Answers
Answer: Choice A) [tex]\boldsymbol{78.67\% \ \pm \ 9.46\%}[/tex]
======================================================
Explanation:
phat = 59/75 = 0.7867 = 78.67% approximately is the sample proportion
n = 75 is the sample size
Your teacher doesn't mention a confidence level, so I'll assume it's the default 95%.
Let's compute the margin of error at 95% confidence
E = z*sqrt(phat*(1-phat)/n)
E = 1.96*sqrt(0.7867*(1-0.7867)/75)
E = 0.0927 approximately
E = 9.27% approximately
Unfortunately the margin of error 9.27% isn't listed among the four answer choices, but let's change the z = 1.96 to z = 2 instead.
Recalculate the margin of error.
E = z*sqrt(phat*(1-phat)/n)
E = 2*sqrt(0.7867*(1-0.7867)/75)
E = 0.0946 approximately
E = 9.46% approximately
This margin of error is listed among the four answer choices.
------------------
We found that
phat = 78.67% approximatelyE = 9.46% approximatelyThe confidence interval in the format [tex]\text{phat} \ \pm \ \text{E}[/tex] is approximately [tex]78.67\% \ \pm \ 9.46\%[/tex] which points us to choice A as the answer.
Answer:
[tex]\textsf{a)} \quad 78.67\% \pm 9.46\%[/tex]
or d) None of the answers are correct. (Please see notes below).
Step-by-step explanation:
P-hat is the probability that a given outcome will occur given a specified sample size.
[tex]\boxed{\begin{minipage}{7.5 cm}\underline{P-hat formula}\\\\$\hat{p}=\dfrac{X}{n}$\\\\where:\\\phantom{ww}$\bullet$ $\hat{p}$ is the probability. \\ \phantom{ww}$\bullet$ $X$ is the number of occurrences of an event. \\ \phantom{ww}$\bullet$ $n$ is the sample size.\\\end{minipage}}[/tex]
Given:
X = 59n = 75Substitute the given values into the formula to find p-hat:
[tex]\implies \hat{p}=\dfrac{59}{75} =0.78666666...[/tex]
The critical value for a 95% confidence level using normal distribution is:
[tex]z=1.9600\;\;\sf (4\;d.p.)[/tex]
[tex]\boxed{\begin{minipage}{5.2 cm}\underline{Margin of error}\\\\$ME=z \cdot \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$\\\\where:\\\phantom{ww}$\bullet$ $z$ is the critical value. \\ \phantom{ww}$\bullet$ $\hat{p}$ is the sample proportion. \\ \phantom{ww}$\bullet$ $n$ is the sample size.\\\end{minipage}}[/tex]
Substitute the given values into the margin of error formula:
[tex]\implies ME=1.9600 \cdot \sqrt{\dfrac{\dfrac{59}{75}\left(1-\dfrac{59}{75}\right)}{75}}[/tex]
[tex]\implies ME=0.092715036...[/tex]
Therefore, an estimate of the proportion of young-adult novels that include a love triangle (including a margin of error) is:
[tex]\implies \hat{p}\pm ME[/tex]
[tex]\implies 0.7867\pm 0.0927[/tex]
[tex]\implies 78.67\% \pm 9.27\%[/tex]
This result if not given in the list of answer options. However, the final result depends on the accuracy of the z-score and p-hat used in the calculations.
If we round the critical value to the nearest integer then:
[tex]\implies z=2[/tex]
Substitute the rounded z-value into the margin of error formula:
[tex]\implies ME=2\cdot \sqrt{\dfrac{\dfrac{59}{75}\left(1-\dfrac{59}{75}\right)}{75}}[/tex]
[tex]\implies ME=0.094607180...[/tex]
Therefore, an estimate of the proportion of young-adult novels that include a love triangle (including a margin of error) using z = 2 is:
[tex]\implies 78.67\% \pm 9.46\%[/tex]
Note: It is likely that this question required the critical value to be rounded to the nearest integer, however please note that this is not normal practice as it produces a different result, as evidenced above.
Related Questions
in January 2008, the temperature in parts of Minnesota fell from 41 degrees to -13 degrees over a 24 hour period. what was the average temperature change per hour?
Answers
We need to find the average termperature change per hour during January 2008.
We have the information that Minnesota fell from 41 degrees to -13 degrees over 24 hours.
Then, 41 degrees to -13 degrees, there is a difference of 41+13 = 54 degrees over 24 hours.
If the difference is over 24 hours, then:
54 degrees / 24 hours =2.25 F is the rate of change.
However, the termperature is decreasing, so the rate of change must be negative.
Hence, the rate of change = -2.25 F.
The correct answer is the third option.
f(x)= -2x-1
h(x)= -x+5
(hf)(6)=??
Answers
Answer:
[tex]f(x) = - 2x - 1 \\ h(x) = - x + 5 \\ \\ The \: \: value \: \: of \: \: \: f(6) = ( - 2) \times 6 - 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 13 \\ \\ as \: we \: know ,\: \\➪(hf)(x) = h(f(x)) \\ so \:➪( hf)(6) = h(f(6)) \\ \\ put \: the \: value \: \: of \: f(6) \: we \: \: get \\ \\➪ (hf)(6) \: = h( - 13) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - ( - 13) + 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 13 + 5 \\ \: \: \: \: \: \: \: = 18[/tex]
Tʜᴀɴᴋs Hᴏᴘᴇ ɪᴛ ʜᴇʟᴘs..{2x + 3y = 5}{ y= 5 x -4}
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Solve the system using substitutions:
[tex]\begin{gathered} 2x+3y=5 \\ 2x+3(5x-4)=5 \\ 2x+15x-12=5 \\ 17x=5+12 \\ 17x=17 \\ x=\frac{17}{17} \\ x=1 \end{gathered}[/tex]x has a value of 1. Use this value to find the value of y.
[tex]\begin{gathered} y=5x-4 \\ y=5\cdot1-4 \\ y=5-4 \\ y=1 \end{gathered}[/tex]y has a value of 1.
x=1
y=1
Sketch a diagram showing VX intersectingUW at V so that VX is perpendicular toU and U, V, and W are collinear.
Answers
We have to do a diagram with the following characteristics.
• VX has to intersect UW at V.
,• VX is perpendicular to UW.
,• U, V, and W are collinear.
Based on the given information, we have the following diagram
The image above shows the answer.
Type the correct answer in each box. Use numerals instead of words.Consider this expression,-412 + 21 - 5(1 + r)What expression is equivalent to the given expression?12 + I +ResetNext
Answers
To answer this question, we need to expand the original equation, and then simplify to obtain the equivalent expression as follows:
[tex]-4x^2+2x-5(1+x)=-4x^2+2x-5(1)-5(x)[/tex]We used the distributive property for -5 (1 + 5).
Then, we have:
[tex]-4x^2+2x-5-5x=-4x^2+2x-5x-5[/tex]Adding like terms:
[tex]-4x^2-3x-5[/tex]In summary, therefore, the equivalent expression is:
[tex]-4x^2-3x-5[/tex]A bicycle has a listed price of 803.98 before tax. If the sales tax is 9.5%, fins the total cost of the bicycle with sales tax included. Round to the nearest cent its necessary.
Answers
The total cost with taxes included is given by
[tex]803.98+803.98\times\frac{9.5}{100}[/tex]which is equal to
[tex]803.98(1+\frac{9.5}{100})[/tex]which gives
[tex]\begin{gathered} 803.98(1+0.095) \\ 803.98(1.095) \end{gathered}[/tex]then, we have $880.3581. By rounding to the nearest cent, the answer is $880.36
126°r= 15 cmFind the arc length of the shaded sector.
Answers
To determine the arc length of the shaded area you have to use the following formula:
[tex]\text{arc.length}=2\pi r(\frac{\theta}{360º})[/tex]"θ" represents the measure of the central angle, in degrees
"r" represents the radius of the circle
We know that the arc measure is 126º, the central angle has the same measure as the intercepted arc, then its measure is also θ=126º
The radius of the circle is r=15cm
[tex]\begin{gathered} \text{arc.length}=2\pi\cdot15\cdot(\frac{126}{360}) \\ \text{arc.length}=30\pi\cdot\frac{7}{20} \\ \text{arc.length=}\frac{21}{2}\pi \\ \text{arclength}\approx32.98\approx33\operatorname{cm} \end{gathered}[/tex]Using the table, what is the average daily balance of the credit card for the May 1 - May 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00.
Answers
The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13
From the table given, we have
The balance of the credit card from May 1 - May 5 was 2000 which is 5 days, from may 6- may 10 was 1600, which is again 5 days, from may 11 to may 20 was 1350, the interval is 10 days and 21 to may 31, 11 days the balance was 1550.
The avergae daily balance was
=[tex]\frac{(Balance (number of days))}{Total number of days}[/tex]
= [tex]\frac{2000(5)+1350(10)+1550(11)}{5+5+10+11}[/tex]
=[tex]\frac{48550}{31}[/tex]
=1566.13
So The average daily balance for the credit card for the may 1 - may 2 billing period was 1566.13
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Consider the two expressions (6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)/(2x + 3 - 7x - 11) and 4x^2 - 7 + 1/(2x + 3 - 7x - 11)
a) Show that the two expressions represent equal numbers when x = 10
b) Explain why these two expressions do not represent equal numbers when x = -3/2
c) Show that these two expressions represent equal numbers for all x other than -3/2.
Answers
Step-by-step explanation:
a)
(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)(2x + 3 - 7x - 11)
[tex] \sf \frac{(6x^3 + 9x^2 + 4x + 7 - 17x^2 - 8x + 8)}{(2x + 3 - 7x - 11)}[/tex]
[tex] \sf = \frac{(6(10)^3 + 9(10)^2 + 4(10) + 7 - 17(10)^2 - 8(10) + 8)}{(2(10) + 3 - 7(10) - 11)}[/tex]
[tex] = \frac{ - 5175}{58}[/tex]
4x^2 - 7 + 1/(2x + 3 - 7x - 11)
[tex] \sf{ 4x^2 - 7 + \frac{1}{(2x + 3 - 7x - 11)}}[/tex]
[tex] \sf{ 4(10)^2 - 7 + \frac{1}{(2(10) + 3 - 7(10) - 11)}}[/tex]
[tex] = \sf \frac{22793}{58}[/tex]
The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a
followed by a
Answers
A 90 degree counterclockwise rotation about point A, a reflection across the y-axis, and a translation 20 units down may be used on quadrilateral ABCD to demonstrate that it is congruent to quadrilateral GHIJ.
A quadrilateral in geometry is a four-sided polygon with four edges and four corners. A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English term quadrilateral. A four-sided polygon with four angles is known as a quadrilateral. Parallelogram, rhombus, kite, rectangle, trapezoid, square, and isosceles trapezoid are the seven different forms of quadrilaterals.
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How does a reflection affect the properties of a two dimensional
Answers
Reflection:
A reflection is a transformation that flips a figure across a line.
Properties of reflection:
• The length remains the same, the angles remain the same.
,• This means that the image and the pre-image have the same size and shape only the orientation changes.
,• The line segment which connects the corresponding parts of the image and pre-image is perpendicular to the line of reflection.
,• The distance from the line of reflection of the corresponding parts of the image and pre-image is the same.
Following is an example of a reflection
This is called a horizontal reflection since the image and the pre-image is flipped across the x-axis. The line of reflection is the vertical line.
pls help l need to finish this
Answers
The equation of the linear function represented by the table below in slope-intercept form is y = -3x + 5
The linear function that will be obtained by using these values of x and y will be a Equation of line.
The slope-intercept form of line looks like this,
y = mx + c
where,
m is the slope.
c is the y intercept,
Firstly, to find the slope we can use any two points,
we will use (1,2) and (2,-1)
Hence, slope m,
m = (-1-2)/(2-1)
m = -3
Putting the value of slope in equation y = mx + c,
y = -3x + c
To fin the value of c,
Using the coordinate (1,2) and putting the values of x and y,
2 = -3 + c
c = 5.
Putting the values of c and m in the equation,
we get,
y = -3x + 5.
The required equation of the line in slope-intercept form is y = -3x + 5
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The values of x and y
Answers
The values of x and y are 26° and 54° respectively.
Consider the triangle with x is triangle 1
Triangle with y is triangle 2
In triangle 1
Since it is a right angled triangle one angle is already known
Another angle is 64°
We know the sum of interior angles of a triangle is equal to 180
Hence 90 + 64 +x = 180°
154 + x = 180°
x= 180 - 154
x = 26°
From triangle 2 it is evident that x and y are complementary angles which means they sum up to 90°
Hence x + y = 90°
26 + y = 90
y = 90 - 26
y = 54°
Hence the value of x and y are 26° and 54° respectively
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At preseident Obama's inauguration in 2013 the newspaper head lines stated there were about 800.000 people in attendance if the newspaper rounded to the nearest hundred thousand what is the largest number and smallest number of people who could have been there
Answers
The smallest whole number is 750,000, while the largest whole number is 849,999.
Consider the facts offered.
We must determine the smallest whole integer that, when rounded to the nearest hundred thousands, equals 800,000
Rounding a numerical rule
If the number on the right side of the rounding digit is 0, 1, 2, 3, 4, there is no need to modify the rounding digit and replace the remainder of the digit on the right with 0.
If the number on the right side of the rounding digit is 5, 6, 7, 8, 9, the rounding digit rounds up by one number and replaces the remainder of the digit on the right with 0.
Consider the number 800,000 for a moment.
Because we want the smallest number possible, the number at the hundred thousand place should be 7.
As a result, the smallest whole number is 750,000.
We now want the largest whole number that rounds to 800,000
Similarly, the biggest whole number must be bigger than 800,000 We don't want to raise the number at the hundred thousand place, hence the best ten thousand place option is 4. Put 9 at the rest locations to get the highest number.
As a result, the biggest whole number is 849,999.
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I can’t seem to understand this. I need 2 solutions and the work. If you could explain the work so I can do it in the future that would be great!!
Answers
Given:
Ethan is 23 years older than Evan
So, let Ethan is (x) years old
And Evan is (y) years old
So, the difference between them is 23 years old
so, x - y = 23
And the sum of Ethan and Evan's age is 43
so, x + y = 43
So, we have the following system of equations:
[tex]\begin{gathered} x-y=23 \\ x+y=43 \end{gathered}[/tex]add the equations to eliminate (y):
[tex]\begin{gathered} (x-y)+(x+y)=23+43 \\ 2x=66 \\ x=\frac{66}{2}=33 \end{gathered}[/tex]Now, substitute with (x) into the second equation to find (y):
[tex]\begin{gathered} 33+y=43 \\ y=43-33=10 \end{gathered}[/tex]So, the answer will be:
Ethan's age = x = 33
Evan's age = y = 10
Find the coordinates of the points of intersection of the graphs with coordinate axes: y= -1/4x+2
Answers
Answer:
Solutions below.
Step-by-step explanation:
This question is asking us to find the points of intersection, which means its asking to find the x-intercept abd y-intercept.
To find the x-intercept, we know that y = 0.
Therefore we can substitute y = 0 into the line equation:
[tex]0 = - \frac{1}{4} x + 2 \\ - \frac{1}{4} x = - 2 \\ x = - 2 \div - \frac{1}{4} \\ = 2 \times 4 \\ = 8[/tex]
Therefore the point of the x-intercept is (8,0).
Likewise to find the y-intercept, we know x = 0.
Therefore we can substitute x = 0 into the line equation:
[tex]y = - \frac{1}{4} (0) + 2 \\ = 0 + 2 \\ = 2[/tex]
Therefore the point of the y-intercept is (0,2).
Answer:
x-intercept: (8, 0)
y-intercept: (0, 2)
Step-by-step explanation:
Given equation:
[tex]y=-\dfrac{1}{4}x+2[/tex]
The graph intersects the y-axis when x = 0.
To find the graph's y-intercept, substitute x = 0 into the equation and solve for y:
[tex]\begin{aligned}x=0 \implies y&=-\dfrac{1}{4}(0)+2\\y&=0+2\\y&=2\end{aligned}[/tex]
Therefore, the coordinates of the point of intersection with the y-axis are:
(0, 2)The graph intersects the x-axis when y = 0.
To find the graph's x-intercept, substitute y = 0 into the equation and solve for x:
[tex]\begin{aligned}y=0\implies \-\dfrac{1}{4}x+2&=0\\-\dfrac{1}{4}x&=-2\\x&=8\end{aligned}[/tex]
Therefore, the coordinates of the point of intersection with the x-axis are:
(8, 0)4. There are 6 red, 5 white, 3 blue, and 4 green marbles in a bag. What is the probability of selecting a red marble, given that a blue marble was already selected?5. While playing Blackjack, an Ace is dealt. To get Blackjack, or 21, a card worth 10 is needed. This could be a 10, Jack, Queen, or King. What is the probability of not getting Blackjack?
Answers
Let sin 0 = 4/9. Find the exact value of cos 0.
Answers
we have the following
[tex]\sin \theta=\frac{4}{9}[/tex]sin of an angle is the same as:
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]therefore we can create the following right triangle:
we can calculate the adjacent side using the pythagorean theorem
[tex]h^2=a^2+b^2[/tex]where h is the hypotenuse, a is the adjacent side and b the opposite side to the angle.
thus, the adjacent side is:
[tex]a=\sqrt[]{h^2-b^2}=\sqrt[]{9^2-4^2}=\sqrt[]{81-16}=\sqrt[]{65}[/tex]Using that value, we can now calculate cos of the angle
[tex]\cos \theta=\frac{adjacent}{hypotenuse}[/tex][tex]\cos \theta=\frac{\sqrt[]{65}}{9}[/tex]which can't be simplify, thus that is the answer for the exact value
8y=5x-15;y=10 which is the answer
Answers
Since we have that y = 10, then:
[tex]8\cdot(10)=5x-15[/tex][tex]80=5x-15\Rightarrow80+15=5x-15+15\Rightarrow95=5x+0[/tex]Then
[tex]5x=95\Rightarrow\frac{5}{5}x=\frac{95}{5}\Rightarrow x=19[/tex]In the first part, we need to sum 15 to both sides of the equation.
In the second part, we divide both sides by 5.
Then, x = 19.
College Algebra
A winery has a vat with two pipes leading to it. The inlet pipe can fill the vat in 5 hours, while the outlet pipe can empty it in 8 hours. How long will it take to fill the vat if both pipes are left open?
It will take__ hours.
(Simplify your answer. Do not round.)
Answers
Answer:
3 1/13
Step-by-step explanation:
rate(time) of one pipe + rate(time) of the other pipe = 1 job
The rate would be the the number of jobs over the time
The rate of the first pipe is 1/5 and the rate of the second pipe is 1/8.
Together:
1/5t + 1/8t = I job
t(1/5 + 1/8) = 1
t(8/40 + 5/40) = 1
t(13/40) = 1 multiply each side by 40/13
t(40/13)(13/40) = 1(40/13)
t = 40/13
t = 3 1/13
Which of the following numbers represents the place the digit 8 as 80?
Answers
Ai Mi was out at a restaurant for dinner when the bill came. Her dinner came to $9. After adding in a tip, before tax, she paid $11.79. Find the percent tip.
Answers
The percent tip which Ai mi added to the $9 dinner as required in the task content is; 31%.
What percent tip did Ai mi add to the dinner as described?It follows from the task content that the percent tip which Ai mi added to the dinner is to be determined by evaluation.
Since the dinner itself costs; $9 and she paid $11.79 after adding tip, it follows that the percent tip is the percentage change in price paid per unit original price as follows;
Percent tip = { ( 11.79 - 9 ) / 9} × 100%
Percent tip = 2.79/9 × 100%
Percent tip = 31%.
Therefore, the percent tip added by Ai mi to the original price of dinner is ; 31%.
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What is the area of this figure?
5 mm
19 mm
36 mm
7 mm
8 mm
7 mm
13 mm
9 mm
Write your answer using decimals, if necessary.
9 mm
11 mm
Answers
Explanation:
19x5 = 95
8x7 = 56
7x9 = 63
13x9 = 117 but since its a triangle you divide it by 2 so 58.5
Add all of these together and you get 272.5
At an animal shelter, 3/8 of the animals are dogs. Of the
dogs, 2/5 have spots. What portion of the animals at the
shelter are dogs that have spots?
Answers
At an animal shelter, 3/8 of the animals are dogs, of the dogs, 2/5 have spots, 3/20 portion of the animals at shelter are dogs that have spots. A fraction, which derives from Latin word fractus, which means "broken," is a portion of whole or, more broadly, any number of equal pieces.
What is a fraction?A fraction, which derives from Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of particular size there are when stated in ordinary English. A common, vulgar, or simple fraction is one that has a non-zero denominator that is displayed below (or after) line on which the numerator is shown. Compound fractions, complicated fractions, and mixed numeral fractions are the examples of uncommon fractions that use numerators and denominators.
The numerator and the denominator of positive common fractions are both natural integers. The denominator shows how many of numerator's equal parts make up a unit or whole, and the numerator reflects the number of equal parts. Since there can never be zero components in a whole, denominator cannot be zero. For instance, numerator 3 in the fraction 3/4 denotes that the fraction is made up of 3 equal parts, while denominator 4 denotes that the fraction is made up of 4 parts altogether.
Let, [tex]\frac{3}{8} x[/tex] animals are dogs,
[tex]\frac{2}{5} * \frac{3}{8}x = \frac{3}{20}x[/tex]
Therefore, [tex]\frac{3}{20}[/tex] of the animals at shelter are dogs that have spots.
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Jessica evaluates √2 on her calculator which
shows a value of 1.4142136.
She then writes √/2 =1.4142136.
Is she correct explain
Answers
Generally, one should not write down values such as this directly from a calculator. √2 is an irrational number, which means that instead of writing it as a terminating decimal, it is best to write it in its exact form (√2) to ensure accuracy for further calculations.
bvhftfgtfygygfygygftfghh vv g f f fyk jf khvy. ynnnnnnnnnnnnnn
Answers
what the??????????????
Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including allanswers in [0, 2x) and indicating the remaining answers by using n to represent any integer. Round your answer to four decimal places, if necessary. If there is nosolution, indicate "No Solution."cos(x) + cos(x) = 4cos(x) + 4
Answers
The solutions to the quadratic trigonometric equation are given as follows:
x = kπ, k = ± 1, ± 3, ± 5, ± 7.
How to solve the quadratic trigonometric equation?The quadratic trigonometric equation is defined as follows:
cos²(x) + cos(x) = 4cos(x) + 4.
Then the following transformation is applied to solve the equation:
y = cos(x).
Hence:
y² + y = 4y + 4
y² - 3y - 4 = 0
(y - 4)(y + 1) = 0.
Applying the Factor Theorem, the solutions are given as follows:
y - 4 = 0 -> y = 4.y + 1 = 0 -> y = -1.However, we want the solutions for x, hence they are obtained as follows:
cos(x) = 4.
x = arccos(4), which has no solution, as there are no angles with a cosine of four.
cos(x) = -1.
x = arccos(-1)
x = kπ, k = ± 1, ± 3, ± 5, ± 7
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. Lisa, Bret, and Gary harvested apples.
Lisa filled 3 carts with apples. Bret also
filled 3 carts with apples. Gary filled
another 3 carts with apples. Write a
multiplication equation and a division
equation for this story.
Answers
Multiplication:
Lisa, Bret, and Gary harvested apples. If they each harvested 3 carts of apples, how many carts did they harvest in total?
--> 3 * 3 = 9 carts in total
Division:
Lisa, Bret, and Gary harvested apples. If all three of them harvested 9 carts of apples in total, how many carts did each person harvest.
--> 9 / 3 = 3 carts per person
(2a² + 7a - 10) (a – 5)
Answers
2a³ - 3a² - 45a + 50 is the simplified form of the expression ( 2a² + 7a - 10 )( a - 5 ) using FOIL method.
What is the simplified form of the given expression?Given the expression in the question;
( 2a² + 7a - 10 )( a - 5 )
To expand ( 2a² + 7a - 10 )( a - 5 ), multiply each term in the first expression by each term in the second expression.
( 2a² + 7a - 10 )( a - 5 )
a( 2a² + 7a - 10 ) -5( 2a² + 7a - 10 )
a×2a² + a×7a + a×-10 -5×2a² -5×7a -5×-10
Multiply a and 2a²
2a³ + a×7a + a×-10 -5×2a² -5×7a -5×-10
Multiply a and 7a
2a³ + 7a² + a×-10 -5×2a² -5×7a -5×-10
Multiply a and -10
2a³ + 7a² - 10a -5×2a² -5×7a -5×-10
Multiply -5 and 2a²
2a³ + 7a² - 10a - 10a² -5×7a -5×-10
Multiply -5 and 7a
2a³ + 7a² - 10a - 10a² - 35a -5×-10
Multiply -5 and -10
2a³ + 7a² - 10a - 10a² - 35a + 50
Collect and add like terms
2a³ + 7a² - 10a² - 10a - 35a + 50
2a³ - 3a² - 45a + 50
Therefore, the simplified form of the expression is 2a³ - 3a² - 45a + 50.
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Isabel will rent a car for a day. The rental company offers two pricing options: Option A and Option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below.
Answers
(a) Option B, 30
At 180 miles, Option B costs $50, but Option A costs $80.(b) 60, Option A
The cost is the same when the graphs intersect.Before 60 miles, the graph for Option A is lower than the graph of Option B, meaning Option A will cost less money.