The correlation coefficient of 0.203 suggests a weak positive correlation between nasal length and stature. However, further statistical analysis is needed to determine whether this correlation is statistically significant.
To test whether there is any correlation between nasal length and stature in the population of Indian adult males, we can use a hypothesis test with the correlation coefficient.
Null hypothesis (H0): There is no correlation between nasal length and stature in the population.
Alternative hypothesis (HA): There is a correlation between nasal length and stature in the population.
The correlation coefficient between the two variables is given as 0.203.
To test the hypothesis, we can use a t-test for the correlation coefficient. The test statistic can be calculated using the formula:
t = r * sqrt((n - 2) / (1 - r^2))
where r is the correlation coefficient and n is the sample size.
In this case, the sample size is 20 and the correlation coefficient is 0.203. Plugging these values into the formula, we can calculate the test statistic.
t = 0.203 * sqrt((20 - 2) / (1 - 0.203^2))
After calculating the test statistic, we can compare it with the critical value of t at a desired significance level (e.g., α = 0.05 for a 5% significance level) and degrees of freedom (df = n - 2) to determine whether to reject or fail to reject the null hypothesis.
If the calculated t-value is greater than the critical value, we can reject the null hypothesis and conclude that there is a statistically significant correlation between nasal length and stature in the population. Conversely, if the calculated t-value is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a correlation between the two variables.
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Select the correct answer.
30-1
2 2 2 2 2 2 2:
(2
28
26-
22-
20
18-
16-
14-
12-
10-
8-
6-
02 4 6 8 10 12 14 16 18 20 22 24 26
How many triangles in the diagram can be mapped to one another by similarity transformations?
OA 2
O B. 4
O C. 0
OD. 3
The number of triangles in the diagram that can be mapped to one another by similarity transformations include the following: D. 3.
What are the properties of similar triangles?In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of three (3) pairs of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent and similar triangles:
ΔABC
ΔDEF
ΔGHI
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If 15 (2/3)×3 (1/6)+6 (1/3) =11 (7/8) + x ; Then the value of the x is
The value of x is approximately 80419.4861.
To find the value of x in the equation:
15 (2/3) × 3 (1/6) + 6 (1/3) = 11 (7/8) + x
Let's simplify each side of the equation separately:
On the left side:
15 (2/3) × 3 (1/6) can be calculated as follows:
15 (2/3) = 15 + (2/3) = 15 + 2/3 = 45/3 + 2/3 = 47/3
3 (1/6) = 3 + (1/6) = 3 + 1/6 = 18/6 + 1/6 = 19/6
So, on the left side, we have:
47/3 × 19/6 + 6 (1/3)
To multiply fractions, we multiply the numerators and denominators:
(47 × 19) / (3 × 6) + 6 (1/3)
47 × 19 = 893
3 × 6 = 18
So, we have:
893/18 + 6 (1/3)
Now, let's convert 6 (1/3) to a fraction:
6 (1/3) = 6 + (1/3) = 6 + 1/3 = 18/3 + 1/3 = 19/3
Now, we have:
893/18 + 19/3
To add fractions, we need a common denominator, which is the least common multiple (LCM) of 18 and 3, which is 18. Let's convert both fractions:
893/18 + 19/3 = (893 × 1) / (18 × 1) + (19 × 6) / (3 × 6)
= 893/18 + 114/18
Now, we can combine the fractions:
(893 + 114) / 18 = 1007/18
On the right side of the equation, we have 11 (7/8) + x. Let's convert 11 (7/8) to a fraction:
11 (7/8) = 11 + (7/8) = 11 + 7/8 = 88/8 + 7/8 = 95/8
Now, the equation becomes:
1007/18 = 95/8 + x
To solve for x, we need to get rid of the fraction on the right side. We can find a common denominator, which is 18 × 8 = 144:
(1007 × 8) / (18 × 8) = (95 × 18 + x × 144) / (8 × 18)
80456/144 = (1710 + 144x) / 144
Cross-multiplying gives us:
80456 × 144 = 1710 + 144x
11598864 = 1710 + 144x
Rearranging the equation:
144x = 11598864 - 1710
144x = 11597154
x = 11597154/144
Evaluating the expression:
x = 80419.4861
Consequently, x has a value of around 80419.4861.
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What translation would map C onto A?
A. (x – 7, y + 3)
B. (x + 3, y – 7)
C. (x – 3, y + 7)
D. (x + 7, y – 3)
Answer:
A
Step-by-step explanation:
consider the coordinates of points C and A
C (4, - 1 ) and A (- 3, 2 )
4 → - 3 in the x- direction is - 7
- 1 → 2 in the y- direction is + 3
then the translation rule is
(x, y ) → (x - 7, y + 3 )
(Computing rates of return) From the following price data, compute the annual rates of return for Asman and Salinas. Time Salinas 1 $30 2 11 29 3 12 31 4 14 34 (Click on the icon in order to copy its contents into a spreadsheet.) How would you interpret the meaning of the annual rates of return? Asman $9 The rate of return you would have earned on Asman stock from time 1 to time 2 is The rate of return you would have earned on Asman stock from time 2 to time 3 is The rate of return you would have earned on Asman stock from time 3 to time 4 is The rate of return you would have earned on Salinas stock from time 1 to time 2 is 22.22 %. (Round to two decimal places.) 9.09 %. (Round to two decimal places.) 16.67 %. (Round to two decimal places.) %. (Round to two decimal places.)
The annual rates of return for Asman and Salinas are as follows: Asman - 22.22%, 9.09%, 16.67%; Salinas - 60.00%%.
1. To calculate the annual rates of return, we need to determine the percentage change in stock prices from one time period to another.
2. For Asman stock, the price data is as follows:
- Time 1: $30
- Time 2: $11
- Time 3: $29
- Time 4: $12
3. The rate of return you would have earned on Asman stock from time 1 to time 2 can be calculated using the formula:
[(Ending Price - Beginning Price) / Beginning Price] * 100
Substituting the values, we get:
[(11 - 30) / 30] * 100 = -63.33% (rounded to two decimal places)
4. The rate of return you would have earned on Asman stock from time 2 to time 3 can be calculated similarly:
[(29 - 11) / 11] * 100 = 163.64% (rounded to two decimal places)
5. The rate of return you would have earned on Asman stock from time 3 to time 4 can be calculated:
[(12 - 29) / 29] * 100 = -58.62% (rounded to two decimal places)
6. For Salinas stock, the price data is as follows:
- Time 1: $30
- Time 2: $12
- Time 3: $31
- Time 4: $34
7. The rate of return you would have earned on Salinas stock from time 1 to time 2 can be calculated:
[(12 - 30) / 30] * 100 = -60.00% (rounded to two decimal places)
8. Therefore, the annual rates of return for Asman and Salinas are as follows:
- Asman: -63.33%, 163.64%, -58.62% (rounded to two decimal places)
- Salinas: -60.00% (rounded to two decimal places)
9. The annual rates of return indicate the percentage change in the value of the stock over a one-year period. A positive rate of return indicates a gain, while a negative rate of return indicates a loss. These figures help investors assess the performance of their investments and make informed decisions.
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On Sunday, a local hamburger shop sold a combined total of 332 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Sunday?
it is important to label all your variables and expressions clearly because
Labeling variables and expressions clearly is important because it helps ensure clarity, precision, and understanding in mathematical or scientific contexts.
Here are a few reasons why it is important to label variables and expressions:
Avoid confusion: Clear labeling prevents confusion, especially when dealing with complex equations or multiple variables. It helps distinguish between different quantities and ensures that each variable represents a specific aspect of the problem or situation.
Enhance communication: Precise labeling allows for effective communication of mathematical ideas and concepts. It helps convey information accurately to others, whether it's through written work, presentations, or discussions.
Promote understanding: By labeling variables and expressions clearly, it becomes easier for both the reader and the writer to understand the meaning and purpose behind each term. It aids in interpreting the mathematical relationships and allows for a better grasp of the overall problem or equation.
Enable error detection: When variables and expressions are properly labeled, it becomes easier to identify any errors or inconsistencies in calculations or equations. It allows for a systematic review and helps catch mistakes in formulas, units, or overall logic.
Facilitate problem-solving: Clear labeling enables effective problem-solving by providing a clear framework for approaching mathematical or scientific challenges. It helps organize information, track relevant variables, and establish logical connections between different components of a problem.
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Ayaan drank 11/4 bottles of water during a soccer game.what is this fraction as a mixed numeral
Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.
To convert the fraction 11/4 to a mixed numeral, we need to determine the whole number part and the fractional part.
Divide the numerator (11) by the denominator (4).
11 ÷ 4 = 2 remainder 3
The quotient 2 represents the whole number part, and the remainder 3 represents the fractional part.
Write the mixed numeral using the whole number part and the fractional part.
The mixed numeral for 11/4 is:
2 and 3/4
Therefore, Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.
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AA
-2 A
4
2
2
y
B
B'
C
()
C
DD
D'
x
What is the rule for the reflection?
O Ty-axis (x, y) → (-x, y)
Ty-axis (x, y) → (x, y)
Tx-axis (x, y) → (-x, y)
Tx-axis (x, y) → (x, y)
The correct rule for reflection across the y-axis is "Ty-axis (x, y) → (-x, y)."
The rule for reflection depends on the axis of reflection. In this case, we are given the options of Ty-axis (reflection across the y-axis) and Tx-axis (reflection across the x-axis). Let's analyze each option:
Ty-axis (x, y) → (-x, y):
This rule states that for a reflection across the y-axis, the x-coordinate of a point is negated while the y-coordinate remains the same. For example, if we have a point (2, 3) and reflect it across the y-axis, it becomes (-2, 3). The x-coordinate is negated, but the y-coordinate remains the same.
Ty-axis (x, y) → (x, y):
This rule states that for a reflection across the y-axis, both the x-coordinate and y-coordinate remain the same. This means that there is no change in the coordinates of the point after the reflection.
Tx-axis (x, y) → (-x, y):
This rule states that for a reflection across the x-axis, the y-coordinate of a point remains the same while the x-coordinate is negated. For example, if we have a point (2, 3) and reflect it across the x-axis, it becomes (2, -3). The y-coordinate remains the same, but the x-coordinate is negated.
Tx-axis (x, y) → (x, y):
This rule states that for a reflection across the x-axis, both the x-coordinate and y-coordinate remain the same. This means that there is no change in the coordinates of the point after the reflection.
Based on the given options, the correct rule for the reflection is Ty-axis (x, y) → (-x, y). This means that when reflecting a point across the y-axis, the x-coordinate is negated while the y-coordinate remains the same.
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suppose that the functions s and t are defined for all real numbers x as follows. s(x)=4x-5 t(x)=x+6 write the expression for (s+t)(x) and (s•t)(x) and evaluate (s-t)(2)
Answer:
To find the expression for (s+t)(x), we simply add the two functions s(x) and t(x): (s + t)(x) = s(x) + t(x) = 4x - 5 + x + 6 = 5x + 1
To find the expression for (s•t)(x), we multiply the two functions s(x) and t(x): (s•t)(x) = s(x) * t(x) = (4x - 5) * (x + 6) = 4x^2 + 19x - 30
To evaluate (s-t)(2), we substitute 2 for x in the expression for (s-t)(x): (s-t)(2) = s(2) - t(2) = (4*2 - 5) - (2 + 6) = 3 - 8 = -5
Therefore, the expression for (s+t)(x) is 5x+1, the expression for (s•t)(x) is 4x^2+19x-30, and (s-t)(2) is -5.
Step-by-step explanation:
X,(x-36) What is the value of x
The value of x is 63
How to determine the valueTo determine the value of the variable, we have that;
Angles at a point is equal to 360 degreesComplementary angles are defined as angles that sum up to 90 degreesSupplementary angles are defined as angles that sum up to 180 degreesAngles on a straight line is equal to 180 degreesFrom the information given, we have that;
x and x - 36 are complementary angles
Now, equate the angles to 90 degrees, we have;
x + x - 36= 90
collect the like terms, we get;
2x = 90 + 36
add the terms
2x =1 26
Divide by the coefficient
x = 63
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Complete question:
The angles X,(x-36) are complementary. What is the value of x
Question 3 A 44-metres long fire-fighting ladder is leaned against a building, as shown in the diagram. The base of the ladder is 7 metres from the building and 3 metres above the ground. How high on the building will the ladder reach?
The ladder will reach a Height of approximately 43.46 meters on the building.
To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.
Using the Pythagorean theorem, we can set up the equation:
(Height of the building)^2 + 7^2 = 44^2
Simplifying the equation, we have:
(Height of the building)^2 + 49 = 1936
Subtracting 49 from both sides, we get:
(Height of the building)^2 = 1887
To find the height of the building, we take the square root of both sides:
Height of the building = √1887
Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.
Therefore, the ladder will reach a height of approximately 43.46 meters on the building.
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I need a medication to be diluted to 3 mg per liter. I only have 1.5 mg of the medicine to
start with, so how much water should I add?
lla fa
Answer: 1.5mg of medicine is to be added to 500ml of water to gain a solution of 3mg per liter
Step-by-step explanation:
3mg per liter is needed. That is 3mg of medicine in 1000ml of water.
As we have only 1.5 mg of medicine that is half of 3mg. We have to add a half of one liter of water. that is 500 ml of water.
please please help last text then finals l give brainliest
1. The x - intercepts of the parabola are
x = 2.5 s and x = 7.5 s2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s
3. The vertex of the parabola is at (5, 80).
What is a parabola?A parabola is a curved shape
1. Given the parabola above, to find the x - intercepts, we proceed as follows.
The x-intercepts are the points at which the graph cuts the x-axis.
They are
x = 2.5 s and x = 7.5 s2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.
The plane takes of at x = 2.5 s and lands at x = 7.5 s
3. The vertex is the maximum point on the graph.
So, we see that the vertex is at x = 5 s and y = 80 ft
So, the vertex is at (5, 80).
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Need answer please if u can help
Answer:
x>-3
Step-by-step explanation:
x-7<-10
x<-10+7
x<-3
x>-3
Question 2: Benjamin rolls an ordinary six-sided dice and flips a coin. List all the possible outcomes.
Answer:
Step-by-step explanation:
Fred took two of his children to watch a movie at the local theatre. He paid $28 for admission. A month earlier, Fred and his wife took all three children to watch a movie at the same theatre. The cost of admission then was $48. The cost of adult and children's tickets are not the same.
Adult admission costs $18, and child admission costs $5.To check:2(5) + 18 = 28, which is true3(5) + 18 = 48, which is also true.
Let's begin by letting x be the cost of adult admission, and y be the cost of a child admission, so we have two equations:2y + x = 28
3y + x = 48
Subtracting the first equation from the second one, we get:3y + x - (2y + x) = 48 - 28y = 20Therefore, we can solve for x by plugging in y=5 in either equation.
Using the first equation, we have:2(5) + x = 28x = 18
Thus, adult admission costs $18, and child admission costs $5.To check:2(5) + 18 = 28, which is true3(5) + 18 = 48, which is also true.
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Write down the first two terms and the 5th term of the following series (i) nothing term=25(2/3)n
ii) nth term =3(n-1)²
i. The first two terms of the series are 50/3 and 100/9, and the fifth term is 800/243.
ii. The first two terms of the series are 0 and 3, and the fifth term is 48.
How to find the nth terms of the sequenceThe first term of the series is can be obtained by substituting n=1 into the formula
Thus;
first term = 25(2/3[tex])^1[/tex]= 25(2/3) = 50/3
The second term of the series is obtained by substituting n=2 into the formula
second term = 25(2/3[tex])^2[/tex] = 25(4/9) = 100/9
The fifth term of the series is obtained by substituting n=5 into the formula
fifth term = 25(2/3[tex])^5[/tex] = 25(32/243) = 800/243
Therefore, the first two terms of the series are 50/3 and 100/9, and the fifth term is 800/243.
(ii) The first term of the series is obtained by substituting n=1 into the formula
first term = [tex]3(1-1)^2 = 3(0)^2 = 0[/tex]
The second term of the series is obtained by substituting n=2 into the formula
second term = [tex]3(2-1)^2 = 3(1)^2 = 3[/tex]
The fifth term of the series is obtained by substituting n=5 into the formula
fifth term = [tex]3(5-1)^2 = 3(16) = 48[/tex]
Therefore, the first two terms of the series are 0 and 3, and the fifth term is 48.
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1.tossing a coin, find the probability of an event to get:
a) head
b) tail
2.tossing two coins find the probability to get:
а)НН
b)TT
c)HT,TH
So the probability of getting one head and one tail is 50%.since there are no other possible outcomes.
When we flip a coin, there are two possible outcomes: heads (H) or tails (T). Tossing a coin is a random experiment that follows a binomial distribution since each toss is independent, and there are only two possible outcomes.
We can use the binomial probability formula to find the probability of a specific event happening.Here are the answers to each part of the question:b) TT (two tails)
To calculate the probability of getting two tails in a row, we multiply the probability of getting tails on the first toss by the probability of getting tails on the second toss.
P(TT) = P(T) x P(T) = 0.5 x 0.5 = 0.25 = 25%So the probability of getting two tails in a row is 25%.c) HT and TH (one head and one tail)To calculate the probability of getting one head and one tail,
we multiply the probability of getting a head on the first toss by the probability of getting a tail on the second toss, and then add it to the probability of getting a tail on the first toss and a head on the second toss.
P(HT or TH) = P(H) x P(T) + P(T) x P(H) = 0.5 x 0.5 + 0.5 x 0.5 = 0.5 = 50%
Note that the probability of getting two heads is the same as the probability of getting two tails (25%), and the probability of getting any combination of heads and tails is 100% (1),
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What are the new coordinates if the figure were rotated 90 degrees counterclockwise
Answer:
third option
Step-by-step explanation:
under a counterclockwise rotation of 90° about the origin
a point (x, y ) → (y, - x )
Then
A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )
B (2, - 2 ) → (- 2, - 2 )
C (1, - 4 ) → (- 4, - 1 )
The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)
How to determine the new coordinates rotating by 90 degrees counterclockwiseFrom the question, we have the following parameters that can be used in our computation:
The figure,
Where, we have
A = (-1, -2)
B = (2, -2)
C = (1, -4)
The rule of 90 degrees counterclockwise is
(x, y) = (-y, x)
Using the above as a guide, we have the following:
A = (2, -1)
B = (2, 2)
C = (4, 1)
Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)
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how many solutions does the system of equations have?
Step-by-step explanation:
The ONE solution to this system of two lines is the point where the two lines cross at (1,4)
The image of B translated using (x + 2, y + 3) would have what coordinates?
Answer:
(5, 4)
Step-by-step explanation:
(x + 2, y + 3)
Substitute x and y for that of B's position.(3 + 2, 1 + 3)
(5, 4)
Answer:
B' (5, 4 )
Step-by-step explanation:
the translation rule (x, y ) → (x + 2, y + 3 )
means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then
B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )
Express 3.75 into Fraction
Answer:
375/100
Reduce to lowest term
15/4 or 3 3/4
What should be subtracted from minus 3 / 4 so has to get 5 / 6 ?
Answer:
Step-by-step explanation:
Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and
6,which is 12.
3*3/4*3=9/12
5*2/6*2=10/12
Step 2:Subtract 9/12 from 10/12,which is 1/12.
Mr. Chen is parking in a lot downtown. The graph shows the relationship
between the time and the total cost of parking. Evaluate the function for an
input of 2.
For an input of 2, the output value of the function include the following: D. after 2 hours, the cost is $6.
What is a linear function?In Mathematics and Geometry, a linear function refers to a type of function whose equation is graphically represented by a straight line on the xy-plane or cartesian coordinate.
This ultimately implies that, a linear function has the same (constant) slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.
In this context, we can logically deduce that the total cost of parking after 2 hours is equal to 6 dollars based on the graph shown above.
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3!6!
5!7!
Evaluate and simplify
The simplified values of each given expressions involving factorials are:
1) 3!6! = 4,320 2) 5!7! = 604,800
How to Evaluate and Simplify Factorials?Factorials are the product of a given number and all positive integers smaller than it, denoted by an exclamation mark (!).
To evaluate and simplify the expressions involving factorials, calculate the factorials and then simplify the resulting values you get:
1. 3!6!
To calculate 3! (3 factorial), we multiply all the integers from 1 to 3:
3! = 3 × 2 × 1 = 6
Next, we calculate 6! (6 factorial) by multiplying all the integers from 1 to 6:
6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
Therefore, 3!6! = 6 × 720 = 4,320.
2. 5!7!
5! = 5 × 4 × 3 × 2 × 1 = 120
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
Therefore, 5!7! = 120 × 5,040 = 604,800.
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Alex and Juana went on a 32-mile canoe trip with their class. On the first day they traveled 24 miles. What percent of the total distance did they canoe?
Alex and Juana canoed 75% of the total distance on the first day of their trip.
To find the percentage of the total distance they canoed on the first day, we need to divide the distance they traveled on the first day by the total distance and then multiply by 100.
Total distance of the canoe trip = 32 miles
Distance traveled on the first day = 24 miles
Calculate the percentage.
Percentage = (Distance traveled on the first day / Total distance) [tex]\times[/tex] 100
Percentage = (24 miles / 32 miles) [tex]\times[/tex] 100
Percentage = (3/4) [tex]\times[/tex] 100
Percentage = 75%
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Graph the following system of equations. y = 3x + 15 3x + 3y = 9 What is the solution to the system? There is no solution. There is one unique solution (−3, 6). There is one unique solution (0, 15). There are infinitely many solutions.
The solution to the system of equations, y = 3x + 15 and 3x + 3y = 9 is one unique solution, which is (-3, 6) [see image attached below].
What is the Solution to a System of Equations?To graph the system of equations and determine the solution, let's start with each equation individually:
y = 3x + 15
3x + 3y = 9
To graph the first equation, y = 3x + 15, we can plot a line with a slope of 3 and a y-intercept of 15. This line will have a positive slope, meaning it goes upward from left to right.
To graph the second equation, 3x + 3y = 9, we can rearrange it to the slope-intercept form y = (-1)x + 3, or simplified as y = -x + 3. This equation represents a line with a slope of -1 and a y-intercept of 3. This line will have a negative slope, meaning it goes downward from left to right.
Now, let's analyze the graphed lines and their intersection to determine the solution:
From the graphs as shown in the image attached below, we can see that the lines intersect at the point (-3, 6). This means that the solution to the system of equations is a single unique solution.
Therefore, the correct answer is option b. There is one unique solution (-3, 6).
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A to D is an example of _____________?
A. reflection across the line y = 1
B. reflection across the line y = x
C. y-axis symmetry
D. x-axis symmetry
Answer:
D
Step-by-step explanation:
A and D are both equidistant from the x- axis, that is
A is 3 units above the x- axis and D is 3 units below the x- axis
then the x- axis is the line of symmetry
Match each pair of angle measures of a triangle with the remaining angle measure
The angles are matches as;
a. 65 degrees
b. 62 degrees
c. 33 degrees
d. 38 degrees
How to determine the anglesFirst, we need to know the properties of a triangle.
These properties are given as;
A triangle has three sidesIt has three anglesIt is a polygonThe sum of the interior angles of a triangle is equal to 180 degreesThen, we have from the information given that;
1. x + 28 + 87 = 180
collect the like terms, we have;
x = 180 - 115
x = 65 degrees
2. x + 16 + 102 = 180
collect like terms
x = 180 - 118
x = 62 degrees
3. x + 96 + 51 = 180
collect like terms
x = 180 - 147 = 33 degrees
4. x + 119 + 23 = 180
x = 38 degrees
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A 78.0 kg sprinter starts a race with an acceleration of 1.64 m/s2. If the sprinter accelerates at that rate for 25 m, and then maintains that velocity for the remainder of the 100 m dash, what will be his time (in s) for the race?
The sprinter will complete the race in approximately 17.07 seconds.
To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.
Acceleration Phase:
The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:
v = u + at
Here:
v = final velocity (which is the velocity at the end of the acceleration phase)
u = initial velocity (which is 0 since the sprinter starts from rest)
a = acceleration
t = time
Rearranging the equation, we have:
t = (v - u) / a
Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:
t = v / a
Plugging in the values, we get:
t = 25 m / 1.64 m/s²
Constant Velocity Phase:
Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:
t = d / v
Here:
d = distance
v = velocity
Plugging in the values, we get:
t = 75 m / (v)
Since the velocity remains constant, we can use the final velocity from the acceleration phase.
Now, let's calculate the time for each phase and sum them up to get the total race time:
Acceleration Phase:
t1 = 25 m / 1.64 m/s²
Constant Velocity Phase:
t2 = 75 m / v
Total race time:
Total time = t1 + t2
Let's calculate the values:
t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)
Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:
v = u + at
Here:
u = initial velocity (0 m/s)
a = acceleration (1.64 m/s²)
t = time (25 m)
Plugging in the values, we get:
v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s
Now, let's calculate the time for the constant velocity phase:
t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)
Finally, let's calculate the total race time:
Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)
Therefore, the sprinter will complete the race in approximately 17.07 seconds.
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