1/3 and 3/9
Simplify 3/9 by 3
(3/3) / (9/3 ) = 1 /3
So, both fractions are equal
1/3 is not greater than 3/9
A model rocket is launched with an initial upward velocity of 156 ft/s. The rocket's height h (In feet) after t seconds is given by the following.
h=156t-16t²
Find all values of t for which the rocket's height is 60 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Explanation
Check
ground
t = 0 seconds
☐or D
X
5
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I need help
The quadratic equation that gives the height of the rocket, h = 156·t - 16·t² is evaluated at h = 60 feet to give the two times the rocket's height is 60 feet as 0.40 seconds and 9.35 seconds.
What is a quadratic equation?A quadratic equation is an equation of the second degree that can be expressed in the form; a·x² + b·x + c = 0, where the letters, a, and b represents the coefficients of x and c is a constant.
The initial velocity of the rocket = 156 ft./s upwards
The given equation of the rocket is: h = 156·t - 16·t²
The times when the rocket height is 60 feet are found by plugging in the value h = 60, in the equation of the vertical height of the rocket as follows:
h = 60 = 156·t - 16·t²
156·t - 16·t² - 60 = 0
4·(39·t - 4·t² - 15) = 0
Therefore: [tex]39\cdot t - 4\cdot t^2 - 15 = \dfrac{0}{4} =0[/tex]
39·t - 4·t² - 15 = 0
-4·t² + 39·t - 15 = 0
From the quadratic formula which is used to solve the quadratic equation of the form; f(x) = a·x² + b·x + c, is presented as follows;
[tex]x = \dfrac{-b\pm\sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}[/tex]
The solution of the equation, -4·t² + 39·t - 15 = 0, is therefore:
[tex]t = \dfrac{-39\pm\sqrt{(39)^2-4\times (-4) \times (-15)} }{2\times (-4)}= \dfrac{-39\pm\sqrt{1281} }{-8}[/tex]
Therefore, when the height of the rocket is 60 feet, the times are: [tex]t = \dfrac{-39-\sqrt{1281} }{-8}\approx 9.35[/tex] and [tex]t = \dfrac{-39+\sqrt{1281} }{-8}\approx 0.40[/tex]
The times when the height of the rocket is 60 feet, the times are:
t ≈ 9.35 s, and t ≈ 0.40 s
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find the height of the trapezoidA=51CM2b=10cmb=7cmH?
we must find b one of the parallel sides before proceeding to find h
from the diagram b = 7cm
[tex]\begin{gathered} \text{Area = }\frac{10\text{ +7}}{2}\times h \\ 51\text{ = }\frac{17}{2}\times h \end{gathered}[/tex][tex]\begin{gathered} 51\text{ x 2 = 17h} \\ h\text{ =}\frac{51\times2}{17} \\ h\text{ =6cm} \end{gathered}[/tex]A cylinder truck all paint cans to be inches across the top diameter in about 10 inches high. How many cubic inches of pink it all to the nearest hundredth?
Given:
A cylinder truck all paint cans to be inches across the top diameter in about 10 inches high.
[tex]\begin{gathered} r=1.5in \\ h=10in \end{gathered}[/tex]Required:
To find the volume of the cylinder.
Explanation:
The volume of the cylinder is,
[tex]V=\pi r^2h[/tex]Therefore,
[tex]\begin{gathered} V=3.14\times1.5^2\times10 \\ \\ =3.14\times2.25\times10 \\ \\ =70.65in^3 \end{gathered}[/tex]Final Answer:
70.65 cubic inches of paint it hold.
Two legs of a step ladder are each 4 metres long. The angle formed between the two legs is 30degrees.Make a labelled scale drawing of the ladder using the scale Icm=0.5 metres and fill in the blanksbelow.
assume the figure as two step ladder
Can you help me find the answer to this equation
Given:
K is the mid-point of FG and L is the mid-point FH.
To find:
The measure of Angle H
Step-by-step solution:
As we are given that K and L are the midpoints of FG and FH respectively.
According to the mid-point theoram,
The segment that connects the mid-point of two sides, is parallel to the third side of that triangle.
Thus,
KL||GH and ∠KLF = ∠GHL
As both of these angles are corresponding angles.
So we can say that m∠H = 85 degrees.
Hello this is a multi step question and I am struggling to help my son with this. It is 1 of 3 so hoping to get guidance with this first one to be able to know how to apply it to the others in his activities. Thank you as I know this is multiple steps and time consuming. The help is greatly appreciated as a parent.
In the first part of this problem, we must compute some statistic variables of two distributions:
0. the mean value,
,1. the median,
,2. the standard deviation.
,3. the interquartile range.
1. The mean of a data set is the sum of all the data divided by the count n:
[tex]\mu=\frac{x_1+x_2+\cdots+x_n}{n}\text{.}[/tex]2. The median is the data value separating the upper half of a data set from the lower half, it is computed following these steps:
• arrange data values from lowest to the highest value,
,• the median is the data value in the middle of the set
,• if there are 2 data values in the middle the median is the mean of those 2 values.
3. The standard deviation for a sample data set is given by the following formula:
[tex]\sigma=\sqrt[]{\frac{(x_1-\mu)^2+(_{}x_2-\mu)^2+\cdots+(x_n-\mu)^2}{n-1}_{}}\text{.}[/tex]4. The interquartile range (IQR) is given by:
[tex]\text{IQR}=Q_3-Q_1\text{.}[/tex]Where Q_1 and Q_3 are the first and third quartiles. The lowest quartile (Q1) covers the smallest quarter of values in your dataset.
--------------
Using the definitions above, we compute the mean, the median and the standard deviation for the samples taken by Manuel and Gretchen.
Manuel's sample
• Sample = {3, 6, 8, 11, 12, 8, 6, 3, 10, 5, 14, 9, 7, 10, 8}
,• Count = 15
1. Mean
Using the formula above, we get:
[tex]\mu=\frac{120}{5}=8.[/tex]2. Median
We order the data set:
[tex]3,3,5,6,6,7,8,(8),8,9,10,10,11,12,14.[/tex]From the ordered data set, we see that the central number 8 divides the data set into two equal parts.
So the median of this sample is:
[tex]\bar{x}=8.[/tex]3. Standard deviation
Using the formula above, we get:
[tex]\sigma=\sqrt[]{\frac{138}{15-1}}\cong3.14.[/tex]4. Interquartile range
Dividing the data sample into quartiles, we have:
[tex]3,3,5,6|6,7,8|8|8,9,10|10,11,12,14.[/tex]We have:
• Q_1 = 6,
,• Q_3 = 10.
So the interquartile range is:
[tex]\text{IQR }=Q_3-Q_1=10-6=4.[/tex]Gretchen's sample
• Sample = {22, 4, 7, 8, 12, 15, 10, 7, 9, 6, 13, 3, 8, 10, 10}
,• Count = 15
1. Mean
[tex]\mu=\frac{144}{15}=9.6.[/tex]2. Median
We order the data set:
[tex]3,4,6,7,7,8,8,(9),10,10,10,12,13,15,22.[/tex]From the ordered data set, we see that the central number 8 divides the data set into two equal parts.
So the median of this sample is:
[tex]\bar{x}=9.[/tex]3. Standard deviation
[tex]\sigma=\sqrt[]{\frac{307.6}{15-1}}\cong4.69.[/tex]4. Interquartile range
Dividing the data sample into quartiles, we have:
[tex]3,4,6,7|7,8,8|9|10,10,10|12,13,15,22.[/tex]We have:
• Q_1 = 7,
,• Q_3 = 12.
So the interquartile range is:
[tex]\text{IQR }=Q_3-Q_1=12-7=5.[/tex]Answers
Manuel's sample
0. Mean = 8
,1. Median = 8
,2. Standard deviation ≅ 3.14
,3. Interquartile range = 4
Gretchen's sample
0. Mean = 9.6
,1. Median = 9
,2. Standard deviation ≅ 4.69
,3. Interquartile range = 5
The following statements "If you are wearing a helmet, you are riding a bike." and "If you are not riding a bike, you are not wearing a helmet." are an example of a _____ statement.Select one:a.inverseb.conversec.contrapositive
Given:
The given statements are,
"If you are wearing a helmet, you are riding a bike."
"If you are not riding a bike, you are not wearing a helmet."
Required:
To identify the kind of statements.
Explanation:
We have the given statement:
"If you are wearing a helmet, you are riding a bike."
Here, p : you are wearing a helmet
q : you are riding a bike
Thus, taking negation of both the parts of the statement as follows:
If not q, then not p.
Hence, the statement formed is,
"If you are not riding a bike, you are not wearing a helmet."
This is the contrapositive statement.
Final Answer:
Given statements are an example of contrapositive.
put the numbers in order from least to greatest2.3,12/5,5/2,2.2,21/10
Express the fraction in terms of decimal.
[tex]\frac{12}{5}=2.4[/tex][tex]\frac{5}{2}=2.5[/tex][tex]\frac{21}{10}=2.1[/tex]The numbers are,
2.3, 2.4, 2.5, 2.2, 2.1.
Now we arrange the number from least to greatest.
[tex]2.1,2.2,2.3,2.4,2.5[/tex]So answer is,
[tex]\frac{21}{10},2.2,2.3,\frac{12}{5},\frac{5}{2}[/tex]By creating a General Court made up of delegates from each town in the colony, this document reflects the principle of:
federalism
individual rights
checks and balances
republicanism
By creating a General Court made up of delegates from each town in the colony, this document reflects the principle of: D. republicanism.
What is federalism?Federalism simply refers to a form of government in which the federal government and other institutional bodies such as states, towns, smaller units, and provinces share power and authority.
What is republicanism?Republicanism can be defined as a form of government that is centered around citizenship in a state and emphasizes their participation for the common good of a geographical area such as states, towns, and other smaller units in a colony.
This ultimately implies that, republicanism involves citizens selecting their representatives (delegates) from each town in a colony, especially through an electoral process such as in Article 8, Fundamental Orders of Connecticut.
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Answer:
republicanism
Step-by-step explanation:
The table shows claims and their
probabilities for an insurance
company.
Amount of claim
(to the nearest $20,000)
$0
$20,000
$40,000
$60,000
$80,000
$100,000
Probability
0.70
0.16
0.09
0.03
0.01
0.01
Answer:
Step-by-step explanation:
This is an equation! Solutions: x=1.
Graphical form: Equation 3%2Ax-x%2B2=4 was fully solved.
Text form: 3*x-x+2=4 simplifies to 0=0
Cartoon (animation) form: simplify_cartoon%28+3%2Ax-x%2B2=4+%29
For tutors: simplify_cartoon( 3*x-x+2=4 )
If you have a website, here's a link to this solution.
TELL ANSWER ASAP PLS WHAT IS 15.5 MULTIPLIED BY 3.75??????
Multiplied by 15.5 to 3.75 is 58.125.
To solve the:
15.5 is multiplied by 3.75
Now,
15.5 × 3.75
= 58.125
What is the process of Multiplication ?
Multiplication is the process of calculating the total of one number multiplied by another. There will be simple tests in addition, subtraction, multiplication and division. 2. uncountable noun. The multiplication of things of a particular kind is the process or fact of them increasing in number or amount.
Hence, Multiplied by 15.5 to 3.75 is 58.125.
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Find the area of a circle with a Diameter = 12 ft. Use 3.14 for π and round to 2 decimal places.
Given:
Diameter of circle = 12ft
pi = 3.14
Solution
The area (A) of a circle can be calculated using the formula:
[tex]\begin{gathered} A\text{ = }\pi r^2 \\ \text{where r is the radius of the circle} \end{gathered}[/tex]Recall that the diamter (d) and radius (r) are related by the formula:
[tex]\begin{gathered} \text{radius = }\frac{diameter}{2} \\ r\text{ = }\frac{d}{2} \end{gathered}[/tex]We can now find the radius (r) of the circle to be:
[tex]\begin{gathered} r\text{ = }\frac{12}{2} \\ r\text{ = 6 ft} \end{gathered}[/tex]We can now find the area by the applying the formula given above:
[tex]\begin{gathered} A\text{ = }\pi\times r^2 \\ A\text{ = 3.14 }\times6^2 \\ =113.04ft^2\text{ (2.dp)} \end{gathered}[/tex]Answer: 113.04 square feet
Solve using elimination.–2x − 7y = 9x − 7y = –15
The question wants us to solve the following system of equations by elimination:
[tex]\begin{gathered} -2x-7=9 \\ x-7y=-15 \end{gathered}[/tex]Solution
[tex]\begin{gathered} -2x-7y=9\text{ (Equation 1)} \\ x-7y=-15\text{ (Equation 2)} \\ \\ \text{Subtract both equations} \\ -2x-7y-(x-7y)=9-(-15) \\ -2x-7y-x+7y=9+15 \\ -2x-x-7y+7y=24 \\ -3x=24 \\ \text{Divide both sides by -3} \\ -\frac{3x}{-3}=\frac{24}{-3} \\ \\ \therefore x=-8 \\ \\ \text{Substitute the value for x into Equation 1}.\text{ This will help us find y.} \\ -2x-7y=9 \\ -2(-8)-7y=9 \\ 16-7y=9 \\ \text{Subtract 16 from both sides} \\ -7y=9-16 \\ -7y=-7 \\ \text{Divide both sides by -7} \\ -\frac{7y}{-7}=-\frac{7}{-7} \\ \\ \therefore y=1 \end{gathered}[/tex]Answer
The answer to the system of equations is:
x = -8
y = 1
hello I need help answering this homework question please thank you
Solution:
Case: Area
Given: A house to be painted
Method/ Final answers
a) Find the area of the garage to be painted.
(i) Front.
A = l X w - Garage door area
l= 15 ft, b= 10-4 gives 6ft
A= 15 X 6 - (10 X 7)
A= 90 - 70
A= 20 square feet
ii) Side
A= l X w
A= 6 X 5
A= 30 square feet
iii) The sum of areas
A= 20 + 30
A= 50 square feet
b) Area of the painted region around windows 5 and 6.
Since 12 in = 1 ft
Area of front door converted to feet is (20/3) ft by 3 ft
Areas of windows 5 and 6 converted to feet is 3 ft by (5/3) ft each
A= Area of space - (Area of front door + window 5 + window 6)
A= (30 X 10) - [(20/3) X 3 + 3 X (5/3) + 3 X (5/3)]
A= 300 - [20 + 5 + 5]
A= 300 - 30
A= 270 square feet.
c) Area of the painted region around windows 3
A= Total face - Area of window 3
A= (Rectangle + Parallelogram + Triangle) - Area of window 3
A= [(10 X 4) + (5 X 4) + (0.5 X 4 X 3)] - [1 X (5/3)]
A= [40+20+6] - [5/3]
A= 66 - (5/3)
A= 193/3 square feet
A= 63.33 square feet
d) Area of the region on the second floor with 2 rectangles and the region around window 4
i) region with rectangle 1 from left to right
A= 10 X (15- 6)
A= 10 X 9
A = 90
ii) region with rectangle 2 from left to right
A= 10 X (15- 6)
A= 10 X 9
A = 90
iii) Area of region around window 4
Area of space - area of window
A= 10 X (30-9-12) - [3 X (5/2)]
A= 10 X 9 - (15/2)
A= 82.5.
Total area= 90 + 90 + 82.5
= 262.5 square feet
e) Total area of the painted region (white)
262.5 + 63.33+ 270 + 50
= 645.83 square feet.
f) Additional question
The total cost if it cost $8 per sq ft
645.83 square feet X $8 per sq ft
=$5166.64
Complete the table .....Which parts of the arithmetic sequence in the left of the table match up with the linear function on the right?
Let's expand the formula for arithmetic sequence.
[tex]\begin{gathered} a_n=a_1+d(n-1) \\ a_n=a_1+dn-d \\ a_n=dn+(a_1-d) \end{gathered}[/tex]The linear function is:
[tex]f(x)=ax+b_{}[/tex]Matching both equations, we can say:
[tex]\begin{gathered} a_n\gg\gg f(x) \\ d\gg\gg a \\ n\gg\gg x \\ a_1-d\gg\gg b \end{gathered}[/tex]A machinist must follow part drawing with scale 1 to 16. Find the dimensions (in inches) of the finished stock shown in the figure. That is find the lengths A, B, C, and D.
Length of the dimensions of the finished stock shown are as follow:
A = 13/4 inches , B = 3/4 inches , C =5/2 inches , D = 3/16 inches.
As given in the question,
Mechanist must follow part drawing with scale 1 to 16.
Dimensions of the finished stock shown in the figure
A represents the length .
B represents the height
C represents the length
D represents the height
Length of A is
= 3 1/4 inches
= 13 /4 inches
Height of B is
=3/4 inches
Length of C is
= 2 1/2 inches
= 5/2 inches
Height of D is
= 3/16 inches
Therefore, length of the dimensions of the finished stock shown are as follow: A = 13/4 inches ,B = 3/4 inches ,C =5/2 inches , D = 3/16 inches.
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help meeeeeeeeee pleaseee !!!!!
The value of the composite function is determined as: (g o f)(5) = 6.
How to Determine the Value of a Composite Function?To determine the value of a composite function, first evaluate the inner function by plugging in the value of x given, then use the output of the inner function as an input to evaluate the outer function.
Given the following:
f(x) = x² - 6x + 2
g(x) = -2x
Therefore:
(g o f)(5) = g(f(5))
Find f(5):
f(5) = (5)² - 6(5) + 2
f(5) = 25 - 30 + 2
f(5) = -3
Find g(f(5)) by substituting x = -3 into g(x) = -2x:
g(f(5)) = -2(-3)
g(f(5)) = 6
Therefore, (g o f)(5) = 6.
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Data Set A has a Choose... interquartile range than Data Set B. This means that the values in Data Set A tend to be Choose... the median.
The median of the given data set will be 35.
What do we mean by media?In statistics and probability theory, the median is the number that separates the upper and lower half of a population, a probability distribution, or a sample of data. For a data set, it might be referred to as "the middle" value.
So, The variability metrics for each class are listed below:
The further classifications: Class A; Class B;
Range: 30 Range: 30IQR: 12.5 IQR: 20.5MAD: 7.2 MAD: 9.2Greater variability in the data set is suggested by class B's wider interquartile range and mean absolute deviations.
Set A's median will be:
median = (20 + 32+ 36+ 37 + 50) / 5median = 175 / 5median = 35Therefore, the median of the given data set will be 35.
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Solve the equation using the justification given for each step.
Multiplicative property of equality
[tex]\begin{gathered} Multiply\text{ both sides by 3} \\ (5x+7)3=\frac{3(-15x-1)}{3}+3(\frac{4}{3}) \end{gathered}[/tex]Distributive property of equality
[tex]3(5x+7)=-15x-1+4[/tex]Associative property
[tex]\begin{gathered} 15x+21=-15x-1+4 \\ 15x+21=-15x+3 \end{gathered}[/tex]Subtraction property of equality
[tex]\begin{gathered} 15x+21-21=-15x+3-21 \\ 15x=-15x-18 \end{gathered}[/tex]Addition property of equality
[tex]\begin{gathered} 15x+15x=-15x+15x-18 \\ 30x=-18 \end{gathered}[/tex]Division property of inequality
[tex]\begin{gathered} \text{divide both sides by 30} \\ \frac{-18}{30}=\frac{30x}{30} \\ x=-\frac{18}{30}=-\frac{3}{5} \end{gathered}[/tex]sean earns $300 in a regular work week. A regular work week for sean consists of 5 work days with 8 hours a day. How much money does sean earn each hour
Solution:
According to the problem, a regular work week consists of 5 work days with 8 hours a day. This is equivalent to say:
5 x 8 hours every regular work week.
That is:
40 hours every regular work week
then, the money earned per hour is:
[tex]\frac{300\text{ }dollars}{40\text{ hours}}\text{ = 7.5 dollars per hour}[/tex]then we can conclude that the correct answer is:
$7.5
14#An ecologist randomly samples 12 plants of a specific species and measures their heights. He finds that this sample has a mean of 14 cm and a standard deviation of 4 cm. If we assume that the height measurements are normally distributed, find a 95% confidence interval for the mean height of all plants of this species. Give the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)Lower limit:Upper limit:
Answer:
Lower limit: 11.7 cm
Upper limit: 16.263
Explanation:
The formula to find the lower and upper limits of the confidence interval (given the data is normally distributed) is :
[tex]CI=\mu\pm Z^*\frac{\sigma}{\sqrt{n}}[/tex]Where:
• μ = sample mean
,• σ = sample standard deviation
,• Z* = critical value of the z-distribution
,• n = is the sample size
In this case:
• μ = 14cm
• σ = 4cm
,• n = 12
The critical value of the z-distribution for a confidence interval of 95% is Z* = 1.96
Now, we can use the formula above to find the upper and lower limit:
[tex]CI=14\pm1.96\cdot\frac{4}{\sqrt{12}}=14\pm\frac{98\sqrt{3}}{75}=\frac{1050\pm98\sqrt{3}}{75}[/tex]Thus:
[tex]Lower\text{ }limit=\frac{1050-98\sqrt{3}}{75}\approx11.736cm[/tex][tex]Upper\text{ }limit=\frac{1050-98\sqrt{3}}{75}\approx16.263cm[/tex]Rounded to one decimal:
Lower limit: 11.7cm
Upper limit: 16.3cm
how many drahms areequivalent to 300 grains?
hello
to solve this question, we need to know how many grains is in 1 gram
[tex]\begin{gathered} 1\text{grams}=15.43\text{grains} \\ \end{gathered}[/tex]now let 300 grains be equal to x grams
[tex]\begin{gathered} 1\text{grams}=15.43\text{grain} \\ \text{xgrams}=300\text{grains} \\ \text{cross multiply both sides and solve for x} \\ x\times15.43=1\times300 \\ 15.43x=300 \\ \text{divide both sides by 19.44} \\ \frac{15.43x}{15.43}=\frac{300}{15.43} \\ x=\frac{300}{15.43} \\ x=19.44 \end{gathered}[/tex]300 grains will weigh 19.44g
6.724x
Melinda went for a run. She was doing a great job until she got to a hill. She was so tired
running up the hill that she tripped over a rock at the top of the hill. She rolled all the way
down the hill. It took her 90 seconds to reach the bottom of the hill. She rolled for 225
feet. What is Melinda's rate of decent?
The Melinda's rate of decent from the top of the hill is 3.75 ft/sec.
What is termed as the rate of decent/speed?Speed is defined as the proportion of distance traveled to time spent traveling. Because it has only one direction and no magnitude, speed is a scalar quantity. When an object travels the same distance in equal time intervals, it is said to be moving at a uniform speed.For the given question;
The distance covered by the Melinda after she tripped over a rock at the top of the hill is 225 feet.
The time taken by Melinda to reach the bottom of the hill is 90 seconds.
Then, the rate of decent will be the speed at which she will fall.
Speed = distance/ time
Speed = 225/60
Speed = 3.75
Thus, the Melinda's rate of decent from the top of the hill is 3.75 ft/sec.
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David is laying tiles on his kitchen floor. His kitchen measures 16 feet by 20 feet Each tile is a square that measures 2 feet by 2 feet (a) What is the area of his kitchen floor? (b) How many tiles will David need to purchase to cover the floor? One Tile 2 ft 2 ft
(a) To find the area of the kitchen floor, we just have to multiply
[tex]A=16ft\times20ft=320ft^2[/tex](b) To find the number of tiles needed, we have to find the area of each tile, which is
[tex]A_{\text{tile}}=2ft^{}\times2ft^{}=4ft^2[/tex]Then, we divide the total area of the kitchen floor by the area of each tile.
[tex]n=\frac{320ft^2}{4ft^2}=80[/tex]Hence, David will need 80 tiles to cover the floor.
At an all-you-can-eat barbeque fundraiser, adults pay $6 for a dinner and children pay $4 for a dinner. 212 people attend and you raise $1,128. What is the total number of adults and the total number of children attending? A)140 adults and 72 children B)72 adults and 140 children C)142 adults and 70 children D)70 adults and 142 children
A)140 adults and 72 children
Explanation
Step 1
Let x represents the number of childrend attending
Let y represents the number of adults attending
then
total cost for the children=4x
total cost for the adults=6y
if you raise 1128,
[tex]4x+6y=1128\text{ Equation(1)}[/tex]Now, 212 people attend,Hence
[tex]x+y=\text{212 Equation(2)}[/tex]Step 2
solve for x and y
a)isolate x in equation (2), then replace in equation (1)
[tex]\begin{gathered} x+y=212 \\ x=212-y \\ \text{now, replace} \\ 4x+6y=1128 \\ 4(212-y)+6y=1128 \\ 848-4y+6y=1128 \\ 2y+848=1128 \\ \text{subtract 848 in both sides} \\ 2y+848-848=1128-848 \\ 2y=280 \\ d\text{ivide boths ides by 2} \\ \frac{2y}{2}=\frac{280}{2} \\ y=140 \end{gathered}[/tex]it means 140 adults are attending
b)replace y=140 in equatin (2) to find x
[tex]\begin{gathered} x+y=212 \\ x+140=212 \\ \text{subtract 140 in both sides} \\ x+140-140=212-140 \\ x=72 \end{gathered}[/tex]so, the number of children is 72 and 72 children
determine the sample space of all the possible outcomes of choosing a card number 1 2 3 or 4 and a blue green or yellow marble how many outcomes involves choosing a Blue Marble
There are a total of 4 outcomes that involve choosing a blue marble
Here, we want to write a sample space for the selection
For us to have the sample space, we will have to write out the possible outcomes
We shall be representing the blue marble by b, the green by g and the yellow by y
We have the sample space as follows;
{1B,1G,1Y,2B,2G,2Y,3B,3G,3Y,4B,4G,4Y}
From the sample space, we can see that there are actually 12 possible results
Now, to get the outcomes involving blue marbles, we simply select the members of the sample space having B at the back
We have these as 1B, 2B, 3B and 4B
This is a total of 4 outcomes
The measures of the angles of a triangle are shown in the figure below. Solve for x.
44°
61°
(8x+11)°
I need help with my math homework question please. Plus it has a second part of the question
The given quadratic equation is
y = - x^2 + 25
a) The leading coeffiecient is the coefficient of the term with the highest exponent. Thus, the leading coefficient is the coefficient of x^2.
Leading coefficient = - 1
Since the leading coefficient is negative, the graph would open downwards. Thus, the correct option is
Down
b) The standard form of a quadratic equation is
y = ax^2 + bx + c
By comparing both equations,
a = - 1
b = 0
c = 25
The formula for calculating the x coordinate of the vertex of the graph is
x = - b/2a
By substituting the given values,
x = - 0/2 * - 1 = 0
We would calculate the y coordinate of the vertex by substituting x = 0 into the original equation. We have
y = - 0^2 + 25
y = 25
The coordinate of the vertex is (0, 25)
c) To find the x intercepts, we would equate the original equation to zero and solve for x. We have
- x^2 + 25 = 0
x^2 = 25
Taking the square root of both sides,
x = square root of 25
x = ± 5
Thus, the x intercepts are
(5, - 5)
d) The y intercept is the value of y when x = 0
Substituting x = 0 into the orignal equation,
y = - 0^2 + 25
y = 25
y intercept = (0, 25)
e) We would find another point on the graph. Let us substitute x = 6 into the equation. We have
y = - (6)^2 + 25 = - 36 + 25
y = - 11
We would plot (6, - 11) and (0, 25) on the graph. The graph is shown below
The table below shows the average annual cost of health insurance for a single individual, from 1999 to 2019, according to the Kaiser Family Foundation.YearCost1999$2,1962000$2,4712001$2,6892002$3,0832003$3,3832004$3,6952005$4,0242006$4,2422007$4,4792008$4,7042009$4,8242010$5,0492011 $5,4292012$5,6152013$5,8842014$6,0252015$6,2512016$6,1962017$6,4352017$6,8962019$7,186(a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).Pt = (b) Using this linear model, predict the cost of insurance in 2030.$ (c) = According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020)..
The given data plot will look thus:
a) Building a model using just the 1999 and 2019 years:
[tex]\begin{gathered} 1999\rightarrow0\rightarrow2196 \\ 2019\rightarrow20\rightarrow7186 \\ \text{Havng} \\ x_1=0,y_1=2196 \\ x_2=20,y_2=7186 \\ \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}_{} \\ \text{The model will be:} \\ P_t=249.5t+2196 \end{gathered}[/tex]b) The cost of insurance in 2030
[tex]\begin{gathered} P_t=249.5t+2196 \\ t=2030-1999=31 \\ \text{The cost of insurance in 2030 therefore will be:} \\ =249.5(31)+2196 \\ =7734.5+2196 \\ =\text{ \$9930.5} \end{gathered}[/tex]c) When do we expect the cost to reach $12,000
[tex]\begin{gathered} P_t=249.5t+2196 \\ 12,000=249.5t+2196 \\ 12000-2196=249.5t \\ 9804=249.5t \\ \frac{9804}{249.5}=\frac{249.5t}{249.5} \\ 39.2946=t \\ Since\text{ t = year -1999} \\ 39.2946+1999=\text{year} \\ 2038.2946=\text{year} \\ Since\text{ we are to give our answer as an exact year} \\ \text{The year will be }2039. \end{gathered}[/tex]HELP ME OUT PLEASE!!!!!!
Answer:
The First one (1.7,3.1)
Step-by-step explanation:
3x-2=-0.5x+4
3.5x=6
x=12/7
x≈1.7
sub x back into to find y
y≈3.1
