Minimum number is 33+4*6= 57
Give us two positive numbers, x and y.
196 is the result: x*y = 19
The minimum is the product of the first plus four times the second: x + 4y.
The first equation results in y = 196/x. Put that into the second equation as a replacement:
x + 4y = x + 4(196/x) = x + 784/x
Taking the first derivative now, we can solve for x by setting it to zero.
d(x + 784/x)/dx = 1 - 784/[tex]x^{2}[/tex]
0 = 1 - 784/[tex]x^{2}[/tex]
0 = [tex]x^{2}[/tex]- 784 [[tex]x^{2}[/tex] multiplied on both sides]
784 = [tex]x^{2}[/tex]
[tex]\sqrt{784}[/tex] = [tex]\sqrt{x^{2} }[/tex]
Y = 196/x = 7 since we want a positive integer, hence x = 28
The factors of 196 are 196*1, 99*2, 66*3, 6*33,22*19, and 11*18 as a check.
196 + 4*1 = 200
99 + 4*2 = 107
66 + 4*3 = 78
33+4*6= 57
22 + 4*19 = 98
11 + 4*18=82
In fact, 33+4*6= 57 is minimum.
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in a survey, 24 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $35 and standard deviation of $15. construct a confidence interval at a 90% confidence level.
The confidence interval at a 90% is 29.533 ≤ μ ≤ 40.467
Given that
mean = 35
standard deviation = 15
We compute the confidence interval as follows:
μ =¯ˣ± ME
Where:
μ = is the population mean,¯x = 35 is the sample mean and,ME = is the margin of error.To calculate the margin of error, we will use the t-distribution since the sample is very small n<30. Thus, our margin of error will be calculated as:
ME = t ×[tex]\frac{s}{\sqrt{n} }[/tex]
Where:
t = is the t-score at the 90% confidence level
degree of freedom df = 24 -1 =23
s = 15 is the standard deviation and,
n =24 is the sample size.
From the t-distribution tables, we will read the values of t at a critical value [tex]\alpha[/tex] = 0.10, and the degree of freedom is 23. This will give t= 1.714.
Thus, the margin of error is:
ME = 1.714 ×[tex]\frac{15}{\sqrt{23} }[/tex]
ME = 1.714 ×3.19
ME = 5.467
the confidence interval for the population mean is equal to:
μ = 35 ± 5.467
29.533 ≤ μ ≤ 40.467
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The graph represents the number y of computers infected by a virus after x hours. Find the number of computers infected after 90 minutes and after 6 hours.
Examining the given graph the number of computers infected in
90 minutes = 8 computers6 hours = 4096 computersHow to find the number of computers infectedThe graph shows that the function is an exponential function
represented as
The starting term of the function f(x) = 4^t is 1, and base is 4
f(x) = number of computer infected
t = time in hours
90 minutes in hours
90 / 60 = 1.5 hours
for t = 1.5 hours
f(x) = 4^1.5
f(x) = 8
for t = 6 hours
f(x) = 4^6
f(x) = 4096
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A 3/8-pound piece of cheese contains 4 servings. How much cheese is in 1 serving?
Answer:
3/32-pound cheese in 1 serving
Step-by-step explanation:
(3/8)/4=3/32 or 0.09375 lbs
3- (pogil) a friend claims that flipping a coin 100 times and finding that it comes up heads only 45% of the time shows that the coin is biased. how should you reply?
with 100 flips, the outcome is very likely to be 45 heads or even less.
just because you have a 50% chance of getting heads, does not necessarily mean that you will get heads at exactly 50%.
100 coin flips will not always produce a 50-50 outcome of heads or tails. This is due to the fact that random events, while predictable in the long run, are not 100% predictable in small cases. For example, if we flipped a fair coin a quadrillion times, the variability in the outcomes caused by the coin's randomness would amount to a fractional value so small that calculators might even round the percentage of heads to 50%. However, with 100 flips, the outcome is very likely to be 45 heads or even less.
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suppose the true proportion of voters in the county who support a restaurant tax is 0.55. consider the sampling distribution for the proportion of supporters with sample size n
The mean of this distribution is 0.55
The standard error of this distribution is 0.0384
We have the following:
p=0.55
sample size, n=168
Mean of distribution:
Mean=true proportion of voters who support a restaurant
Mean=p=0.55
Hence, the mean of distribution is 0.55
Standard error of the distribution:
[tex]=\sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]=\sqrt{\frac{0.55(1-0.55)}{168} }[/tex]
=0.0384
Hence, the standard error is 0.0384
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The questions was incomplete, the complete question is given below:
Suppose the true proportion of voters in the county who support a restaurant tax is 0.55. Consider the sampling distribution for the proportion of supporters with sample size n = 168.
What is the mean of this distribution?
What is the standard error of this distribution?
What type of angles are < 3 and < 6
Answer:
Obtuse Angles
Step-by-step explanation:
Both < 3 and < 6 are visibly over 90° and less than 180°, so both are obtuse.
In the equation, what is the value of s?
3(s + 1) − 8 = 6s(2 − 4)
Answer:
[tex]\boxed{\boxed{\sf s=\frac{1}{3}}\sf \:or\:\boxed{\sf s=0.33...}}[/tex]
Step-by-step explanation:
[tex]\sf 3\left(s+1\right)-8=6s\left(2-4\right)[/tex]
Expand ( Apply the Distributive Property):-
[tex]\sf 3s-5=-12s[/tex]
Add 5 to both sides:-
[tex]\sf 3s-5+5=-12s+5[/tex]
Simplify:-
[tex]\sf 3s=-12s+5[/tex]
Add 12s to both sides:-
[tex]\sf 3s+12s=-12s+5+12s[/tex]
Simplify:-
[tex]\sf 15s=5[/tex]
Divide both sides by 15:-
[tex]\sf \cfrac{15s}{15}=\cfrac{5}{15}[/tex]
Simplify:-
[tex]\sf s=\cfrac{1}{3}[/tex]
___________________
Hope this helps!
Have a great day! :)
Which graph represents the function
f(x)=√x+3-4
Answer:
I believe it is the last option but I'm not completely sure because the pic is blurry. But if the beginning of the graph is at (-3, -4) then the last option is definitely correct.
Step-by-step explanation:
Remember h controls horizontal movement k controls vertical movements.
always remember to take the opposite of h.
;)
h - 2 > 10; h = 12
is that true?
Answer:
no, h=anything greater than 12
Step-by-step explanation
Answer:
No. It is false.
Step-by-step explanation:
h - 2 > 10; h = 12
Substitute 12 in place of h.
12 - 2 >? 10
Simplify.
10 >? 10
10 is NOT > 10
10 is not greater than 10. 10 is equal to 10. If the symbol had the "or equal to" underline under it, then it would be true. See image.
Choose the graph of Y=1/2|x|+3
What is the equation for the constant of proportionality that
matches the table?
y = 9x
y=18x
y = Ox
y = x
Answer:
y=9x
Step-by-step explanation:
For these x's and y's, we can notice that y is always equal to 9 times the value of x. 0 equals 9 * 0, 9 equals 9 * 1, 18 equals 9 * 2, 27 equals 9 * 3, and 36 equals 9 * 4.
We have just shown that y equals 9 times x, which is just y=9*x, or y=9x.
A regular hexagon with a perimeter of 45 meters is dilated by a scale factor of 4/3 to create a new hexagon. What is the perimeter of the new hexagon?
The perimeter of the resulting hexagon is 60 meters.
What is the perimeter of the image of a hexagon as a result of a dilation?
In this problem we find the perimeter of a regular hexagon, which is dilated around its center. Regular hexagons are polygons with six sides of equal length. Dilations are rigid operations of the form:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilation.k - Scale factorP(x, y) - Original pointP'(x, y) - Resulting pointThe perimeter is the sum of the side lengths of the hexagon and by dilation we find the following relationship between original and resulting perimeters (p, p'):
p' = k · p
If we know that p = 45 and k = 4 / 3, then the resulting perimeter is:
p' = (4 / 3) · (45)
p' = 60
The resulting hexagon has a perimeter of 60 meters.
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g(x) is a vertical shift of f(x) , as shown in the graph. How do the two equations relate to each other?
Answer:
A
Step-by-step explanation:
g(x) = f(x) + 3
9y + 4.1 -6y someone help me on this question
Answer:
3y + 4.1
Step-by-step explanation:
You can't add unlike terms, so you collect like terms:
9y - 6y + 4.1
= 3y + 4.1
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is placed. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Write the expression in exponential form.
log₆ M = y
21a5b³-14a³b² +63a²b
———————————-
7ab
Answer:
[tex]3a^4b^2-2a^2b+9a[/tex]
Step-by-step explanation:
Because multiplication is the inverse of division, we're able to split this fraction into three separate fractions, which will simplify nicely at the end:
[tex]\frac{21a^5b^3}{7ab}; \frac{-14a^3b^2}{7ab}; \frac{63a^2b}{7ab}[/tex]
We can start by simplifying each fraction since 21, -14, and 63 are all divisible by 7:
[tex]\frac{3a^5b^3}{ab}; \frac{-2a^3b^2}{ab}; \frac{63a^2b}{ab}[/tex]
Finally, when dividing quotients with exponents, we subtract the exponents and we put all of our answers back together since everything was multiplied by each other at the beginning of the problem:
[tex]3a^4b^2-2a^2b+9a[/tex]
A 3 gallon bucket of paint costs $116.64. What is the price per cup?
Answer:
Step-by-step explanation:
You can use proportions to solve this.
You are paying $116.64 for 3 gallons of paint, so you could write this as:
\frac{116.64}{3}
Since the question is asking for price PER CUP, you want to convert 3 gallons to cups. 3 gallons = 48 cups. So now you can rewrite this as:
\frac{116.64}{48 cups}
In order to find the cost per cup, you can set up a proportion that solves for the price, x
\frac{116.64}{48 cups} = \frac{x}{1 cup}
Solve for x by cross multiplying:
48x = 116.64
x = $2.43
It costs $2.43 per cup of paint
If f(x) = -8m + 3 and g(x) = -8m^2 + m - 5, what is (f times g)x?
A.) 64m^3 - 16m^2 + 43m - 15
B.) 64m^3 +43m - 15
C.) 64m^3 - 32m^2 + 43m - 15
D.) -16m^2 + 43m - 15
Answer: Choice C
[tex]64m^3-32m^2+43m-15[/tex]
==================================================
Explanation:
Multiply out the expressions using the distribution rule as shown below.
[tex](-8m+3)(-8m^2+m-5)\\\\n(-8m^2+m-5) \ \ \text{ ... see note1}\\\\-8m^2n+mn-5n\\\\-8m^2( n )+m( n )-5( n )\\\\-8m^2( -8m+3 )+m( -8m+3 )-5( -8m+3 ) \ \ \text{ ... see note2}\\\\( 64m^3-24m^2 )+( -8m^2+3m )+( 40m-15 )\\\\64m^3+(-24m^2-8m^2)+(3m+40m)-15 \\\\64m^3-32m^2+43m-15 \\\\[/tex]
I used the tool WolframAlpha to confirm the answer is correct. GeoGebra is another free tool that offers similar capabilities.
Footnotes:
Note1: I let n = -8m+3, and replaced -8m+3 with n. That way the distribution on the next step could happen.Note2: I plugged in n = -8m+3. After which distribution happens 3 more times.pls explain how to do this
The x value for each of the equation.
1)The x is 10 when the equation is 8=x-2
2)If x+2=-2, then the value of x is -4.
3)If 2=x+8, then the value of x is -6.
4)The x is -10 when the equation is x+8=-2
Given that,
The given equation are
1) 8=x-2
2) x+2=-2
3) 2=x+8
4)x+8=-2
We have to find the x value for each of the equation.
Take the equations,
1) 8=x-2
Adding 2 on both sides
8+2=x-2+2
10=x
The x is 10 when the equation is 8=x-2
2) x+2=-2
Adding 2 on both sides
x+2+2=-2+2
x+4=0
Adding -4 on both side
x+4-4=0-4
x=-4
If x+2=-2, then the value of x is -4.
3) 2=x+8
Subtracting 8 on both sides
2-8=x+8-8
-6=x
x=-6
If 2=x+8, then the value of x is -6.
4)x+8=-2
Adding -8 on both sides
x+8-8=-2-8
x=-10
The x is -10 when the equation is x+8=-2
Therefore, the x value for each of the equation.
1)The x is 10 when the equation is 8=x-2
2)If x+2=-2, then the value of x is -4.
3)If 2=x+8, then the value of x is -6.
4)The x is -10 when the equation is x+8=-2
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Body-mass index, or BMI, takes both weight and height into account when assessing whether an individual IS
underweight or overweight. BMI varies directly as one's weight, in pounds, and inversely as the square of one's height,
in inches. In adults, normal values for the BMI are between 20 and 25, inclusive. Values below 20 indicate that an
individual is
underweight and values above 25 indicate that an individual is overweight. A person who weighs 180
pounds and is 5 feet, or 60 inches, tall has a BMI of 35.15. Use the four-step procedure for solving variations to
determine what the BMI is, to the nearest tenth, for a 210-pound person who is 5 feet 9 inches tall. Is this person
underweight, normal, or overweight?
The person is overwieght as his BMI is 31.00 (approx)
What is Proportion?
In general, proportion refers to a part, share, or quantity assessed in comparison to a total. According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios or fractions are equivalent.
Solution:
Since, BMI is directly proportionate with weight and indirectly proportionate with square of height, we need to use a constant to make proportion to an equation.
According to the question,
BMI of a person who weighs 180 pounds and is 5 feet tall is 35.15.[tex]BMI = k*weight/height^{2}[/tex]
here, k is any constant value
35.15 = k*180/(60*60)
(35.15 * 3600)/180 = k
k = 703
Calculating BMI of a person weighing 210 pound and is 5 feet 9 inch tall.
First of all we need to convert 5 feet 9 inches into inches
5 feet = 60 inches
so, 5 feet 9 inch means 69 inches
BMI = 210*703/(69*69)
BMI = 31.00 (after rounding off)
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4. The first three terms of an infinite geometric sequence are m – 1,6, m + 8.
(a)write down two expressions for r.
(b) the find two possible values of m.
(c) Hence, find two possible values of (r)
In the given geometric sequence
a) The expression of the common ratio r = -6 and (m+8)/2
b) The possible value of m = -28
c) The possible value of r = -6
The geometric sequence is
-1 , 6, m+8
The the common ratio = second term / first term
= 6 / -1
= -6
The common ratio = third term / second term
= (m+8)/6
The two expressions of common ratio is -6 and (m+8)/6
Part b
The third term = second term × common ratio
= 6 × -6
= -36
Then,
m +8 = -36
m = -36 + 8
m = -28
The possible value of m = -28
Part c
The possible value of r = -6
Hence, in the given geometric sequence
a) The expression of the common ratio r = -6 and (m+8)/2
b) The possible value of m = -28
c) The possible value of r = -6
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A waitress sold 19 ribeye steak dinners and 12 grilled salmon dinners, totaling $581.52 on a particular day. Another
day she sold 24 ribeye steak dinners and 6 grilled salmon dinners, totaling $581.59. How much did each type of
dinner cost?
The each type of dinner cost is ribeye steak dinner cost is $20.05 and grilled salmon dinner cost is $16.74 by using the equation.
Given that,
On one particular day, a waitress served 12 grilled salmon dinners and 19 ribeye steak dinners for a total of $581.52. She made $581.59 on another day by selling 24 ribeye steak dinners and 6 grilled salmon entrees.
We have to find what was the price of each kind of dinner.
So,
We take R as a ribeye steak dinner and S as grilled salmon dinners.
We get,
19R+12S=$581.52 ---> equation(1).
24R+6S=$581.59 ----> equation(2).
Now Take the equation (2)
24R+6S=$581.59
6S=$581.59-24R
Multiply 2 on both sides of equation.
12S=$1163.18-48R
Now take the equation(1)
19R+12S=$581.52
Take the 12S as 12S=$1163.18-48R
19R+$1163.18-48R=$581.52
-29R=$581.52-$1163.18
-29R=-581.66
29R=581.66
R=581.66/29
R= $20.05
Now substitute R in 12S=$1163.18-48R
We get,
12S=$1163.18-48($20.05)
12S=$1163.18-962.4
12S=200.78
S=200.78/12
S=$16.74
Therefore, The each type of dinner cost is ribeye steak dinner cost is $20.05 and grilled salmon dinner cost is $16.74 by using the equation.
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What is the first step to find the volume of the solid?
Answer: c
Step-by-step explanation:
The population of a specific species of nocturnal mammal is decreasing at a rate of 3.5%/year. The graph models the number of mammals x years after they were originally counted.
Identify and interpret the key features of the exponential function modeled in terms of this situation.
Select each correct answer.
Question 1 options:
The y-intercept represents the number of mammals when they were originally counted.
The line y = 0 is an asymptote of the graph.
The y-intercept.is 75.
The y-intercept is 120.
The asymptote indicates that the number of mammals counted when the study began was 120.
The asymptote indicates that as years pass, the number of mammals will approach 0.
The line x = 0 is an asymptote of the graph.
The key features of the graph of the exponential function are given as follows:
The y-intercept represents the number of mammals when they were originally counted.The y-intercept is 120.The line y = 0 is an asymptote of the graph.The asymptote indicates that as years pass, the number of mammals will approach 0.What are the key features of the graph?The y-intercept of a function gives the value of the function when it crosses the y-axis, that is, when x = 0, hence it is the initial number of mammals, which is of 120.
As x goes to infinity, the number of mammals will never be of zero but it will get very close to zero, hence the line y = 0 is the horizontal asymptote of the graph.
Missing InformationThe graph is shown by the image given at the end of the answer.
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In the coordinate plane, line p has slope 8 and y-intercept (0, 5). Line r is the result of dilating line p by a factor of 3 with center (0, 3). What are the slope and y-intercept of line r?.
In the given coordinate plane, based on the given dilation the line r has slope 8 and coordinate (0,8)
Dilation:
Dilation refers the ratio of the given line to line by the scale factor.
Given
In the coordinate plane, line p has slope 8 and y-intercept (0, 5). Line r is the result of dilating line p by a factor of 3 with center (0, 3).
Here we need to find the the slope and y-intercept of line r.
Here we know that scale factor is 3.
Let us consider the slope of the line r will not change and the intercept is the addition of their ordinate will be.
So, it can be written as,
=> Intercept = 5 + 3
=> Intercept = 8
Therefore, the line r has slope 8 and coordinate (0.8).
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Which graph represents f(x)=5⋅3x?
Answer:
the first one, the top left corner
Step-by-step explanation:
y- int = 5
no x int
Luke claims two circles are always isometric because the shape never changes. Is he correct?
Group of answer choices
Yes - an isometry preserves shape.
Yes - all circles are similar.
No - the center may be located on a difference coordinate.
No - an isometry preserves both size and shape.
Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.
Given that,
Luke asserts that since the shape is constant, two circles are always isometric.
We have to say is he accurate.
The answer is
No, an isometry keeps the size and shape intact.
Because a shape-preserving transformation (movement) in the plane or in space is called an isometric transformation (or isometry). The isometric transformations include translation, rotation, and combinations thereof, such as the glide, which combines a translation with a reflection.
Therefore, Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.
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Write 180 as a product of primes. Use index notation when giving your answer.
Answer: 5x2x2x3x3 is the answer to your question
Are the lines parallel? y=-3x+2 and 3x+y=6
A. Yes, they have the same slope and a different y intercept
B. No they are not parallell
Answer:
A. Yes, they have the same slope and a different y-intercept.
Step-by-step explanation:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Rearrange 3x + y = 6 to y = mx + c form.
y = -3x + 6
Parallel lines have the same slope.
Since slope of both lines is -3, the lines are parallel.
Identify a reasonable domain and range.
Tickets that cost $125 dollars each
Well the domain is the number of tickets and the range is the cost for those tickets.
So x = 1 when y = 125 (1 ticket is 125 dollars). Here is a reasonable domain and range comparision:
x = 1 , y = 125
x = 2, y = 250
x = 3, y = 375
x = 4, y = 500
ect...
The lower limit of the domain is 0 because you cannot have less than 0 tickets.
I hope this helps!