Answer:
The answer to your problem is, -3000
Step-by-step explanation:
:Write down the points through which the line passes through
:The line is passing through a point at (0, 80000) and (10, 50000)
Next, ( important )
Find the slope of the line
Since the line is passing through the point (0, 80000) and (10, 50000)
So the slope of the line:
= m
[tex]\frac{80,000 - 50,000}{0 - 10}[/tex]
= [tex]\frac{30,000 }{-10}[/tex]
= -3,000
Techniquelly the answer is, 30,000 but for more explanation here it is :)
Find the number that will complete the point-slope equation that models this scenario
The required point-slope equation that models this scenario is
[tex]y - y_{1} - m( x - x_{1} )[/tex]
y - 50,000 = -30,000 ( x - 10 )
Thus the answer to your problem is, - 3,000
Any questions? Write them down below \/
Find the probability of
drawing a spade, then
drawing a face card out of a
deck
The likelihood of pulling a spade followed by a face card from a deck is 3/52, or roughly 0.0588. (rounded to four decimal places).
What is the probability?The probability of drawing a spade from a deck of 52 cards is 13/52, or 1/4, since there are 13 spades in the deck.
Once a spade has been drawn and not returned to the deck, there are now 51 cards left in the deck, of which 12 are face cards (the Jack, Queen, and King of each suit). Therefore, the probability of drawing a face card given that a spade has already been drawn is 12/51.
To find the probability of both events happening together (drawing a spade and then a face card), we can multiply the probabilities of each event:
P(drawing a spade, then drawing a face card) = P(drawing a spade) x P(drawing a face card given that a spade has been drawn)
= (1/4) x (12/51)
= 3/52
Therefore, the probability of drawing a spade, then drawing a face card out of a deck is [tex]3/52[/tex] , or approximately [tex]0.0588[/tex] (rounded to four decimal places).
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Five percent of my students suffer from a terrible malady called Lazybrain(LB). A blood test detects LB accurately 90% of the time. Yusuke is told that his blood test is positive for LB. Yusuke hopes that this is a "flase positive" and he actually doesn't have LB. i. Draw the tree with all the probabilities. Indicate which branches are false positive, false negative, correct positive, and correct negative.
The tree diagram with probabilities that shows all possible outcomes for Yusuke's situation is mentioned below .
What is tree diagram?A tree diagram is a visual tool used to represent hierarchical structures or relationships.
It consists of a branching structure where each branch represents a different category or possibility, allowing for easy visualization of complex systems or decision-making processes.
LB (+) LB (-)
Test (+) 0.045 (true) 0.055 (false positive)
Test (-) 0.005 (false negative) 0.895 (true negative)
The probabilities are as follows:
0.05 (5%) of the students have LB, and therefore the probability of Yusuke having LB is 0.05.
The blood test detects LB accurately 90% of the time, meaning that the probability of a correct positive test result (i.e., Yusuke has LB and the test detects it) is 0.05 * 0.9 = 0.045.
The probability of a false positive test result (i.e., Yusuke does not have LB but the test detects it) is 0.95 * 0.1 = 0.055.
The probability of a true negative test result (i.e., Yusuke does not have LB and the test does not detect it) is 0.95 * 0.9 = 0.855.
The probability of a false negative test result (i.e., Yusuke has LB but the test does not detect it) is 0.05 * 0.1 = 0.005.
Note that the sum of the probabilities for each possible outcome (i.e., correct positive, false positive, true negative, false negative) should add up to 1.
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Yusuke having LB is 0.05. Yusuke has LB, the test detects it is 0.05 * 0.9 = 0.045. Yusuke does not have LB, the test detects it is 0.95*0.1 = 0.055. Yusuke does not have LB , the test does not detect it is 0.95 0.9 =0.855.
What is tree diagram?A tree diagram is a visual tool used to represent hierarchical structures or relationships.
It consists of a branching structure where each branch represents a different category or possibility, allowing for easy visualization of complex systems or decision-making processes.
LB (+) LB (-)
Test (+) 0.045 (true) 0.055 (false positive)
Test (-) 0.005 (false negative) 0.895 (true negative)
The probabilities are as follows:
0.05 (5%) of the students have LB, and therefore the probability of Yusuke having LB is 0.05.
The blood test detects LB accurately 90% of the time, meaning that the probability of a correct positive test result (i.e., Yusuke has LB and the test detects it) is 0.05 * 0.9 = 0.045.
The probability of a false positive test result (i.e., Yusuke does not have LB but the test detects it) is 0.95 * 0.1 = 0.055.
The probability of a true negative test result (i.e., Yusuke does not have LB and the test does not detect it) is 0.95 * 0.9 = 0.855.
The probability of a false negative test result (i.e., Yusuke has LB but the test does not detect it) is 0.05 * 0.1 = 0.005.
Note that the sum of the probabilities for each possible outcome (i.e., correct positive, false positive, true negative, false negative) should add up to 1.
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The expression tan(0) cos(0) simplifies to sin(0) . Prove it
As the tangent of an angle is given by the division of the sine of the angle by the cosine of the angle, the expression is simplified to the sine of the angle.
How to obtain the tangent of an angle?To calculate the tangent of an angle, you need to divide the length of the side opposite to the angle by the length of the side adjacent to the angle. The side opposite is the side that is opposite to the angle, while the side adjacent is the side that is adjacent to the angle.
An equivalent way to describe the calculation of the tangent is that it is the division of the sine of the angle by the cosine of the angle.
Hence the expression in the context of this problem is simplified as follows:
tan(θ)cos(θ) = sin(θ)/cos(θ) x cos(θ) = sin(θ).
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Can you help me with this question please.
Answer:
[tex]x = 4\sqrt{3}[/tex]
Step-by-step explanation:
The triangle is right-angled
In a right-angled triangle, the following equality holds
[tex]\tan x = \dfrac{\text{Side Opposite x}}{\text{Side adjacent to x}}\\\\\tan 30 = \dfrac{4}{x}\\\\[/tex]
[tex]\tan 30 = \dfrac{1}{\sqrt{3}}\\\\\dfrac{1}{\sqrt{3}} = \dfrac{4}{x}\\\\[/tex]
Cross multiply:
[tex]1 \times x = 4 \times \sqrt{3}\\\\x = 4\sqrt{3}[/tex]
I want you to put Ronaldo in this cartesian plane it has to be measured!! The best one wins 45pt and I will rate you best ! Send me your worked document in the answers
Love you guys!
Answer:
Step-by-step explanation:
what?
Select the correct answer.Adam constructed quadrilateral PQRS inscribed in circle O. How can he prove PQRS is a square?A.He needs to show only that the diagonals are perpendicular.B.He needs to show only that the diagonals are perpendicular and congruent.C.He needs to show only that the diagonals are perpendicular and bisect each other.D.He needs to show that the diagonals are perpendicular, congruent, and bisect each other.
Adam needs to show that the diagonals are perpendicular, congruent, and bisect each other.Therefore Option D is correct.
To prove that PQRS is a square, Adam needs to show that all four sides are congruent and that all four angles are right angles.
One way to do this is by showing that the diagonals of PQRS are perpendicular, congruent, and bisect each other.
If the diagonals are perpendicular, then opposite angles are congruent and the quadrilateral is a kite.
If the diagonals bisect each other, then opposite sides are congruent and the kite is a rhombus.
If the diagonals are also congruent, then all sides are congruent and the rhombus is a square.
Therefore, He needs to show that the diagonals of PQRS are perpendicular, congruent, and bisect each other to prove that PQRS is a square.
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a researcher is interested in exploring the relationship between calcium intake and weight loss. two different groups, each with 26 dieters, are chosen for the study. group a is required to follow a specific diet and exercise regimen, and also take a 500-mg supplement of calcium each day. group b is required to follow the same diet and exercise regimen, but with no supplemental calcium. after six months on the program, the members of group a had lost a mean of 15.6 pounds with a standard deviation of 1.2 pounds. the members of group b had lost a mean of 10.3 pounds with a standard deviation of 1.9 pounds during the same time period. assume that the population variances are not the same. construct a 90% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not. let population 1 be the amount of weight lost by group a, who took a 500-mg supplement of calcium each day, and let population 2 be the amount of weight lost by group b, who did not take a calcium supplement. round the endpoints of the interval to one decimal place, if necessary.
The 90% confidence interval for the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not is: resulting in a confidence interval of (4.337, 6.263) pounds.
To construct a 90% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not, we can use a two-sample t-test with unequal variances.
The null hypothesis is that the true difference between the mean amounts of weight lost by the two groups is zero, and the alternative hypothesis is that the true difference is not zero.
We can use the following formula to calculate the confidence interval:
CI = (x_1 - x_2) ± tα/2 * √((s_1)²/n_1 + (s_2)²/n_2)
where
x_1 = 15.6 (mean amount of weight lost by group a)
x_2 = 10.3 (mean amount of weight lost by group b)
s_1 = 1.2 (standard deviation of group a)
s_2 = 1.9 (standard deviation of group b)
n_1 = n_2 = 26 (sample size of both groups)
tα/2 = t0.05/2,24 = 1.711 (degrees of freedom = n_1 + n_2 - 2 = 50)
Plugging in the values, we get:
CI = (15.6 - 10.3) ± 1.711 * √(1.2²/26 + 1.9²/26)
CI = 5.3 ± 0.963
CI = (4.337, 6.263)
Therefore, with 90% confidence, we can estimate that the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not is between 4.337 and 6.263 pounds.
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uessing on an exam: in a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers. what is the probability that: (please round all answers to four decimal places)
In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). nancy has not studied for the exam at all and decides to randomly guess the answers, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977
How to calculate the probability?In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers.
The probability of guessing on an exam can be calculated by using the formula:n(C)/(n(T))where n(C) is the number of favorable events and n(T) is the total number of events. Let's solve the given problem:
Probability of getting the first question correct: P (1st) = 1/4 Probability of getting the second question correct: P (2nd) = 1/4Probability of getting the third question correct: P (3rd) = 1/4 Probability of getting the fourth question correct: P (4th) = 1/4Probability of getting the fifth question correct: P (5th) = 1/4 The probability of guessing all questions correctly can be calculated by multiplying the probability of each question together. P (all) = P (1st) * P (2nd) * P (3rd) * P (4th) * P (5th)= 1/4 * 1/4 * 1/4 * 1/4 * 1/4= 1/1024Therefore, the probability that Nancy will correctly answer all 5 questions by guessing is 0.000977. (rounded to four decimal places)Answer: 0.000977
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What is the Smallest Positive Integer with at least 8 odd Factors and at least 16 even Factors?
Answer:
Step-by-step explanation:
120
Doug is selling his autographed baseball. He bought it for $26 and wants to mark it up 20%. What will the new price be?
Answer:
The answer is $31.20
Step-by-step explanation:
do 20% of 26 and add it to the $26
Which property is (n · p) · q = n · (p · q)
The associative characteristic of multiplication is what the equation (n · p) · q = n · (p · q) represents.
what is equation ?A mathematical assertion that establishes the equality of two expressions is known as an equation. It usually consists of two sides, divided by an equal sign (=), with one or more terms on each side, which could be variables, constants, or both. The objective of equation solving is to identify the value(s) of the variable(s) necessary to make the equation correct. There are many mathematical methods for solving equations, including factoring, simplification, substitution, and the quadratic formula.
given
The associative characteristic of multiplication is what the equation (n · p) · q = n · (p · q) represents.
According to this characteristic, a multiplication expression's outcome is unaffected by the way its factors are organized.
In other words, you can arrange the variables however you like and still arrive at the same conclusion.
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what is the specificity for the test based on these screening results (rounded to three decimal places)?
The specificity of the test based on the given screening results is 0.967 (rounded to three decimal places).
To calculate the specificity, divide the number of true negatives (TN) by the total number of negative results (TN+FP). In this case, that would be 687/(687+22), which is equal to 0.967 (rounded to three decimal places).
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Stanley left his home at 8:00 a. M. And went to Peter's house. For the first 48 minutes of his trip, his average driving speed was 50 km/h. (a) Find the distance travelled (in km) for the first 48 minutes of his trip. (b) For the remaining journey, Stanley drove at a speed of 90 km/h for 1 minutes. It is given that his average driving speed for the whole journey is 70 km/h. Hours if he -Example 73) (i) Express, in terms of 1, the distance travelled (in km) for the remaining journey. (ii) Did Stanley arrive at Peter's house before 9:30 a. M. ? Explain your answer
(a) Distance travelled in first 48 minutes = 40 km. (b)(i) Distance travelled in remaining journey = 30 km. (ii) Yes, Stanley arrived at Peter's house before 9:30 a.m. as he reached there at 9:28 a.m.
(a) To find the distance travelled for the first 48 minutes, we can use the formula:
distance = speed x time
The speed is 50 km/h and the time is 48/60 hours (since 48 minutes is 0.8 hours). So,
distance = 50 x 0.8
distance = 40 km
Therefore, Stanley travelled 40 km for the first 48 minutes of his trip.
(b) Let's use the formula for average speed:
average speed = total distance ÷ total time
We know that the total distance is the distance travelled in the first 48 minutes plus the distance travelled for the remaining journey. Let's call the distance for the remaining journey "d". We also know that the total time is 1 hour (60 minutes).
So,
70 = (40 + d) ÷ 1
40 + d = 70
d = 30
Therefore, the distance for the remaining journey is 30 km.
(i) To express the distance travelled for the remaining journey in terms of 1, we can use the formula we found in part (b):
d = 30 km
(ii) To find out if Stanley arrived at Peter's house before 9:30 a.m., we need to know the total time of his journey. We know that he left his home at 8:00 a.m. and his average speed was 70 km/h. So, the total distance he travelled is:
distance = speed x time
distance = 70 x time
We also know that the total distance is the distance for the first 48 minutes plus the distance for the remaining journey:
distance = 40 + 30
distance = 70 km
Therefore, the total time of his journey is:
time = distance ÷ speed
time = 70 ÷ 70
time = 1 hour
Since he arrived at Peter's house at 9:00 a.m. (1 hour after he left his home), we can conclude that he arrived before 9:30 a.m.
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Rosa wants to Invest $1400 a savings account that pays 4.4% simple Interest. How long will take for this investment to double In value? Round your answer to the nearest tenth.
Answer: 31.8 years
Step-by-step explanation:
The formula to calculate the simple interest is:
I = Prt
where:
I = Interest
P = Principal amount
r = Rate of interest
t = Time (in years)
We want to know how long it will take for the investment to double in value. That means the interest earned should be equal to the principal amount. So, we can write:
2P = P + I
Simplifying:
P = I
Now, we can substitute the values given in the problem:
1400 = 14000.044t
Simplifying:
t = 1400/(1400*0.044) = 31.82 years
Therefore, it will take approximately 31.8 years for the investment to double in value.
For what values of the variables must ABCD be a parallelogram?
The for the values of the variables x = 7 and y = 10, the given must be a parallelogram.
What is parallelogram?A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.
A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base and height of the parallelogram determine its area.
For the given quadrilateral to be parallelogram the opposite sides need to be parallel and equal.
For the given quadrilateral we have:
2y - 16 = y - 6
2y - y = -6 + 16
y = 10
Also,
2x + 2 = y + 6
Substitute the value of y = 10:
2x + 2 = 10 + 6
2x = 16- 2
2x = 14
x = 7
Hence, the for the values of the variables x = 7 and y = 10, the given must be a parallelogram.
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Maggie crochets squares to make a blanket. She has 6 squares made. She then makes 6 squares each hour for 3 hours. Determine which of the following represent the linear relationship described.
The linear relationship of Maggie crocheting squares is y = 6 + 6x graph (b)
How to determine the linear relationshipLet x be the number of hours Maggie spends crocheting squares, and let y be the total number of squares she has made.
Initially, Maggie has 6 squares made,
so y = 6 when x = 0.
For each hour that she spends crocheting squares, Maggie makes 6 more squares.
Therefore, the relationship between x and y is:
y = 6 + 6x
This is a linear relationship with a slope of 6, which means that Maggie is crocheting squares at a rate of 6 squares per hour.
This is represented by graph (b)
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What shape is this cross-section?
The crοss-sectiοn in the image shοwn appears tο be a trapezοid.
What is trapezοid?A quadrilateral with at least οne pair οf parallel sides. In this crοss-sectiοn, the tοp and bοttοm sides are parallel, while the οther twο sides are nοt parallel is trapezοid. There are times when people define trapezoids as having at least one pair of opposite sides that are similar, and other times they say there is just one pair.
The parallelogram satisfies the "at least one" interpretation of the definition because it has two pairs of opposite sides that are similar, which qualifies it as both a trapezoid and a parallelogram. The parallelism does not support the "one and only one" interpretation of the description. How students respond to this depends on how they describe themselves.
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The ordering and transportation cost €C for components used in manufacturing process is approximated by the function below, where C is measured in thousands of dollars and is the order size in hundreds_ C(x) = s(x x+3 (a) Verify that C(3) C(6) _ c(3) (b) According to Rolle's Theorem, the rate of change of the cost must be for some order size in the interval (3 answer to the nearest whole number:) components Find that order size (Round vour Need Help? Ialkto Tutor
The value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.
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The Tire Rack, America’s leading online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and driving conditions. In addition, the Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences. The following data show survey ratings (1 to 10 scale with 10 the highest rating) for 18 maximum performance summer tires (Tire Rack website, February 3, 2009). The variable Steering rates the tire’s steering responsiveness, Tread Wear rates quickness of wear based on the driver’s expectations, and Buy Again rates the driver’s overall tire satisfaction and desire to purchase the same tire again. (Data is in TireRack file)
1. Develop an estimated regression equation that can be used to predict the Buy Again rating given based on the Steering rating. At the .05 level of significance, test for a significant relationship. Interpret the coefficients (Say what they mean in terms of change in you corresponding to a change in x)
2. Did the estimated regression equation developed in part (a) provide a good fit to the data? Explain.
3. Develop an estimated regression equation that can be used to predict the Buy Again rating given the Steering rating and the Tread Wear rating.
4. Is the addition of the Tread Wear independent variable significant? Use 0.05 level of significance.
1 Tire Steering read WeaBuy Again 2 Goodyear 8.9 8.5 8.1 3 Michelin F89 9 8.3 4 Michelin H 8.3 8.8 8.2 5 Dunlop SI 8.2 8.5 7.9 6 Goodyear 7.9 7.7 7.1 7 Yokoham 84 8.2 8.9 8 Yokoham 7.9 7 7.1 9 Kumho P 7.9 7.9 8.3 10 Goodyear 7.6 5.8 4.5 11 Hankook 7.8 6.8 6.2 12 Michelin E 7.4 4.8 13 IMichelin N7 14 Michelin S 6.9 15 Kumho 776.6 16 Dunlop SI 6.2 4.2 17 Bridgestof 5.7 5.5 18 Goodyear 5.7 5.4 19 Dunlop SI57 5 5 34 3.6 2.9 3.3
Tire Steering Tread Wear Buy Again
Goodyear Assurance TripleTred 8.9 8.5 8.1
Michelin HydroEdge8.9 9 8.3
Michelin Harmony 8.3 8.8 8.2
Dunlop SP 60 8.2 8.5 7.9
Goodyear Assurance ComforTred 7.9 7.7 7.1
Yokohama Y372 8.4 8.2 8.9
Yokohama Aegis LS4 7.9 7 7.1
Kumho Power Star 758 7.9 7.9 8.3
Goodyear Assurance 7.6 5.8 4.5
Hankook H406 7.8 6.8 6.2
Michelin Energy LX4 7.4 5.7 4.8
Michelin MX4 7 6.5 5.3
Michelin Symmetry 6.9 5.7 4.2
Kumho 722 7.2 6.6 5
Dunlop SP 40 A/S 6.2 4.2 3.4
Bridgestone Insignia SE200 5.7 5.5 3.6
Goodyear Integrity 5.7 5.4 2.9
Dunlop SP20 FE 5.7 5 3.3
Show transcribed image text
The survey ratings provide valuable feedback for drivers who are looking for quality tires for their vehicles. These ratings can give insight on steering responsiveness, how quickly a tire wears, and overall customer satisfaction. Drivers can also see how their tire of choice stacks up against other tires, making it easier to make an informed decision when shopping for tires.
The Tire Rack is America’s leading online distributor of tires and wheels. They conduct extensive testing to ensure that customers are provided with the most suitable tires for their vehicles, driving styles, and driving conditions. They also use an independent consumer survey to help drivers gain insight on long-term tire experiences.
The following data show survey ratings on a 1-10 scale, with 10 being the highest rating, of 18 maximum performance summer tires, as of February 3, 2009 (Tire Rack website). The variables are Steering (steering responsiveness), Tread Wear (quickness of wear), and Buy Again (overall tire satisfaction and desire to purchase the same tire again). The Yokohama Aegis LS4 has a Steering rating of 7.9, Tread Wear rating of 7, and Buy Again rating of 7.1. The Dunlop SP20 FE has a Steering rating of 5.7, Tread Wear rating of 5, and Buy Again rating of 3.3.
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What is 16/15 in simplest form
42 Développer chaque produit, puis réduire les expres-
sions obtenues.
A= 5x-3(x+12)
C = 2x² + x(4x - 5)
B=3x-6+7(2x+4)
D=4x²-x+x(5x-9)
Which function models the area of a rectangle with side lengths of 2x – 4 units and x + 1 units? What is the area when x = 3?
A. f(x) = 2x2 – 4x + 4; A = 10 B. f(x) = 2x2 + 8x – 4; A = 38 C. f(x) = 2x2 – 8x + 4; A = 2 D. f(x) = 2x2 − 2x − 4; A = 8
Draw and label a rectangle with an area of 32 square units and a perimeter of 36 units
If the area of the rectangle is 32 square units and its perimeter is 36 units, then the length and width of the rectangle will be given as 16 units and 2 units respectively.
Area is defined as the measure of a specific region on ground which is enclosed by a closed polygon figure. The area of a rectangle is given as the product of its length (l) and its width (b) . Perimeter on the other hand is the sum of all four sides of a rectangle and is given by the formula as follows:
Perimeter of rectangle = 2 (length + width)
Now its is given that Area= length x width
32 = l*b ... 1
36 = 2(l+b) ... 2
Using equation 1, we get b = 32/l. Putting this value in equation 2, we get:
36 = 2 (32/l + l)
18 = 32/l + l
⇒ l^2 - 18l + 32 = 0
Solving this quadratic equation we get,
l = 16, 2
Thus the length and width of the rectangle will be equal to 16 units and 2 units respectively or vice versa.
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Refer to complete question below:
On a separate piece of paper, draw and label rectangle with an area of 32 sq. Unit and a perimeter of 36 units. Use numbers or words to show that you are correct.
Graph the line with slope 3 passing through the point (1,-5),
Can somebody help me
Answer:
Step-by-step explanation:
To graph the line with slope 3 passing through the point (1,-5), we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is a point on the line.
Substituting the given values, we get:
y - (-5) = 3(x - 1)
Simplifying the equation, we get:
y + 5 = 3x - 3
Subtracting 5 from both sides, we get:
y = 3x - 8
Now we have the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Comparing this equation to the one we just found, we can see that the slope is 3 and the y-intercept is -8.
To graph the line, we can plot the y-intercept at (0,-8) and then use the slope to find other points on the line. Since the slope is 3, we can go up 3 units and to the right 1 unit to find another point on the line. We can repeat this process to find more points on the line, and then connect them to graph the line.
Bernard's rectangular bedroom is 12 feet by 16 feet. What is the diagonal distance from one corner to the opposite corner?
Answer: 20 feet
Step-by-step explanation: To find the diagonal distance from one corner to the opposite corner of Bernard's rectangular bedroom, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two other sides are the length and the width of the room, so we have:
diagonal^2 = 12^2 + 16^2
diagonal^2 = 144 + 256
diagonal^2 = 400
Taking the square root of both sides, we get:
diagonal = √400
diagonal = 20 feet
Therefore, the diagonal distance from one corner to the opposite corner of Bernard's rectangular bedroom is 20 feet.
A floor is shaped like a regular pentagon. Each side length is represented by (2×+ 4) inches and (4×-2) inches. Find the length of each side
The length of each side of the regular pentagon is 10 units
Let's use the fact that the floor is a regular pentagon to set up an equation involving the side lengths.
A regular pentagon has five sides of equal length, so we can set the two expressions for the side lengths equal to each other:
2× + 4 = 4 × - 2
Solving for x, we get:
2x = 6
x = 3
Now that we have the value of x, we can substitute it back into either expression for the side length to find the length of each side. Let's use the expression (2× + 4) inches:
2× + 4 = 2(3) + 4
= 6 + 4
= 10 units
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a college student takes the same number of credits each semester. before beginning college, the student had some credits earned while in high school. after 2 semesters, the student had 45 credits, and after 5 semesters, the student had 90 credits. if c(t) is the number of credits after t semesters, write the equation that correctly represents this situation.
The equation that correctly represents this situation is c(t) = 45 + 45(t-2). This equation states that the total number of credits the student will have after t semesters is equal to 45 (the number of credits they had before beginning college) plus 45 times the number of semesters after two (t-2).
To explain this equation in more detail, we need to break it down. First, the student had some credits earned while in high school, so the equation starts off with c(t) = 45, which is the number of credits the student had before beginning college.
Next, 45(t-2) represents the number of credits earned in the additional semesters since college began. The t-2 part of the equation means that the total number of credits earned in the additional semesters starts at zero for t = 2. Then, for each additional semester, 45 credits are added. So, for example, when t = 5, 45 credits are added to the initial 45 credits the student had before beginning college, resulting in 90 credits.Therefore, the equation c(t) = 45 + 45(t-2) correctly represents this situation.
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6. The desks at Ryder Middle School are shaped
like a rectangle with an area of 2x²-3x - 2
square inches. The length of the desk is 2x + 1
inches. Write an expression to represent the
width of the desk. (Hint: A = lw)
The equation for the area of a rectangle is A = lw, where l is the length and w is the width. We are given the area (2x² - 3x - 2) and the length (2x + 1). To solve for the width, we can rearrange the equation to w = A/l.
Therefore, the expression to represent the width of the desk is w = (2x² - 3x - 2)/(2x +1).
you have spent $2,500 on liquor for your bar. your bar sales have been $12,890. what is your cost of sales for liquor, expressed as a percentage?
The cost of sales for liquor, expressed as a percentage is 19.39%.
What is the cost of sales for liquor in percentage?To compute for the cost of sales for liquor, expressed as a percentage given that you have spent $2,500 on liquor for your bar and your bar sales have been $12,890, you can use the formula:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
where, Cost of Goods Sold (COGS) = Beginning Inventory + Purchases - Ending Inventory (or the total cost of goods sold during the period)
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
Let's compute for the COGS first:
COGS = Beginning Inventory + Purchases - Ending Inventory
= $0 + $2,500 - $0
= $2,500
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
= $12,890 - $0 - $0
= $12,890
Cost of sales is obtained as follows:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
= ($2,500 / $12,890) × 100
= 19.39%.
Therefore, the cost of sales for liquor, expressed as a percentage is 19.39%.
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8. Students were asked to simplify the following expressions on a test. (154 Four different student answers are shown below: Student A 21 - 3h 15-4h+6+h Student B 18h Student C 3h + 21 600p Student D 21 +- 3h Which student or students simplified the expression correctly? Explain
Student A and Student D have correctly simplified the expression. The expression 154 can be written as 3h + 21 + 15-4h+6+h, which is the same as 21 - 3h + 3h + 21. Student A and Student D both simplified the expression to 21 - 3h. Student B simplified the expression to 18h and Student C simplified the expression to 600p, which are both incorrect.
