Answer:
It is C
Step-by-step explanation:
Find two positive integers whose sum is 16 and the sum of squares is minimum.
x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.
According to the question,
The two numbers are positive and the sum of the two numbers is 16 and the sum of the squares of the two numbers is the minimum.
Now to solve the question we will consider,
x and y are the two numbers, such that x > 0 and y > 0
Sum of the numbers : x + y = 16
Sum of squares of the numbers: S = x²+ y²
x + y = 16 y = (16 - x)
Assume, S = x² + y²
S = x² + (16 - x)²
Now we will differentiate with respect to x
dS/dx = 2x+ 2(16-x)(-1)
2x-2(16-x)=0
2x-32+2x=0
4x-32=0
4x=32
x=32/4
x=8
As x > 0, x = 8
d²S/dx² = d/dx [2x+ 2(16-x)(-1)]
d²S/dx² = d/dx (2x) - 2 d/dx (16-x)
d²S/dx² = 2 - 2[0-1]
d²S/dx² = 4
Now when x=8
d²S/dx² = 4 ≥0
Therefore, the function S = sum of the squares of the two numbers is minimum at x = 8.
y = 16-8 = 8
Therefore, x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.
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Tony planned to spend $100 for food this week. On Monday he spent $22 and on Thursday he spent $52. How much money dose he have left for the week
Answer:$26
Step-by-step explanation:
52+22=74
100-74=26
suppose that among the 6000 students at a high school, 1500 are taking honors courses and 1800 prefer watching basketball to watching football. if taking honors courses and preferring basketball are independent, how many students are taking both honors courses and prefer basketball to football?
Students taking both honors courses and prefer basketball to football is 450.
Total number of students at a high school = 6000
Number of students who has taken honors courses = 1500
Number of students who prefer watching basketball to football = 1800
Let event of taking honors courses be A
and event of preferring watching basketball be B
P(A) = 1500 / 6000 = 0.25
P(B) = 1800 / 6000 = 0.3
If both the event of taking honors courses and preferring watching basketball is independent then
By using property of independent events ,
P(A∩B) = P(A) . P(B)
= (0.25)(0.3) = 0.075
Number of students taking both honors courses and prefer basketball to football = 0.075 × 6000
= 450 Students
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a research team believes that a recently discovered treatment will have an effect on the dependent variable. they randomly selects a sample of 12 people, and with their permission, provides them a treatment. they then evaluate the evidence regarding whether their treatment had an effect. here's the data: the mean for their sample is 99. the mean for the population is 102, with a standard deviation of 11. assume a normal distribution for the individual scores. the research team sets their alpha level to .05. . calculate the z test, and decide whether the research team should: 0 - retain the null hypothesis 1 - reject the null hypothesis.
Using the z test the value of z is -0.9404 and the value of z the research team should 0 - retain the null hypothesis.
In the given question,
They randomly selects a sample of 12 people, and with their permission, provides them a treatment.
So n = 12
The mean for their sample is 99.
x = 99
The mean for the population is 102.
μ=102
A standard deviation of 11.
σ = 11
Test statistic z:
z = (x-μ)/σ /√n
Now putting the value
z = 99-102/11/√12
z=-3/11/3.45
z=-3/3.19
z= -0.9404
Test statistic z = -0.9404
From the value of z the research team should 0 - retain the null hypothesis.
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4(y-4)=8
ANSWER WITH EXPLINATION PLEASE
Answer:
y=6
Step-by-step explanation:
4(y-4)=8
4×y-16=8
4×y=8+16
4×y=24
y=6
4(6-4)=8
4×2=8
Savio leaves his home 9.00 to drive to a work appointment. He drives a distance of 40miles.
Savio thinks he drives at an average speed of 60 miles per hour.
If Savio is correct what time will he arrive at his appointment
Answer:
9:40
Step-by-step explanation:
Distance = rate x time
Let t = time
40 = 60t Divide both sides by 60
[tex]\frac{40}{60}[/tex] = t An hour would be 60 minutes so the number of minutes out of the total would be 40.
the sat math scores of 1,000 future engineers and physicists are recorded. what will be the relationship between the mean and median of the collected data? think about if you would expect the distribution of sat math scores to be a normal distribution, skewed right distribution, or skewed left distribution.
The relationship between the mean and median of the collected data is that the mean will be smaller than the median.
Since the SAT Math scores for these students will be mostly high scores, the distribution will be skewed to the left. Thus, the few low scores (outliers) will make the mean smaller than the median.
Outliers that do not change the mean have an impact just on the mean. As a result, the mean is frequently lower than that of the median when the distribution of data is skewed to the left. The mean is frequently higher than the median when the distribution is tilted toward the right. We anticipate that the mean and median in symmetrical distribution will be about identical in value. This is a crucial link between the connection here between mean and median as well as the distribution's form. Nevertheless, it isn't applicable to all sets of data. Collections of data sets are where exceptions happen much more frequently.
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(1 point) college officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. how many randomly selected student
Probability Theory
P (K) =[tex]\frac{n (K) }{n (S)}[/tex]
P(K) : probability of selected K
n (K) : number of occurence of K
n (S) : number of all occurence
In question is not contain information about the number of students who curry a gun, knife, or other weapon and the number of all students. so, we can desribe that :
n (A) : the number of occurence of students who curry a gun
n (B) : the number of occurence of students who curry a knife
n (C) : the number of occurence of students who curry other weapon
and the number of all students is n ( A U B U C) -> union of sets
how many randomly selected student? in question, there is no specific about the student. so, we can answer with :
1) probability of students who curry a gun
P (A) = [tex]\frac{n (A) }{n (AUBUC)}[/tex]
2) probability of students who curry a knife
P (B) = [tex]\frac{n (B) }{n (AUBUC)}[/tex]
3) probability of students who curry other weapon
P (C) = [tex]\frac{n (C) }{n (AUBUC)}[/tex]
and if question want to estimate with percentage, we can multiply with 100%. example :
1) percentage of probability of students who curry a gun
P (A) = [tex]\frac{n (A) }{n (AUBUC)}[/tex] x 100%
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Francesca has 2615 comic books.
She wants to put them into groups of 8.
How many comic books would be left over
after putting them into groups?
Answer: 7 comic books would be left after putting them into groups of 8.
Step-by-step explanation: There will be 326 groups of comic books. 326 x 8 = 2,608 which means that there will be 7 comic books left after putting them all into groups of 8.
Two trains are traveling at constant speeds on different tracks. Trains Train A is traveling 12.5 meters per second. What speed is Train B traveling? meters per second.
Train B is traveling faster because it traveled 100 meters in four seconds.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
We have to determine which train is moving faster based on the image.
We can tell by looking at the train speeds.
As per the formula,
distance/time = speed
Train A travels 12.5 metres in one second = 12.5/1 = 12.5 metres per second
Train B travels 100 meters in four seconds, hence its speed is 100/4 = 25 meters per second.
This is because it traveled 100 meters in four seconds, whereas train A covered 12.5 meters in one second.
Hence, train B is traveling faster.
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The question seems to be incomplete the correct question has been in attached file
A company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122. 5 grams per apple. Calculate and interpret a 95% confidence interval for the mean weight per apple.
The average apple weight's 95% confidence interval is (119.14, 125.86).
According to one manufacturer, an apple weighs 120 grams on average with a 12-gram standard variation. According to statistics generated from a sample of 49 apples randomly selected from a shipment, the average weight per apple was 122. 5 grams.
Let,
n = 49
x = 122.5
σ = 12
To figure up and analyze a 95% confidence interval for the average apple weight;
The formula for a 95% confidence interval is
(x ± 1.96*σ√n)
(122.5 ± 1.96*12/√49)
(119.14, 125.86)
Consequently, a 95% confidence interval for the average apple weight is (119.14, 125.86).
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Justin wants to find the volume of a rectangular box. He starts by placing a layer of cubes in the bottom of the box (as shown).
Each cube has a length, width, and height of `1/2` inches. He continues placing cubes in the box until it is full. What is the volume of the box?
The volume of the given rectangular box is given by 225 cubic inches.
We know that the volume of the rectangular box with length L and width W and height H is given by,
V = LWH
So given the length of rectangular box is = 12 1/2 inches = 25/2 inches
The width of rectangular box is = 4 1/2 inches = 9/2 inches
The height of box is = 4 inches
So the volume of the rectangular box = (25/2)*(9/2)*4 = 25*9 = 225 cubic inches.
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(-5,6)
(-3,3)
(-1,0)
(1,-3)
(3,-6)
Find the range of the relation.
(-6, -3, 0, 3, 6)
(-5, -3, -1, 1, 3)
(-6, -5, -3, -1, 0, 3, 6}
(-6,6)
The range of the given relation is (-6, -3, 0, 3, 6).
Range:
Basically the set contains 2 elements in it, in which set contains all the second elements, on the other hand, is known as the range of the relation.
Given,
Here we have the relation (-5,6), (-3,3), (-1,0), (1,-3) and (3,-6)
Here we need to find the range of the relation.
According to the definition of the relation,
Range refers the y values of the coordinates,
So, based on this the value of the given coordinates are extracted as,
(-5, 6) => 6
(-3, 3) => 3
(-1, 0) => 0
(1, -3) => -3
(3, -6) => -6
Now we have arrange the range values from the smallest to largest,
Therefore, the range of the relation is (-6, -3, 0, 3, 6).
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Algbra 2 help please asap
Answer:
3√10 units
Step-by-step explanation:
[tex] \sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \sqrt{10} = 5 \sqrt{10} [/tex]
[tex]3x + 2x = 5 \sqrt{10} [/tex]
[tex]5x = 5 \sqrt{10} [/tex]
[tex]x = \sqrt{10} [/tex]
So the length of the longer piece is 3√10 units.
f(x) = x
f(x) = 3
f(x) = 5-x
f(x) = 3-x
Domain
x=2
2
0≤x<2
3
f(x) = 1
f(x) = 2
Function Equation
Given f(x)=2−∣x−5∣
Domain of f(x) is defined for all real values of x.
Since, ∣x−5∣≥0⟹−∣x−5∣≤0
⟹2−∣x−5∣≤2⟹f(x)≤2
Hence, range of f(x) is (−∞,2].
The volume of this prism is 378 cm*.
What is the length of x?
27 cm*
Answer:14
Step-by-step explanation:All you have to do is Divide 378 by 27 to get x
Hope This Helps!
How do I solve this Quadratic expression by factoring?
Answer:
Step-by-step explanation:
Step-by-step explanation:
the highest exponent is 2, so, we expect to get 2 factors in x (as the multiplication of x×x = x²).
3 is a prime number, and the only factors to get 3 are 3 and 1
3 = 3×1
so, we expect to get factors that look like
(3x + a)(x + b)
when we do the multiplication, we get
3x² + 3bx + ax + ab = 3x² +(3b + a)x + ab
now we compare this to our original expression
3x² +(3b + a)x + ab = 3x² - 13x + 12
3b + a = -13
ab = 12
so, we know a and b must both be negative
(-×- = +, - - - = -).
the negative factors of 12 are
-12 × -1
-6 × -2
-4 × -3
which one of these pairs can make
3b + a = -13
be true ?
3×-12 + -1 = -37 no
3×-1 + -12 = -15 no
3×-6 + -2 = -20 no
3×-2 + -6 = -12 no
3×-4 + -3 = -15 no
3×-3 + -4 = -13 yes
so, our factors are
(3x - 4)(x - 3)
I need help please!!!
The slope of the line that passes through (9, 1) and (-8, 2) is -1/17
How to find the slope?If we have a linear equation or a segment that passes through two points (x₁, y₁) and (x₂, y₂), then the slope is given by the formula:
slope = (y₂ - y₁)/(x₂ - x₁)
In this case, we know that the two points are (9, 1) and (-8, 2), using the above formula we can find the slope to be:
slope = (2 - 1)/(-8 - 9)
slope = 1/-17 = -1/17
That is the slope of the line or segment that passes through the given points.
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Distribute and then Combine Like Terms: 5(3x + 4) + 7x
Answer:
22x + 20
Step-by-step explanation:
Distribute:= (5)(3x) + (5)(4) + 7x
= 15x + 20 + 7x
Combine Like Terms:= 15x + 20 + 7x
= (15x + 7x) + (20)
= 22x + 20
Answer:
22x +20
Step-by-step explanation:
5(3x + 4) + 7x
5 x 3x + 5 x 4 +7x
15x + 5 x 4 + 7x
15x + 20 + 7x
22x + 20
Doughnuts are sold in bags and cartons.
A bag holds 4 doughnuts and a carton holds 10 doughnu*
Tom buys B
bags of doughnuts and C cartons of doughnuts.
He buys a total of T doughnuts.
Write down a formula for T in
terms of B and C.
Answer:
Step-by-step explanation:
Answer:
b= c + t (the amount bought)
Step-by-step explanation:
Janet buys 4 bags of potatoes.
The first bag has 8 potatoes in it.
The second bag has 6 potatoes in it.
The third bag has 10 potatoes in it.
She has not yet counted the number of potatoes in the fourth bag.
To represent the total number of potatoes she has, Janet writes (8+6+10)
+x, where x is the number of potatoes in the fourth bag. Which expression
also represents the total number of potatoes Janet has?
2(4+3+5+x)
O 25+1+B)4x
O (8+6)(10+x)
O (8+6)+(10+x)
Answer:
(8+6)+(10+x)Step-by-step explanation:
2(4+3+5+x) Not valid since x represents the total number of potatoes in the fourth bag. The expression expands to (8+6+10 + 2x), not just x.25+1+B)4x Not valid as written, the expression has a new, undefined variable, B. Plus the 25+1 are not related to the actual inforamation. (8+6)(10+x) Not valid since there is no logic in multiplying the two expressions.(8+6)+(10+x) Valid: The expression can also be writte as 8+6+10+x, which matches the potatoe count in the four bags.Which equation represents the line parallel to the line whose equation is 2y=4x+14
The parallel line has an equation of y = 2x + 3
How to determine the line equation?The equation is given as
2y = 4x + 14
Make y the subject
2y = 4x + 14
Divide through by 2
y = 2x + 7
The equation of a line can be represented as
y = mx + c
Where
slope = m
By comparing the equations, we have:
m = 2
This means that the slope of 2y = 4x + 14 is 2
The slopes of parallel lines are equal
This means that the slope of the other line is 2
i.e. m = 2
Recall that:
The equation of a line can be represented as
y = mx + c
Where
slope = m
So, we have
y = 2x + c
Assume any value for c
This gives
y = 2x + 3
Hence, the equation of the parallel line is y = 2x + 3
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I need help please!!
Answer:
-5/3 or -1.67
Step-by-step explanation:
Answer:
-5/3
Step-by-step explanation:
Oh it's you again, I am just gonna copy paste my format from your previous question.
Use the slope formula: s=(y2-y1)/(x2-x1)
It doesn't matter the order.
Let's say -6 is x2 and 8 is y2; 3 is x1 and -7 is y1
Plug in the equation: s=[(8)-(-7)]/[(-6)-(3)]
Simplify and solve: s=[8+7]/[-9]
s = -15/9
s = -5/3
True or false: The numerical coefficient of 14xy4z5 is 4.
Answer:
False
Step-by-step explanation:
The numerical coefficient is 14, not 4.
Answer:
it's False
Step-by-step explanation:
Trust me IT worth it
A dog kennel charges $40 for each night the dog stays in the kennel. Each day includes a 2 hour play time and
1 hour etiquette training. The kennel also charges a $10 bathing fee for a bath before the dog returns home.
Think of the linear function that demonstrates the cost of putting a dog in the kennel (c) in terms of the number
of nights (n)
Answer:
c=40n+10
Step-by-step explanation:
They charge 40$ per night from which we get 40n
The extra 10$ is from the bathing fee
The rest of the information they give us isn't useful in this case because they didn't ask us the cost per hour
Sketch and Solve. A rectangular page is 2 inches longer than it is wide. If the diagonal of the pag is 52 inches, what is the perimeter of the page
The Perimeter of the Rectangle is 144cm;
What is the Perimeter of a Rectangle?
The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in meters, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.
A rectangle has four 90° angles.
The lengths of a rectangle's diagonals are equal. Rectangle perimeter is calculated using the formula perimeter of a rectangle = 2(l + w), where l is the rectangle's length and w is its width.
According to the question
Let the length of the rectangle be x cm;
So, The breadth of the rectangle will be: (x+2) cm;
And, we have the diagonal = 52 cm;
So,
we can use the Pythagoras triangle to find the value of x cm;
⇒[tex]x^{2} + (x+2)^{2} = (52)^{2}[/tex]
⇒[tex]2x^{2} +4+4x = 2704;\\[/tex]
⇒[tex]2x^{2} +4x = 2700[/tex]
⇒[tex]2x^{2} +4x - 2700 =0;[/tex]
By solving the above equation, we get:
x = 35 cm;
So, the length of the rectangle = is 35 cm;
Breadth of the rectangle = 37 cm;
and
Perimeter of the Rectangle = 2(35 + 37) cm;
The perimeter of the Rectangle = = 144 cm;
Hence,
The perimeter of the Rectangle = = 144 cm;
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I need help with this, I "apparently get it wrong"
Answer:
Step-by-step explanation:
Which one adds up to 14 is the question? There are dots on the dice which correspond to numbers. The dots are saying that they are numbers. And if you get to 14 with the dices, you pick it.
b to the power of −6 times b to the power of 11
Answer: B^5
Step-by-step explanation: truss
In the space provided below, solve the equation 4x² 768 = 0 for x algebraically. Write your answer in simplest radical form. Show all work.
Answer:
Step-by-step explanation:-b± √b²-4ac. X =
What is the maximum or minimum value of the function what is the range y=-2x^2+32x-12.
The maximum or minimum value of the function y = -2x² + 32x - 12 is (8, 116) and the range of the function y = -2x² + 32x - 12 lies in the interval
(−∞ ,116).
Given, the function is y = -2x2 + 32x - 12
According to the question we have to extract the maximum or minimum value of the function.
The maximum or minimum of a function which is a quadractic function occurs at the point x = -b/2a.
If a is negative, then the maximum value of the function is f(-b/2a).
If a is positive, then the minimum value of the function is f(-b/2a).
According to this, we can derive the general equation as
fmax(x) =ax²+bx+c occurs at x = -b/2a.
From the given equation, comparing we get
a = -2, b = 32, c = -12
Substitute the value of a and b in in the general equation and we get
x = -32/2(-2)
x = -32/-4
x = 8
Put x = 8 in the given general equation,
y = -2(8)² + 32(8) - 12
y = -2(64) + 256 - 12
y = -128 + 256 - 12
y = 256 - 140
y = 116
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