Let's denote the width of the printed material on the poster as "x" cm and the height as "y" cm.
According to the given information, the top and bottom margins are each 6 cm, and the side margins are each 8 cm. This means that the actual width of the entire poster, including the margins, is "x + 2(8)" cm, and the actual height, including the margins, is "y + 2(6)" cm.
Given that the area of the printed material on the poster is fixed at 380 square centimeters, we can set up the following equation:
Actual Area of Poster = Area of Printed Material on Poster
(x + 2(8))(y + 2(6)) = 380
(x + 16)(y + 12) = 380
To find the dimensions of the poster with the smallest area, we need to minimize the product (x + 16)(y + 12).
Since the given area of the printed material on the poster is fixed at 380 square centimeters, the actual area of the entire poster, including the margins, will be minimized when (x + 16)(y + 12) is minimized.
To minimize the product (x + 16)(y + 12), we need to minimize both x + 16 and y + 12, as they are both positive quantities.
Since x and y represent the width and height of the printed material on the poster, respectively, the smallest possible values for x + 16 and y + 12 would be 0, which means x = -16 and y = -12. However, since width and height cannot be negative, we need to find the next best option.
The smallest possible values for x + 16 and y + 12 that are greater than or equal to 0 would be when x = 0 and y = 0. This means that the width of the printed material on the poster should be 0 cm and the height should be 0 cm, which would make the dimensions of the poster with the smallest area:
Width = 0 cm
Height = 0 cm
However, please note that this would mean there is no printed material on the poster, as the width and height are both 0. If you want to have a non-zero width and height for the printed material on the poster, you would need to adjust the given area of the printed material on the poster accordingly.
Maths
Find y using the graph
Answer:
y = 4x² -8x +10
Step-by-step explanation:
You want to write the equation y = 4(x -1)² +6 in standard form.
Distributive propertyThe distributive property is used to eliminate parentheses.
y = 4(x -1)² +6 . . . . . . given equation
y = 4(x -1)(x -1) +6 . . . . . the meaning of the exponent of 2
y = 4((x(x -1) -1(x -1)) +6 . . . . . distributive property applied once
y = 4(x² -x -x +1) +6 . . . . . . . . . . distributive property applied again
y = 4(x² -2x +1) +6 . . . . . . collect terms inside parentheses
y = 4x² -8x +4 +6 . . . . . . . distributive property applied
y = 4x² -8x +10 . . . . . . . . . collect terms
evaluating Outcomes with Probability: Tutorial Question Select the correct answer. Students voted in an election for class president, but there was a tie for first place between two people. The school principal suggested the following methods could be used to decide who the class president should be. Use probability to determine which method could be used to fairly choose the class president. O flipping a fair coin O asking a group of senior teachers O rolling a biased die Oletting the two candidates mutually decide who should win
Answer:
The method that could be used to fairly choose the class president in the given scenario is flipping a fair coin. This is because flipping a fair coin is a random process and both candidates have an equal chance of winning. This ensures fairness in the selection process. Asking a group of senior teachers or letting the two candidates mutually decide who should win may introduce biases and may not be fair to both candidates. Rolling a biased die may also introduce unfairness as the outcome is not random and is predetermined.
Suppose that $2000 is invested at an interest rate of 4.75% per year, compounded continuously. After how many years will the initial investment be doubled?
Answer: it will take approximately 14.62 years for the initial investment to double at an interest rate of 4.75% per year, compounded continuously.
Step-by-step explanation: Given an investment of $2000 at a continuously compounded interest rate of 4.75%, the balance in the account can be calculated using the following mathematical expression after t years:
The aforementioned equation, A = P * e^(rt), denotes the relationship between the accrued amount (A) and the principal amount (P), compounded continuously at a fixed annual rate of interest (r) over a specific time period (t), as governed by the mathematical constant "e."
In the context of financial calculations, the symbol 'P' denotes the initial capital investment. The interest rate, represented by the variable 'r', is expressed in the form of a decimal. Additionally, 'e' is the mathematical constant, roughly equivalent to 2.71828. Finally, 't' refers to the duration of the investment, measured in years.
In order to determine the duration of time required for the investment to achieve a twofold increase, it is necessary to solve the corresponding equation:
The equation expressed as 2P = P * e^(rt) can be restated more formally as follows. Given a principal investment amount represented by P and a rate of return indicated by r, compounded over time t, the equation can be expressed as the product of P and the exponential function of e^(rt), yielding twice the initial investment amount.
The variable 2P represents the monetary value acquired through doubling the initial investment.
Upon division of both sides by P, the resulting expression is as follows:
The equation 2 equals the exponential function of the base e raised to the power of the product of r and t.
By applying the natural logarithm function to both expressions, the resultant outcome is:
The natural logarithm of 2 can be represented as rt, where r denotes the logarithmic base and t denotes the logarithm of the argument, in accordance with the conventions of academic mathematical writing.
Upon resolving for the variable t, an outcome is yielded:
The mathematical expression t = ln(2) / r can be written in a formal academic style as follows: The equation determines the relationship between time t and the rate of decay r, where t is equal to the natural logarithm of 2 divided by r.
Upon substitution of the provided values, the resultant output is:
The calculated value of the variable t, representing the length of time in years, is approximately equal to 14.62 years, obtained through the algebraic manipulation of the natural logarithmic function of 2 divided by the constant value of 0.0475.
Please help me with this question!!!
Charlie works as a salesperson and receives a monthly salary of $2,000 plus a commission of $100 for every item that they sell. Find the model of Charlie's monthly pay, using P for pay and q for the number of items they sell in a month.
Enter your answer as a formula including "P(q)="
(do not include the dollar sign)
Step-by-step explanation:
Charlie's monthly pay, P, can be represented as a linear function of the number of items sold, q. The monthly salary of $2,000 represents the y-intercept of the line, and the commission of $100 per item sold represents the slope of the line.
Thus, the model for Charlie's monthly pay, P(q), can be expressed as:
P(q) = 100q + 2000
where q is the number of items sold in a month, and P(q) is Charlie's monthly pay in dollars.
Use the information in the charts to answer the questions.
Barbara- 3 3/10
Donna - 2 4/5
Cindy - Find
Nicole - 2 1/10
1. The four girls ran in a relay race as a team. Each girl ran one part of
the race. The team’s total time was
3 11 /5 minutes. What was Cindy’s
time?
2. Find the difference between the fastest girl’s time and the slowest
girl’s time.
3. To break the school’s record, the girls’ time had to be faster than
2 12/5 minutes. Did the girls break the record? If so, how much faster were
they? If not, how much slower were they?
Answer:
Step-by-step explanation:
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...
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..
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this is what I don’t know
Answer:
84 degrees for number 6
Step-by-step explanation:
the area of a circle is 360 degrees, so just subtract the other angles by 360 i think that's how you do it
More than 56% of people support stricter gun laws. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage).
Null hypothesis: H0: p ≤ 0.56
Alternative hypothesis: H1: p > 0.56
We have,
Let p be the true proportion of people in the population who support stricter gun laws.
The null and alternative hypotheses in symbolic form for the claim that more than 56% of people support stricter gun laws are:
Null hypothesis: H0: p ≤ 0.56
Alternative hypothesis: H1: p > 0.56
Thus,
The null hypothesis states that the proportion of people in the population who support stricter gun laws is less than or equal to 56%, while the alternative hypothesis states that the proportion is greater than 56%.
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Find a.the mean b.the median wage
The mean is 4746
The median wage is #4618
The wages for the five local government trainees are
#4,166, #4,618, #3,742, #5,838 and #5,366
= 4166+ 4618+ 3742+5838+5366/5
= 23,730/5
Mean = 4,746
The median wage is
Arrange the wages orderly
3,742, 4166, 4618, 5366, 5838
The median wage is #4618
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Find the slope of the line shown belowpp
Answer: the slope is 6
Step-by-step explanation: the line y=6x-3
Given this equation what is the value of x at the indicated point?
Answer:
x = -1
Step-by-step explanation:
You will plug in 8 for y then solve for x:
[tex]\frac{12}{3} = (x-1)^2\\4 = (x-1)^2\\\frac{+}{-}2 = x-1 \\ x= +3, and -1[/tex]
Then the answer is -1 because the graph shows the point in the 2nd quadrant meaning x is negative
Use z scores to compare the given values.
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The tallest living man at one time had a height of 222 cm. The shortest living man at that time had a height of 98.4 cm. Heights of men at that time had a mean of
171.59 cm and a standard deviation of 5.47 cm. Which of these two men had the height that was more extreme?
Since the z score for the tallest man is z- and the z score for the shortest man is z-. the
(Round to two decimal places.)
man had the height that was more extreme.
the more extreme height was the case for the shortest living man (13.38 standard deviation units below the population's mean) compare with the tallest man that was 9.21 standard deviation units above the population's mean.
To answer this question, we need to use standardized values, and we can obtain them using the formula:
z = (x - μ)σ .. [1]
Where,
x is the raw score we want to standardize.
μ is the population's mean.
σ is the population standard deviation.
A z-score "tells us" the distance from in standard deviation units, and a positive value indicates that the raw score is above the mean and a negative that the raw score is below the mean.
In a normal distribution, the more extreme values are those with bigger z-scores, above and below the mean. We also need to remember that the normal distribution is symmetrical.
Heights of men at that time had:
μ = 171.59 cm
σ = 5.47 cm.
Let us see the z-score for each case:
Case 1: The tallest living man at that time
The tallest man had a height of 222 cm.
Using [1], we have (without using units):
z = (x - μ)σ
z = (222 - 171.59)/5.47
z = 50.41 / 5.47
z = 9.21
That is, the tallest living man was 9.21 standard deviation units above the population's mean.
Case 2: The shortest living man at that time
The shortest man had a height of 98.4 cm.
Following the same procedure as before, we have:
z = (x - μ)σ
z = (98.4 - 171.59)/5.47
z = - 13.38
That is, the shortest living man was 13.38 standard deviation units below the population's mean (because of the negative value for the standardized value.)
The normal distribution is symmetrical (as we previously told). The height for the shortest man was at the other extreme of the normal distribution in standard deviation units more than the tallest man.
Then, the more extreme height was the case for the shortest living man (13.38 standard deviation units below the population's mean) compare with the tallest man that was 9.21 standard deviation units above the population's mean.
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A survey of the wine market has shown that the preferred wine for 17 percent of Americans is merlot.
A wine producer in California, where merlot is produced, believes the figure is higher in California. She
contacts a random sample of 550 California residents and asks which wine they purchase most often.
Suppose 115 replied that merlot was the primary wine.
(a) Calculate the appropriate test statistic to test the hypotheses.
(b) Calculate the p-value associated with the test statistic, and test the claim at α = 0.01.
The sample data provides sufficient evidence to conclude that the population proportion is greater than 0.17 at 1% level of significance.
What is a Null Hypothesis?
One can define a null hypothesis as a declaration that postulates no noteworthy variance or association between two or more variables existing within a populace.
Usually utilized in statistical hypothesis testing, it evaluates if an observed effect or relation is statistically meaningful or arises purely by chance.
It often bears the insignia H0 and subject to an alternative proposition (Ha) signifying a significant outcome or connection instead. Whenever the null hypothesis gets dismissed, one may deduce that there are ample findings to sustain the alternate assertion's validity.
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In October, Meg's pumpkin weighed 3 pounds and 11 ounces. In November, it weighed 8 pounds and 2 ounces. How many more ounces did it weigh in November?
Result:
The weight of the pumpkin in November = 71 ounces more than in October.
How to compare the weights?
To compare the weights, we need to convert both weights to the same unit of measurement, either pounds or ounces.
Let's convert the first weight, which is 3 pounds and 11 ounces, to ounces:
3 pounds = 3 x 16 = 48 ounces
11 ounces = 11
So the first weight is 48 + 11 = 59 ounces.
Now, let's convert the second weight, which is 8 pounds and 2 ounces, to ounces:
8 pounds = 8 x 16 = 128 ounces
2 ounces = 2
So the second weight is 128 + 2 = 130 ounces.
To find how many more ounces the pumpkin weighed in November, we subtract the October weight from the November weight:
130 - 59 = 71
Therefore, the pumpkin weighed 71 more ounces in November than it did in October.
Find the measures of angle BED
keeping in mind that twin sides make twin angles, Check the picture below.
The table below shows the earnings, in thousands of dollars, for three different commissioned employees.
Employee #1
Employee #2
Employee #3
$2,000 - 3% on all
7% on all sales
5% on the first $40,000
sales
8% on anything over
$40,000
December
4.4
5.6
5.2
January
3.5
3.85
3.6
February
4.7
4.9
4.4
Which employee did not have the same dollar amount in sales for the month of February as the other two employees?
a. Employee #1.
b.
Employee #2
c. Employee #3
They each had the samè dollar amount in sales.
I am pretty sure the answer is b. emplyee 2# but im not 100% sure since your graph is really weird and hard to uunderstand
Complete each ordered pair so that it is a solution of the given linear equation.
y=1/4×−8; (4, ), ( ,−11)
The first ordered pair is (4, )
The second ordered pair is ( ,-11)
Answer:
(4, -3)
(-28,-11)
Step-by-step explanation:
y = [tex]\frac{1}{4}[/tex] x - 4 Substitute 4 for x
y = [tex]\frac{1}{4}[/tex][tex](\frac{4}{1})[/tex] - 4 another name of 4 is [tex]\frac{4}{1}[/tex]
y = 1 - 4
y = -3
(4,-3)
y = [tex]\frac{1}{4}[/tex] x - 4 Substitute -11 for y
-11 = [tex]\frac{1}{4}[/tex] x - 4 Add 4 to both sides
-11 + 4 = [tex]\frac{1}{4}[/tex]x - 4 + 4
-7 = [tex]\frac{1}{4}[/tex]x Multiply both sides by 4
-7(4) = [tex]\frac{1}{4}[/tex][tex](\frac{4}{1})[/tex]x
-28 = x
(-28,-11)
Helping in the name of Jesus.
How many of each size of cube can fill a 1-inch cube: Edge= 1/4 inch
Please help and if answer please give how you solved it
The number of cubes needed with an edge length of 1/3 inches is needed to build a cube with an edge length of 1 inch is 27.
We have,
the edge length of smaller cube, a = 1/3 inches
the edge length of the cube to be built, S = 1/3 inches
Now, Volume of cube = a³
= (1/3)³
= 1/27 in³
Volume of the cube to be build = S³
= 1³
= 1 in.³
Thus, Cubes of smaller length are needed for the larger cube
= 1/ (1/27)
= 27
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Prove that (A-B)xC=(AXC)-(BXC)
Step-by-step explanation:
supposedly
A=3
B= -2
C=2
(3-(-2)×2=(3×2)-(-2×2)
5×2=6-(-4)
10=6+4
10=10
In an experiment, the probability that event A occurs is 1 3 , the probability that event B occurs is 5 6 , and the probability that events A and B both occur is 1 5 . What is the probability that A occurs given that B occurs?
Note that where the above events are described, the probablity of A occurring given that B occurrs is 6/25.
How did we arriave at that?We can use Bayes' theorem to find the conditional probability
P (A| B) = P(A and B ) / P( B)
From the problem statement, we know that P(A) = 1/3,
P(B) = 5/6, and
P (A and B) = 1/5.
Substituting to get .....
P(A | B) = (1/5) / (5/6)
= 1/5 x (6 /5)
= 6/25
Hence, we are corect to state that the probability of A occurring given that B occurs is 6/25.
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****
Atte
THINK
What is the volume of the triangular prism shown below?
13 cm
8 cm
3 cm
The volume of the Triangular prism above is 156 cm^3
What is a Triangular Prism?
Triangular Prism is a three-dimensional shape consisting of two triangular ends connected by three rectangles. It has two identical triangles as parallel bases and if it is a right prism all lateral faces are rectangles.
How to determine this
The volume of a Triangular prism is calculated as
Volume = 1/2 * base * height * length
Where the Base = 8 cm
Height = 3 cm
Length = 13 cm
Volume = 1/2 * 8 * 3 *13
Volume = 1/2 *312
Volume = 156 cm^3
Therefore, the volume of the triangular prism is 156 cm^3
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Susan is going for a walk. She walks for 2 hours at a speed of 3.2 miles per hour. For how many miles does she walk?
Solve completely the system of equations :
x + 3y - 22 = 0 , 2x - y + 42 = 0 , x - 11y + 142 = 0.
Answer:
x = -16/7 and y = 38/7.
Step-by-step explanation:
To solve the system of equations:
x + 3y - 22 = 0 --- equation (1)
2x - y + 42 = 0 --- equation (2)
x - 11y + 142 = 0 --- equation (3)
We will use the method of substitution to find the values of x and y that satisfy all three equations.
From equation (1), we can express x in terms of y:
x = 22 - 3y --- equation (4)
We can substitute equation (4) into equation (2) and simplify:
2(22 - 3y) - y + 42 = 0
44 - 6y - y + 42 = 0
-7y = -38
y = 38/7
Now, we can substitute the value of y into equation (4) to find x:
x = 22 - 3(38/7)
x = -16/7
Therefore, the solution to the system of equations is:
x = -16/7 and y = 38/7.
A soft drink machine outputs a mean of 24
ounces per cup. The machine's output is normally distributed with a standard deviation of 3
ounces. What is the probability of filling a cup between 26
and 27
ounces?
2/7
Assuming I know what standard deviation is, it is there is a 3 ounce "range" that the machine can give, based on that 24 oz mean. So there can be 21,22,23,24,25,26, and 27. Out of those 7, 2 are the numbers we are looking for, so it is 2/7.
A laptop company has discovered their cost and revenue functions for each day:
C(x) = 4x²10x + 150 and R(x) = - 3x² +150x + 75. If they want to make a profit, what is the
range of laptops per day that they should produce? Round to the nearest nunber which would generate a
profit.
to
laptops
The range of laptops that they should produce per day to make profit is: 1 to 21 laptops
How to solve Inequality word problems?When dealing with inequalities, we could make use of any of the following:
Greater than(>)
Less than (<)
Greater than or equal to (≥)
Less than or equal to (≤)
We are given:
Cost function: C(x) = 4x² - 10x + 150
Revenue function: R(x) = -3x² + 150x + 75
Now, if they want to make profit, then:
R(x) > C(x)
Thus:
4x² - 10x + 150 > -3x² + 150x + 75
Rearranging to get:
7x² - 160x + 75 > 0
Solving using quadratic calculator gives:
x ≈ 1 and 21
Thus the range of laptops that they should produce per day to make profit 1 to 21
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Find the square root of 3 whole numbe 6 over 25
The value of the square root 3 6/25 is 1⅘
What is square root?The square root of a number is a value that can be multiplied by itself to give the original number. For example the square root of 225 is 15.
Another example is the square of 16, which can be gotten by finding the prime product of 16
16 = 2×2×2×2. we can group the 2s into two i.e (2×2) × (2×2) . We can now take one out of 2 .
= 2 × 2 = 4. Therefore the the square root of 16 is 4.
Therefore the square root of 3 6/25 can be found by converting the fraction into improper fraction.
= 81/25
therefore the √81/25 = 9/5 = 1⅘.
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Gerald is constructing a line parallel to line l through point P. He begins by drawing line m through points P and Q. He then draws a circle centered at Q, which intersects line l at point N and line m at point S. Keeping the compass measure, he draws a congruent circle centered at point P, which intersects line m at point T.
Which next step will create point R, such that when a line is drawn through points P and R, the line will be parallel to line l?
Lines m and n intersect at point Q. A circle is drawn around point Q and forms point S on line m and forms point N on line l. Point P is also on line m. A circle is drawn around point P and forms point T on line m.
To create point R such that a line through points P and R is parallel to line l, Gerald needs to draw a line through points T and N.
We have,
We know that line l is parallel to line m since both lines intersect at point Q and no other point.
The circle centered at Q intersects line m at point S and line l at point N, which means that QS is perpendicular to line l.
Similarly, the circle centered at P intersects line m at point T, which means PT is perpendicular to line l.
To create a line parallel to line l, Gerald needs to find a line perpendicular to line l.
This can be achieved by drawing a line through points T and N. This new line will be parallel to QS and perpendicular to line l.
Finally, Gerald can find the intersection of this new line with the circle centered at P to find point R, which will be equidistant from points P and T. Drawing a line through points P and R will be parallel to line l.
Thus,
To create point R such that a line through points P and R is parallel to line l, Gerald needs to draw a line through points T and N.
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PLEASE HELP WILL GIVE BRAINLEST FOR CORRECT ANSWER ONLY !!
(Enlarge photo)
The answer is D :) )
Solve for the length of the missing side in the triangle. Leave your answer in radical form. Show your work and
explain the steps you used to solve.
17
The length of the missing side is given as follows:
[tex]x = \sqrt{155}[/tex]
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.For the triangle in this problem, the sides and the hypotenuse are given as follows:
Sides of 13 and x.Hypotenuse of 18.Hence the missing side is given as follows:
x² + 13² = 18²
x = sqrt(18² - 13²)
x = sqrt(155) -> most simple radical form.
Missing InformationThe triangle is given by the image presented at the end of the answer.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
The first and second one
Step-by-step explanation:
Since they are one-to-one functions, the first table and the first graph (under the table) are the answers.
Be sure to mark this as brainliest and hope this helps!
Answer: The first one and second one.
Step-by-step explanation:
It's a bit cut-off but for the very first function, each x-value has a corresponding y-value so it is a function. For the second one (the graph), if we do the vertical line test, it will pass it (vertical line touches only one point of the function). The third one (the loop graph) , however, will not pass the vertical line test as there's a point on the graph where if we were to draw a vertical line, it would be touch 2 or 3 points of the function.
You are sent to the local tea shop to pick up 12 drinks. You purchase 8 sweet teas and 4 unsweetened teas. Unfortunately, you forgot to label them. If you pick 3 drinks at random, find the probability of each event below. Give your answers as simplified fractions.
a) All of the 3 drinks picked are sweet teas.
b) Exactly one drink is sweetened.
a) The probability of picking a sweet tea on the first draw is 8/12. Since we did not replace the first tea, the probability of picking another sweet tea on the second draw is 7/11. Similarly, the probability of picking a sweet tea on the third draw is 6/10. Therefore, the probability of picking 3 sweet teas in a row is:
(8/12) * (7/11) * (6/10) = 0.2545 or 127/500
b) There are 3 ways to pick exactly one sweet tea: S U U, U S U, U U S, where S represents a sweet tea and U represents an unsweetened tea. The probability of picking a sweet tea on the first draw is 8/12, and the probability of picking an unsweetened tea is 4/12. Therefore, the probability of picking exactly one sweet tea is:
(8/12) * (4/11) * (3/10) + (4/12) * (8/11) * (3/10) + (4/12) * (3/11) * (8/10) = 0.4364 or 48/110