The equation and graph of a polynomial are shown below. The graph reachesits minimum when the value of xis 4. What is the y-value of this minimum?--y= 2x2-16x + 30ys
Answers
We can find the y-value of the minimum using the graph or using the equation. Let's use the equation and evaluate it when x = 4.
[tex]\begin{gathered} y=2x^2-16x+30=2(4)^2-16(4)+30 \\ y=2\cdot16-64+30=32-64+30=-2 \end{gathered}[/tex]Hence, the y-value of the minimum is -2.Related Questions
What is the range of the function f(x) = |x| + 5? R: {f(x) ∈ ℝ | f(x) < 5} R: {f(x) ∈ ℝ | f(x) ≥ 5} R: {f(x) ∈ ℝ | f(x) > 5} R: {f(x) ∈ ℝ | f(x) ≤ 5}
Answers
Given:
[tex]f(x)=|x|+5[/tex]Find-: Range of a function.
Sol:
For |x| is always positive because |x| function is:
[tex]|x|=\begin{cases}-x\text{ at x<0} \\ x\text{ at x>0}\end{cases}[/tex]So the range is:
[tex]\lbrace f(x)\in\Re|f(x)\ge5\rbrace[/tex]What is your favorite song and why? Does it mean something to you or do you just enjoy the sound of it/the lyrics? Enjoy the points :)
Answers
Answer:
Step-by-step explanation:
my favorite song is Sia's unstoppable song. I think it conveys a lot of energy and always while I listen to it I get points and am inspired to do better.
A catering service offers 3 appetizers, 7 main courses, and 4 desserts. A customer is to select 2 appetizers, 3 main courses,and 3 desserts for a banquet. In how many ways can this be done?
Answers
General category: Mathematics
Sub-category: Probability
Topic: counting techniques
Introduction:
The combination formula C(n,r) shows us the number of ways of picking r unordered outcomes from n possibilities. For n ≥ r ≥ 0, C(n,r) is given by the following formula:
[tex]C(n,r)=\frac{n!}{r!(n\text{ -r})!}[/tex]Explanation:We can use combinations and fundamental counting principles to answer this question.
Let us denote by "a", the number of selection of appetizers. This number can be calculated as follows:
[tex]C(3,2)=\frac{3!}{2!(3\text{ -2})!}=3[/tex]Now, let us denote by "b", the number of selection of main courses. This number can be calculated as follows:
[tex]C(7,3)=\frac{7!}{3!(7\text{ -3})!}=35[/tex]Finally, let us denote by "c", the number of selection of desserts. This number can be calculated as follows:
[tex]C(4,3)=\frac{4!}{3!(4\text{ -3})!}=4[/tex]Now, applying the multiplication principle we get the desired number:
[tex]C(3,2)\cdot C(7,3)\cdot C(4,3)=3\cdot35\cdot4\text{ = 420}[/tex]We can conclude that the correct answer is:
A water sample shows 0.036 grams of some trace element for every cubic centimeter of water. Hudson uses a container in the shape of a right cylinder with a radius of 7.3 cm and a height of 12.2 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Hudson collected? Round your answer to the nearest tenth.
Answers
We have a water that has a concentration of 0.036 grams per cm³ of some trace element.
We have to find how much of this trace element will be in the container with the sample of water.
This amount will be equal to the volume of the container times the concentration of the trace element.
We start by calculating the volume.
The container is a cylinder. Its volume will be the base area times the height.
We can calculate it as:
[tex]\begin{gathered} V=A_bh \\ V=(\pi r^2)h \\ V=\pi(7.3)^2(12.2) \\ V=\pi(53.29)(12.2) \\ V\approx2042.4688\text{ }cm^3 \end{gathered}[/tex]We can multiply this volume by the concentration as:
[tex]\begin{gathered} m=C\cdot V \\ m=0.036\text{ }\frac{g}{cm^3}\cdot2042.4688\text{ }cm^3 \\ \\ m\approx73.5\text{ }g \end{gathered}[/tex]Answer: 73.5 grams.
Lyle is a car salesman and is planning to work 5 days this week. His goal is to sell 3 cars per day. How many carsdoes Lyle hope to sell by the end of the week?cars
Answers
Firstly, there are 7 days in a week but from the information given, Lyle is planning to work for only 5 days in the week. Since his goal is to sell 3 cars per day, then the total number of cars that he would sell by the end of the week would be
5 * 3 = 15
Lyle would hope to sell 15 cars by the end of the week
Can I get help with question 1? a,b,c and d? I couldn’t take a picture of question “d”but it says “construct a frequency histogram”
Answers
The frequency histogram for the given data is attached below and the mean of the distribution is approximately 52.94°
The given frequency distribution table is given .
Using the data from the table we have to find the mean
We know that :
Mean = sum of all data/ total frequency.
From the table we see that
Mean = 52 + 7 × 5 /37 = 52.94
Standard deviation:
The formula for calculating this is given by:
[tex]{\displaystyle s_{N}={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\bar {x}}\right)^{2}}}.}[/tex]
substituting the values we get :
sd = √(73.67/37)×5
sd = 7.0056
sd ≈ 7.01
When that is not possible, the standard deviation is determined by analysing a sample of the population that is representative of the entire population and creating a statistic that is used to estimate the standard deviation of the population as a whole.
This type of statistic is called an estimator, and the estimator itself is known as a sample standard deviation .
Hence the mean of the grouped data is 52.94 and the standard deviation is 7.01 .
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How is the function in the following picture graphed on a chart?
Answers
Okay, here we have this:
which question is the odd one out
III + MMM = 3003
L - XXIX = XXI
45 x 2 = 90.00000000000000000000000000000000000000000000000000001
Answers
Here the odd one out is 45×2=90.00000000000000000000000000000000000000000000000000001.
What is roman numerals?These are the symbols used in the system of numerical notation. We can convert a natural number to a Roman numeral by modifying the placement of seven symbols. The symbol I stands for 1, V stands for 5, X stands for 10, L stands for 50, C stands for 100, and M stands for 1000. In this system, the numbers are represented by combinations of letters from the Latin alphabet. In roman numerals, alphabets are used to represent fixed positive numbers. There are mainly used by Romans. These are the symbols that are representing the numbers that do not follow the base 10 in the number system.
The numbers III + MMM = 3003 and L - XXIX = XXI are roman numerals but the number 45 × 2 = 90.00000000000000000000000000000000000000000000000000001 is a rational number.
So, the number 45 × 2 is the odd one out.
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Which of the following is not a solution for x < 8?x = 9x = 4.3x = 7.95x = -3
Answers
The expression is given as x < 8.
ExplanationThe expression x less than 8 has values
4.3 , 7.95 , -3.
AnswerHence x=9 is not a solution for x < 8.
Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true?
f(x) is decreasing for all x < 6
f(x) is increasing for all x > 6
f(x) is decreasing for all x < 3
f(x) is increasing for all x < 3
Answers
Answer: f(x) is increasing for all x < 3
D
Step-by-step explanation: I got the answer right on FLVS
Trust me I got 100%
What is the purchase price of a 50-day T-bill with a maturity value of S1,737 that eams an annual interest rate of 2 802% (Assume a 360 day year)The purchase price is (Round to two decimal places)
Answers
We need to use the next simple interest formula:
[tex]A=P(1+rt)[/tex]Where
P= Present value
r= annual interest rate in decimal form
T=time in years
A=amount after time
Hence, we have that
A= S1,737
r=2.802%/100=0.02802
t=50/360
P=?
Replacing on the given formula:
[tex]\begin{gathered} 1,737=P(1+0.02802\cdot\frac{50}{360}) \\ P=\frac{1,737}{1+0.02802\cdot\frac{50}{360}} \\ P=1730.27 \end{gathered}[/tex]Hence, the purchase price is $1730.27
Try AgainAt the city museum, child admission is $6.00 and adult admission is $9.20. On Monday, twice as many adult tickets as childtickets were sold, for a total sales of $780.80. How many child tickets were sold that day?
Answers
32 child tickets were sold on that day
Explanation:Given:
The cost per child = $6.00
let the number of child tickets = c
The cost per adult ticket = $9.20
let the number of adult tickets = a
To find:
the number of child tickets sold
On Monday:
Adult tickets = 2(children tickets)
a = 2c
Total sales on Monday = $780.80
Total sales = The cost per child (number of child tickets) + The cost per adult (number of adults tickets)
780.80 = 6(c) + 9.2(a)
substitute for a:
780.8 = 6c + 9.2(2c)
780.8 = 6c + 18.4c
780.8 = 24.4c
divide both sides by 24.4:
[tex]\begin{gathered} \frac{780.8}{24.4}\text{ = }\frac{24.4c}{24.4} \\ \\ c\text{ = 32} \end{gathered}[/tex]Hence, 32 child tickets were sold on that day
please solve it and identify what was wrong in solving it the first time
Answers
we have that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
In the triangle ABE
A+B+E=180
substitute given values
60+55+E=180
E=65 degrees
so
mRemember that
m by vertical angles
so
mIn the triangle EDC
msubstitute given values
65+85+D=180
D=30 degreesmIf a woman making $36,000 a year receives a cost-of-living increase of 2.1%, what will her new salary be?
Answers
Answer:
Her new salary is $36756
Explanation:
We need to know how much 2.1% of 36000 is, so:
[tex]\begin{gathered} \frac{x}{2.1}=\frac{36000}{100} \\ x=\frac{36000\cdot2.1}{100} \\ x=756 \end{gathered}[/tex]That corresponds to the cost of living increase.
Given the surface area of a sphere is 324ππ sq km, what is the radius of the sphere?
Answers
The surface area S of sphere is given by
[tex]S=4\pi r^2[/tex]In our case
[tex]S=324\pi[/tex]Then, we have
[tex]324\pi=4\pi r^2[/tex]By moving 4Pi to the left hand side, we have
[tex]\frac{324\pi}{4\pi}=r^2[/tex]We can cancel Pi out in numerator and denominator, then ,we get
[tex]\begin{gathered} \frac{324}{4}=r^2 \\ 81=r^2 \\ \text{therefore} \\ r=\sqrt[]{81} \end{gathered}[/tex]and the answer is r= 9 kilometers, that is, the radius is 9 km
Solve: XC - XV. Show your answer as a Roman Numeral. Standard Number 1 5 10 50 100 500 1,000 Roman Numeral 1 V X Х L с D M A) V B) VI C) VIL
Answers
To make this substraction, it is better to first convert into standard numbers then make the substraction.
In Romans,
Multiply (x + x2 + x + 1) (3x2 + 3x-3) (x3 + x2 + x + 1) (3x2 + 3x - 3) = 3x5 6x4 + 3x + 3x2 - 3 (Simplify your answer.)
Answers
Problem:
Multiply (x + x2 + x + 1) (3x2 + 3x-3) (x3 + x2 + x + 1) (3x2 + 3x - 3)
Solution:
[tex](x+x^2+x+1)(3x^2+3x-3)(x^3+x^2+x+1)(3x^2+3x-3)[/tex]this is equivalent to:
[tex](2x+x^2+1)(3x^2+3x-3)(x^3+x^2+x+1)(3x^2+3x-3)[/tex]this is equivalent to:
[tex](2x+x^2+1)(x^3+x^2+x+1)(3x^2+3x-3)^2[/tex]this is equivalent to:
[tex]9x^9+45x^8+\text{ 81}x^7+63x^6+18x^5-18x^4-45x^3-27x^2+9x+9[/tex]Then, the correct answer is:
[tex]9x^9+45x^8+\text{ 81}x^7+63x^6+18x^5-18x^4-45x^3-27x^2+9x+9[/tex]Hello I really need help with this question I’m not understanding it
Answers
The subset of the event " The two spins have a sum of 5 " is { (2,3), (3,2), (1,4) and (4,1) }
It is given that the sum of Jae's two spins was 5.
S is the sample space of spinning the spinner twice.
The collection of all the possible outcomes is termed the sample space
Subset: If every element in set A is also an element in set B, then set A is a subset of set B. Set A is therefore contained within set B.
Now, the subset of the event " The two spins have a sum of 5 "
In the spinner, there are 1, 2, 3, and 4.
So, the values that would give us a 5 are (2,3), (3,2), (1,4), and (4,1)
These are the terms that will be in the required subsets,
So, Required subset = { (2,3), (3,2), (1,4) and (4,1) }
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please help, thank you!by the way this is a two-step equation with decimals
Answers
Given data:
The given equaion is -0.9p+3.2= -1.7p.
The given equation can be written as,
[tex]\begin{gathered} -\text{0}.9p+3.2=-1.7p \\ 1.7p-0.9p=-3.2 \\ 0.8p=-3.2 \\ p=-4 \end{gathered}[/tex]Thus, the value of p is -4.
You're having a breakfast party for 483 of your closet friends and 271 like chocolate donuts. In a dozen donuts, the probability of getting a chocolate donut is 1/5. How many dozen donuts would you have to buy to ensure that all 271 people get a chocolate donut?
Answers
In a dozen donuts the probability of getting a chocolate donut is 1/5, meaning 1/5 of the 12 donuts are chocolate donuts.
Step 1.- Calculate how much 1/5 out of 12 is:
[tex]\frac{1}{5}(12)=\frac{12}{5}=2.4[/tex]In each dozen we would get 2.4 chocolate donuts
Step 2.- Calculate how many dozen are needed to get 271 chocolate donuts.
We divide 271 by 2.4 to get the answer:
[tex]\frac{271}{2.4}=112.92[/tex]Step 3: We round the answer to the nearest integer value, and we need 113 dozens of donuts to ensure that all 271 people get a chocolate donut.
Answer: 113
find the slope of the line through each pair of points (3,0) , (-11, -15)
Answers
Given:
points (3,0) , (-11, -15)
Required:
Slope
Solution:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{slope}=\frac{-15-0}{-11-3_{}}=\frac{-15}{-14}=\frac{15}{14}[/tex]Answer:
[tex]\text{slope}=\frac{15}{14}[/tex]A. Make box-and-whisker plots to represent the temperature data for Oakville and Fairview.
B. What conclusions can you make about the temperatures in August in the two cities?
C. Luis finds that the average August temperature in Fairview in 2004 was 73°. How would including this additional data value change the box-and-whisker plot you made in part (a)? Would it change the conclusions you made in part (b)?
Answers
Answer:
In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.
lower air temperature and less precipitation
Graphs that Describe Climate Climographs show monthly average temperatures and precipitation totals on a single graph.
Step-by-step explanation:
Carey creates the table to him determine 75% of 36
Answers
The table made is correct, so we conclude that 3/4 is equivalent of 75%. However, we must apply this percentage, or fraction, to the whole number we want to take the percentage of, that is, 36.
The number 27 is the actuall result of taking this percentage.
So, the correct expression would be:
[tex](\frac{3}{4})(36)[/tex]Thus, we need to change the 27 to 36, first alternative.
Explain two ways to evaluate 32(13+18)
Answers
The given expression is
[tex]32(13+18)[/tex]To evaluate this expression, first, we use the distributive property
[tex]32(13+18)=32\cdot13+32\cdot18=416+576=992[/tex]Therefore, the answer is 992.Liam placed 24 patio pavers as shown below.
A rectangular array shows four patio pavers wide by six patio pavers long. The total length of the side of the rectangle that has four patio pavers is sixty-three and two-tenths inches.
What is the length of a single patio paver?
A.
18.2 in.
B.
15.8 in.
C.
10.53 in.
D.
2.63 in.
Answers
4 patio pavers = 63.2 inches
1 patio pavers = 15.8 inches.
The length of one patio paver is 15.8 inches.
What is a rectangle?
A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The total length of the side of the rectangle that has four patio pavers is sixty-three and two-tenths inches.
This means,
Length of the side with 4 patio pavers.
= 63(2/10) inches
= 632/10
= 63.2 inches
Now,
The length of one patio paver.
4 patio pavers = 63.2 inches
Divide both sides by 4.
1 patio pavers = 63.2/4
1 patio pavers = 15.8 inches.
Thus,
The length of one patio paver is 15.8 inches.
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Charlotte spent $26 at the hair salon. She wants to leave a 12% tip. About how much money should she leave?
Answers
We will have the following:
[tex]t=26+(0.12)(26)\Rightarrow t=29.12[/tex]So, she shoulld leave $29.12 in total.
Hello I'M Having trouble with this problem
Answers
Percent decrease in average number of visit is 50%.
Define average.The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average. Because it offers a single, typical value to represent an entire data collection, the mean is useful. It is one of many approaches to identify central tendency and represents the arithmetic average.
Given,
Average in first week = 48000
Average in second week = 24000
Average decrease = 48000 - 24000
Average decrease = 24,000
Percent decrease in average number of visit:
24000/48000 × 100
1/2 × 100
50%
Percent decrease in average number of visit is 50%.
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The initial value of your new car was $20,000. After one year, the value of the car is $18,000.What will the approximate value of the car be in 7 years?$8,000.00O $8,565.94$9,000.00$9,565.94
Answers
Answer:
The approximate value of the car after 7 years is;
[tex]\text{ \$9,565.94}[/tex]Explanation:
Given that the initial value of the car is;
[tex]P=\text{ \$20,000}[/tex]after 1 year its new value is;
[tex]\text{ \$18,000}[/tex]The rate of depreciation is;
[tex]r=\frac{18000}{20000}=0.9\text{ per year}[/tex]After 7 years the value of the car can be calculated using the formula;
[tex]F=P(r)^t[/tex]where t equals 7 years.
substituting the values;
[tex]\begin{gathered} F=20000(0.9)^7 \\ F=\text{ \$9,565.94} \end{gathered}[/tex]Therefore, the approximate value of the car after 7 years is;
[tex]\text{ \$9,565.94}[/tex]Hello I don't know if you can help me with this
Answers
we have that
In this problem we have an arithmetic sequence
the general equation is equal to
an=a1+D(n-1)
where
a1 is the first term
D is the common difference
n is the number of terms
so
a1=7
D is the difference between consecutive terms
D=11-7=4
an=7+4(n-1)
change the variables
d=7+4(n-1)
d=7+4n-4
d=4n+3
For n=30
d=4(30)+3
d=123When finding the composition of f (g (x) )substitute f (x) for the x in g (x)multiply f (x) by g (x)substitute g (x) for the x in f (x)
Answers
Okay, here we have this:
Considering that the composition of function is formed by taking the outputs of one function and converting them into the inputs of another function. We obtain that, f(g(x)), consists of taking the result obtained by evaluating g (x) and replacing it by x in f (x). Then the correct answer is the third option.