Answer:
axis of symmetry x=3
vertex (3, 52)
Step-by-step explanation:
y = -5x² + 30x + 7
x = -b/2a = -30/2(-5) = -30/-10 = 3
y = -5(3)² + 30(3) + 7
y = -45 + 90 + 7
y = 52
Shawn has 25 coins, all nickels and dimes. The total value is $2.00. How many of each coin does he have ?
Answer:
[tex]\boxed{15 \ dime \ and \ 10 \ nickel \ coins}[/tex]
Step-by-step explanation:
1 dime = 10 cents
1 nickel = 5 cents
So,
If there are 15 dimes
=> 15 dimes = 15*10 cents
=> 15 dimes = 150 cents
=> 15 dimes = $1.5
Rest is $0.5
So, for $0.5 we have 10 nickels coins
=> 10 nickels = 10*5
=> 10 nickels = 50 cents
=> 10 nickel coins = $0.5
Together it makes $2.00
4x + 12 = 20y Solve for x.
Answer:
x=5y-3
Step-by-step explanation:
[tex]4x+12=20y\\4x=20y-12\\x=\frac{20y-12}{4} \\x=\frac{20y}{4}- \frac{12}{4} \\x=5y-3[/tex]
Please help!! Over several years, Stephon gathered data about his age and the time it took him to run two laps on the school track. The scatter plot shows the data he gathered and the line of best fit. The equation of the line of best fit is y = -2.1x + 565.6. Based on the line of best fit, approximately how long will it take Stephon to run two laps on the track when he is 192 months old?
Answer:
Time taken by Stephen = 162 seconds
Step-by-step explanation:
Stephan gathered data which fits in the line of best fit,
y = -2.1x + 565.6
Where x represents the age (in months)
And y represents the time (in seconds) taken by Stephen to run two laps on the track.
Time taken to run 2 laps at the age of 192 months,
By substituting x = 192 months,
y = -2.1(192) + 565.6
= -403.2 + 565.6
= 162.4 seconds
≈ 162 seconds
Therefore, time taken by Stephen to cover 2 laps was 162 seconds when he was 192 months old.
what is the volume of the specker below volume of a cuboid 50cm 0.4m 45cm
Answer:
50*0.4*45=900cm²
6th grade math, help me please:)
Answer:
A. 3/5
Step-by-step explanation:
Simple math, 9/15. Divide both by 3.
3*3=9 and 3*5=15 so answer is 3/5!
Answer:
answer is A
Step-by-step explanation:
this is a probability question
divide the number of baskets made by the total number of attempts
9/15 = 3/5
Plz help this is an evil question
Answer:
18.9 units of fencing
Step-by-step explanation:
First find the perimeter
P = 2(l+w)
P = 2( 2.5+1.28)
P = 2( 3.78)
P =7.56m
We need 2.5 units of fencing for each meter
Multiply by 2.5
7.56*2.5
18.9 units of fencing
Answer:
Julio needs to purchase 18.9 units of fencing.
Step-by-step explanation:
I meter of the perimeter accounts for 2.5 units of fencing. Respectively 2 meters account for 2 times as much, and 3 meters account for 3 times as much of 2.5 units. Therefore, if we determine the perimeter of this rectangular garden, then we can determine the units of fencing by multiplying by 2.5.
As you can see this is a 2.5 by 1.28 garden. The perimeter would be two times the supposed length, added to two times the width.
2.5 x 2 + 1.28 x 2 = 5 + 2.56 = 7.56 - this is the perimeter. The units of fencing should thus be 7.56 x 2.5 = 18.9 units, or option d.
Find the sum of the cubes of first three composite numbers.
Answer:
792
Step-by-step explanation:
The first three composite numbers are 4, 6 ,8
so 4^3+6^3+8^3=64+216+512=792
A casino offers a game wherein a player can roll one six sided die. If the player rolls a 1or 2, they
win. If the player rolls a 3, 4, 5, or 6, they lose. If a player bets $2.00 and wins, they will be paid out
an additional $3.00. If they lose, they lose their initial $2.00. Find the expected value of the $2.00
bet.
Enter your answer rounded to the nearest cent and don't forget, expected values can be negative!
Answer:
Expected Value of $2:
Expected Value of $2:
Win, 0.3333 x $3 = $1
Plus
Loss, 0.6667 x -$2 = -$1.33
Expected value = ($0.33)
Step-by-step explanation:
Probability of a win = 2/6 = 0.3333
Probability of a loss = 4/6 = 0.6667
Expected Value of $2:
Win, 0.3333 x $3 = $1
Plus
Loss, 0.6667 x -$2 = -$1.33
Expected value = ($0.33)
The casino game player's expected value is computed by multiplying each of the possible outcomes by the likelihood (probability) of each outcome and then adding up the values. The sum of the values is the expected value, which amounts to a loss of $0.33.
x=7 what would match this soulotion
Answer:
x = 7
Step-by-step explanation:
7 = 7
It's given
What is the measure of o?
Answer:
2π radians
Step-by-step explanation:
Intelligence quotients (IQs) measured on the Stanford Revision of the Binet Simon Intelligence Scale are normally distributed with a mean of 100 and a standard deviation of 16. Determine the percentage of people who have an IQ between 115 and 140.
Answer:
the percentage of people who have an IQ between 115 and 140 is 16.79%
Step-by-step explanation:
From the information given:
We are to determine the percentage of people who have an IQ between 115 and 140.
i.e
P(115 < X < 140) = P( X ≤ 140) - P( X ≤ 115)
[tex]P(115 < X < 140) = P( \dfrac{X-100}{\sigma}\leq \dfrac{140-100}{16})-P( \dfrac{X-100}{\sigma}\leq \dfrac{115-100}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq \dfrac{140-100}{16})-P( Z\leq \dfrac{115-100}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq \dfrac{40}{16})-P( Z\leq \dfrac{15}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.9375)[/tex]
[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.938)[/tex]
From Z tables :
[tex]P(115 < X < 140) = 0.9938-0.8259[/tex]
[tex]P(115 < X < 140) = 0.1679[/tex]
Thus; we can conclude that the percentage of people who have an IQ between 115 and 140 is 16.79%
Using the normal distribution, it is found that 82.02% of people who have an IQ between 115 and 140.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of [tex]\mu = 100[/tex].The standard deviation is of [tex]\sigma = 15[/tex].The proportion of people who have an IQ between 115 and 140 is the p-value of Z when X = 140 subtracted by the p-value of Z when X = 115, hence:
X = 140:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 100}{16}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a p-value of 0.9938.
X = 115:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{115 - 100}{16}[/tex]
[tex]Z = -0.94[/tex]
[tex]Z = -0.94[/tex] has a p-value of 0.1736.
0.9938 - 0.1736 = 0.8202.
0.8202 = 82.02% of people who have an IQ between 115 and 140.
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An appliance company determines that in order to sell x dishwashers, the price per dishwasher must be p = 420 - 0.3x. It also determines that the total cost of producing x dishwashers is given by C(x) = 5000 + 0.3x2. How many dishwashers must the company produce and sell in order to maximize profit? g
The company must produce and sell 350 dishwashers in order to maximize profit.
How to determine the number of dishwashersTo determine the number of dishwashers the company must produce and sell in order to maximize profit, we need to find the value of x that corresponds to the maximum point of the profit function.
The profit (P) is given by the equation:
P(x) = Revenue - Cost
The revenue is calculated by multiplying the price per dishwasher (p) by the number of dishwashers sold (x):
Revenue = p * x
The cost is given by the function C(x):
Cost = C(x)
Therefore, the profit function can be expressed as:
P(x) = p * x - C(x)
Substituting the given expressions for p and C(x):
P(x) = (420 - 0.3x) * x - (5000 + 0.3x²)
Expanding and simplifying the equation:
P(x) = 420x - 0.3x² - 5000 - 0.3x²
Combining like terms:
P(x) = -0.6x² + 420x - 5000
To find the value of x that maximizes profit, we need to find the vertex of the quadratic function. The x-coordinate of the vertex can be determined using the formula:
x = -b / (2a)
In our case, a = -0.6 and b = 420:
x = -420 / (2 * -0.6)
x = -420 / (-1.2)
x = 350
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350 dishwashers must the company produce and sell in order to maximize profit.
Maxima means a point at which the function attains the maximum value.
Given the following information:
Price per dishwasher, p = 420 - 0.3x
Total cost of producing x dishwashers, C(x) = 5000 + 0.3x2
Profit= Total Selling price- Total Cost Price
Total Selling price of x dishwasher, S.P= xp
S.P=x(420 - 0.3x)
S.P=420x - 0.3x²
Profit= 420x - 0.3x² - ( 5000 + 0.3x²)
Profit= 420x - 0.3x² - 5000 - 0.3x²
Profit= -0.6x²+420x-5000
So, profit, f(x)=-0.6x²+420x-5000
To determine the value of x so that maximum profit is possible:
1. Calculate the first derivative of profit function and calculate the value of x by equating it to zero.
2. Select that value of x for which the profit function attains the maximum value, to check the maxima calculate 2nd derivative, if it gives a negative value for the value of x. Then, x is the point of maxima for the given function.
[tex]f(x)=-0.6x^2+420x-5000\\f\prime(x)=-1.2x+420\\f\prime(x)=0\\-1.2x+420=0[/tex]
Calculating the value of x by transposing,
x=420/1.2
x=350
To check maxima, calculating second derivative.
[tex]f\prime(x)=-1.2x+420=0\\f\prime\prime(x)=-1.2[/tex]
2nd derivative is negative, it means that x=350 is the point of maxima.
Thus, a company must produce and sell 350 dishwashers in order to maximize profit.
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What is the equation perpendicular to -x+y= 7 and passes through (-1,1)
Answer:
Step-by-step explanation:
First , let us rewrite the given equation into y= mx+b format
.y= -x +7
Slope is -1
Slope of the line perpendicular to the given equation is -(-1) ie., 1
Let us find the y-intercept by plugging in the values of x,y and slope into the equation y= Mx +b
1 = -1 +b
2 = b
Equation of the line perpendicular to the given equation and passing through (-1,1) is
y=x +2
Need Answers ASAP!!!! (due today)
Answer:
1.
a. 20 m²: barn door is 5m x 4m
b. 468 m²:surface area of barn
i. left and right barn walls: 2(15 x 7) = 210
ii. back wall: 7 x 8 = 56
iii. front wall: (7 x 8) - 20* = 36
*20 for the barn door
iv. front of roof: (4 x 4) / 2 = 8 x 2* = 16
*I split the triangle into 2 smaller triangles
v. sides of roof: 2(5 x 15) = 150
2.
a. 15 m²: silo door is 3m x 5m
b. 244.18 m²: surface area of silo
i. SA(silo)=2πrh+2πr²
ii. SA(silo) = 2π(2.5)(14) + 2π(2.5)²
iii. SA(silo) = 259.18
iv. SA(silo - door) = 259.18 - 15
v. SA(silo - door) = 244.18
3.
a. 712.18 m²: total surface area painted red
i. add both surface areas: 468 + 244.18 = 712.18 m²
hope this helps :)
You are tossing a coin, then rolling a die, then drawing a card from a deck of cards. What is the probability that you will get: a tail AND an even number on the die AND a card less than 5 (assume the ace is equal to 1) from the deck?
[tex]|\Omega|=2\cdot6\cdot52=624\\|A|=1\cdot3\cdot16=48\\\\P(A)=\dfrac{48}{624}=\dfrac{1}{13}[/tex]
Answer:
1/13
Step-by-step explanation:
f(x)=2x+1 and g(x)=3x2+4, find (f∘g)(−2) and (g∘f)(−2).
Answer:
Step-by-step explanation:
Fog=2(g)+1
2(3x+2+4)+1
2{3x+6)+1
6x+12+1
=6x+13
Fog(-2)=6(-2)+13
-12+13
=1
Gof=3(f)+2+4
=3(2x+1)+6
6x+3+6
=6x+9
Gof(-2)=6(-2)+9
-12+9
=-3
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 8 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 22 feet high
Answer:
(11π/9 )ft/s
Step by step Explanation
Let us denote the height as h ft
But we were told that The diameter of the base of the cone is approximately three times the altitude, then
Let us denote the diameter = 3h ft, and the radius is 3h/2
The volume of the cone is
V = (1/3)π r^2 h
Then if we substitute the values we have
= (1/3)π (9h^2/4)(h) = (3/4)π h^3
dV/dt = (9/4)π h^2 dh/dt
We were given as 22feet and rate of 8 cubic feet per minute
h = 22
dV/dt = 8
8= (9/4)π (22) dh/dt
= 11π/9ft/s
Therefore, the rate is the height of the pile changing when the pile is 22 feet is
11π/9ft/s
Please helppp!!!!! Geometry
Answer:
[tex]\boxed{Option \ 4}[/tex]
Step-by-step explanation:
∠YVZ = 180 - 52 - 43 - 38 (Angles on a straight line add up to 180 degrees so if we try to find an unknown angle on the straight line, we need too subtract all the other angles from 180 degrees)
=> ∠YUZ = 47 degrees
Step-by-step explanation: In the figure shown, <UVW is a straight angle.
This means it measures 180 degrees.
So to find <YVZ, we add up all the angles and subtract the sum
from 180 to get the answer to this problem.
43 + 52 + 38 gives us a sum of 133.
Now we take 180 - 133 yo get 47.
So m<YVZ is 47 degrees.
John needs to produce a scale diagram of a bedroom using a scale of 1:40. The length of the room is 3.4 metres. What is the length on the diagram? _____ cm
Answer:
8.5cm
Step-by-step explanation:
convert 3.4metres to cm that is by multiplying by 100
3.4×100=340cm
1rep 40
?rep 340
that is 340/40
=8.5cm
Answer:
8.5 cm
Step-by-step explanation:
Scale = 1:40
Length of the room = 3.4 meters
3.4 meters =3.4 X 100 =340 cm
Since 1 unit on the diagram represents 40 units
The length of the diagram
[tex]=\dfrac{340}{40}\\\\=8.5$ cm[/tex]
The length of the room on the diagram is 8.5 cm.
What expression be used to add 3/4 + 1/6
Answer:
11 / 12 or 0.9167
Step-by-step explanation:
Given:
3/4 + 1/6
Find:
Value with expression
Computation:
"3/4 added to number 1/6"
3/4 + 1/6
By taking LCM
[9 + 2] / 12
11 / 12 or 0.9167
6th grade math, help me please.
Answer:
a) [tex]\frac{2}{3} \,\frac{lb}{bread}[/tex]
b) [tex]1\frac{1}{4} \,\frac{in}{domino}[/tex]
Step-by-step explanation:
Part a:
every 4 lbs of flour, she makes 6 loaves of bread. this as a rate in simplest fraction form is:
[tex]\frac{4}{6} \,\frac{lb}{bread} = \frac{2}{3} \,\frac{lb}{bread}[/tex]
Part b:
every 10 inches , 8 dominoes can be placed. then the rate can be written as:
[tex]\frac{10}{8} \,\frac{in}{domino} = \frac{5}{4} \,\frac{in}{domino} =1\frac{1}{4} \,\frac{in}{domino}[/tex]
Please help me identify the rays!!!!
Answer:
D (The last choice)
Step-by-step explanation:
We know that rays are lines with a dot on one side and an arrow on the other. WE also know that lines have two arrows on each end. Keeping this in mind, we can identify which line segments and rays and lines.
can I get a step by step explanation Thnx
Answer:
( 2A - kn) /k = m
Step-by-step explanation:
A = k/2(m+n)
Multiply each side by 2/k
2/k *A =2/k * k/2(m+n)
2A /k = m+n
Subtract n from each side
2A /k - n = m+n -n
2A /k - n = m
Getting a common denominator
2A/k - kn/k = m
( 2A - kn) /k = m
Answer:
Step-by-step explanation:
[tex]A=\frac{k(m+n)}{2}\\2A=k(m+n)\\\frac{2A}{k} =m+n\\\frac{2A}{k}-n=m\\2A-kn=km\\\frac{(2A-kn)}{k}=m[/tex]
Identify any outlier(s) in the data. {52, 61, 42, 46, 50, 51, 49, 44, 40, 66, 53, 67, 45, 64, 60, 69}
An outlier in statistics is a data point that deviates considerably from other observations. The given data set has no outlier.
What is an outlier?An outlier in statistics is a data point that deviates considerably from other observations. An outlier can be caused by measurement variability or by experimental mistake; the latter is sometimes eliminated from the data set.
To find the outlier for the given data set follow the given steps.
Step one: The first step is to find the quartiles for the data set.
For this data set, the quartiles are:
Q1 = 45.5
Q3 = 62.5
Step Two: Find the Interquartile Range
The interquartile range is the difference between the first and third quartiles.
IQR = Q3 - Q1
IQR = 45.5 - 62.5
IQR = 17
Step Three:
The next step is to set up a fence beyond the first and third quartiles using the interquartile range.
Lower Fence = Q1 - (1.5 × IQR)
Lower Fence = 45.5 - (1.5 × 17)
Lower Fence = 20
Upper Fence = Q3 + (1.5 × IQR)
Upper Fence = 62.5 + (1.5 × 17)
Upper Fence = 88
Step Four: Find the Outliers
Any numbers in the data that are above or below the fences are outliers.
Since there are no numbers outside the two fences. Hence, it can be concluded that the given data set does not have, any outlier.
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45% of 80.374 is a number between
Answer:
36.1683
Step-by-step explanation:
45*80.374/100=
Enter the correct answer in the box by replacing the values of a and b. f(x) = a(b)^x
Answer:
f(x)= 8(0.5)^x
Step-by-step explanation:
As you can see on the graph there are two specific points labeled:
(0,8) and (1,4)
The 8 would be the initial value and starting point of the "design"
A is always the initial value so replace that.
Then proceed to divide 4 by 8 to figure out the percentage change its 0.5
leave x as it is
Find the length L of the curve
[tex]y = \sqrt{x} [/tex]
from the point P(0,0) to the point Q(4,2)
Answer:
4.647 to the nearest thousandth.
Step-by-step explanation:
The formula for the length of an arc between x = a and x = b is
a
∫ √( 1 + (f'(x))^2) dx
b
Here f(x) = √x so
we have ∫ (√( 1 + (1/2 x^-1/2))^2 ) between x = 0 and x = 4.
= ∫ ( √( 1 + 1/(4x)) dx between x = 0 and x = 4.
This is not easy to integrate but some software I have gives me the following
length = √17 + 1/8 log(33 + 1/8 √17)
= 4.647.
The line passing through points
(4,0) and (-2, 1) has a slope of?
A. -6
B. -1/6
C. 1/2
D. 2
E. 1/6
Answer:
b. -1/6
Step-by-step explanation:
slope = (difference in y)/(difference in x)
slope = (1 - 0)/(-2 - 4) = 1/(-6) = -1/6
Answer:
m = -1/6 = B
Step-by-step explanation:
[tex]m = \frac{y_2-y_1}{x_2-x_1} \\ x_1=4\\ y_1=0\\ x_2=-2\\y_2=1.\\m = \frac{1-0}{-2-4} \\m = \frac{1}{-6}[/tex]
CAN SOMEONE PLEASE HELP ME! To find x
ANSWERS
A-(11)
B-(14)
C-(7)
D-(3)
Answer:
C-(7)
Step-by-step explanation:
Given figure is a trapezoid and 21 - x is the mid segment.
Therefore by mid-segment formula of a trapezoid, we have:
21 - x = 1/2(17 + 11)
21 - x = 1/2 * 28
21 - x = 14
21 - 14 = x
7 = x
x = 7
I NEED HELP ASAP choose one of the multiple choice
Answer:
B. Square both sides of the equation.
Step-by-step explanation:
You cannot do anything to the equation unless you square both sides to eliminate the square root on the left (squaring each individual term of the equation does not help; you need to square the entire square root to eliminate it).
Hope this helps!