The probability that the total grade for these 39 students is less than 2652.0 is 0.8289.
When answering a question, it is essential to be factually accurate, professional, and friendly. It is also important to be concise and provide step-by-step explanations. Additionally, relevant terms such as "unimodal," "deviation," and "random" should be used where appropriate. HTML formatting should be used where necessary.The solutions to the given problems are:a) The distribution of student's grades is unimodal and skewed left.b) If n=39 students are selected at random, the distribution of the sample mean grade is normal with a mean of μ=65 and a standard deviation of σ=2.5681.c) The probability that the sample mean grade for these 39 students is less than 68 is 0.8461.d) If n=39 students are selected at random, the distribution of the sample total grade is normal with a mean of 2535 and a standard deviation of 30.3848.e) The probability that the total grade for these 39 students is less than 2652.0 is 0.8289.
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If Bill starts work at 8:15, works until 4:45, and has 90 minutes of breaks. How many hours does Bill work in 5 days?
If Bill starts work at 8:15, works until 4:45, and has 90 minutes of breaks. Bill works for 36.25 hours in 5 days.
What is work per day?Work per day typically refers to the amount of time or effort expended by an individual during a typical working day.
According to question:First, let's find out how many hours Bill works in one day.
From 8:15 AM to 4:45 PM, Bill works for 8 hours and 30 minutes (since there are 60 minutes in an hour, we can convert the 45 minutes to 0.75 hours, so 8 hours and 45 minutes is the same as 8.75 hours):8 hours and 45 minutes - 90 minutes of breaks
= 7 hours and 15 minutes
= 7.25 hours of work per day.
To find out how many hours Bill works in 5 days, we can simply multiply his daily hours by the number of days:7.25 hours per day x 5 days = 36.25 hours.
Therefore, Bill works for 36.25 hours in 5 days.
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Let X be a normally distributed random variable. Given that the
mean is 2 and P(X < 2.24) = 0.7257, what is the variance?
a. 0.5266
b. None of the suggested answers are correct
c. 0.6
d. 0.4
e. 0.1
e [0.1}
We know that P(X < 2.24) = 0.7257. Also, the mean is 2.Let us calculate the variance of the given normal distribution random variable. Given that P(X < 2.24) = 0.7257, we have to find variance. Let us solve this question as follows:We know that mean of normally distributed random variable is μ and standard deviation is σ. As the mean is 2, μ = 2.We have the z-score: z = (2.24 - 2) / σFrom the normal distribution table, we can find out that P(Z < 0.80) = 0.7881Now, we have the following equation:0.7881 = (2.24 - 2) / σσ = 0.3158Finally, we can find the variance (σ^2) = 0.3158^2 = 0.0995 ≈ 0.1Therefore, the correct answer is option e. 0.1.
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PLEASE HELP I OS EASY\
Find the surface area of the rectangular prism.
A storage container is in the shape of a rectangular prism. The container has a length of 5 feet, and a width of 9 feet, and a height of 8 feet. What is the surface area of the container?
360 ft2
314 ft2
157 ft2
22 ft2
ANswer __________________
The surface area οf the cοntainer is 314 ft².
What is rectangle?A rectangle is a geοmetric shape that has fοur sides and fοur right angles (90 degrees) with οppοsite sides being parallel and equal in length. It is a type οf quadrilateral, a pοlygοn with fοur sides.
Tο find the surface area οf a rectangular prism, we need tο add the areas οf all six faces. The fοrmula fοr the surface area οf a rectangular prism is:
Surface area = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height οf the rectangular prism.
Substituting the given values, we get:
Surface area = 2(5)(9) + 2(5)(8) + 2(9)(8)
Surface area = 90 + 80 + 144
Surface area = 314 square feet
Therefοre, the surface area οf the cοntainer is 314 ft².
Answer: 314 ft².
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How many terms are in the expression: 12p + 8m + 2
Answer: I THINK 4.
Step-by-step explanation:
Sorry if it is wrong!! :'D
Leeanne plans to sell her car and places an x-line ad. The newspaper charges p dollars for the
first k lines and e dollars per extra line, to run the ad for a week.
When x > k, write an algebraic expression for the cost of running the ad for a week.
a.
b. When x
Answer:
a. When x > k, the cost of running the ad for a week can be expressed as:
C = p + e(x - k)
where C is the cost in dollars, p is the cost per k lines, e is the cost per extra line, and (x - k) is the number of extra lines over k.
b. When x ≤ k, the cost of running the ad for a week can be expressed as:
C = p
where C is the cost in dollars and p is the cost per k lines. Since the number of lines x is less than or equal to k, there are no extra lines and the cost is simply the base cost of p dollars for k lines.
Hope this helped! I'm sorry if it's wrong. If you need more help, ask me! :]
Solve 5(p−3q)<12 for q
The value of q in the question is q>-12/15
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions
The given inequality is 5(p−3q)<12
Opening the bracket we have
5p - 15q < 12
The solution can only be gotten if we assume p = 0
the substitute p=0 in the inequality to have
-15q < 12
dividing both sides by -15 to have
-15q/-15 < 12/-15
therefore q > 12/-15
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The populations P (in thousands) of Horry County, South Carolina, from 1971 through 2018 can be modeled by P-75.9e0.0316 where t represents the year, with t= 1 corresponding to 1971.
(a) Use the model to find the population in 1980, 1990, 2000, and 2010. (Round your answers to the nearest whole number.)
1980
1990
2000
2010
(b) According to the model, when will the population of Horry County reach 390,000? (Round your answer down to the nearest year.)
(c) Do you think the model is valid for long-term predictions of the population? Explain.
O Yes, as t increases, the population increases rapidly.
O Yes, as t increases, the population decreases rapidly.
O Yes, as t increases, the population remains constant.
O No, as t increases, the population decreases rapidly.
O No, as t increases, the population increases rapidly.
a) The populations in 1980, 1990, 2000, and 2010 are 157,000, 218,000, 269,000, and 308,000 respectively.
b) the population will reach 390,000 in 270 years
c) No, as t increases, the population increases rapidly
How to find the populations as required(a) To find the population in 1980, 1990, 2000, and 2010, we substitute the corresponding values of t into the given model and round the answers to the nearest whole number.
Population in 1980: P = 75.9e^(0.0316*10) = 156,604
Population in 1990: P = 75.9e^(0.0316*20) = 217,643
Population in 2000: P = 75.9e^(0.0316*30) = 269,099
Population in 2010: P = 75.9e^(0.0316*40) = 308,227
(b) To find when the population of Horry County will reach 390,000, we need to solve the equation 390 000 = 75.9e^(0.0316t) for t.
Taking the natural logarithm of both sides, we get:
ln(390,000/75.9) = 0.0316t
Simplifying, we get:
t = ln(390,000/75.9)/0.0316 ≈ 270.395
Rounding down to the nearest whole year, we get that the population will reach 390,000 in 270 years
(c) The model assumes that the population growth rate will remain constant over time. However, in reality, population growth rates can be affected by a variety of factors, such as changes in birth and death rates, immigration, emigration, and natural disasters.
Therefore, it is unlikely that the model will be valid for long-term predictions of the population. The model can provide a good estimate of the population for the short-term, but it is not reliable for predictions far into the future.
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Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?
Step-by-step explanation:
Divya is cooking dinner. she goes to the market to buy ingredients. the price per pound of different ingredients is shown in the table below. Diyva recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2 pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus How much will diyva pay for all the ingredients in the recipe?
Given: S is on the segment RT. RS = x + 2, ST = 3x + 1, and RT = 15.
On solving the question we have that We can see that RS + ST = RT, equation confirming that S is on segment RT: RT = RS + ST = 5 + 10 = 15
What is equation?A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.
Because S is on the section RT, we know that RS + ST = RT. As a result, we may construct the following equation:
RS + ST = 3x + 1 + (x + 2) = 15
To simplify this equation, we can combine similar terms:
4x + 3 = 15
Subtraction of 3 from both sides yields:
4x = 12
When we divide both sides by 4, we get:
x = 3
RS = x + 2 = 5 and ST = 3x + 1 = 10 as a result.
We can see that RS + ST = RT, confirming that S is on segment RT:
RT = RS + ST = 5 + 10 = 15
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the daily high temperature for chattanooga is normally distributed with mean 79 and standard deviation 4. find the probability that a randomly chosen temperature is between 70 and 75.
The probability of randomly selecting a temperature between 70 and 75 is approximately 0.8291.
To find the probability that a randomly chosen temperature is between 70 and 75, we need to use the z-score formula as shown below:
z = (x - μ) / σ
Where:x = 70 and 75μ = 79σ = 4z1 = (70 - 79) / 4 = -2.25z2 = (75 - 79) / 4 = -1P(70 < x < 75) = P(-2.25 < z < -1)
To find the probability for the above inequality, we need to use a calculator. We know that the probability of the standard normal distribution is equal to 1.
Hence, P(-2.25 < z < -1) = Φ(-1) - Φ(-2.25) = 0.8413 - 0.0122 ≈ 0.8291. Therefore, the probability is about 0.8291.
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Harrison has a rectangular plank of wood that is 29 inches long. He creates a ramp by resting the plank against a wall with a height of 14 inches, as shown. Using Pythagoras' theorem, work out the horizontal distance between the wallI and the bottom of the ramp. Give your answer in inches to 1 d.p.
Answer:
Horizontal distance between the wall and the bottom of ramp = 25.4 inches.
Step-by-step explanation:
Pythagorean theorem:
AB -> wall ; AB = 14 inches
AC -> Wooden plank ; AC = 29 inches
BC -> horizontal distance between the wall and the bottom of ramp(pank).
Pythagorean theorem,
[tex]\boxed{\bf base^2 + altitude^2 = hypotenuse^2}[/tex]
BC² + AB² = AC²
BC² + 14² = 29²
BC² + 196 = 841
BC² = 841 - 196
= 645
BC = √645
BC = 25.4 inches
Horizontal distance between the wall and the bottom of ramp = 25.4 inches.
Given,
Length = 29 inches
Height = 14inches
Here,
Pythagorean theorem:
AB -> wall ; AB = 14 inches
AC -> Wooden plank ; AC = 29 inches
BC -> horizontal distance between the wall and the bottom of ramp (plank).
Pythagorean theorem,
Base² + Perpendicular² = Hypotenuse²
BC² + AB² = AC²
BC² + 14² = 29²
BC² + 196 = 841
BC² = 841 - 196
= 645
BC = √645
BC = 25.4 inches
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Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation 15 . Find
P 9
, which is the IQ score separating the bottom9%from the top 91%
. The IQ score that separates the bottom 9% from the top 91% is P 9
=
(Round to the nearest hundredth as needed.) Assume that adults have IQ
scores that are normally distributed with a mean of 105 and a standard deviation of 15 . Find the third quartile
Q 3
which is the IQ score separating the top 25% from the others. The third quartile, Q 3
is . (Round to one decimal place as needed.)
Value of Q3 is approximately 114.1 given mean and standard deviation.
We must identify the IQ score that separates the bottom 9% from the top 91% in order to determine P9. The normal distribution of IQ scores has a mean of 100 and a standard deviation of 15, as is well known. The z-score for the 9th percentile can be calculated using a calculator or a typical normal distribution table.
[tex]z = invNorm(0.09) = -1.34[/tex]
The formula for converting a z-score to an IQ score is as follows:
IQ equals z * standard deviation + mean, or -1.34 * 15 + 100, or 79.1.
P9 is therefore roughly 79.1.
We must identify the IQ score that distinguishes the top 25% from the rest in order to determine Q3. Assuming a normal distribution, IQ values have a mean of 105 and a standard deviation of 15. Since the top 25% and the 75th percentile are the same, we can use a calculator or a conventional normal distribution table to determine the z-score that represents the 75th percentile:
[tex]z = invNorm(0.75) = 0.67[/tex]
We can then use the formula for transforming a z-score to an IQ score:
IQ = z * standard deviation + mean = 0.67 * 15 + 105 = 114.05
Therefore, Q3 is approximately 114.1.
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HELPPPPPPPPPPPPpppppppppppppppppppppppp
Answer:C
Step-by-step explanation:
[tex](x-3)^2=5\\we \ should \ find \ square \ root \ of \ each \ side,\\\sqrt{(x-3)^2}=\sqrt{5}\\1)x-3=\sqrt{5}x=\sqrt{5}+3\\2)3-x=\sqrt{5}\\x=3-\sqrt{5}\\\\so,x=3\± \sqrt{5}[/tex]
PLEASE HELP ASAP WILL GIVE BRAINLIEST
Answer:
3x+5x=8x
-3t+-t=-4t
3p+3p=6p
2n+n=3n
5g+-g=4g
7y+y=8y
4+12=16
Step-by-step explanation:
I dont know what 28x76 is
Answer:
28
x 76
----
168 (units digit of 76 multiplied by 28)
1408 (tens digit of 76 multiplied by 28)
----
2128
Therefore, 28x76 is equal to 2128.
Step-by-step explanation:
Please I really need help the blank boxes are from 0-9.
For no solution 7x+10
For one solution8x+0
For infinite solution 7x+5
Define infinite solutionAn infinite solution is a solution to a system of equations that has an infinite number of possible solutions. In other words, any value for the variables in the system will satisfy all the equations.
2x+5+2x+3x
On adding the values with variables, x=7
On adding constant values=5
2x+5+2x+3x=7x+5
For no solution
7x+5=7x+10
For one solution
7x+5=8x
x=5
For infinite solution
7x+5=7x+5
Hence, For no solution 7x+10
For one solution 8x+0
For infinite solution 7x+5.
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1. Draw a scatter plot that shows a positive linear association and clustering.
2. Draw a scatter plot that shows a negative non-linear association and no clustering.
The grouping of data or sample points is a component of the machine learning process known as clustering.
What is Clustering?The task of arranging a set of objects into an identical group in a way that makes them more similar to one another than those found in different groups is known as cluster analysis or clustering.
A scatter plot is an unique type of plot or mathematical diagram that displays data for usually 2 parameters for a collection of data. It uses Cartesian coordinates.
Coordinates, it is a set or group of values that show an exact or accurate position.
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Determine the value of x
Answer:
12 × 3 = 36
the top of the diagram will also equal 36
138-72=66
66 ÷2= 33
33÷3 =11
therefore x=11
Answer:
perimeter = 138
p=2(138+12)
p=2×150
p=300
x=300
URGENTTTTT!!!!!!!!!! please complete the chart with the correct angle measures
(numbers 6-9 please!)
Answer:
9 hope u get it right budddyyyy
Use the equation y = 7x to complete the table. What are the missing values of
y?
O A. When x = 2, y = 16.
When x = 4, y = 30.
O B. When x = 2, y = 14.
When x = 4, y = 28.
C. When x = 2, y = 8.
When x = 4, y = 22
D. When x = 2, y = 12.
When x = 4, y = 24.
Using the equation y = 7x , we can compute that when x = 2, y = 14 and when x = 4 , y = 28. So, correct option is B.
The equation y = 7x relates the variables y and x, where y is a function of x. To compute the value of y for a given value of x, we simply substitute that value of x into the equation and solve for y.
When x = 2, we can substitute this value into the equation:
y = 7(2) = 14
Therefore, when x = 2, y = 14.
Similarly, when x = 4, we can substitute this value into the equation:
y = 7(4) = 28
Therefore, when x = 4, y = 28.
So, the correct option is B: When x = 2, y = 14 and when x = 4, y = 28.
In summary, to compute the value of y for a given value of x using an equation, we substitute that value of x into the equation and solve for y. In this case, when x = 2, y = 14, and when x = 4, y = 28, according to the given equation y = 7x.
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The table contains the number of M&M’s of each color that were found in a case.
M&M Distribution
Blue Brown Green Orange Red Yellow Total
399 538 364 393 507 351 2552
Round answers to four decimal places, if necessary.
Find the probability of choosing a green or red M&M.
P(green or red) =
Find the probability of choosing a blue, red, or yellow M&M.
P(blue, red, or yellow) =
Find the probability of not choosing a brown M&M.
P(not brown) =
Find the probability of not choosing a green M&M.
P(not green) =
(a) P(green or red) = 0.3946
(b) P(blue, red, or yellow) = 0.7606
(c) P(not brown) = 0.7807
(d) P(not green) = 0.6559
What is probability?
Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.
The total number of M&M's is 2552.
(a) P(green or red) = P(green) + P(red)
= 364/2552 + 507/2552
= 0.2692
(b) P(blue, red, or yellow) = P(blue) + P(red) + P(yellow)
= 399/2552 + 507/2552 + 351/2552
= 0.4917
(c) P(not brown) = 1 - P(brown)
= 1 - 538/2552
= 0.7891
(d) P(not green) = 1 - P(green)
= 1 - 364/2552
= 0.8575
Hence,
(a) P(green or red) = 0.3946
(b) P(blue, red, or yellow) = 0.7606
(c) P(not brown) = 0.7807
(d) P(not green) = 0.6559
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Identify which functions have complex roots by selecting the function names on the provided coordinate plane.
From the graphs in the given coordinate plane, the functions that have complex roots are function b, function d and function f.
Determining the functions that have complex rootsFrom the question, we are to determine the functions that have complex roots in the given coordinate plane.
In a quadratic graph, if the vertex of the quadratic function lies above the x-axis, and the parabola opens upward, there will be NO x-intercepts. The graph will have complex roots.
Also, if the vertex of the quadratic function lies below the x-axis, and the parabola opens downward , there will be NO x-intercepts.
The graph will have complex roots.
In the given coordinate plane, the functions that have complex roots are function b, function d and function f.
Hence, the functions b, d, and f have complex roots.
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Baxter’s Hardware has some followers on their social media account on Friday. On Saturday, the account gains 18 new followers. On Sunday, 20 people stop following the Baxter’s Hardware account. Baxter’s Hardware has 25 followers on Monday morning. The equation f + 18 - 20 = 25 represents the situation. Solve the equation. Be sure to show your work.
Please answer quick!!!
According to given equation Baxter’s Hardware had 27 followers on Sunday morning.
What is equation?
Equations can take many forms, including linear, quadratic, polynomial, trigonometric, and exponential, and can be used to model and solve a wide range of real-world problems.
The given equation is:
f + 18 - 20 = 25
Adding the numbers on the left side, we get:
f - 2 = 25
Adding 2 to both sides, we get:
f - 2 + 2 = 25 + 2
Simplifying, we get:
f = 27
Therefore, Baxter’s Hardware had 27 followers on Sunday morning.
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help me find the missing sides to solve this equation
For the equilateral triangles we have:
1) x = 5, y = √50
2) a = 2, b = √8
3)y = 8, x = √128
4) a = b = 7/√2
How to find the missing sides?We can see some triangles, remember that for a right triangle whose angles are 45°, we have an equilateral triangle.
So the two legs have the same measure.
1) Here we can see that x = 5, and the hypotenuse is given by:
y^2 = 5^2 + 5^2
y^2 = 50
y = √50
2) Here we have a = 2, then the hypotenuse is:
b^2 = 2^2 + 2^2
b^2 = 8
b = √8
3) Here we have y = 8, then the hypotenuse is:
x^2 = 8^2 + 8^2
x^2 = 128
x = √128
On the last triangle we can see that the hypotenuse is 7, and we know that a = b
then:
7^2 = a^2 + b^2
7^2 = a^2 + a^2
49 = 2*a^2
(49/2) = a^2
√(49/2) = a
7/√2 = a = b
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find the values of a, b, and c in the equation 5x^2-2=2x^2+10x+6
The value οf a = 3, b=-10, c-8
What is quadratic equatiοn?it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm. A nοn-zerο term (a 0) fοr the cοefficient οf x² is a prerequisite fοr an equatiοn tο be a quadratic equatiοn.
The x² term is written first, then the x term, and finally the cοnstant term is written when cοnstructing a quadratic equatiοn in standard fοrm. In mοst cases, the numerical values οf letters a, b, and c are expressed as integral values rather than fractiοns οr decimals.
The equatiοn given 5x²-2=2x²+10x+6
3x²-10x-8=0
values οf a = 3, b=-10, c-8
Hence the value οf a = 3, b=-10, c=8
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the basis for using a normal probability distribution to approximate the sampling distribution of the sample means and population mean is . a. the empirical rule b. chebyshev's theorem c. bayes' theorem d. the central limit theorem
The cοrrect answer tο the given questiοn is d. the central limit theοrem.
What is frequency distributiοn?The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.
The basis fοr using a nοrmal prοbability distributiοn tο apprοximate the sampling distributiοn οf the sample means and pοpulatiοn mean is the central limit theοrem.
The central limit theοrem states that fοr a sufficiently large sample size, the sampling distributiοn οf the sample means will be apprοximately nοrmal, regardless οf the shape οf the pοpulatiοn distributiοn. This theοrem allοws us tο make statistical inferences abοut the pοpulatiοn mean based οn the sample mean using the prοperties οf the nοrmal distributiοn, such as the mean and standard deviatiοn.
Therefοre, the cοrrect answer tο the given questiοn is d. the central limit theοrem.
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A company's profit (in millions of dollars) can be represented by y=x^2 -16x +67 where x is the number of years since the company started. When did the company have a profit of 7 million dollars?
For given quadratic equation, the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.
What exactly are quadratic equations?
A quadratic equation is a second-degree polynomial equation of the form:
ax²+ bx + c = 0
where x is the variable and a, b, and c are constants, with a ≠ 0. The term "quadratic" comes from the Latin word "quadratus", which means "square". In other words, a quadratic equation is an equation that involves the square of the variable x.
Now,
We are given that the profit of the company (in millions of dollars) can be represented by the equation y = x² - 16x + 67, where x is the number of years since the company started.
We want to find when the company had a profit of 7 million dollars.
So, we can set y = 7 in the equation:
7 = x² - 16x + 67
Rearranging and simplifying:
x² - 16x + 60 = 0
Now, we can solve for x using the quadratic formula:
x = (-(-16) ± √((-16)^2 - 4(1)(60))) / 2(1)
x = (16 ± √(16)) / 2
x = 8 ± 2
Therefore, the solutions are x = 10 or x = 6.
This means that the company had a profit of 7 million dollars in either its 6th year or its 10th year of operation.
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Karen has two dogs. The larger dog weighs 1. 4 pounds more than the smaller dog. The combined weight of the two dogs is 12. 6 pounds
The weight of the smaller dog is 5.6 pounds.
Let the weight of the smaller dog be x, then,
The weight of the larger dog = 1.4 pounds.
The combined weight of the dogs = 12.6 pounds.
Therefore,
The sum of the weight of the larger dog and smaller dog = the combined weight of the dogs.
That is,
1.4 + x + x = 12.6
1.4 + 2x = 12.6
2x = 12.6 - 1.4
2x = 11.2
x = 11.2 ÷ 2
x = 5.6.
Hence, the weight of the smaller dog is 5.6 pounds.
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Your question is incomplete, and the complete question would be:
Karen has two dogs. the larger dog weighs 1.4 pounds more than the smaller dog. the combined weight of the two dogs is 12.6 pounds. what is the weight of the smaller dog?
I choose 10 consecutive numbers. if I exclude one of the numbers the remaining 9 sum to 2023 which number did I exclude?
Answer:
the number 228
Step-by-step explanation:
Let's call the smallest number in the consecutive sequence "x". Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.
If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:
(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) or 9x + 36.
We know that the sum of the remaining 9 numbers is 2023, so we can set up the equation:
9x + 36 = 2023
Solving for x, we get:
9x = 1987
x = 221
Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.
If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.
The pH of a solution is given by the formula pH=−logH+, where H+ is the concentration of hydrogen ions in moles per liter in the solution. Lye has a pH of 12.13. Use this formula to find the hydrogen ion concentration, [H+]. Round to one decimal place if necessary.
Given data:
pH of lye = 12.13
Using the formula pH = -log[H+], we have to find the hydrogen ion concentration, [H+].
Now, putting the given values in the formula, we get:
pH = -log[H+]
12.13 = -log[H+]
log[H+] = -12.13
[H+] = 10^-12.13 = 5.01187 x 10^-13
So, the hydrogen ion concentration, [H+] is 5.01187 x 10^-13 moles/liter. Therefore, the answer is 5.01187 x 10^-13.
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