Answer: Let's assume that the zeros of the given quadratic equation are a and 1/a, since they are reciprocals of each other. By the sum-product relationships for zeros of a quadratic equation, we have:
a + 1/a = -b/a1 = -4/(1-3k) (where b = 4 and a1 = 1-3k)
Multiplying both sides by a1, we get:
a1(a + 1/a) = -4
Expanding the left-hand side, we get:
a1a + a1/a = -4
Multiplying both sides by a, we get:
a1a² + a1 = -4a
Substituting a1 = 1-3k, we get:
(1-3k)a² + (1-3k) = -4a
Rearranging, we get:
(1-3k)a² + 4a + (3k-1) = 0
Since a is one of the zeros of the quadratic, we know that the quadratic can be factored as:
(1-3k)(a - r)(a - s) = 0
where r and s are the other two roots of the quadratic. By expanding the left-hand side, we get:
(1-3k)(a² - (r+s)a + rs) = 0
Comparing with the expanded form of the quadratic, we see that:
r + s = -4/(1-3k)
rs = (3k-1)/(1-3k)
By Vieta's formulas, we know that rs = c/a1, where c is the constant term of the quadratic. Substituting c = -5 and a1 = 1-3k, we get:
rs = -5/(1-3k)
Equating this with the expression we obtained earlier for rs, we get:
-5/(1-3k) = (3k-1)/(1-3k)
Multiplying both sides by 1-3k and simplifying, we get:
-5 = (3k-1)(3k-2)
Expanding the right-hand side, we get:
-5 = 9k² - 15k + 2
Simplifying, we get:
9k² - 15k - 7 = 0
Using the quadratic formula, we get:
k = (15 ± sqrt(15² + 497))/18
k = (15 ± sqrt(429))/18
Therefore, the two possible values of k are:
k = (15 + sqrt(429))/18 ≈ 1.57
k = (15 - sqrt(429))/18 ≈ -0.24
Note that both of these values of k satisfy the condition that the zeros of the quadratic are reciprocals of each other.
Step-by-step explanation:
It is $150 to rent a room at local skating rink, and it is $5 extra per child for pizza, drink, and a party bag. Write the equation in slope intercept form for the situation above
A) x+y=1050
B) y=150
C) y=150x+5
D) y=5x+150
Answer:
Let's start with the fixed cost, which is the cost to rent the room: $150. This is the y-intercept of the equation. Now, for each child attending the party, there is an additional cost of $5. We can represent the number of children attending with the variable x. Therefore, the equation in slope-intercept form is: y = 5x + 150 So the correct answer is D) y = 5x + 150
the daily high temperature in a town in Alaska has been colder than -4f for three weeks
This statement implies that the daily high temperature in the town in Alaska has been below -4°F (minus four degrees Fahrenheit) for three consecutive weeks.
Suki purchased $9,600 worth of stock and paid her broker a 2.5% broker
fee. She had an immediate need for cash and was forced to sell the stock
when it was worth $8,000. She used a discount broker who charged
$33.97 per trade transaction.
Compute Suki's net loss(-) after the broker fees were taken out.
The net loss is $1873.97.
What is the selling price?
The selling price formula is Selling Price = Cost Price + Profit Margin. Cost price is the price a retailer paid for the product. The profit margin is a percentage of the cost price.
Here, we have
Given: Suki purchased $9,600 worth of stock and paid her broker a 2.5% broker fee. She had an immediate need for cash and was forced to sell the stock when it was worth $8,000. She used a discount broker who charged $33.97 per trade transaction.
Purchase price: $9,600
Fee purchase: 2.5%
Selling price: $8,000
Fee scale: $33.97
The broker fee is the product of the broker fee rate of 2.5% and the purchase price:
Broker fee purchase = 2.5%× 9,600
= 240
The total purchase cost is the sum of the purchase price and the broker fee of the purchase:
Total purchase cost Purchase price = Broker fee purchase
= 9600 + 240
= 9840
The total selling cost is the selling price decreased by the broker fee of the sale (flat rate):
Total selling cost = Selling price - Broker fee sale
= 8,000 - 33.97
= 7966.03
The net loss is then the difference between the total purchase cost and the total selling cost:
Net loss = Total purchase cost - Total selling cost
= 9840 - 7966.03
= 1873.97
Hence, the net loss is $1873.97.
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3n + 9 = 11n -23 Please
Answer: N=4
Step-by-step explanation:
Answer: n = 4
Step-by-step explanation:
subtract 9 from both sides simplify subtract 11n from both sides then combine like terms, simplify, divide both sides by the same factor, then simplify then boom :)
WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
Find the value of x.
Let a = 10, b = 6, c = 12, and d = x
ab=cd
x = ab/c
x = 10(6)/12
x = 5
What is the result when the number 94 is decreased by 50%?
Answer:
47
Step-by-step explanation:
Given: 94 decreased by 50%
First, we will change the percentage to a decimal, by moving the decimal two nodes to the left.
50% = .50
Next, we will multiply the decimal with the number.
94 · .50 = 47
check attached image for further explanation
Pablo is mailing packages. Each small package costs him $2.80 to send. Each large package costs him $3.80. How much will it cost him to send 5 small packages and 4 large packages?
Step-by-step explanation & Answer
———-———-———-———-———-———-———-———-———-———-———-——
Page 1
So first we need to multiply the small packages by 5 because he needs to said 5 of them which is:
5 x 2.80 = 14 Which is our answer for the first part of the question.
Next we need to multiply the big/large packages by 4 because he is going to send 4 of them.
4 x 3.80 = 15.2 / ( money terms ) = 15.20
[tex]\left \{ {{small= 14} \atop {big=15.20}} \right.[/tex]
———-———-———-———-———-———-———-———-———-———-———-——
Page 2
We can them add them up or we can leave it at this but just in case lets add them up:
15.20 + 14 = 29.20 Which is the answer.
[tex]\left[\begin{array}{ccc}An&sw&r\\&=&\\22&.&9\end{array}\right][/tex]
In the circle below, suppose m VUX = 228° and mZUVW=121°. Find the following.
U
X
(a) m/VUX = °
(b) m LUXW =
0.
Assume that m arc VUX = 228° and m ∠UVW = 121° in the circle below.
m∠VUX = 66° and m m∠UXW = 59° respectively.
1) The given information is;
The angle of arc m∠VUX = 228°, the measured angle of ∠UVW = 121°
Given that m∠VUX = 228°, therefore, arc ∠XWV = 360 - 228 = 132°
Therefore, the angle subtended by arc ∠XWV at the centre = 88°
The angle subtended by arc ∠XWV at the circumference = m∠VUX
∴ m∠VUX = 132°/2 = 66° (Angle subtended at the center = 2×angle subtended at the circumference)
m∠VUX = 66°
2) Similarly, m∠XWV is subtended by arc m∠VUX, therefore, m∠XWV = (arc m VUX)/2 = 228°/2 = 114°
A quadrilateral's angles add up to 360°.
Therefore;
m∠VUX + m∠XWV + m∠UVW + m∠UXW = 360° (The sum of angles in a quadrilateral XWVU)
m∠UXW = 360° - (m∠VUX + m∠XWV + m∠UVW)
m∠UXW = 360° - (66 + 114 + 121)
m∠UXW = 360° - 301
m∠UXW = 59°.
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What is the size of angle a?
Answer:
60 degrees
Step-by-step explanation:
The total angles of a circle add up to 360 so to find a missing angle, subtract the figures already given from 60. The angles given total to (140+125+35) = 300. To find angle a, you subtract the 300 from 360. 360-300 = 60 degrees. Therefore, angle a is 60 degrees
The preimage shown above is dilated by a scale factor of 4 about the center (-2,-2). What is the coordinate location of the point C'.
Type your answer as an ordered pair, (x,y) with no spaces.
The coordinate location of point C' after the dilation is (-10, 2).
What is coordinate location?
To find the coordinate location of point C' after the dilation by a scale factor of 4 about the center (-2,-2), we can use the following formula:
(x', y') = (k * (x - h) + h, k * (y - k) + k)
where (x, y) are the coordinates of the original point, (h, k) are the coordinates of the center of dilation, k is the scale factor, and (x', y') are the coordinates of the corresponding point after dilation.
For point C, the coordinates are (x, y) = (-2, -1) and the center of dilation is (h, k) = (-2, -2) with a scale factor of k = 4.
Plugging in these values, we get:
(x', y') = (4 * (-2 - (-2)) - 2, 4 * (-1 - (-2)) - 2)
= (-10, 2)
Therefore, the coordinate location of point C' after the dilation is (-10, 2).
What is coordinate?
A coordinate is a set of numbers or values that indicate the position or location of a point or object in a given space or system. Coordinates are often used in mathematics, geometry, physics, and other fields to describe the location of objects or points in a two- or three-dimensional space. The most common type of coordinates are Cartesian coordinates, which are represented by an ordered pair of numbers (x,y) that describe the location of a point on a two-dimensional plane, or an ordered triplet of numbers (x,y,z) that describe the location of a point in a three-dimensional space.
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Complete question is: The preimage shown above is dilated by a scale factor of 4 about the center (-2,-2). the coordinate location of the point C'after the dilation is (-10, 2).
a surveyor determines that the angle of elevation to the top of a building from a point on the ground is . he then moves back 51.3 feet and determines that the angle of elevation is . what is the height of the building?
The height of the building is approximately 62.4369 feet. The solution involves using trigonometry and solving for the opposite side of the triangle using the tangent function.
Let h be the height of the building, and x be the distance between the first point and the base of the building. Then we have:
tan(26.8°) = h/x ----(1)
tan(19.5°) = h/(x + 43.9) ----(2)
From equation (1), we have x = h/tan(26.8°)
Substituting this value of x in equation (2) and solving for h, we get:
h = (43.9 tan(19.5°) tan(26.8°))/(tan(26.8°) - tan(19.5°))
Plugging in the values, we get:
h ≈ 62.4369 feet
Therefore, the height of the building is approximately 62.4369 feet.
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Can I have some help with this math problem
The answer is A. 1/4.
An outline of a city map is shown. The population of the city is 23,023 people. What is the population density of the city?
Answer:148.38
Step-by-step explanation:
Population Density=Population of country÷Area of country
Population of country=23,023
Area of country=(18*8)+(4*5)=164 m²
Population Density=23023÷164=148.38 people/m²
Which of the following is a valid application of the distributive property?
A. 5 x 2 + 3 = 5 X (2 + 3)
B. 5 x 2 + 3 = 5 x (2) + 5 x (3)
B only
A only
Neither A nor B
Both A and B
Answer:
B only
Step-by-step explanation:
The correct answer is B only.
The distributive property states that a multiplication of a number by a sum or difference can be rewritten as the sum or difference of the products of the number with each term in the sum or difference. In other words, a(b + c) = ab + ac and a(b - c) = ab - ac.
Option A, 5 x 2 + 3 = 5 X (2 + 3), does not use the distributive property correctly. It tries to distribute the 5 over the sum 2 + 3, which is not possible.
Option B, 5 x 2 + 3 = 5 x (2) + 5 x (3), correctly applies the distributive property by distributing the 5 over each term in the sum 2 + 3.
Therefore, the valid application of the distributive property is B only.
the waiting time at a drive-through window has an exponential distribution with a mean of 6 minutes. what is the probability that the waiting time is greater than 5 minutes? enter your answer as a percentage accurate to two decimal places. for example, a probability of 0.4567 is 45.67%, so it should be entered as 45.67.
The probability that the waiting time is greater than 5 minutes is 0.3012
Given that the waiting time at a drive-through window has an exponential distribution with a mean of 6 minutes.
The probability density function of an exponential distribution is given by
f(x) = (1/μ) × e^(-x/μ)
where μ is the mean of the distribution.
Therefore, the probability that the waiting time is greater than 5 minutes is
P(X > 5) = ∫[5, ∞] f(x) dx
= ∫[5, ∞] (1/6) × e^(-x/6) dx
= [-e^(-x/6)]_[5, ∞]
= e^(-5/6)
Using a calculator, e^(-5/6) is approximately 0.3012.
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45,52,17,63,57,42,54,58 outlier
Answer: 31363022. or 17
Step-by-step explanation:
a chair is normally $30.00. it's now on sale for 10% off. what is the sale price?
- ugly person
Answer:27
Step-by-step explanation:First you find 10% of 30 which is 3 then you subtract 30-3=27
as the size of a sample increases, the mean of the distribution of sample means increases always. (true/false). group of answer choices
As the size of a sample increases, the mean of the distribution of sample means increases always. - False
The mean of the distribution of sample means does not always rise as sample number rises. The population mean is not changed by increasing the sample number because the population mean is equivalent to the mean of the distribution of sample means. The variation of the distribution of the sample means does, however, decline as the sample number rises.
The distribution of sample means approximates normality with a mean equal to population mean and a standard deviation equal to population standard deviation divided by square base of the total sample size. This is known as the central limit theorem. As a result, the distribution of sample means becomes more tightly focused around the community mean and less variable as the sample number rises.
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The volume of a rectangular prism is 768 ft3. What is the volume of the same shape if the width is changed by a scale factor of 1/3?
The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively. If the width is changed by a scale factor of 1/3, then the new width is (1/3)w. The length and height remain the same. Therefore, the new volume of the rectangular prism is:
V' = l(1/3w)h
Multiplying both sides by 3 to simplify the expression, we get:
3V' = lw(3h)
Since the original volume of the rectangular prism is 768 ft3, we have:
V = lwh = 768
Multiplying both sides by 3 to simplify the expression, we get:
3V = lw(3h)
Substituting 3V for lw(3h), we get:
3V' = 3V(1/3w) = Vw
Therefore, the new volume of the rectangular prism is:
V' = Vw = (768 ft3)(1/3) = 256 ft3
So, the volume of the same shape if the width is changed by a scale factor of 1/3 is 256 ft3.
last month alex sold his bike for 50.00 and deposited 80 percent of the money into his savings account he made the tqo other deposits of 24 and 35 before he withdrew 2/3 of the total to buy a used skate board write the amounts of alex transmission in order as inergets
The amounts of Alex's transactions in order are $50.00, $40.00, $24.00, $35.00, $149.00, and $98.67.
The amounts of Alex's transactions can be listed in the following order:
The amount he received from selling his bike: $50.00
The amount he deposited into his savings account, which is 80% of $50.00: $40.00
The first deposit he made of $24.00
The second deposit he made of $35.00
The total amount he had in his account before withdrawing 2/3 of it: $149.00 (which is the sum of $50.00, $40.00, $24.00, and $35.00)
The amount he withdrew to buy the used skateboard, which is 2/3 of $149.00: $98.67
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a mosaic table top has triangular and rectangular peices for every 8 rectangular pieces there are 12 triangular pieces there are a total of 80 pieces how many of each shape are used
in classical variables sampling, the evidence supports the conclusion that the account is not materially misstated if both the upper and lower limits are within the bounds of
The evidence supports the conclusion that the account is not materially misstated if both the upper and lower limits are within the bounds of tolerable misstatement.
after running a classification model, we have the following confusion matrix: confusion matrix what is this model's overall accuracy ?
The overall classification accuracy of this model on the test set is 0.179
The overall classification accuracy of the model can be calculated by dividing the number of correctly classified instances (the sum of true positives and true negatives) by the total number of instances in the test set
Accuracy = (TP + TN) / (TP + TN + FP + FN)
where TP = True Positives, TN = True Negatives, FP = False Positives, and FN = False Negatives.
From the confusion matrix given
True Positives (TP) = 124
True Negatives (TN) = 116
False Positives (FP) = 77
False Negatives (FN) = 851
Plugging these values into the formula, we get
Accuracy = (124 + 116) / (124 + 116 + 77 + 851)
Accuracy = 0.179
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The given question is incomplete, the complete question is:
The following classification confusion matrix shows the results of a model's classifications on a test set: Test Set Results Model Prediction FALSE TRUE FALSE 116 TRUE 77 124 851 (The rows refer to the model's classifications, and the columns to the actual results in the test set.) a. What is the overall classification accuracy of this model on the test set?
David is driving on a road with a speed limit of 60 mph. It is possible for him to get a ticket if she goes more than 7mph over the speed limit. Is it possible to David to get a ticket while she is on cruise control.
This is a inequality problem.
It is possible for her to exceed the speed limit and get a ticket if she is not paying attention or if the road conditions change.
What is speed?
she should always be aware of her speed and adjust it as necessary to stay within the legal limit.
Yes, this is an inequality problem. We can use an inequality to represent the situation:
David's speed ≤ Speed limit + 7 mph
Let's substitute the given values:
David's speed ≤ 60 mph + 7 mph
David's speed ≤ 67 mph
If David's speed is less than or equal to 67 mph, then she will not get a ticket, because she is within the allowable limit of going 7 mph over the speed limit. However, if David's speed is greater than 67 mph, then she will be going too fast and is at risk of getting a ticket.
Since David is driving on cruise control, it is possible for her to exceed the speed limit and get a ticket if she is not paying attention or if the road conditions change. Therefore, she should always be aware of her speed and adjust it as necessary to stay within the legal limit.
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Graph the equation below by plotting the
y-intercept and a second point on the
line. When you click Done, your line will
appear.
1=1/√x-2
Click on the point(s). To change your selection, drag the
marker to another point. When you've finished, click Done.
-8-6-4
Done
N
8
co
F
2
-2
$
-6-
-8-
2
4 6 8
Edit
so it is 2o bevuse
hi
please help
Given POQ = 0 rad, the length of the arc PQ is twice the radius OP and OR = 4cm, find
a) the value of 0
b) the area of the shaded region if the length of the arc PQ is twice the length of the arc RS
As a result, the shaded region's area sector is **10.62 cm² cm.²
What is a sector?
A sector is a section of a circle in geometry that is bounded by two radii and an arc. It is a pie-shaped portion of a circle that touches the circle's center, has two straight edges (the two radius lines), and a curved edge created by the arc.
Arc Length = r is the formula for the arc length of a circle,
where is the radius of the circle and r is the radian measurement of the arc (or central angle).
The formula for arc length, L = r *, can be used to determine the value of zero. L is the length of the arc, r is the radius of the circle, and is the centre angle in radians. We can deduce from the facts provided that PQ equals 2 * OP.
Also obvious is that OR = 4 cm. We can claim that PQ = 2 * OR = 8cm because PQ is twice as long as OP. Now, we can calculate's value using the formula:
L = r * θ 8 = 4θ θ = 2
Consequently, = 2 radians.
We must know the length of arc RS in order to calculate the size of the shaded zone. PQ is twice RS, as we are aware. RS = PQ/2, which equals 4 cm. Now, we may apply the area of a formula.We may now apply the formula A = (1/2) * r² *, where A is the sector's area, r is the circle's radius, and is the centre angle in radians.
Sector PQR area equals (1/2) * OR2 * sector PQR area equals (1/2) * 16 * 2 sector PQR area equals (16)
Sector PSR area equals (1/2) * OR²2 * Sector PSR area equals (1/2) * 16 * π/3 Sector PSR area equals (8)/3
Sector PQR minus Sector PSR is equal to the area of the shaded region. Area of the shaded area is 16 - (8π)/3. Shaded area size: 10.62 cm²
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a part of a population chosen in such a way that every member had an equal chance of being selected.
This is called random sampling.
What is random sampling?
Random sampling is commonly used in research and statistical analysis, as it helps to reduce the potential for bias in the sample selection process. There are several techniques for conducting random sampling, such as simple random sampling, stratified random sampling, and cluster sampling, each with its own specific method of selection.
Random sampling is an important tool in statistical inference and research. By selecting a random sample from a population, researchers can obtain an estimate of the population parameters (such as the mean or proportion) with a known level of precision and confidence.
There are several techniques for conducting random sampling:
Simple random sampling: In this technique, each member of the population has an equal chance of being selected. This can be done by assigning each member of the population a unique number and using a random number generator to select the sample.
Stratified random sampling: In this technique, the population is divided into subgroups (strata) based on some characteristic (such as age or gender). A random sample is then selected from each stratum.
Cluster sampling: In this technique, the population is divided into clusters (such as neighborhoods or schools). A random sample of clusters is then selected, and all members within those clusters are included in the sample.
Random sampling has several advantages over non-random sampling methods, such as convenience sampling or purposive sampling. First, it helps to ensure that the sample is representative of the population, reducing the potential for bias in the sample selection process. Second, it allows for the calculation of sampling error, which is the degree of error that is inherent in any sample due to chance variation. Finally, random sampling allows for the use of inferential statistics, which enables researchers to make inferences about the b based on the sample data.
However, random sampling also has some limitations. It can be expensive and time-consuming to select a truly random sample from a large population. Additionally, it may be difficult to ensure that all members of the population are included in the sampling frame, which could result in some members being excluded from the sample. Finally, the sample size must be large enough to ensure a sufficient level of precision in the estimates of the b parameters.
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what's the answer The area of a square is A = s², where s is the length of one side of the square.
What is the side length s for each square?
Drag the answer into the box to match each description.
The square with A = 225 in²
The side length of each square is √225 in = 15 inches so the option B is correct
What do you mean by term Square root ?The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √. For example, the square root of 9 is 3 because 3 multiplied by 3 equals 9. The square root of 16 is 4 because 4 multiplied by 4 equals 16. The square root of a number is always a positive number, although it can be irrational (a non-repeating, non-terminating decimal) for some numbers.
The formula to find the length of one side of a square, s, when given the area, A, is:
s = √(A)
So, for the square with A = 225 in², the side length would be:
s = √(225) in
s = 15 inches
Therefore, the side length of the square with an area of 225 in² is 15 inches.
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Which statement is not true for the function notation of the volume of a cube, V(s) = s3?
Answer:
Step-by-step explanation:
The statement that is not true for the function notation of the volume of a cube, V(s) = s3, is not specified. Please provide the statement you are referring to.
joy is giving ice cream cones to some children at a carnival. she has 8 chocolate ice cream cones, 10 vanilla ice cream cones, and 6 strawberry ice cream cones. if joy selects an ice cream cone randomly without looking, what is the probability that she will give a chocolate ice cream cone to the first child and then a vanilla ice cream cone to the second child?
The required probability that Joy will give a chocolate ice cream cone to the first child and then second child get a vanilla ice cream cone is equal to 3/16.
Number of chocolate ice cream cones = 8
Number of vanilla ice cream cones = 10
Number of strawberry ice cream cones = 6
Total number of ice cream cones = 8+10+6
= 24 cones,
The probability of Joy giving a chocolate ice cream cone to the first child is 8 cones,
P(chocolate) = 8/(8+10+6) = 8/24 = 1/3
Now,
Assuming that Joy gave away a chocolate ice cream cone to the first child,
There are 8-1=7 chocolate ice cream cones left.
Similarly, there are 10-1=9 vanilla ice cream cones left.
Probability of Joy giving a vanilla ice cream cone to the second child,
given that she gave a chocolate ice cream cone to the first child, is,
P(vanilla | chocolate)
= 9/(7+9)
= 9/16
Probability of Joy giving a chocolate ice cream cone to the first child and a vanilla ice cream cone to the second child is,
P(chocolate and vanilla)
= P(chocolate) × P(vanilla | chocolate)
= (1/3) × (9/16)
= 3/16
Therefore, the probability that Joy will give a chocolate ice cream cone to the first child and then a vanilla ice cream cone to the second child is 3/16.
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