In order to complete the square for the given equation x^2+16x=18, the number added to both sides is 64.
Complete the square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial. To complete the square, add or subtract the same value to both sides. In this case, add the square of half the coefficient of the x -term, (b/2)^2 to both sides of the equation. Hence, the number to add would be (16/2)^2 = 64.
Thus,
x^2+16x + 64 =18 + 64
x^2+16x + 64 =82
x^2+ 2*8x + 64 =82
(x + 8)^2 = 82
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Use partial quotients to find the quotient for 590 divided by 6
Answer:98.3333333333 (98)
The number 590 is called the numerator or dividend, and the number 6 is called the denominator or divisor.
The quotient of 590 and 6, the ratio of 590 and 6, as well as the fraction of 590 and 6 all mean (almost) the same:
590 divided by 6, often written as 590/6. The answer is actually 98 but if I am wrong sorry.
A theme park sells adult tickets (a) for $159.50 and child tickets (c) for $109.00. The theme park needs to make at least 5.49 million dollars to make a profit each day. Which inequality could the theme park use to determine how many of each ticket must be sold in a day to make a profit?
A. 159.50a + 109c ≤5,490,000
B. 159.50a + 109c ≥5,490,000
C. 159.50a + 109c <5,490,000
D. 159.50a + 109c >5,490,000
Answer:A
Step-by-step explanation:
Inequality could the theme park use to determine the Total number of tickets that must be sold in a day to make a profit is 159.50a + 109c ≥5,490,000.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
Given, Tickets for an amusement park are available for adults (a) for $159.50 and for kids (c) for $109.00. The theme park requires daily revenue of at least $5.49 million to turn a profit.
total earning per day = 159.50a + 109c
this should be greater than (>) or at least equal to 5.49 million.
Therefore, The total number of tickets that must be sold in a day to generate a profit is 159.50a + 109c ≥ 5,490,000. Inequality might be used by the theme park to calculate this amount.
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If 15 baseballs weigh 75 ounces, how many baseballs weigh 15 ounces?
1: 5 baseballs
2:10 baseballs
3: 3 baseballs
4:75 baseballs
If 15 baseballs weigh 75 ounces, how many baseballs weigh 15 ounces?
1: 5 baseballs
2:10 baseballs
3: 3 baseballs
4:75 baseballs
75oz / 15 baseballs = 5 oz each
15 oz / 5 oz = 3 baseballs
Which of the fractions below are less than 3/4? Select four. A)3/5 B)5/8 C')5/6 D)1/2 E)7/12
a satellite in a circular orbit 1250 kilometers above earth makes one complete revolution every 110 minutes. find its linear speed, round your answer to 2 decimal places. assume that earth is a sphere of radius 6400 kilometers.
Its linear speed would be 1637.75 miles/hour
Vt = 435,49 Km/min
Vt = 26129 Km/hour
Vt = 16630, 35 miles/hour
The distance from the earth center up to the satellite position is:
Earth radius + distance above the earth
radius of satellite 6400 + 1250 = 7650 Km
linear speed = Vt = 2π*r/T
where
r is the radius of the satellite and T period = 110 min
Then
Vt = 6,28* 7650 / 110
Vt = 4804/110
Vt = 43,674.54 Km/min
To get it in Km/h we must multiply by 60
Vt = 26204m/hour
And finally, to get it in miles per hour we divide it by 16
Vt = 1637.75 miles/hour
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amc 12a 2014] let a < b < c be three integers such that a, b, c is an arithmetic progression and a, c, b is a geometric progression. what is the smallest possible value of c?
The smallest possible value of c is 1 in this case.
If the integer a, b and c are in arithmetic progression.
Then we can write,
b = (a+c)/2
If the integer a, b and c are in geometric progression,
Then, we can write,
b = √(ac)
Now, we can write,
a+b = 2√(ac)
Squaring both sides,
a²+c²+2ac = 4ac
(a-c)² = 0
So,
a = c.
If a = c.
Then,
b = (a+a)/2
b = a
So, a = b = c.
Smallest possible positive integer is 1.
So, the smallest possible value of c is 1.
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on a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. if 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
The percent of the ship's passengers held round-trip tickets is 50/100 = 50%.
Since the number of passengers on the ship is immaterial, let the number of passengers on the ship be 100 for convenience.
Let x be the number of passengers that held round-trip tickets.
Then, since 20 percent of the passengers held a round-trip ticket and took their cars aboard the ship, 0.20(100) = 20 passengers held round-trip tickets and took their cars aboard the ship.
The remaining passengers with round-trip tickets did not take their cars aboard, and they represent 0.6x (that is, 60 percent of the passengers with round-trip tickets).
Thus, 0.6x + 20 = x, from which it follows that 20 = 0.4x, and so x = 50.
The percent of passengers with round-trip tickets is, then, 50/100 = 50%
A roundtrip flight is a flight itinerary that includes one flight to a vacation spot and some other flight lower back from that destination, which include flying from NYC to Paris after which Paris lowers back to NYC. The direction might also include layovers or connections, however, the beginning and endpoint are equal.
Ask the enterprise to alter the round-trip ticket for one-way usage. although airways exercise a varying degree of flexibility, many airlines will regulate a round-ride fare to permit one-manner use, though a few airlines might also charge a penalty or charge for this provider.
also known as “return air tickets,” round-journey tickets are flights from and again to the equal place beginning. A one-manner price tag, then again, simplest lets you to fly your destination, now not back from it.
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Look at this table:
X Y
-4 7
-3 5
-2 3
-1 1
0 -1
Write a linear function (y = mx + b) or an exponential function (y = a(b)*) that models the
data.
Answer:
y= -2x -1
Step-by-step explanation:
m= (5-7)/(-3- -4) = -2/1 = -2
y-intercept = -1
y= -2x -1
suppose a sample of bone fossil contains 5.2% of the carbon-14 found in an equal amount of carbon in present-day bone. estimate the age of the fossil, assuming an exponential decay model. the half-life of carbon-14 is approximately 5700 years.
The age of the fossil is 24, 312 years assuming an exponential decay model.
Exponential decay model refers to model in which the amount of something decreases at a rate proportional to the amount left and this rate is given by a constant ratio k. The formula for remaining quantities of a substance is given by:
P = 100 e^(-kt)
Where P is the remaining quantity, k is the constant of decay, and t is time.
As the half life of the carbon 14 is 5700, when 50% of the substance remains,
50 = 100 e^(-5700k)
1/2 = e^(-5700k)
In(1/2) = In(e^(-5700k))
- In (2) = -5700k
k = In(2)/5700 = 0.0001216
Since, 5.2% carbon-14 remains,
5.2 = 100 e^(-0.0001216t)
0.052 = e^(-0.0001216t)
In(0.0052) = - 0.0001216
t = In(0.052) * - 0.0001216
t ≈ 24, 312 years.
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I need help with this one please
Answer:
A
Step-by-step explanation:
3 - (-1.5)
when you open the backet it will be 3 - - 1.5
minus and minus makes plus
therefore it will be 3+1.5
so the answer is 4.5
TRUE/FALSE. inferential statistics allows a researcher to make inferences about a specific population based on data taken from a sample.
A researcher can draw conclusions about a particular group using inferential statistics, which is a "true" statement.
Explain the term inferential statistics?Inferential statistics use data from the experiment's sample of subjects to compare the different treatments and draw conclusions about the subject population as a whole.
Inferential statistics come in a wide variety, and each form is suitable for a particular research methodology and set of sample characteristics. A statistical field known as inferential statistics is one that employs analytical tools to make inferences about the larger population by analyzing samples taken at random. Generalizations about than a population are what inferential statistics are intended to do.Thus, a researcher can draw conclusions about a particular group using inferential statistics, which is a "true" statement.
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Eleanor and billie make 752 brownies this give them to their 9 friends to share. what impact did the remainder have on this answer
Answer:
Step-by-step explanation:
This impact shows the Eleanor and Billie will have some leftover brownies.
Lets see.
752/9
752=720+27+5
720/9=80, 27/9=3, and 5/9 has a Remainder of 5.
80+3=83 R 5
consider the following binomial experiment: the probability that a fuse produced by a certain company will be defective is 37⁄100 . if 500 fuses are produced each day, how many can we expect to find each day that are defective ? a) 189 b) 187 c) 185 d) 183 e) 188 f) none of the above.
We can expect to find 185 defective fuses each day.
The correct answer is c) 185.
At first we have to find the expected number of defective fuses each day, we can use the formula for the expected value of a binomial distribution:
Expected Value (μ) = n * p
where:
n = number of trials (in this case, the number of fuses produced each day) = 500
p = probability of success (in this case, the probability that a fuse is defective) = 37/100 = 0.37
Expected Value (μ) = 500 * 0.37 = 185
So, we can expect to find 185 defective fuses each day.
The correct answer is c) 185.
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Rank the population sizes (N) from fastest to slowest growth. If two population sizes have the same growth, overlap them.
The rank of population size from fastest to slowest growth is N = 1250, N = 1500, N = 1000, N = 750, N = 500, and N = 250.
The population growth rate is the measure that helps to determine how much the population size changes over time. The population growth rate shows either logistic growth or exponential growth. The formula for logistic population growth is given by [tex]\frac{dN}{dt}=r_{\text{max}}N\left(\frac{K-N}{N}\right)[/tex]. Here, N is the population size, t is time, r (max) is the maximum rate of increase, and K is the carrying capacity.
The one that grows fast will have a large population size, and the one that grows slowly will have a small population size. To rank the population size, arrange the given population size from the largest to the smallest. As a result, we get,
Fastest growth rate N=1250, N=1500 , N=1000, N= 750, N= 500, N= 250 Slowest growth rate
The complete question is -
Arrange the following population sizes in the order of decreasing growth rate. Rank the population sizes (N) from fastest to slowest growth. If two population sizes have the same growth, overlap them.
N = 1250, N = 1500, N = 1000, N = 750, N = 500, N = 250
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PLEASE HELP
For this graph, determine whether x and y are proportional.
If x and y are proportional, fill in the blank with a number in simplest form.
Answer:
Proportional
y is 0.4 times x
or
y is 2/5 times x
Both numbers are the same, I don't know which form the computer expects you to enter
Step-by-step explanation:
x and y are proportional since there is a linear relationship between y and x.
Let's verify this
When x = 5, y = 2. So y/x = 2/5 = 0.4
So y = 0.4x
When x = 10, y = 4
So y/x = 4/10 = 2/5 = 0.4
Again y = 0.4x
So the answer is 0.4, same as 2/5
Answer:
Step-by-step explanation:
the x and y are proportional because the number increases by the same number each time. so y =2 and x=5 then on the next one, if it's proportional, y will = 4 and x will = 10. another way you can be sure that it is proportional is that every time you add the first number you can divide it and get the first number. for example if you divide 4 by 2 you will get 2. if you divide 10 by 2 you get 10. so in a short answer yes it is proportional
a rectangular prism with dimensions of (x-3),(x-1), and (x-8) has a volume of 33x cubic units. what are the dimensions of the prism?
The dimensions of the rectangular prism with the volume 33x cubic units are 11units, 9units, 4 units.
As given in the question,
Dimension of the rectangular prism in form of x are :
( x - 3 ) , ( x - 1 ) , and ( x - 8 )
Volume of the rectangular prism = 33x cubic units
⇒ ( x - 3 )( x - 1 )( x - 8 ) = 33x
⇒ ( x² -4x + 3 )( x - 8) = 33x
⇒ x³ -12x² + 35x -24 = 33x
⇒ x³ -12x² + 2x -24 = 0
⇒ x² ( x - 12 ) + 2 ( x - 12 ) = 0
⇒ ( x - 12 )( x² + 2 ) = 0
⇒ x = 12 or x = √ -2
Dimensions cannot be square root of negative.
⇒ x = 12
x - 3 = 9 units
x -1 = 11 units
x - 8 = 4 units
Therefore, the dimensions of the rectangular prism are 9 units, 11unitsm and 4 units.
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The temperature went from -16°F to 7°F. What was the change in temperature?
-9°F
23°F
-23°F
9°F
Answer:
23°F
Step-by-step explanation:
because its from a negative temp to a positive the inc is positive and -16-+7 is 16+7 = 23
3. Can you find the ratio of AB to AC and the ratio of DE to EF?
Its a written response type answer, so yes, no. And why or why not
Answer: Yes
Step-by-step explanation:
If you were to be given the numbers for the corresponding coefficient you can solve this question just like as if they were real numbers. Even if you weren't given values, The coefficients unknown value is usually presumed as 1.
if a= 10 b=5 c=6 d=50 e=100 f=1
ab= 10:5
ac= 10:6
de= 50:100
ef= 100:1
if they were all one then they would just be 1:1
help me rq pls it wont take long
Answer:
52[tex]a^{2}[/tex] + 26
urgenttt sorryyy thankss tooo
Answer:
7/10
Step-by-step explanation:
30 : 5 = 6 to Sali
10 : 100 = x : 30
x = 30 * 10 / 100
x = 3 * 1 = 3 to Jane
30 - (6+3) = 30 - 9 = 21
21/30
(21 : 3)/(30:3)
7/10
Rami's grandfather paid $67.83 for a length of rope that cost $0.95 per foot. He then cut the rope into pieces that were each 3 feet long. How many 3-foot pieces of rope did Rami's grandfather make? Enter your answer in the box.
The number of 3-foot pieces of rope that Rami's grandfather could make would be = 23.8 pieces.
What is rope?Rope is a thick cord that is material up of synthetic or organic materials that are interwoven together which can be used to support a structure.
The amount of money paid by Rami's grandfather for the rope = $67.83
The amount that the rope is sold per foot = $0.95/ft
To calculate the number of ft he bought;
= 67.83/0.95
= 71.4ft of rope
The number of 3-foot piece that he can cut
= 71.4/3
= 23.8 pieces.
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the scores on a standardized test have an average of 1200 with a standard deviation of 60. a sample of 50 scores is selected. what is the probability that the sample mean will be between 1195 and 1205? round your answer to three decimal places.
The probability that the sample mean will be between 1195 and 1205 is 0.445
What is a probability distribution?
In mathematics, a probability distribution is a function that expresses the likelihood of many possible values for a variable. Graphs and probability tables are common ways of displaying probability distributions.
Given, mean = [tex]\mu[/tex] = 1200
standard deviation = [tex]\sigma[/tex] = 60
n = 50
[tex]\mu_{\bar x} = 1200\\\sigma_{\bar x} =\sigma / \sqrt(n) = 60/ \sqrt50=8.485[/tex]
[tex]P(1195 < \bar x < 1205 ) = P[(1195-1200) / 8.485 < (\bar x - \mu\bar x ) / \sigma\bar x < (1205-1200) / 8.485)][/tex]
= P(-0.59 < Z <0.59 )
= P(Z <0.59 ) - P(Z <-0.59 )
Using the z table, we get
=0.7224-0.2776
=0.4448 = 0.445 ( rounded to 3 decimal places)
Hence, the probability that the sample mean will be between 1195 and 1205 is 0.445
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Under her cell phone plan, Jocelyn pays a flat cost of $35 per month and $5 per gigabyte. She wants to keep her bill under $55 per month. Use the drop-down menu below to write an inequality representing gg, the number of gigabytes she can use while staying within her budget.
A company manufactures and sells shirts. The daily profit the company makes depends on how many shirts they sell. The profit, in dollars, when the company sells xx shirts can be found using the function f(x) = 6x - 70. Find and interpret the given function values and determine an appropriate domain for the function.
The numeric values of the function are given as follows:
f(-2) = -82, meaning that if the company sells -2 shirts, it would have a profit of -82 dollars. This interpretation does not make sense in the context of the problem.f(12) = 2, meaning that if the company sells 12 shirts, it would have a profit of 2 dollars. This interpretation makes sense in the context of the problem.f(17.5) = 35, meaning that if the company sells 17.5 shirts, it would have a profit of 36 dollars. This interpretation does not make sense in the context of the problem.An appropriate domain for the situation is of:
{x ∈ N | x ≥ 0.}
What are the numeric values of the function?The function in this problem is defined as follows:
f(x) = 6x - 70.
In which the variables are given as follows:
x is the number of shirts sold.f(x) is the profit when x shirts are sold.Hence when x = -2, the numeric value is given as follows:
f(-2) = 6(-2) - 70 = -82.
This point is outside of the domain, as the number of shirts cannot be negative, hence an appropriate domain for the function is of:
{x ∈ N | x ≥ 0.}
As the number of shirts is also a countable amount.
When x = 12, the numeric value is given as follows:
f(12) = 6(12) - 70 = 72 - 70 = 2.
When x = 17.5, the numeric value is given as follows:
f(17.5) = 6(17.5) - 70 = 35.
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1+1 = ??????????????????
Answer:
2
Step-by-step explanation:
one apple and another equals to 2.
Answer: 11
Step-by-step explanation: you put one and one together lol
compare using >, =, or <. 3 _____ -3
Answer:
=
Step-by-step explanation:
HELP I WILL GIVE BRAINLIEST!!!
Answer:
ITS B
Step-by-step explanation:
(10,0) and (-2, 4)
Find the slope
The slope is -1/3.
The slope of a line, also known as the gradient is defined as the value of the steepness or the direction of a line in a coordinate plane. Slope can be calculated using different methods, given the equation of a line or the coordinates of points lying on the straight line.
Slope = m = tan θ = (y2 - y1)/(x2 - x1)
Slope = 2−1 / 2−1
= 4-0 / -2-10
= 4 /-12
= −1/3.
The slope is -1/3.
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a cone has volume of 98cm the radius of the cone is 5.13 what is the hight of the cone
Step-by-step explanation:
v=1/3πr²h
98=1/3×22/7×(5.13)²×h
98=1/3×22/7×(27.2403)×h
98=28.537×h
h=28.537/98
h=0.291m
hope it helps. please mark brainliest
Answer:
Answer to your question is in the attachment
9) John and Sarah are each saving money for a car. The total amount of money John will
save is given by the function J = 28 + 4x.
The total amount Sarah will save is given
by the function S = x2 + 2x + 20. After
how many weeks, x, will they have the same amount of money saved? Explain how you arrived at your answer.
To find out how many weeks it will take for John and Sarah to save the same amount of money, we must set their respective functions equal to each other and solve for x.
J = S
28 + 4x = x2 + 2x + 20
x2 + 2x - 4x - 8 = 0
x2 - 2x - 8 = 0
(x - 4)(x + 2) = 0
x = 4 or x = -2
Since x must be a positive value, the answer is that it will take John and Sarah 4 weeks to have the same amount of money saved.