound at the school bake sale Dave sold 14 84 pounds of cookies and Theo sold 21.45 pounds of cookies How many pounds did they sell altogether? A 35 29 OB 36 39 C36 25 0 D. 36 29
For tis problem we have that Dave sold 14.84 pounds of cookies and Theo sold 21.45 pounds of cookies.
If we want to find the total of pounds that they sold together we just need to add the two values and we have:
[tex]14.84+21.45=36.29\text{pounds}[/tex]The reason is because 0.84+0.45=1.29
14+21=35. And finally 35+1.29=36.29
And the best answer for this case would be D. 36.29
What is the value of x in the proportion2 1/4 = 1 1/2_________x = 3 3/5A. 2 2/5B. 5 2/5C. 8 1/10D. 12 3/20
First, we transform the mixed fractions
[tex]\begin{gathered} 2\frac{1}{4}=2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4} \\ 1\frac{1}{2}=1+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{3}{2} \\ 3\frac{3}{5}=3+\frac{3}{5}=\frac{15}{5}+\frac{3}{5}=\frac{18}{5} \end{gathered}[/tex]Then, we use cross multiplication
[tex]\begin{gathered} \frac{\frac{9}{4}}{x}=\frac{9}{4}\times\frac{1}{x}=\frac{9}{4x} \\ \frac{\frac{5}{2}}{\frac{18}{5}}=\frac{3}{2}\times\frac{5}{18}=\frac{15}{36} \end{gathered}[/tex]so, we have
[tex]\frac{9}{4x}=\frac{15}{36}[/tex]Finally, we solve for x, we multiply x on both sides
[tex]\begin{gathered} \frac{9}{4x}x=\frac{15}{36}x \\ \frac{15}{36}x=\frac{9}{4} \\ x=\frac{\frac{9}{4}}{\frac{15}{36}} \\ x=\frac{9}{4}\times\frac{36}{15} \\ x=\frac{9\times9\times4}{15\times4} \\ x=\frac{81}{15} \\ x=\frac{27}{5} \end{gathered}[/tex]Since 27/5 = 5+2/5.Then,
[tex]x=5\frac{2}{5}[/tex]Then the answer is the second one.
is there one solution to the following system of equations by elimination 3x + 2y equals 3 3x + 2y equals 19
3x+2y= 3 (a)
3x+2y= 19 (b)
Subtract (b) to (a) ; elimination method.
3x+ 2y = 3
-
3x+2y= 19
_________
0 = 19
Since both variables were eliminated, the system has no solutions.
option c.
Can someone help me with this geometry question I don’t know if I’m right or wrong?
Given:-
A circle has a central angle 135 degrees.
The radius of the circle is 24.
To find the arc length.
So now we use the formula,
[tex]s=r\theta[/tex]Now we convert 135 degrees to radians. so we get,
[tex]135=\frac{135}{180}\times\pi[/tex]So now we substitute the value. so we get,
[tex]\begin{gathered} s=24\times\frac{135}{180}\times\pi \\ s=18\pi \end{gathered}[/tex]So the required value is,
[tex]18\pi[/tex]So the correct option is OPTION D.
Trini bought some jeans that she had been saving up for. She purchased them for $88 but has wornthem 4 times already. So far, what is the cost of wear for the jeans?
In order to find the cost of wear for the jeans, we just need to divide the cost of the jeans by the number of times Trini worn it.
So we have:
[tex]\frac{88}{4}=22[/tex]Therefore the cost of wear so far is $22.
Identify the minimum from the tableType your answer as an ordered pair (x,y)
By definition, a function is a relation in which each input value has one and only one output value.
The input values are also known as x-values and the output values are also called y-values.
By definition, the Minimum is the lower point of the function.
Having the table shown in the exercise, you can identify the following points:
[tex]\begin{gathered} (-2,10) \\ (-1,8) \\ (0,6) \\ (1,4) \end{gathered}[/tex]You can identify that the lower y-value of all those points is:
[tex]y=4[/tex]Therefore, you can determine that the lower point of the function is:
[tex](1,4)[/tex]The answer is:
[tex](1,4)[/tex]Which sequence of transformations will change figure PQRS to figure P'Q'R'S'?
Explanation:
A counterclockwise rotation about the origin by 90 degrees rule is:
[tex](x,y)\rightarrow(-y,x)[/tex]The reflection about the x-axis is:
[tex](x,y)\rightarrow(x,-y)[/tex]If we take for example point P (-3, -2) we can see it ends at P'(2,3). The counterclockwise rotation about the origin by 90º gives:
[tex](-3,-2)\rightarrow(2,-3)[/tex]And now with a reflection about the x-axis:
[tex](2,-3)\rightarrow(2,3)[/tex]Which is point P'
Answer:
Counterclockwise rotation about the origin by 90 degrees followed by reflection about the x-axis
A cylinder whose height is 3 times its radius is inscribed in a cone whose height is 6 times its radius. What fraction of the cone's volume lies inside the cylinder? Express your answer as a common fraction.
The fraction of the cone's volume that lies inside the cylinder would be; V = 44/21 r^4
How to find the volume of a right circular cone?Suppose that the radius of the considered right circular cone is 'r' units.
And let its height be 'h' units. The right circular cone is the cone in which the line joining the peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
Then, its volume is given :
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
Let the radius of the cylinder is r
The height of the cylinder is h = 3r
The height of the cone is h = 6r
The fraction of the cone's volume that lies inside the cylinder would be;
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
[tex]V = \dfrac{1}{3} \times 3.14 \times r^3 \times 6r \: \rm unit^3[/tex]
V = 44/21 [tex]r^{4}[/tex]
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Answer:
4/9
Step-by-step explanation:
