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
5+10+15+...+100 write the series using summation notation
The Solution.
To determine that the series is an arithmetic progression,
[tex]\begin{gathered} T_{2_{}}-T_1=T_3-T_2=d \\ \text{Where d = common difference} \end{gathered}[/tex][tex]d=10-5=15-10=5[/tex]The sum of n terms of an arithmetic progression is given as
[tex]\begin{gathered} S_n=\frac{n}{2}(a+l) \\ \text{Where S}_n=\sum ^{\square}_{\square} \\ n=n\text{ umber of terms}=\text{?} \\ a=\text{first term=5} \\ l=\text{last term=100} \end{gathered}[/tex]But we need to first find the number of terms (n), by using the formula below:
[tex]\begin{gathered} l=a+(n-1)d \\ \text{Where a = 5, l=100, d = 5 and n =?} \end{gathered}[/tex]Substituting the values, we get
[tex]\begin{gathered} 100=5+(n-1)5 \\ 100=5+5n-5 \\ 100=5n \\ \text{Dviding both sides by 5, we get} \\ n=\frac{100}{5}=20 \end{gathered}[/tex]Substituting into the formula for finding the sum of terms of the series, we get
[tex]\begin{gathered} S_{20}=\frac{20}{2}(5+100) \\ \text{ } \\ \text{ = 10(105) = 1050} \end{gathered}[/tex]Therefore, the correct answer is 1050.
6. Suppose that wedding costs in the Caribbean are normally distributed with a mean of $6000 and a standard deviation of $735. Estimate the percentage of Caribbean weddings that cost (a) between $5265 and $6735. % (b) above $6735. % (c) below $4530. % (d) between $5265 and $7470. %
To solve this problem, the first thing we must do is find the Z-Score of the given costs: $5265 , $6735 , $4530 ,and $7470
Then we proceed to find the percentages for each interval based on the graph
z-score for $5265 )
[tex]Z_{5265}=\frac{5265-6000}{735}=-1[/tex]z-score for $6735 )
[tex]Z_{6735}=\frac{6735-6000}{735}=1[/tex]z-score for $4530 )
[tex]Z_{4530}=\frac{4530-6000}{735}=-2[/tex]z-score $7470 )
[tex]Z_{7470}=\frac{7470-6000}{735}=2_{}[/tex]now, let's analyze the intervals
a ) between $5265 and $6735
This interval goes from (μ-σ) to (μ+σ)
if we look at the graph we find that this corresponds to a percentage of 68%
b) above $6735
This corresponds to what is to the right of (μ+σ)
This is a percentage of 16%
[tex]\frac{100-68}{2}=\frac{32}{2}=16[/tex]c ) below $4530
This corresponds to what is to the left of (μ-2σ)
This is a percentage of 2.5%
[tex]\frac{100-95}{2}=\frac{5}{2}=2.5[/tex]d ) between $5265 and $7470
This interval goes from (μ-σ) to (μ+2σ)
This is a percentage of 81.5%
[tex]\begin{gathered} 100-\frac{100-68}{2}-\frac{100-95}{2} \\ =100-16-2.5 \\ =81.5 \end{gathered}[/tex]Find the slope and the equation of the line having the points (0, 2) and (5, 5)
Answer:
The slope is 3/5 and the equation is:
[tex]y=\frac{3}{5}x+2[/tex]Explanation:
Given the points (0,2) and (5, 5)
The slope of a line is the ratio of the difference between the y coordinates to the x coordinates. The x coordinates are 0 and 5, the y coordinates are 2 and 5.
[tex]\begin{gathered} m=\frac{5-2}{5-0} \\ \\ =\frac{3}{5} \end{gathered}[/tex]The equation of a straight line is given as:
y = mx + b
Where m is the slope and b is the y-intercept
Using any of the given points, we can find b
Use (0, 2), with x = 0, y = 2
2 = (3/5)(0) + b
b = 2
Now the equation is:
[tex]y=\frac{3}{5}x+2[/tex]Factor each polynomial by factoring out the greatest common factorminimum steps please
we are given the following expression:
[tex]12x^4+6x^3-8x^2[/tex]The greatest common factor between 12, 6, and 8 is 2. And the greatest common factor between the variables is:
[tex]\text{GCF(x}^4,x^3,x^2)=x^2[/tex]Therefore, the factorization is:
[tex]12x^4+6x^3-8x^2=2x^2(6x^2+3x-4)[/tex]Refer to attached image.
213 and 131 are incorrect.
Answer:
P(X<16) = 0.64P(X>12) = 0.64Step-by-step explanation:
Given a graph of a probability density function, you want the probabilities ...
P(X < 16)P(X > 12)Probability from PDFThe probability of a given range of values of X is the area under the density curve for those values of x.
P(X < 16)The triangular area to the left of X=16 has a base of 16 and a height of 0.08. Its area is given by the area formula for a triangle:
A = 1/2bh
A = 1/2(16)(0.08) = 0.64
The probability is P(X<16) = 0.64.
P(X > 12)The area to the right of X=12 is a trapezoid with parallel "bases" of 0.06 and 0.10. The "height" of the trapezoid is 20-12 = 8. The area is given by the formula ...
A = 1/2(b1 +b2)h
A = 1/2(0.06 +0.10)(8) = 0.64
The probability is P(X>12) = 0.64.
The graph of a function is shown below. find the following, g(10), g(-3)
According to the graph, the value of the function g(-3) is 4 and g(10) is out of view
What are graphs?Graphs are graphical representations of equations, ordered pairs, tables of a relation
How to evaluate the function?From the question, the function is represented by the attached graph
Also from the question, the function to calculate is given as g(10) and g(-3)
This means that we calculate the values of the function, when x = 10 and -3
i.e.
We calculate g(x), when x = -3
We calculate g(x), when x = 10
So, we look at the graph for this function value
From the graph of values, we have
When x = -3, g(x) = 4
When x = 10, g(x) = not visible
This means that
g(-3) = 4
g(10) = out of view
Hence, the function g(-3) has a value of 4 and g(10) is out of view
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assume the rate of inflation is 7% per year for the next 2 years. what will be the cost of goods 2 years from now adjusted for inflation if the goods cost $330.00 today? round to the nearest cent
To find the cost of the goods after two years we are going to use the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where P is the cost now, r is the inglation rate in decimal form, n is the number of times the interest is taken per year and t is the time.
In this case we have P=$300.00, r=0.07, n=1 (once per year) and t=2 (two years). Plugging this values we have:
[tex]A=330(1+\frac{0.07}{1})^{1\cdot2}=377.82[/tex]Therefore after two years the cost will be $377.82
Select all the situations in which a proportional relationship is described.
Jackson saves $10 in the first month and $30 in the next 3 months.
Mia saves $8 in the first 2 months and $4 in the next month.
Piyoli spends $2 in the first 2 days of the week and $5 in the next 5 days.
Robert spends $2 in the first 3 days of the week and $5 in the next 4 days.
The situations that describe a proportional relationship are:
Jackson saves $10 in the first month and $30 in the next 3 months.
Mia saves $8 in the first 2 months and $4 in the next month.
Piyoli spends $2 in the first 2 days of the week and $5 in the next 5 days.
What is a proportional relationship?A relation is proportional if the rate of change of the variables is constant. The variables can either increase or decrease at a constant rate. A proportional relationship can be modelled with a linear equation.
Is Jackson's saving proportional?
Average of the amount saved in the next 3 months: $30 / 3 = $10
The relationship is proportional because the amount saved in the first month and the average is equal.
Is Mia's saving proportional?
Average of the amount saved in the first 2 months: $8 / 2 = $4
The relationship is proportional because the amount saved in the thir month and the average is equal.
Is Piyoli's spending proportional?
Average of the amount spent in the first 2 days: $2 / 2 = $1
Average of the amount spent in the next 5 days = $5 / 5 = $1
The relationship is proportional because the averages are equal.
Is Robert's spending proportional?
Average of the amount spent in the first 3 days: $2 / 3 = $0.67
Average of the amount spent in the next 4 days = $5 / 4 = $1.25
The relationship is not proportional because the averages are not equal.
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The shaded triangle has an area of 4 cm?Find the area of the entire rectangleBe sure to include the correct unit in your answer.
Given:
Area of a shaded region of a rectangle is given.
[tex]\text{Area of the triangle=}4cm^2[/tex]Area of the rectangle is twice the area of the triangle given.
[tex]\begin{gathered} \text{Area of a rectangle=2}\times Area\text{ of a triangle} \\ =2\times4 \\ =8cm^2 \end{gathered}[/tex]Nov 28,Quadrilateral ABCD is dilated by a scale factor of to form quadrilateral A'B'C'D'.What is the measure of side DA?Dal1515301B2162А
The quadrilateral ABCD was dilated by a scale factor of 3/4 to form the quadrilateral A'B'C'D'
This means that each side of the quadrilateral was multiplied by 3/4 to make the dilation.
You know that the scale factor is 3/4 and the length of D'A' is equal to 30 units, then:
[tex]\begin{gathered} D^{\prime}A^{\prime}=\frac{3}{4}DA \\ 30=\frac{3}{4}DA \end{gathered}[/tex]Multiply both sides by the reciprocal of 3/4
[tex]\begin{gathered} 30\cdot\frac{4}{3}=(\frac{4}{3}\cdot\frac{3}{4})DA \\ 40=DA \end{gathered}[/tex]The length of side DA is 40 units.
50 points.
Daisy is a botanist who works for a garden that many tourists visit. The function f(s) = 3s + 30 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 12w represents the number of seeds she plants per week, where w represents the number of weeks.
Part A: Write a composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks.
Part B: What are the units of measurement for the composite function in Part A?
Part C: Evaluate the composite function in Part A for 36 weeks.
From the situation described in this problem, it is found that:
A. The composite function is: f(s(w)) = 36w + 30.
B. The unit of measurement of the composite function is: flowers.
C. After 36 weeks, Daisy can expect to bloom 1326 flowers.
Composite functionFor a composite function, the output of the inner function serves as the input of the outer function.
In the context of this problem, the functions are given as follows:
f(s) = 3s + 30.s(w) = 12w.Hence the composite function that represents how many flowers Daisy can expect to bloom over a certain number of weeks is:
f(s(w)) = f(12w) = 3(12w) + 30 = 36w + 30.
The unit of measurement of the composite function is the unit of the outer function, which is flowers.
After 36 weeks, the number of flowers that Daisy can expect to bloom is given as follows:
f(s(36)) = 36(36) + 30 = 1326 flowers.
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find the slope that goes through the points (1, -4) and (-3, 8)
Given the points:
(x1, y1) ==> (1, -4)
(x2, y2) ==> (-3, 8)
To find the slope, use the slope formula below:
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]\begin{gathered} m\text{ = }\frac{8-(-4)}{-3-1} \\ \\ m=\frac{8+4}{-3-1} \\ \\ m=\frac{12}{-4} \\ \\ m\text{ = -3} \end{gathered}[/tex]Therefore, the slope is -3.
ANSWER:
-3
Identify each pair of angles as corresponding, alternate interior, alternate exterior, consecutiveinterior, vertical, or adjacent.
SOLUTION
Given the image on the answer tab;
Explanation;
The two angles are said to be adjacent angles when they share the common vertex and side.
Considering our question;
Find the value of this expression if x = 1 andy = -7x2y-9
We are asked to evaluate the expression:
[tex]\frac{x^2y}{-9}[/tex]when x = 1 and y = -7
so we replace them as shown below, making sure we include them inside parenthesis to keep clear that the expressions in x and in y are multiplying each other:
[tex]\frac{x^2y}{-9}=\frac{(1)^2(-7)}{-9}=\frac{-7}{-9}=\frac{7}{9}[/tex]So we see that x^2 becomes 1 and the factor y stays as -7. The final expression cancels out the negative sign in numerator (from -7) and in denominator (from -9) and gives 7/9.
Sketch the vectors u and w with angle θ between them and sketch the resultant.|u|=20, |w|=50, θ=80°
Vectors are represented by arrows, where the norm of a vector determinate its length.
Since θ = 80° is the angle between them, a sketch for our vectors is
The resultant of their sum is given by the parallelogram law. If we draw two vectors parallel to u and w, we're going to have a sketch of a parallelogram, and the diagonal connecting the angle between u and w to the opposite vertice represents the resultant.
Can someone please help me with this problem? I’ve been struggling with it
Consider the following table for interval notation:
First row:
x<0 is the same as:
[tex]-\inftyThen, the graph of that interval looks like:And the interval notation for that inequality is:
[tex](-\infty,0)[/tex]Second row:
-2
The graph of this inequality is:
The interval notation is:
[tex](-2,1\rbrack[/tex]Third row
The inequality that is represented by that interval is:
[tex]-3\le x[/tex]Its graph is:
Fourth row
The interval represented in that graph is:
[tex]\lbrack0,6)[/tex]The inequality represented by that interval is:
[tex]0\le x<6[/tex]An amusement park's owners are considering extending the weeks of the year that it is opened. The owners would like to survey 100 randomly selected families to see whether an extended season would be of interest to those that may visit the amusement park.What is the best way to randomly choose these 100 families? Have the owners of the amusement park ask the first 100 people they see.Choose a neighborhood near the amusement park and ask 100 families in this neighborhood.Ask the first 100 families that enter the amusement park on a busy weekend day.Allow a random number generator to come up with 100 families within a 50 radius of the amusement park.
Solution
Option 1:
- The owners asking the first 100 people they see would mean that they would see only those around them. This could be anyone at all from workers in the amusement park to people outside the park; these would not be random, and would not necessarily be a family but the survey is talking about randomly choosing 100 families. Because of these reasons, this is not the best way to randomly choose 100 families.
Option 2:
- Choosing a neighborhood near the amusement park would mean that they go to a neighborhood with families that might visit the amusement park and there would be many families to randomly choose from.
- This option seems like a good choice to randomly choose these 100 families that might visit the amusement park.
Option 3:
- Asking the first 100 families that enter the amusement park on a busy weekend would definitely bias the survey since families that you find in the amusement park are families that definitely want to be there and if they are there on a busy weekend, they certainly would not mind extending the season
which statement is true of the system of equations shown below
3x + 7y= 14
3x+7y= 10
Subtract the second equation to the first.
3x +7y= 14
-
3x + 7y= 10
_________
0x +0y = 4
0 = 4
0 is no
The lengths of two sides of the right triangle ABC shown in the illustration givena=12 cm and c= 20cm
In the right triangle of sides a, b, and c
[tex]a^2+b^2=c^2[/tex]Since a = 12 and c = 20
Substitute them in the given rule
[tex]\begin{gathered} (12)^2+b^2=(20)^2 \\ 144+b^2=400 \end{gathered}[/tex]Subtract 144 from both sides
[tex]\begin{gathered} 144-144+b^2=400-144 \\ b^2=256 \end{gathered}[/tex]Take a square root for both sides
[tex]\begin{gathered} \sqrt[]{b^2}=\sqrt[]{256} \\ b=16 \end{gathered}[/tex]The answer is b = 16
65+ (blank) =180
11x + (blank)=180
11x =
x =
The angle x has a measure of 13 degrees
What are angles?Angles are the measure of space between lines
How to determine the measure of the angle x?The figure represents the given parameter
On the figure, we have the following parameters:
Angle 1 = 54
Angle 2 = 11x - 7
Angle 5
From the figure, angles 1 and angle 5 are corresponding angles
Corresponding angles are congruent angles
So, we have
Angle 1 = Angle 5
This gives
Angle 5 = 54
Also, we have
Angle 5 and Angle 2 are supplementary angles
This means that
Angle 5 + Angle 2 = 180
Substitute the known values in the above equation
So, we have
54 + 11x - 17 = 180
Evaluate the like terms
11x = 143
Divide both sides by 11
x = 13
Hence, the value of x is 13 degrees
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A classic car is now selling for $2000 more than two times its original price. If the selling price is now $12,000, what was the car's original price?
A chocolate factory has a goal to produce10121012pounds of chocolate frogs per day. If the machines operate for712712hours per day making215215pounds of chocolate frogs per hour, will the chocolate factory make it’s goal?The chocolate factory meet their goal with the total being10121012pounds of chocolate frogs produced.
First, rewrite all the mixed fractions as impropper fractions:
[tex]\begin{gathered} 10\frac{1}{2}=10\times\frac{2}{2}+\frac{1}{2}=\frac{20}{2}+\frac{1}{2}=\frac{21}{2} \\ \\ 7\frac{1}{2}=7\times\frac{2}{2}+\frac{1}{2}=\frac{14}{2}+\frac{1}{2}=\frac{15}{2} \\ \\ 2\frac{1}{5}=2\times\frac{5}{5}+\frac{1}{5}=\frac{10}{5}+\frac{1}{5}=\frac{11}{5} \end{gathered}[/tex]Next, multiply the rate of chocolate production over time by the the operating time of the machines to find the total amount of pounds of chocolate frogs produced in one day:
[tex]7\frac{1}{2}\times2\frac{1}{5}=\frac{15}{2}\times\frac{11}{5}=\frac{15\times11}{2\times5}=\frac{3\times11}{2}=\frac{33}{2}=16\frac{1}{2}[/tex]Then, the chocolate factory can produce 16 1/2 pounds of chocolate frogs per day.
Since 16 1/2 is greater than 10 1/2, then the chocolate factory will meet their goal with the total being over 10 1/2 pounds of chocolate frogs produced.
how long is the hypotenuse of this right triangle?28 519023
To calculate the hypotenuse of a right angled triangle as shown in the diagram, we can apply the Pythagoras theorem which states as follows;
AC^2 = AB^2 + BC^2
Where AC is the hypotenuse (the longest side) 28 units, AB is one of the other two sides, 23 units and BC is the third side.
We can now re-write the formula as follows;
28^2 = 23^2 + BC^2
784 = 529 = BC^2
Subtract 529 from both sides of the equation
255 = BC^2
Add the square root sign to both sides of the equation and you have
BC = 15.9687
BC is approximately 16 units
Give. ∆ABC Angle B = 42°, Angle C = 71° and BC = 22. Find AB and round your answer to nearest integer.
Let's make a diagram to visualize the problem.
First, let's find angle A.
[tex]\begin{gathered} A+B+C=180 \\ A+42+71=180 \\ A=180-71-42 \\ A=67 \end{gathered}[/tex]Then, we use the law of sines to find AB.
[tex]\begin{gathered} \frac{AB}{\sin71}=\frac{BC}{\sin A} \\ \frac{AB}{\sin71}=\frac{22}{\sin 67} \\ AB=\frac{22\cdot\sin 71}{\sin 67} \\ AB\approx23 \end{gathered}[/tex]Therefore, AB is 23 units long, approximately.There are 130 people in a sport centre.
76 people use the gym
60 people use the swimming pool.
32 people use the track.
23 people use the gym and the pool.
8 people use the pool and the track.
20 people use the gym and the track.
6 people use all three facilities.
Given that a randomly selected person
uses the gym and the track, what is
the probability they do not use the
swimming pool?
The probability is 0.57
What is meant by probability?
Probability is a discipline of mathematics that deals with appropriate units of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number ranging from zero and 1, where 0 denotes the event's feasibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.
Probability of using the pool = 97/225 = 0.43
Probability that they do not use the swimming pool = 1 - 0.43 = 0.57
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the Missing Angles (plus angle review)<8 of 16Whats the measure of each of the angle in degrees? Label the angles, then answer,Subm104056°
A is angle opposite by the vertex with the angle of 104 degrees, that is why it also measure 104 degrees
The three inner angles of any triangle add 180 degrees, then 56 + A + B = 180
Solving for B: B = 180 - 56 - A = 180 - 56 - 104 = 20
The number of inequality’s and signs can be changed by the way
Linear Optimization
It consists of finding the optimum solution to a problem where all the conditions are related as linear functions.
We'll use the graphic method to solve the problem.
The problem is as follows:
Ava sells burritos amd tacos. Let's call x to the number of tacos sold and y to the number of burritos sold.
The first condition we find is that she can only produce a maximum of 130 units between tacos and burritos. This gives us the first inequality:
x + y ≤ 130 (1)
She sells each taco for $3.75 and each burrito for $6. She must sell a minimum of $600 worth of both products, so:
3.75x + 6y ≥ 600
Multiply this inequality by 4:
15x + 24y ≥ 2400
And divide it by 3:
5x + 8y ≥ 800 (2)
We are given a final condition that she can sell a minimum of 80 burritos, thus:
y ≥ 80 (3)
There are two obvious conditions not explicitly said but they can be deducted by the wording of the problem. Both x and y must be greater or equal to zero:
x ≥ 0 (4)
y ≥ 0 (5)
Let's put this all together:
x + y ≤ 130 (1)
5x + 8y ≥ 800 (2)
y ≥ 80 (3)
x ≥ 0 (4)
y ≥ 0 (5)
The optimum solution must satisfy all the conditions. They form a feasible region in the x-y coordinates system. One of the corners of that region will eventually be the best solution, depending on the objective function (not given here).
We need to graph all five lines in one common grid. It's shown below.
According to the graph, one possible solution is to sell x=50 tacos and y=80 burritos
RATIOS, PROPORTIONS, AND PERCENTSCalculating income taxTeresa made $20,000 in taxable income last year.Suppose the income tax rate is 10% for the first $7500 plus 16% for the amount over $7500.How much must Teresa pay in income tax for last year? I need help with this math problem.
We need find the tax on the first 7500
7500 * 10%
7500 * .10 = 750
Now we find the tax on what is over 7500
20000 -7500 =12500
The tax rate for this amount is 16%
12500 * 16%
12500 * .16
2000
Add the tax for both amounts together
750 + 2000
2750
The total tax paid is 2750
Make a tree diagramPlease be quick, I am in a hurry.
Explanation
The question wants us to obtain all the outcomes possible when a coin and a cube is tossed
A coin has two possible outcomes
[tex]\mleft\lbrace\text{Head, Tail}\mright\rbrace[/tex]A cube has 6 surfaces, so the outcomes are
[tex]\mleft\lbrace1,2,3,4,5,6\mright\rbrace[/tex]Thus, we can have the diagram showing the outcomes to be
find the first second and third derivatives of the function
Given the function
[tex]f(x)=\frac{8}{5}x-9[/tex]Finding the derivative we have
[tex]f^{^{\prime}}(x)=\frac{8}{5}[/tex]Also
[tex]f^{\doubleprime}(x)=0^{}[/tex]Finally
[tex]f^{^{\doubleprime}^{\prime}}(x)=0[/tex]