The zero of x = 3 will be x - 3 = 0
The zero of x = 8 will be x - 8 = 0
Therefore, the quadratic equation will be
(x - 3) and (x - 8)
(a) How high is the javelin when it was thrown? How do you know?(b) How far from the thrower does the javelin strike the ground?
The height of the javelin is given by
[tex]h(x)=-\frac{1}{20}x^2+8x+6[/tex]Here, x is the horizontal distance from the point at which the javelin is thrown.
a)
When the javelin is thrown, the horizontal distance from the point at which the javelin is thrown is zero. So, put x = 0 to find the height of the javelin when thrown. So, the distance:
[tex]\begin{gathered} h(0)=-\frac{1}{20}(0)^2+8(0)+6 \\ =0+0+6 \\ =6 \end{gathered}[/tex]Thus, the height of the javelin when it was thrown is 6 ft.
b)
When the javelin strikes the ground the value of h(x) is zero.
Find the value of x when h(x) is zero.
[tex]\begin{gathered} h(x)=0 \\ -\frac{1}{20}x^2+8x+6=0 \\ -x^2+160x+120=0 \\ x^2-160x-120=0 \end{gathered}[/tex]Now, the roots of the equation are x = 160.74 and x = -0.74.
The distance cannot be negative. So, the javelin is 160.74 ft far from the thrower when it strikes the ground.
You are a landscaper working on the design of a parking lot in a new shopping center. You are measuring the length of a grass median that will be exactly as long as four parking spots and their dividing lines. One of these spots is a handicapped spot, which is 1018 feet wide and next to the curb. The other three spots are 838 feet wide. There are four dividing lines between the spots, and each measures 18 foot. What is the length of the grass median, D?
SOLUTION
From the given information:
one of the spots is
[tex]10\frac{1}{8}ft[/tex]Other three spots are
[tex]8\frac{3}{8}ft\text{ wide}[/tex]There are four dividing line of
[tex]\frac{1}{8}\text{foot}[/tex]The total length of the grass median is:
[tex]10\frac{1}{8}+3(8\frac{3}{8})+4(\frac{1}{8})[/tex]Calculate the value
[tex]\begin{gathered} \frac{81}{8}+3(\frac{67}{8})+\frac{4}{8} \\ =\frac{81}{8}+\frac{201}{8}+\frac{4}{8} \\ =\frac{81+201+4}{8} \\ =\frac{286}{8} \end{gathered}[/tex]Reduce the fraction
[tex]\frac{286}{8}=35\frac{6}{8}=35\frac{3}{4}[/tex]Therefore the length of the grass median is
[tex]35\frac{3}{4}[/tex]I need help with solving this: what is the 8th term to 1,5,25,125,..
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
1,5,25,125,..
Step 02:
[tex]an=5^{n-1}[/tex]if n = 8
[tex]a_8=5^{8-1}=5^7=78125[/tex]The answer is:
8th term is 78125
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
Ethan's income is 4500 per month a list of some of his expenses appear below what percent of Ethan's expenses is food?
Ethan's earns 4500$ per month*
the amount spent on the food is 600 $
so percentage will be'
[tex]=\frac{4500}{600}=\frac{1500}{200}=7.5\text{ \%}[/tex]so the answer is the percentage amount spent on food is, 7.5 %
JCPenney sells jeans for $49.50 that cost $38.00. What is the percent markup on cost? Check the cost. (Round your answer to the nearest hundredth percent.)
The percent mark up on the cost is 30.26%.
How to find the percent mark-up on cost?JCPenney sells jeans for $49.50 that cost $38.00.
The percent mark up can be calculated as follows:
Mark up percentage is calculated by dividing the gross profit of a unit by the cost of that unit.
In other words, Mark-up percentage is the difference between a product's selling price and cost as a percentage of the cost.
Hence,
selling price = $49.50
cost price = $38.00
mark up = 49.50 - 38 = 11.5
Therefore,
percent mark up = 11.5 / 38 × 100
percent mark up = 1150 / 38
percent mark up = 30.2631578947
Therefore,
percent mark up = 30.26%
learn more on percent mark up here: brainly.com/question/12284542
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Find the perimeter of the isosceles triangle in simplest form. x2 + 20 units 2x units
The perimeter of an isosceles triangle is given by:
[tex]P\text{ = 2a + b}[/tex]From the question, b = 2x; a = x^2 + 20
[tex]P\text{ = 2a }+b=2(x^2+20)+2x=2x^2+40\text{ + 2x}[/tex][tex]P=2x^2\text{ + 2x + 40}[/tex]To beA train started from City A to City B at 13:30. The train travelledat an average speed of 180 miles per hour. If the distancebetween City A and City B is 756 miles, at what time did thetrain arrive at City B? Give your answer in a 24-hour clockformat, such as 19:00. DEnter the answer
Remember that
the speed is equal to divide the distance by the time
speed=d/t
solve for t
t=d/speed
we have
d=756 miles
speed=180 miles per hour
substitute
t=756/180
t=4.2 hours
4.2 hours=4 hours +0.20 hours
Convert 0.20 hours to minutes
Multiply by 60
0.20 h=0.20*60=12 minutes
so
4.2 hours=4 h 12 min
therefore
A train started from City A to City B at 13:30.
13:30+ 4h 12 min=17:42 hrs
3x - 4y = 65x + 8y = -1
multiply mentally to find the product
8 * 404 = 8(----- + 4)
At first, we will split 404 into two numbers one of them is 4
To find the other number subtract 4 from 404
404 - 4 = 400
8 * 404 = 8(400 + 4)
Now we will multiply 8 by 40 and 8 by 4
8(400 + 4) = 8 * 400 + 8 * 4
It is easy to find the product of 8 and 4
8 * 4 = 32
8 * 400 = 3200
Let us add them
3200 + 32 = 3232
The answer is 3232
0.25(60) + 0.10x = 0.15(60 + x)
Answer: X = 120
Step-by-step explanation:
lol:
V = (−∞,∞)
X = 120
10 ptsQuestion 3Find the measure of each interior angle. Round to the nearest hundredth.4x(6x - 90)(3x + 31)(7x+19)X=(4x)" =(6x - 90)(7x + 19)° =(3x + 31)º =
Alexandre, this is the solution:
Let's recall that the interior angles of a rhombus add up to 360 degrees.
Upon saying that, we have:
4x + 3x + 31 + 6x - 90 + 7x + 19 = 360
20x - 40 = 360
Adding 40 at both sides:
20x - 40 + 40 = 360 + 40
20x = 400
Dividing by 20 at both sides:
20x/20 = 400/20
x = 20
Now, we can calculate each of the angles and prove they add up to 360 degrees, as follows:
• 4x = 4 * 20 =, 80
,• 3x + 31 = 3 * 20 + 31 = 60 + 31 =, 91
,• 7x + 19 = 7 * 20 + 19 = 140 + 19 = ,159
,• 6x - 90 = 6 * 20 - 90 = 120 - 90 = ,30
80 + 91 + 159 + 30 = 360
figure0123456vehicles4122028364452linear ?pattern ?constant?
Problem
Solution
For this case we need to verify if the pattern is linear so we cna check this doing the following operations:
(12-4)/(1-0) =8
(20-12)/(2-1) =8
(28-20)/(3-2) =8
(36-28)/(4-3) =8
(44-36)/(5-4) =8
(52-44)/(6-5) =8
And as we can see we have the same constant so we can conclude that we have a linear pattern with a constant value of k=8
That means for every increase in the figure the vehicles increase by 8
We can also find the formula for the linear pattern and we have:
4 =8 (0)+b
And solving for b we got
b= 4
And the equation y=mx+b is:
y= 8x +4
This is a non graded practice that I am doing. I don’t under these questions 5-11
7. The intersection of two intersecting lines is a point.
In the given image, we see that lines NQ and ML intersect at point P.
Therefore, the intersection of NQ and ML is P.
find the volume and total surface area of a right circular cone whose base diameter is 10 cm and whose altitude is 20 cm.
SOLUTION
Given the question in the question tab, the following are the solution steps to calculate the required measurements.
Step 1: write the given parameters
[tex]\begin{gathered} \text{diameter}=10\operatorname{cm},\text{altitude}=\text{height}=20\operatorname{cm} \\ r=\frac{d}{2}=\frac{10}{2}=5\operatorname{cm} \end{gathered}[/tex]Step 2: Calculate the volume of the right circular cone
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{\pi\times5\times5\times20}{3} \\ V=\frac{500\pi}{3}=523.5987756 \\ V\approx523.5988\operatorname{cm}^3 \end{gathered}[/tex]Step 3: Calculate the total surface area of the right circular cone
[tex]\begin{gathered} \text{TSA}=\pi r(r+\sqrt[]{h^2+r^2)} \\ \text{TSA}=\pi(5)(5+\sqrt[]{20^2+5^2)} \\ \text{TSA}=5\pi(5+\sqrt[]{400+25)} \\ \text{TSA}=5\pi(5+\sqrt[]{425})=5\pi(5+20.61552813) \\ \text{TSA}=5\pi(25.615528134) \\ \text{TSA}=402.3677749 \\ \text{TSA}\approx402.3678cm^2 \end{gathered}[/tex]Hence, the volume and the total surface area of the given right circular cone are approximately 523.5988cm³ and 402.3678cm² respectively
Triangle BCA is similar to Triangle STR . What is the value of x?
Sin the triangles are similar the ratio 4 to 6 should hold for any side, this means that:
[tex]\frac{4}{6}=\frac{x}{9}[/tex]Solving for x we have:
[tex]\begin{gathered} \frac{4}{6}=\frac{x}{9} \\ x=9(\frac{4}{6}) \\ x=\frac{36}{6} \\ x=6 \end{gathered}[/tex]Therefore. x=6.
Factor out the greatest negative common factor for the expression.- 8mºn - 40m?n4Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.OA. - 8mºns - 40mºn4-(Factor completely.)OB. There is no common factor other than 1.
Solution
- The question tells us to factor out the greatest negative common factor of the expression below:
[tex]-8m^3n^5-40m^3n^4[/tex]- The greatest negative common factor is the negative monomial with the largest magnitude, which divides evenly into each term of the given expression.
- Let us factorize the expression to derive this greatest negative common factor below:
[tex]\begin{gathered} -8m^3n^5-40m^3n^4 \\ -8,m^3,\text{ and }n^4\text{ are all co}mmon\text{ in the expression above.} \\ \text{Thus, we have:} \\ \\ -8m^3n^4(n-5) \end{gathered}[/tex]Final Answer
The answer is
[tex]-8m^3n^4(n-5)[/tex]The annual rainfall in a town has a mean of 54.11 inches and a standard deviation of 12.59 inches. Last year there was rainfall of 48 inches. How many standard deviations away from the mean is that? Round your answer to two decimal places.
SOLUTION
Mean=54.11, standard deviation = 12.59
X=48
Using the z formula
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substituting values gives
[tex]z=\frac{48-54.11}{12.59}[/tex]Solve for z
[tex]z=-0.4853[/tex]This shows that the result shows that the value x=48 is 0.4853 standard deviation to the left of the mean.
Please it’s due todayAre there any limitations on the inputs of the equation?Does the graph have any symmetry?If so, where? When will the graph point upward? When will it point downward?
We have the following:
1.
There is no limitation on the input values, the domain is all real numbers.
2.
Yes, it has an axis of symmetry at the point (0,0)
3.
The graph point upward in the interval:
[tex](0,\infty)[/tex]The graph point downward in the interval:
[tex](-\infty,0)[/tex]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.)
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%
32Lucky Lanes Bowling Alley is putting this design on its roof.4 feet4 feet20 feet4 feet4 feet10 feet
In order to find the volume of the design, we want to find the volume of the figures that compound it:
Total volume = volume 1 + volume 2
Volume 1The volume of each box is given by the product of its sides:
side 1 x side 2 x side 3.
In this case, we have that
side 1 = 4 ft
side 2 = 4 ft
side 3 = 20 ft - 4 ft = 16 ft
Then,
side 1 x side 2 x side 3.
↓
volume 1 = 4 ft x 4 ft x 16 ft = 256 ft³
volume 1 = 256 ft³
Volume 2For the second part we have that:
side 1 = 4 ft
side 2 = 4 ft
side 3 = 10 ft
Then,
side 1 x side 2 x side 3.
↓
volume 2 = 4 ft x 4 ft x 10 ft = 160 ft³
volume 2 = 160 ft³
Total volumeThe total volume is given by
Total volume = volume 1 + volume 2
↓
Total volume = 256 ft³ + 160 ft³
Total volume = 416 ft³
Answer: 416 ft³
A company charges $7 dor a t-shirt and ships any order for $22 a school principal ordered a number of t-shirts for the school store the total cost of the order was 1,520 how many t-shirts did the principal buy
the equation is
[tex]7x+22=1520[/tex]then solve for x
[tex]\begin{gathered} 7x+22-22=1520-22 \\ 7x=1498 \\ \frac{7x}{7}=\frac{1498}{7} \\ x=214 \end{gathered}[/tex]answer: the principal bought 214 t-shirts
Below, the two-way table is given for aclass of students.Freshmen Sophomore Juniors Seniors TotalMale 462. .Female 33246TotalIf a student is selected at random, find theprobability the student is a junior. Roundto the nearest whole percent.
The final answer is: 27%
We are asked to find the probability that a student chosen at random is a junior. This requires that we know the total number of students in each level from Freshmen to Seniors.
Totals:
Freshmen = 4 + 3 = 7
Sophomore = 6 + 4 = 10
Juniors = 2 + 6 = 8
Seniors = 2 + 3 = 5
Thus we can calculate the total number of students considered:
7 + 10 + 8 + 5 = 30 students in total.
Now we can calculate the probability as:
[tex]\begin{gathered} P(\text{choosing juniors) = }\frac{Number\text{ of Juniors}}{\text{Total Number of Students}} \\ \end{gathered}[/tex]The number of Juniors was calculated earlier as: Juniors = 8
We have the total number of students as 30
Therefore, we can solve:
[tex]P(\text{choosing juniors)=}\frac{8}{30}=\frac{4}{15}[/tex]But we were asked to round to the nearest whole percent, which means we are required to put the fraction into percentage.
The way we do this is to multiply the fraction by 100%
[tex]\begin{gathered} \frac{4}{15}\times100=26.6667. \\ \\ \therefore P(\text{choosing juniors)=27\% (to the nearest whole percent)} \end{gathered}[/tex]Therefore the final answer is: 27%
The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 30.8 miles per gallon, with a standard deviation of 4.1 miles per gallon. Assume that a Normal model applies. Find the probability that a randomly selected automobile will average: 1. Less than 28 miles per gallon. Chapter 6 Assignment 2. More than 26 miles per gallon.
I need much help with this normal distribution question.
The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean.
What is meant by normal distribution?The probability density function for a continuous random variable in a system defines the Normal Distribution.
A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction.
The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean. This shows that data close to the mean occur more frequently than data far from the mean. On a graph, the normal distribution is represented by a "bell curve."
To learn more about normal distribution refer to:
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A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table. (a) Make a scatter plot of the data. (b) Find and graph a linear regression equation that models the data. (c) Use the model to predict soft-drink sales if the temperature is 95°F.
ANSWER and EXPLANATION
a) First we have to make a scatter plot. We do this by plotting the calues of High Temperature on the x axis and Number of cans sold on the y axis:
b) We want to find and graph the linear regression equation that models the data.
The linear regression equation will be in the form:
y = a + bx
[tex]\begin{gathered} \text{where} \\ a\text{= }\frac{(\sum ^{}_{}y)(\sum ^{}_{}x^2)\text{ - (}\sum ^{}_{}x)(\sum ^{}_{}xy)}{n(\sum ^{}_{}x^2)\text{ }-\text{ (}\sum ^{}_{}x)^2} \\ \text{and b = }\frac{n(\sum ^{}_{}xy)\text{ - (}\sum ^{}_{}x)(\sum ^{}_{}y)}{n(\sum ^{}_{}x^2)\text{ }-\text{ (}\sum ^{}_{}x)^2} \end{gathered}[/tex]We have from the question that:
x = High Temperature
y = Number of cans added
So, we have to find xy and x^2. We will form a new table:
Now, we will find a and b:
[tex]\begin{gathered} a\text{ = }\frac{(4120)(39090)\text{ - (}554)(297220)}{8(39090)\text{ }-554^2} \\ a\text{ = }\frac{\text{ 161050800 - 164659880}}{312720\text{ - 306916}} \\ a\text{ = }\frac{-3609080}{5804} \\ a\text{ }\cong\text{-62}2 \end{gathered}[/tex][tex]\begin{gathered} b\text{ = }\frac{8(297220)\text{ - (554})(4120)}{5804} \\ b\text{ = }\frac{2377760\text{ - 2282480}}{5804} \\ b\text{ = }\frac{95280}{5804} \\ b\text{ }\cong\text{ 16} \end{gathered}[/tex]Therefore, the linear regression equation is:
y = -622 + 16x
Now, let us graph it using values of x (High Temperature):
That is the Linear Regression Graph.
c) To predict soft drink sales if the temperature is 95 degrees Farenheit, we will put the x value as 95 and find y. That is:
y = -622 + 16(95)
y = 898
The model predicts that 898 cans of soft drinks will be sold when the High Temperature is 95 degrees Farenheit.
Which of the following represents the translation of R (-3, 4), along the vector <7, -6> <-1, 3>.
Solution
Step 1:
The translation is a term used in geometry to describe a function that moves an object a certain distance.
Step 2:
Pre-mage R = (-3,4)
Step 3:
When moved along (7, -6) the new coordinates become:
R' = (-3+7 , 4 - 6 ) = (4 , -2)
R' = ( 4 , -2 )
Step 4:
When moved along (-1, 3) the new coordinates become:
R'' = ( 4-1 , -2+3 ) = ( 3 , 1 )
R'' = (3 , 1)
Final answer
[tex]R(-3\text{ , 4\rparen }\rightarrow\text{ R'\lparen4 , -2\rparen }\rightarrow\text{ R''\lparen3 , 1\rparen}[/tex]Solve each equation for the given variable.-2x + 5y = 12 for ySolve each equation for y. Then find the value of y for each value if x.y + 2x = 5; x = -1, 0, 3
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
-2x + 5y = 12
y = ?
Step 02:
We must apply algebraic rules to find the solution.
-2x + 5y = 12
5y = 12 + 2x
y = 12 / 5 + 2x / 5
[tex]y\text{ =}\frac{12}{5}\text{ + }\frac{2x}{5}[/tex]The answer is:
y = 12 / 5 + 2x / 5
What is the slope of this line? :(
Answer:
y=1/4x+1
Step-by-step explanation:
Answer:
m=1/4
Step-by-step explanation:
Got it correct
Hello! I think the answer is 398. Would you mind guiding me?
Given -
Total Personal Videos Players = 400
Video Players with no defects = 398
Number of Video Players sent = 2000
To Find -
The number of Video Players with no defects =?
Step-by-Step Explanation -
Total Personal Videos Players = 400
Video Players with no defects = 398
So,
Two video players in every 400 are defected
So,
2000 = 5 × 400
So,
Total number of Video Players with defects = 5 × 2 = 10
Hence,
The number of Video Players with no defects = 2000 - 10 = 1990
Final Answer -
The number of Video Players with no defects = 1990
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
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]