Answers
Diagram 1.
Strategy 1.
[tex]A_{Total}=253\cdot31=(200+50+3)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]\begin{gathered} A_{Total}=A_1+A_2+A_3+A_4+A_5+A_6 \\ =(200\cdot30)+(50\cdot30)+(3\cdot30)+(200\cdot1)+(50\cdot1)+(3\cdot1) \\ =6000+1500+90+200+50+3 \\ =7843 \end{gathered}[/tex]Diagram 2.
Strategy 2.
[tex]A_{Total}=253\cdot31=(253)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]A_{Total}=A_1+A_2=253\cdot30+253\cdot1=7590+253=7843[/tex]We can see that we got the same answer: Total area = 7843 quare units
The strategies are similar because they are dividing the total area into smaller ones and then add them together.
However, they are different in that diagram 1 has more areas that are smaller compared to diagram 2. Also, the divisions in diagram 1 are designed to make multiplications easier compared to diagram 2.
Related Questions
This is not from a test or graded assessment. The Question is included in the picture.
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Given:
[tex]\begin{gathered} g(x)=-x^5-4x^3+6x \\ \\ h(x)=x^4+2x^3-2x^2+x-7 \\ \\ j(x)=3x^4+7x^2 \end{gathered}[/tex]It's required to determine if the functions are odd, even, or neither.
An even function satisfies the property:
f(-x) = f(x).
And an odd function satisfies the property:
f(-x) = -f(x)
We substitute x by -x on each function as follows:
[tex]\begin{gathered} g(-x)=-(-x)^5-4(-x)^3+6(-x) \\ \\ g(-x)=x^5+4x-6x \end{gathered}[/tex]Note the function g(-x) is the inverse (negative) of g(x), thus,
g(x) is odd
Now test h(x):
[tex]\begin{gathered} h(-x)=(-x)^4+2(-x)^3-2(-x)^2+(-x)-7 \\ \\ h(-x)=x^4-2x^3-2x^2-x-7 \end{gathered}[/tex]Comparing h(-x) and h(x) we can see none of the properties are satisfied, thus:
h(x) is neither odd nor even
Let's now test j(x):
[tex]\begin{gathered} j(-x)=3(-x)^4+7(-x)^2 \\ \\ j(-x)=3x^4+7x^2 \end{gathered}[/tex]Since j(-x) and j(x) are equal,
j(x) is even
What is an example of a situation from your professional or personal life that requires you to compare, understand, and make decisions based on quantitative comparison? Be sure to describe the types of quantitative comparisons you had to make, what decisions you made, and why.
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An example of situation involving quantitative comparison is:
The game-plan of an offensive coach for a NFL game.
What are quantitative variables?
Quantitative variables are variable that assume numbers as results, instead of labels such as yes/no or good/bad.
When an NFL offensive coordinator is game-planning, he has to consider numeric stats of the opponent defense, such as these ones:
Average passing yards allowed per play.Average rushing yards allowed per play.These stats are also compared to the NFL average to verify if the weak point of the opponent defense is the run or the pass, hence the game-plan is adjusted accordingly as follows:
Bad run defense: the coordinator should call more running plays.Bad pass defense: the coordinator should call more passing plays.A similar problem, also about quantitative variables, is given at https://brainly.com/question/15212082
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How do you know when an equation has infinite many solution?A. The coefficients are differentB. The coefficients are the same and the constants are differentC. The coefficients are the same and the constants are same
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Solution:
An equation has infinitely many solutions when the coefficients are the same and the constants are the same.
This is illustrated as shown below:
[tex]\begin{gathered} 2a+5+a=\text{ 5+3a,} \\ thus,\text{ we have infinitely many solution} \end{gathered}[/tex]Hence, the correct option is C.
I haven’t got a clue about what it is or what to do
Answers
EXPLANATION
Rotating the shape , give us the third shape form.
A gumball machine contains orange, yellow, and purple gum balls. The probability of getting an orange gumball is 3/4. The probability of getting a yellow gumball is 1/6. If there are 36 gumballs in the machine, how many are there of each color number of purple marbles _______ number of yellow marbles_____ number of orange marbles______
Answers
Given:
Probability of getting orange gumball is, p(o) = 3/4.
Probability of getting yellow gumball is, p(y) = 1/6.
The objective is to find the number of each colored gumballs.
Since, the sum of the events of probability is always 1.
Then, the probability of purple ball p(p) can be calculated as,
[tex]\begin{gathered} \frac{3}{4}+\frac{1}{6}+p(p)=1 \\ p(p)=1-\frac{3}{4}-\frac{1}{6} \\ p(p)=\frac{12-3(3)-1(2)}{12} \\ p(p)=\frac{1}{12} \end{gathered}[/tex]Since, it is given that the total number of gumball is N = 36.
Then, the number of orange ball can be calculated as,
[tex]\begin{gathered} p(o)=\frac{n(o)}{N} \\ \frac{3}{4}=\frac{n(o)}{36} \\ n(o)=36\cdot\frac{3}{4} \\ n(o)=27\text{ balls.} \end{gathered}[/tex]Similarly, the number of yellow ball can be calculated as,
[tex]\begin{gathered} p(y)=\frac{n(y)}{N} \\ \frac{1}{6}=\frac{n(y)}{36} \\ n(y)=\frac{36}{6} \\ n(y)=6 \end{gathered}[/tex]And the number of purple ball can be calculated as,
[tex]\begin{gathered} p(p)=\frac{n(p)_{}}{N} \\ \frac{1}{12}=\frac{n(p)}{36} \\ n(p)=\frac{36}{12} \\ n(p)=3 \end{gathered}[/tex]Hence, the number of orange ball is 27, number yellow ball is 6 and number of purple ball is 3.
Based on a recent study, the pH level of the arterial cord (one vessel in the umbilical cord) is normally distributed with mean 7.38 and standard deviation of 0.14. Find the percentageof preterm infants who have the following arterial cord pH levels.a. pH levels between 7.00 and 7.50.b. pH levels over 7.46A.The percentage of arterial cord pH levels that are between 7.00 and 7.50 is ____%.(Round to two decimal places as needed.)B.The percentage of arterial cord pH levels that are over 7.46 is ___%.(Round to two decimal places as needed.)
Answers
We have the pH level as a random normal variable with mean 7.38 and standard deviation of 0.14.
A) We have to calculate the percentage of infants that are expected to have pH levels between 7.00 and 7.50.
We can approximate this as the probability of selecting a random infant and it has a pH level within this interval.
Then, to calculate the percentage we will use the z-scores for each boundary of the interval:
[tex]z_1=\frac{X_1-\mu}{\sigma}=\frac{7-7.38}{0.14}=\frac{-0.38}{0.14}\approx-2.7143[/tex][tex]z_2=\frac{X_2-\mu}{\sigma}=\frac{7.5-7.38}{0.14}=\frac{0.12}{0.14}\approx0.8571[/tex]Then, we can use the standard normal distribution to look for the probabilities for each z-score and calculate the probability as:
[tex]\begin{gathered} P(7.00Given that the probability is 0.80099, we can express the percentage as:[tex]P=0.80099\cdot100\%=80.01\%[/tex]B) We now have to calculate the percentage that is above 7.46.
We start by calculating the z-score as:
[tex]z=\frac{X-\mu}{\sigma}=\frac{7.46-7.38}{0.14}=\frac{0.08}{0.14}\approx0.571428[/tex]Then, we can calculate the probability as:
[tex]P(X>7.46)=P(z>0.571428)\approx0.28385[/tex]This correspond to a percentage of 28.39%.
Answer:
A) 80.01%
B) 28.39%
Question HelpMultiple Representations A vehicle ses 7 gallons of gasoline to travel 147 miles. The vehicle uses gasoline at a steady rate. Use pencil and paper to draw a picture that models the situation Write a table of equivalent ratiosThen use the table to find the number of gallons of gasoline the vehicle uses to travel 63 milesComplete the tableGallons Miles1231411421
Answers
We know a vehicle uses 7 gallons of gasoline to travel 147 miles.
This gives us a ratio: 147/7 = 21
The vehicle travels 21 miles per gallon of gasoline
The situation can be modeled as a line with a constant slope of 21 miles/gallon
If we use the horizontal axis for the number of gallons and the vertical axis for the miles traveled, we can draw an approximate graph
Let's give the gallons (g) some values to fill up the table:
For g=1, miles = 21
For g=2, miles = 42
For g=3, miles = 63
For g=7, miles = 147
For g=14, miles = 294
For g=21, miles = 441
The graph is shown below
a coral reef grows 0.15 m every week. how much does it grow in 13 weeks? in centimeters
Answers
Given:
A coral reef grows 0.15 m every week.
Coral reefs grow 13 times 0.15m for 13 weeks.
[tex]=13\times0.15m[/tex][tex]=1.95\text{ m}[/tex]We need to convert m into cm.
[tex]1m=100cm[/tex]Multiply 1.95m by 100, we get
[tex]1.95\times100=195cm[/tex]Hence a coral reef grows 195cm in 13 weeks.
How can you use transformations to verify that the triangles are similar?
Answers
We need to know about congruency to solve the problem. Two pairs of congruent angles prove that the triangles are similar.
We can define similarity of two geometrical objects on a plane as possibility to transform one into another using dilation optionally combined with congruent transformations of parallel shift, rotation and symmetry. We need to use transformation to verify whether the triangles in the diagram are similar. The two triangles have a common angle D and angles ABD and ECD are equal. Thus we can say that we have two pairs of congruent angles in the two triangles, so the two triangles are similar.
Therefore the triangles are similar since they have two pair of congruent angles.
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need help with a question
Answers
From the image, we have the equation:
3x - 6 = -2x + 4
Let's solve for x:
3x - 6 = -2x + 4
Add 2x to both sides of the equation:
3x - 6 + 2x = -2x + 2x + 4
3x + 2x - 6 = 4
5x - 6 = 4
Add 6 to both sides:
5x - 6 + 6 = 4 + 6
5x = 10
Divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{10}{5} \\ \\ x\text{ = 2} \end{gathered}[/tex]ANSWER:
x = 2
help meeeeeeeeee pleaseee !!!!!
Answers
The values of the composition of the functions are:
(f o g)(x) = -x³ - x + 1
(g o f)(x) = -x³ - x - 1
How to Determine the Composition of a Function?To find the value of the composition of a given function, the inner function is first evaluated, then the output of the inner function is then replaced into the outer function and simplified.
Given the functions:
f(x) = x³ + x + 1g(x) = -x(f o g)(x) = f(g(x))
Substitute -x for x into the function f(x) = x³ + x + 1:
f(g(x) = (-x)³ + (-x) + 1
f(g(x) = -x³ - x + 1
(g o f)(x) = g(f(x))
Substitute x³ + x + 1 for x into the function g(x) = -x:
g(f(x)) = -(x³ + x + 1)
g(f(x)) = -x³ - x - 1
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can you please help me? I'm having trouble with algebra 2 doing online school
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Brianna, this is the solutiuon:
Part 2: Recalling that the perfect square trinomial has the form:
ax² + bx + c
(x - 1)² = (x - 1) * (x - 1)
x² - x - x + 1
x² - 2x + 1
Thus, b = -2. The correct answer is A.
Part 3: Recalling that the perfect square trinomial has the form:
ax² + bx + c
(x + 25)² = (x + 25) * (x + 25)
x² + 25x + 25x + 625
x² + 50x + 625
Therefore, c = 625. The correct answer is D.
In the right trapezoid ABCD, BC is parallel to AD, and AD is contained in the line whose equation is y=−12x+10 y = − 1 2 x + 10 . What is the slope of the line containing BC? Explain how you got your answer
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the radius of a circle is 9 inches. what is the circumference?give the exact answer in simplest form.
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Step 1
The circumference of a circle is given by;
[tex]2\pi r[/tex]where;
[tex]\begin{gathered} r=9in \\ \end{gathered}[/tex]Step 2
Find the circumference
[tex]\begin{gathered} C=2\times\pi\times9 \\ C=18\pi in\text{ches} \end{gathered}[/tex]Hence, in terms of π the circumference of the circle=18πinches
65+ (blank) =180
11x + (blank)=180
11x =
x =
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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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Graph the line that has an x-intercept of (-1,0) and a y-intercept of (0,5). What is the slope of this line?
Answers
Answer:
The slope is 5.
Step-by-step explanation:
To solve this, you could have plotted the two points, drew a line between them, and then calculated the slope by counting on the graph the line's rise/run.
To slove this by finding the slope with the points:
(5 - 0) / (0 - - 1) = 5 / 1 = 5
The slope is 5
write a word problem in which you divide two fractions into mixed numbers or a mixed number and a fraction solve your word problem and show how you found the answer
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Jade share 4 1/3 cups of chocolate by 1/3 among his friends
The mixed fraction = 4 1/3
Fraction = 1/3
[tex]\begin{gathered} \text{Firstly, we n}eed\text{ to convert the mixed fraction into an improper fraction} \\ 4\frac{1}{3}\text{ = }\frac{(3\text{ x 4) + 1}}{3} \\ 4\frac{1}{3}\text{ = }\frac{12\text{ + 1}}{3} \\ 4\frac{1}{3}\text{ = }\frac{13}{3} \\ \text{Divide }\frac{13}{3}\text{ by 1/3} \\ =\text{ }\frac{13}{3}\text{ / }\frac{1}{3} \\ \text{ According to mathematics, once the numerator and denominator of the LHS is interchanged then the order of operator changes from division to multiplication} \\ =\text{ }\frac{13}{3}\text{ x }\frac{3}{1} \\ =\text{ }\frac{13\text{ x 3}}{3} \\ \text{= }\frac{39}{3} \\ =\text{ 13} \end{gathered}[/tex]Therefore, the answer is 13
What is the solution set of x over 4 less than or equal to 9 over x?
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we have
[tex]\frac{x}{4}\leq\text{ }\frac{9}{x}[/tex]Multiply in cross
[tex]x^2\leq36[/tex]square root both sides
[tex](\pm)x\leq6[/tex]see the attached figure to better understand the problem
the solution is the interval {-6,6}
the solution in the number line is the shaded area at right of x=-6 (close circle) and the shaded area at left of x=6 (close circle)
Wilson paints 40% of a bookcase in 20 minutes.How much more time will it take him to finish the bookcase?1. Write an equation using equal fractions to represent this situation. Use a box to represent the time it takes to paint the whole bookcase. 2 Use your equation to find the amount of time it will take Wilson to paint the whole bookcase. Explain how you found this answer. 3. How much time will it take Wilson to finish painting the bookcase? Explain.
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We can start that, by rewriting 40% as a fraction:
[tex]\frac{40}{100}=\frac{2}{5}[/tex]So let's find how long it will take to finish this painting, by writing the following fractions, and from them an equation:
1)
[tex]\begin{gathered} \frac{2}{5}---20 \\ \frac{3}{5}---x \\ \frac{2}{5}x=\frac{3}{5}\cdot20 \\ \frac{2}{5}x=12 \end{gathered}[/tex]So this is the equation, let's find the time to complete the painting:
[tex]\begin{gathered} \frac{2}{5}x=12 \\ 5\times\frac{2}{5}x=12\times5 \\ 2x=60 \\ \frac{2x}{2}=\frac{60}{2} \\ x=30 \end{gathered}[/tex]So it will take plus 30 minutes for to Wilson finish the bookcase. Note that
5/5 is equivalent to the whole bookcase or 100%
2) The amount of time to paint this whole bookcase, is found taking the initial 20 minutes and adding to them the 30 minutes we can state that the painting overall takes 50 minutes
3) Sorting out the answers:
[tex]\begin{gathered} 1)\frac{2}{5}x=\frac{3}{5}\cdot20 \\ 2)50\min \\ 3)30\min \end{gathered}[/tex]
The graph of a function is shown below. find the following, g(10), g(-3)
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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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What is the equation of the following graph?A. f(x) = 2(3*)OB. f(x) = (4)Oc. f(x) = 3(2)D. f(x) = 5(2") y
Answers
Given
The graph,
To find:
The equation representing the given graph.
Explanation:
It is given that,
That implies,
From the given graph,
It is clear that the curve passes through, (0,5).
Then, for x=0,
Consider the equation,
[tex]\begin{gathered} f(0)=5(2^0) \\ =5\times1 \\ =5 \end{gathered}[/tex]Which is equal to y=5.
Hence, the equation representing the above graph is,
[tex]f(x)=5(2^x)[/tex]I'll send a pic of it
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Solution:
Since the slope of the given function represents the rate at which the temperature changes, the answer is the slope of the equation, that is, the correct solution would be:
[tex]0.7[/tex]
According to the theory of the color yellow + red = orange. If Luisa has x liters of yellow paint and/ 4 liters of red paint. How many liters of orange paint will he get Louise? And if I had 4 liters of yellow paint, could I get exact 5 liters of paint orange?
Answers
Yellow + red = Orange
Yellow paint , x liters
Red paint , 4 liters
a) Because addition applies , adding x liters of Yellow + 4 liters of red and the result is x + 4 liters of orange
b) for second question apply equation
4 • yellow + Red •N = 5
then find N
its possible to obtain 5 liters of paint orange with
2 liters of yellow, 2 liters of red, and adding
0.5 liters of yellow, 0.5 liters of red.
Real world compositions: A manufacturer sells a lawn mower to a store at $75 over the manufacturing cost. The store then sells the lawn mower for 140% of the price paid to the manufacturer. Determine the function of the price of a lawn mower in terms of the cost to manufacture the mower. What price will a customer pay for this mower if the manufacturer's cost was $230? Solve using composite functions
Answers
From the information provided, the lawn mower is sold at a price which is $75 over the cost of manufacture.
If the cost of manufacture is x, then we would have;
[tex]f(x)=x+75[/tex]Also, the store now sells the lawn mower for 140% of the price paid to the manufacturer. Therefore, we would have;
[tex]g(x)=f(x)1.4[/tex]Hence, if the manufacturer's cost is $230, the customer would be paying g(x). When the cost x is now given as 230, we wou;d have;
[tex]\begin{gathered} f(230)=230+75 \\ f(230)=305 \\ \text{Hence;} \\ g(x)=f(x)1.4 \\ g(x)=305\times1.4 \\ g(x)=427 \end{gathered}[/tex]ANSWER:
The function of the price is;
[tex]f(x)=x+75[/tex]The price a customer pays when the cost of manufacturing is $230 would now be $427
determine the area of the shaded regionA. 6 square unitsB. 19 square unitsC.20 square unitsD. 25 square units
Answers
area of the square:
[tex]\begin{gathered} a=l\times l \\ a=5\times5 \\ a=25 \end{gathered}[/tex]area of the rectangle
[tex]\begin{gathered} a=b\times h \\ a=3\times2 \\ a=6 \end{gathered}[/tex]area of the shaded region:
area of the square - area of the rectangle = area of the shaded region
[tex]25-6=19[/tex]answer: B 19 saquare units
andrew went to the store to buy some walnuts. the price pee walnut is $4 per pound and he has a coupon for $1 off the final amount. with the coupon, how much would andrew have to pay to buy 4 pounds of walnuts? what is the expression for the cost to buy p pounds of walnuts , assuming at least one pound is purchased.
Answers
The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts= 4p - 1
Explanation:
Amount per pound of walnut = $4
Amount of coupon = $1
The cost of 4 pounds of walnuts:
[tex]\text{Cost = 4 }\times5=\text{ \$20}[/tex]The amount Andrew have to pay to buy 4 pounds of walnuts:
Amount = cost - coupon
Amount = $20 - $1
The amount Andrew have to pay to buy 4 pounds of walnuts = $19
The expression for the cost to buy p pounds of walnuts:
let number of pounds = p
Cost for p pounds of walnut = Amount per walnut * number of walnut
Cost for p pounds of walnut = $4 * p
= $4p
The expression for the cost to buy p pounds of walnuts= cost for p - coupon
= 4p - 1
A Census Burcau report on the income of Americans says that with 95% confidence themedian income of all U.S. households is $49,841 to $50,625. The point estimate and margin oferror for this interval are: *Point estimate = $49,841; Margin of error = $784Point estimate = $50,233; Margin of error = $784oPoint estimate = $50,233; Margin of error = $392Point estimate = $50,625; Margin of error = $392
Answers
Let the point estimate be x and the margin of error be e.
Then, we must have
[tex]\begin{gathered} x+e=50625----------------------(1) \\ x-e=49841----------------------(2_{}) \end{gathered}[/tex]Add the equation (1) and equation(2) to eliminate the variable e, we have
[tex]\begin{gathered} 2x=100466 \\ \text{ thus} \\ x=\frac{100466}{2}=\text{ \$}50233 \end{gathered}[/tex]Subtracting equation (2) from equation(1) to eliminate the variable x, we have
[tex]\begin{gathered} 2e=784 \\ \text{ thus} \\ e=\frac{784}{2}=392 \end{gathered}[/tex]Hence, the point estimate is $50233 and the margin of error is $392, The Third option
7 ( 7x - 3y) - 6 Expand the expression
Answers
The expanded form of the expression is 49x - 21y - 6
Explanation:[tex]\text{Given: }7(7x\text{ - 3y) - 6}[/tex]To expand, we will multiply the terms outside by the terms inside the parentheiss:
[tex]\begin{gathered} U\sin g\text{ distributive property} \\ a(b\text{ + c) = a9b) + a(c)} \\ \\ 7(7x-3y)-6=\text{ }7(7x)\text{ -7(3y) - 6} \\ =\text{ 49x - 21y - 6} \end{gathered}[/tex]The expanded form of the expression is 49x - 21y - 6
Put these five fractions in order, left to right, from least to greatest. 1 /3 2 /7 3/10 4/13 5/17
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The five fractions can be arranged in order, from the left to right, from least to greatest as : 5/17 , 3/10 , 4/13 , 1 /3.
How can the fraction can be arranged from the from least to greatest?The fraction can be arranged from the from least to greatest by firstly convert the fraction to the decimal numbers so that one c b able to identify the highest and the lowest values.
The given fractions 1 /3 2 /7 3/10 4/13 5/17 can be converted to decimal numbers as 0.33 , 0.67 , 0.30 , 0.31 , 0.29 respectively and this can be arranged as 5/17 , 3/10 , 4/13 , 1 /3.
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16 - 2t = 5t +9 Can you help me solve this?
Answers
1=t
add 2t to the second side, so that it is going to be 16=7t+9
now, subtract 9 from the right side: 16-9=7t
7t=7
t=1
