Answers
C. 6
Explanation
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.so
Step 1
given
[tex]2(x-4)+3x-x^2[/tex]a)let
[tex]x=2[/tex]b) now, replace and calculate
[tex]\begin{gathered} 2(x-4)+3x-x^2 \\ 2(2-4)+3(2)-(2^2) \\ 2(-2)+6-4 \\ -4+6-4 \\ -4+6-4=6 \end{gathered}[/tex]therefore, the answer is
C. 6
I hope this helps you
Related Questions
The heights, in feet, of 12 trees in a park are shown below.8, 11, 14, 16, 17, 21, 21, 24, 27, 31, 43, 47Use the drop-down menus to explain the interquartile range of the data.
Answers
Given:
The heights, in feet, of 12 trees in a park are:
8,11,14,16,17,21,21,24,27,31,43,47.
Required:
To find the interquartile range of the given data.
Explanation:
We have given the heights of 12 trees in feet.
Therefore, the total number of quantitties (elements) in given data is even.
Thus, the median (M) of the data is,
[tex]\begin{gathered} M=\frac{21+21}{2} \\ \Rightarrow M=\frac{42}{2} \\ \Rightarrow M=21 \end{gathered}[/tex]The median (Q) of the first half of the data 8,11,14,16,17 is given by,
[tex]Q=14[/tex]since the number of quantities are odd.
The median (Q') of the second half of the data 24,27,31,43,47 is given by,
[tex]Q^{\prime}=31[/tex]since the number of quantities are odd.
Hence, the interqurtile range (R) is,
[tex]\begin{gathered} R=Q^{\prime}-Q \\ \Rightarrow R=31-14 \\ \Rightarrow R=17 \end{gathered}[/tex]Final Answer:
The interquartile range is,
[tex]R=17[/tex]The first option is spread.
The second option is range.
The third option is 17.
The fourth option is middle 50%.
it snowed 20 inches in 10 days in Montreal. Find the unit rate.
Answers
the expression is
[tex]\frac{20}{10}[/tex]We must divide each value by the value of the denominator to obtain the unit ratio
so
[tex]\frac{\frac{20}{10}}{\frac{10}{10}}=\frac{2}{1}=2[/tex]the unit ratio is 2 inches per day
1. Which expression is equivalent to 2 x (5 x 4)?a. 2+ (5 x 4)b. (2 x 5) x 4c. (2 x 5) x 4d. (5 x 4) x (2 X4)
Answers
We are given the following expression
[tex]2\times(5\times4)[/tex]Recall the associative property of multiplication
[tex]a\times(b\times c)=(a\times b)\times c[/tex]The associative property of multiplication says that when you multiply numbers, you can group the numbers in any order and still you will get the same result.
So, if we apply this property to the given expression then it becomes
[tex]2\times(5\times4)=(2\times5)\times4[/tex]Therefore, the following expression is equivalent to the given expression.
[tex](2\times5)\times4[/tex]use the distributive property to simplify the left side of the equation 2(x/8+3)=7+1/4x
Answers
Given data:
The given expression is 2(x/8+3)=7+1/4x.
The given expression can be written as,
2(x/8)+2(3)=7+1/4x
x/4+6=7+1/4x
x/4-1/4x=7-6
x/4-1/4x=1
x^(2)-1=4x
x^(2)-4x-1=0
Thus, the final expression is x^(2)-4x-1=0 after applying distributve property on left side.
2. Graph the image of Parallelogram WXYZ under a translation 4 units to the left and 6 units up
Answers
Translation 4 units to the left transforms the point (x, y) into (x-4, y). Applying this rule to the parallelogram WXYZ, we get:
W(0, -2) → (0-4, -2) →W'(-4, -2)
X(2, -2) → (2-4, -2) → X'(-2, -2)
Y(2, -5) → (2-4, -5) → Y'(-2, -5)
Z(0, -5) → (0-4, -5) → Z'(-4, -5)
Translation 6 units up transforms the point (x, y) into (x, y+6). Applying this rule to the parallelogram W'X'Y'Z', we get:
W'(-4, -2) → (-4, -2+6) → W''(-4, 4)
X'(-2, -2) → (-2, -2+6) → X''(-2, 4)
Y'(-2, -5) → (-2, -5+6) → Y''(-2, 1)
Z'(-4, -5) → (-4, -5+6) → Z''(-4, 1)
Where the parallelogram W''X''Y''Z'' is the image of Parallelogram WXYZ translated 4 units to the left and 6 units up, as can be seen in the next graph:
martin earns $23.89 per hour proofreading ads at a local newspaper.His weekly wage w can be describe by the equation w= 23.89h, where h is the number of hours worked (a). write the equation in function notation (b). find f(23) f(35) and f(41)
Answers
SOLUTION
(a) The equation in function notation is
[tex]\begin{gathered} w=23.89h=f(h) \\ w=f(h)=23.89h \end{gathered}[/tex]Hence the answer is
[tex]w=f(h)=23.89h[/tex](b). f(23) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(23)=23.89\times23 \\ f(23)=549.47 \end{gathered}[/tex]f(35) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(35)=23.89\times35 \\ f(35)=836.15 \end{gathered}[/tex]f(41) becomes
[tex]\begin{gathered} f(h)=23.89h \\ f(41)=23.89\times41 \\ f(h)=979.49 \end{gathered}[/tex]In the diagram below, if < ACD = 54 °, find the measure of < ABD
Answers
Opposite angles in a quadrilateral inscribed in a circle add up to 180, therefore:
[tex]\begin{gathered} m\angle ACD+m\angle ABD=180 \\ 54+m\angle ABD=180 \\ m\angle ABD=180-54 \\ m\angle ABD=126^{\circ} \end{gathered}[/tex]Answer:
b. 126
determine the value of x nodes following quadrilateral
Answers
The value of x nodes given quadrilateral is 80° which is determined by the measure of the supplemental interior angle.
What is the quadrilateral?A quadrilateral is a polygon with four sides. This also indicates that a quadrilateral has four vertices and four angles.
Exterior Angle is defined as an angle produced on the outside of a polygon by extending the sides of the polygon.
First, we have to find the measure of the supplemental interior angle
Here take the exterior angle1 = 100° and exterior angle2 = 60°, find its interior angles
⇒ 100 + int.1 = 180 ⇒ int.1 = 180 - 100 = 80°
⇒ 60 + int.2 = 180 ⇒ int.2 = 180 - 60 = 120°
Since the sum of all interior angles of a polygon = 360°
As per the given figure,
x + 80 + x + 120 = 360
2x = 360 - 200
2x = 160
x = 80°
Therefore, the value of x nodes given quadrilateral is 80°.
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Assume that 5 cards are drawn from a standard deck of 52 cards. How many ways can I get 3 sevens, 1 six and 1 five?
Answers
Answer
64 ways
Explanation
In a standard deck of 52 cards, there are four 'sevens', four 'sixes' and four 'fives'.
Using Combination formula, the number of ways to pick 3 sevens, 1 six and 1 five is given as
⁴C₃ × ⁴C₁ × ⁴C₁
= 4 × 4 × 4
= 64
Hope this Helps!!!
Solye for x.7(x - 3) + 3(4 - x) = -8
Answers
Explanation
Step 1
apply the distributive property to eliminate the parenthesis
[tex]\begin{gathered} 7(x-3)+3(4-x)=-8 \\ 7x-21+12-3x=-8 \end{gathered}[/tex]Step 2
add similar terms
[tex]\begin{gathered} 7x-21+12-3x=-8 \\ 4x-9=-8 \end{gathered}[/tex]Step 3
add 9 in both sides
[tex]\begin{gathered} 4x-9=-8 \\ 4x-9+9=-8+9 \\ 4x=1 \end{gathered}[/tex]Step 4
divide each side by 4
[tex]\begin{gathered} 4x=1 \\ \frac{4x}{4}=\frac{1}{4} \\ x=\frac{1}{4} \end{gathered}[/tex]Question 2, please let me know if you have any questions regarding the materials, I'd be more than happy to help. Thanks!
Answers
Mean Value Theorem
Supposing that f(x) is a continuous function that satisfies the conditions below:
0. f(x) ,is continuous in [a,b]
,1. f(x) ,is differentiable in (a,b)
Then there exists a number c, s.t. a < c < b and
[tex]f\mleft(b\mright)-f\left(a\right)=f‘\left(c\right)b-a[/tex]However, there is a special case called Rolle's theorem which states that any real-valued differentiable function that attains equal values at two distinct points, meaning f(a) = f(b), then there exists at least one c within a < c < b such that f'(c) = 0.
As in our case there is no R(t) that repeats or is equal to other R(t), then there is no time in which R'(t) = 0 between 0 < t < 8 based on the information given.
Answer: No because of the Mean Value Theorem and Rolle's Theorem (that is not met).
An air plane can cruise at 640mph. How far can it fly in 3/2 Ths of an hour?
Answers
Answer: 960 miles
3/2 of an hour would be 1 hour and 30 min or an hour and a half
640mph (mph = miles per hour)
1/2 of an hour is 30 minutes so its 640 miles in half so 320
now all you gotta do is add it
so 640 + 320 = 960
use accounting principles to find the number of outcomes: How many ways can Mark create a 4-digitcode for his garage door opener?
Answers
To creat a 4 - digit code, we need to consider that for each digit we have 10 options:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 -----> 10 options for each digit.
Next, we multiply the number of options we have for each digit. In this case, since we need the code to have 4 digits:
[tex]10\times10\times10\times10[/tex]We multiply 4 times 10.
And the result is:
[tex]10\times10\times10\times10=10,000[/tex]He has 10,000 ways to create a 4-digit code.
if sound travels at 335 miles per second through air and a plane is 2680 miles away how long will the sound take to reach the people
Answers
It will take 8 seconds for the sound to reach the people
Here, we want to calculate time
Mathematically;
[tex]\begin{gathered} \text{time = }\frac{dis\tan ce}{\text{speed}} \\ \end{gathered}[/tex]With respect to this question, distance is 2680 miles while speed is 335 miles per second
Substituting these values, we have;
[tex]\text{time = }\frac{2680}{335}\text{ = 8}[/tex]2. Mr. Cole took a walk with his wife. They walked 4.4 miles in 1.4 hours. What was their average speed inmiles per hour?
Answers
Mr. Cole took a walk with his wife.
They walked 4.4 miles in 1.4 hours.
So we have
Distance = 4.4 miles
Time = 1.4 hours
We are asked to find the average speed in miles per hour.
The average speed is given by
[tex]S=\frac{D}{t}[/tex]Where D is the distance and t is the time.
[tex]S=\frac{4.4}{1.4}=3.142[/tex]Therefore, their average speed is 3.142 miles per hour.
Justin and poor friends are going to a movie each person buys a movie ticket that costs one 50 less than the square of $3 of the friends bought a bag of popcorn and a small soda that cost $2.25 more than the score of $2 right expression that can be used to find the total amount that Justin is trying to at the movies
Answers
Answer:
4(3² - 1.5) + 3(2² + 2.25)
Explanation:
First, they buy 4 tickets that cost $1.50 less than the square of $3. So, we can express that as follows:
4 x (3² - 1.5)
Then, they buy 3 bags of popcorn and a small soda that cost $2.25 more than the square of $2, so the expression for this is:
3 x (2² + 2.25)
Therefore, the numerical expression that can be used to find the total amount is the sum of the expression above:
4 x (3² - 1.5) + 3 x (2² + 2.25)
4(3² - 1.5) + 3(2² + 2.25)
So, the answer is:
4(3² - 1.5) + 3(2² + 2.25)
Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 12 minutes. Consider 49 of the races.
Let
X = the average of the 49 races.
Please see attachment for questions
Answers
Using the normal distribution and the central limit theorem, it is found that:
a) The distribution is approximately N(145, 1.71).
b) P(143 < X < 148) = 0.8389.
c) The 70th percentile of the distribution is of 145.90 minutes.
d) The median is of 145 minutes.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In the context of this problem, the parameters are defined as follows:
[tex]\mu = 145, \sigma = 12, n = 49, s = \frac{12}{\sqrt{49}} = 1.71[/tex]
The distribution of sample means is approximately:
N(145, 1.71) -> Insert the mean and the standard error.
The normal distribution is symmetric, hence the median is equal to the mean, of 145 minutes.
For item b, the probability is the p-value of Z when X = 148 subtracted by the p-value of Z when X = 143, hence:
X = 148:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (148 - 145)/1.71
Z = 1.75
Z = 1.75 has a p-value of 0.9599.
X = 143:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (143 - 145)/1.71
Z = -1.17
Z = -1.17 has a p-value of 0.1210.
Hence the probability is:
0.9599 - 0.1210 = 0.8389.
The 70th percentile is X when Z has a p-value of 0.7, so X when Z = 0.525, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
0.525 = (X - 145)/1.71
X - 145 = 0.525(1.71)
X = 145.90 minutes.
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Hi I am really confused on this problem and would like help on solving it step by step
Answers
Given:
An exponential function represents the graph of some of the functions given in the option.
Required:
The correct equation represents the given function.
Explanation:
The graph of the function
[tex]y\text{ = 2\lparen}\sqrt{0.3})^x[/tex]is given as
Also, the graph representing the function
[tex]y=2e^{-x}[/tex]is given as
Answer:
Thus the correct answer is option B and option D.
What is the area of the composite figure? 9 in. 12 in. 24 in 20 in 12 in 15 in 30 in. O 1,182 square inches O 1,236 square inches O 978 square inches O 924 square inches
Answers
Given data:
The given figure is shown.
The area of the given figure is,
[tex]\begin{gathered} A=(24\text{ in)}(30\text{ in)+}\frac{1}{2}(24\text{ in)(9 in)+}\frac{1}{2}(15\text{ in)}(20\text{ in)} \\ =720\text{ sq-inches+108 sq-inches+150 sq-inches} \\ =978\text{ sq-inches} \end{gathered}[/tex]Thus, the area of the composite figure is 978 sq-inches.
Can anyone help? I’ve asked this same question 6 times!
Answers
Answer: 54080
Since the first number cannot be 0 or 1, there would be only 8 possible numbers for the first number. For the second number, we can now have all 10 numbers.
The number of different combinations of numbers would then be:
[tex]8\times10=80[/tex]Then, for the first letter, we have 26 possible letters, as well as the second letter. The number of different combinations of letters would then be:
[tex]26\times26=676[/tex]So, for a license plate that has 2 numbers and 2 letters, where the first number cannot be 0 or 1, there would be:
[tex]8\times10\times26\times26=54080[/tex]I inserted a picture of the questionPlease state whether it’s A B C or DCheck all that apply
Answers
Given the initial function,
[tex]f(x)=2^x[/tex]In general, a vertical stretch/compression is expressed by
[tex]f(x)\to k\cdot f(x)[/tex]If k>1, the function gets a vertical stretch; on the other hand, if 0Therefore, in our case,
[tex]g_1(x)=\frac{1}{3}f(x)\to\text{vertical compression by a factor of 1/3}[/tex]A vertical shift is given by the following formula
[tex]\begin{gathered} f(x)+k \\ k>0\to\text{shifted up} \\ k<0\to\text{shifted down} \end{gathered}[/tex]In our case,
[tex]g(x)=g_1(x)-7\to\text{vertical shift down by 7 units.}[/tex]Therefore, the answers are B and D.
Bo rolls a fair 6-sided number cube then chooses one card from a deck of four cards numbered 1through 4. What is the probability that the number cube and the card have the same number?
Answers
the probability is 1 whole number 1 over 2
Kareem ordered some books online and spent a total of . Each book cost and he paid a total of for shipping. How many books did he buy?
(a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers , , and . Let represent the number of books.
(b) Solve the equation in part (a) to find the number of books.
Answers
Answer:
A
Step-by-step explanation:
Select the sequence of transformations that will carry rectangle A onto rectangle A'. A) reflect over y-axis, rotate 90° clockwise, then reflect over x-axis B) rotate 180° clockwise, reflect over y-axis, then translate 3 units left C) rotate 180° clockwise, reflect over x-axis, then translate 2 units left D) rotate 90° clockwise, reflect over y axis, then translate 3 units left
Answers
Let:
[tex]\begin{gathered} A=(3,4) \\ B=(4,2) \\ C=(1,-1) \end{gathered}[/tex]and:
[tex]\begin{gathered} A^{\prime}=(-3,1) \\ B^{\prime}=(-4,-1) \\ C^{\prime}=(-1,-4) \end{gathered}[/tex]After a reflection over the y-axis:
[tex]\begin{gathered} A\to(-x,y)\to A_1=(-3,4) \\ B\to(-x,y)\to B_1=(-4,2) \\ C\to(-x,y)\to C_1=(-1,-1) \end{gathered}[/tex]After a translation 3 units down:
[tex]\begin{gathered} A_1\to(x,y-3)\to A_2=(-3,1) \\ B_1\to(x,y-3)\to B_2=(-4,-1) \\ C_1\to(x,y-3)\to C_2=(-1,-4) \end{gathered}[/tex]Since:
[tex]\begin{gathered} A_2=A^{\prime} \\ B_2=B^{\prime} \\ C_2=C^{\prime} \end{gathered}[/tex]The answer is the option K.
Write an exponential expression: Let 10 be the base and an even number between 1 and 10 be the exponent.
Then write the exponential expression in expanded form and standard form.
Answers
The exponential expression as required to be chosen is; 10⁴.
The expanded form of the expression is; 10 × 10 × 10 × 10.
The standard form of the expression is; 10,000.
Exponential expressions in expanded form and Standard form.It follows from the task content that the exponential expression is to be written in expanded and standard form.
Since the exponential expression must have 10 as the base and an even number between 1 and 10 as the exponent.
An example of such exponential expression is therefore;
10⁴.
Hence, to write the expression in expanded form; it is written as a product of factors as follows;
10 × 10 × 10 × 10
Also, the expression can be written in standard form as the result of the multiplication above;
= 10,000.
Read more on exponential expressions in expanded and standard form;
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Fill in the missing numbers to complete the linear equation that gives the rule for this table.x: 1, 2, 3, 4y: 8, 28, 48, 68Y = ?x + ?
Answers
we have a table that describe the line and we need to finde the slope and the intercept with the y axis, so the slope can be found with this equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So I use the numbers in the table to fill the equation so:
[tex]\begin{gathered} m=\frac{28-8}{2-1} \\ m=\frac{20}{1} \\ m=20 \end{gathered}[/tex]now for the intercept we replace x=0 and use the coordinate (1,8) so:
[tex]20=\frac{y-8}{0-1}[/tex]and we solve for y so:
[tex]\begin{gathered} -20=y-8 \\ -20+8=y \\ -12=y \end{gathered}[/tex]So the equation is:
[tex]y=20x+(-12)[/tex]Finding the intercepts, asymptotes, domain, and range from the graph of a rational function
Answers
From the given graph
The asymptotes are the dotted lines in the graph, then
The vertical asymptote is x = 3
The horizontal asymptote is y = 1
The domain is all values of x that make the function defined
Since x can not equal 3, then
The domain is
[tex]D=(-\infty,3)\cup(3,\infty)[/tex]The range is all values of y corresponding to the values of the domain (x)
Since y can not equal 1, then
The range is
[tex]R=(-\infty,1)\cup(1,\infty)[/tex]The x-intercept is the value of x at the graph intersecting the x-axis
Since the graph intersects the x-axis at the point (6, 0), then
The x-intercept is 6
The answer is the first choice 6
The y-intercept is the value of y at the graph intersection the y-axis
Since the graph intersects the y-axis at point (0, 2_, then
The y-intercept is 2
The answer is the second answer 2
What does the point (2, 24 ) represent in the situation ?K =
Answers
Given point:
(2, 24)
To find the constant proportionality:
In general, the constant proportionality is
[tex]\begin{gathered} k=\frac{y}{x} \\ k=\frac{24}{2} \\ k=12 \end{gathered}[/tex]Hence, the constant proportionality is 12.
write your answer in exponential form. 3^9 * 3^-3
Answers
Step 1
Given;
[tex]3^9\times3^{-3}[/tex]Required; To write the answer in exponential form
Step 2
[tex]\begin{gathered} Using\text{ the index law below;} \\ a^b\times a^c=a^{bc} \\ Hence,\text{ 3}^9\times3^{-3}=3^{9-3}=3^6 \end{gathered}[/tex]Answer;
[tex]3^6[/tex]converting to slope intercept formmatch each equation to an equivalent equation written in slope intercept form.
Answers
Statement Problem: Match each equation to an equivalent equation written in slope-intercept form.
Solution:
A slope intercept form equation is written as;
[tex]y=mx+b[/tex](a)
[tex]2y-6=x[/tex]Add 6 to both sides of the equation;
[tex]\begin{gathered} 2y-6+6=x+6 \\ 2y=x+6 \end{gathered}[/tex]Divide each term by 2;
[tex]\begin{gathered} \frac{2y}{2}=\frac{x}{2}+\frac{6}{2} \\ y=(\frac{1}{2})x+3 \end{gathered}[/tex](b)
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