The direction and magnitude of the vector A + B are approximately 5.22m at an angle of -33.5°.
To find the direction and magnitude of the vector A + B, we need to perform vector addition using the given components. Given: Vector A: [10.22m, 145.1°], Vector B: [10m, 30°]. Step 1: Resolve the vectors into their Cartesian components. Vector A: A_x = 10.22m * cos(145.1°), A_y = 10.22m * sin(145.1°), Vector B: B_x = 10m * cos(30°), B_y = 10m * sin(30°)
Step 2: Add the respective components of vectors A and B. Resultant vector R: R_x = A_x + B_x, R_y = A_y + B_y. Step 3: Calculate the magnitude of the resultant vector. Magnitude of R: |R| = √(R_x^2 + R_y^2). Step 4: Calculate the direction of the resultant vector. Direction of R: θ = atan2(R_y, R_x). Let's calculate these values: Vector A: A_x = 10.22m * cos(145.1°) ≈ -4.329m, A_y = 10.22m * sin(145.1°) ≈ -7.923m
Vector B: B_x = 10m * cos(30°) ≈ 8.66m, B_y = 10m * sin(30°) ≈ 5m. Resultant vector R: R_x = -4.329m + 8.66m ≈ 4.331m, R_y = -7.923m + 5m ≈ -2.923m, Magnitude of R: |R| = √(4.331^2 + (-2.923)^2) ≈ √(18.731 + 8.551) ≈ √27.282 ≈ 5.22m. Direction of R: θ = atan2(-2.923, 4.331) ≈ -33.5°. Therefore, the direction and magnitude of the vector A + B are approximately 5.22m at an angle of -33.5°.
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Marnie packed 18 boxes in 3 hours, which was 72% of the total number of boxes she had to pack. How many boxes did Marnie have to pack? 13 boxes 25 boxes 54 boxes 216 boxes.
Marnie had to pack 25 boxes.
The correct option is 25 boxes.
Let's assume the total number of boxes Marnie had to pack is "x".
According to the information given, Marnie packed 18 boxes, which is 72% of the total number of boxes she had to pack.
We can represent this as an equation:
18 = 0.72x
To find the value of x, we can divide both sides of the equation by 0.72:
18 / 0.72 = x
Simplifying the equation, we have:
x = 25
Therefore, Marnie had to pack 25 boxes.
The correct option is 25 boxes.
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Given △ABC ∼ △DEF, AB=6, BC=7, AC=8, and DF=6. 4, solve for DE and EF
The length of DE is approximately 4.8 units, and the length of EF is approximately 5.6 units.
In similar triangles, corresponding sides are in proportion. We can set up the following ratios based on the given information:
AB/DE = BC/EF = AC/DF
Substituting the given values, we have:
6/DE = 7/EF = 8/(6.4)
Cross-multiplying, we get:
6EF = 7DE
8EF = 48
Simplifying the second equation, we find that EF = 6.
Substituting EF = 6 into the first equation, we can solve for DE:
6(6) = 7DE
36 = 7DE
DE ≈ 36/7 ≈ 4.8
Therefore, DE is approximately 4.8 units and EF is 6 units.
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The soccer league has a total of 272 players on 16 teams. How many players per team are there in the league? 16 players per team 17 players per team 288 players per team 4352 players per team.
In the soccer league with a total of 272 players on 16 teams, there are 17 players per team.
To determine the number of players per team in the league, we divide the total number of players (272) by the number of teams (16).
Dividing 272 by 16, we get:
272 ÷ 16 = 17
Therefore, there are 17 players per team in the soccer league.
To verify this, we can perform a quick check. If there are players per team, and there are 16 teams in total, the total number of players would be:
17 players per team × 16 teams = 272 players
Since this matches the given total number of players in the league, our calculation is correct.
Hence, there are 17 players per team in the soccer league with a total of 272 players on 16 teams.
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find the probability of event B. enter as a decimal rounded to the nearest hundredth.
a. The probability that both events will occur is 0.3
b. The probability that event B will occur is 1
What is probability?Probability is the likelihood of an event
a. To find the probability that both events are likely to occur, we proceed as follows
The probability that both event srae likely to occur P(A n B) = n(A n B)/n(A u B) where
n(A n B) = number of elements common to A and Bn(A u B) = total number of elementsGiven that
n(A n B) = 6n(A u B) = 20P(A n B) = n(A n B)/n(A u B)
= 6/20
= 3/0
= 0.3
So, the probability that both events will occur is 0.3
a. To find the probability of B events, we proceed as follows
The probability that both event B is likely to occur P(B) = n(B)/n(A u B) where
n( B) = number of elements in Bn(A u B) = total number of elementsGiven that
n(B) = 20n(A u B) = 20P(B) = n(B)/n(A u B)
= 20/20
= 1
So, the probability that event B will occur is 1
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Consider a rectangular tank with height 5 m and base 4 × 8 m^2. Suppose the tank is half full of water. Find the work required to empty the tank through a whole at the top of the tank. The density of water is 1000 kg/m^3 and g = 9. 8 m/s^2
The work required to empty the tank through a hole at the top of the tank is 3.92 × 10^5 J Given, Height of the rectangular tank = 5mBase of the rectangular tank = 4 x 8 m^2Volume of the tank = base x height = 4 x 8 x 5 = 160 m^3
Given, the tank is half full of water volume of water in the tank = 1/2 x 160 = 80 m^3Density of water = 1000 kg/m^3g = 9.8 m/s^2Let the hole be at depth h from the top of the water in the tankThe work required to empty the tank through the hole is given by the expression,W = mghwhere m is the mass of water that flows out of the tank, g is the acceleration due to gravity and h is the depth of the hole from the top of the water in the tank.We can find the value of m as follows:Given, density of water = 1000 kg/m^3Volume of water in the tank = 80 m^3Mass of water in the tank = Volume x density = 80 x 1000 = 80000 kgLet the depth of the hole from the top of the water in the tank be h m. Then the volume of water that flows out of the tank is given by the expression,
V = 4 × 8 × h = 32h m^3The mass of water that flows out of the tank is given by the expression,m = density x volume = 1000 x 32h = 32000h kgNow we can substitute the value of m in the expression for W to get the work required to empty the tank through the hole,W = mgh = 32000gh JThe value of h that minimizes the work required to empty the tank is obtained by differentiating W with respect to h and equating the result to zero. This gives,dW/dh = 32000g - 0 = 0Therefore, h = 0The work required to empty the tank through a hole at the top of the tank is 3.92 × 10^5 J.
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Steve is turning half of his backyard into chicken pen . His backyard is a 24 meter by 45 Metter rectangle
An area of 18 x 30 = 540 square meters, which is half the area of his backyard.
Steve is turning half of his backyard into a chicken pen. Given that his backyard is a 24 meters by 45 meters rectangle, the area of the whole backyard is
24 x 45 = 1080 square meters.
If half of the backyard is to be turned into a chicken pen, then the area of the chicken pen will be
1080/2 = 540 square meters.
Since the area of a rectangle is calculated by multiplying its length by its width, the dimensions of the chicken pen will depend on the desired shape of the pen.
Steve can decide to make the chicken pen a square or a rectangle or any other shape.
However, if he decides to make the pen a rectangle, he will have to make sure that the length and width are such that their product is equal to 540 square meters.
For example, he can make the chicken pen a rectangle with a length of 18 meters and a width of 30 meters.
This will give an area of 18 x 30 = 540 square meters, which is half the area of his backyard.
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W = Fd. Find the force, F, needed to move a piano given the amount of work applied, W, and distance moved, d. ?
To find the force, F, needed to move a piano given the amount of work applied, W, and distance moved, d, we can use the equation W = Fd.
Rearranging the equation, we can solve for F by dividing both sides of the equation by d.
The equation W = Fd represents the relationship between work (W), force (F), and distance (d).
In this case, we are given the values of W and d and need to find F.
To isolate F, we can rearrange the equation as F = W/d.
By dividing the work (W) by the distance (d), we obtain the force (F) required to move the piano. The unit of force is typically measured in newtons (N), work in joules (J), and distance in meters (m).
It's important to note that this equation assumes a linear motion, where the force applied remains constant throughout the displacement of the piano. In practical situations, however, additional factors such as friction and the piano's weight distribution may affect the force required to move it.
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1. Use , , or = to compare the ratios. Show your work.(a)5 : 8and7 : 10(b)96and3624
(a) 5:8 < 7:10
To compare the ratios, we can find their equivalent fractions. For 5:8, the equivalent fraction is (5/8), and for 7:10, it is (7/10).
Comparing the fractions, (5/8) is less than (7/10) because the denominator of (8) is larger than the denominator of (10), and the numerators (5 and 7) are the same.
To compare ratios, we can convert them into equivalent fractions. In the first case, 5:8 and 7:10 can be written as fractions (5/8) and (7/10), respectively. To determine which fraction is larger, we compare their numerators and denominators. In this case, both fractions have the same numerator (5 and 7). However, the denominator of (5/8) is 8, which is larger than the denominator of (7/10), which is 10. Since the numerators are equal and the denominator of (5/8) is larger, we can conclude that 5:8 is less than 7:10.
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Justin recently started working for a company that pays him $11. 40 per hour. He is expected to work a total of 251 days for 8 hours each. How much will Justin earn for the year (i. E. Gross annual salary)?.
Justin will earn $22,903.20 for the year as his gross annual salary
To find Justin's gross annual salary, you need to multiply his hourly rate by the number of hours he works in a year. Justin works 8 hours per day and 251 days in a year.
So, the total number of hours he works in a year is:
$$8 \text{ hours/day} \cdot 251 \text{ days/year} = 2,008 \text{ hours/year}
$$Now, multiply this number by Justin's hourly rate:$$2,008 \text{ hours/year} \cdot $11.40/\text{hour} = $22,903.20
$$
Therefore, Justin will earn $22,903.20 for the year as his gross annual salary.
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Justin will earn $550,732.80 as his gross annual salary.
To calculate Justin’s gross annual salary, we will first calculate his daily pay and then multiply it by the total number of days he will work.
Here are the steps to solve the problem:
Step 1: Find the daily pay Justin will earn.
To find Justin's daily pay, we will multiply his hourly pay by the number of hours he will work each day. Justin will work for 8 hours each day, so his daily pay is:
Daily pay = Hourly pay × Number of hours worked per day
= $11.40 × 8
= $91.20
Step 2: Find the total pay Justin will earn.
To find the total pay Justin will earn, we will multiply his daily pay by the number of days he will work.
Total pay = Daily pay × Number of days worked
= $91.20 × 251
= $22,897.20
Step 3: Find Justin’s gross annual salary.Justin’s gross annual salary is the total pay he will earn for the year.
To find this, we will simply multiply his total pay by the number of times he will be paid in a year (assuming he is paid twice a month, which is common in many companies):
Gross annual salary = Total pay × Number of pay periods in a year
= $22,897.20 × 24= $550,732.80
Therefore, Justin will earn $550,732.80 as his gross annual salary.
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Sam has 8 shells and thandeka has 12. What is the ratio,in simplest form,of Sam's shells and thandeka shells?
The ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3. To simplify the ratio of Sam’s shells and Thandeka’s shells, we need to divide both numbers by their greatest common factor, GCF.
In this case, we have:Sam’s shells = 8Thandeka’s shells = 12Factors of 8: 1, 2, 4, 8Factors of 12: 1, 2, 3, 4, 6, 12The common factors of 8 and 12 are 1, 2, and 4.
However, we need to find the greatest common factor of 8 and 12 to simplify the ratio. Therefore, the greatest common factor of 8 and 12 is 4.
Hence, dividing both numbers by 4 gives us:
Sam’s shells ÷ GCF = 8 ÷ 4 = 2
Thandeka’s shells ÷ GCF = 12 ÷ 4 = 3
Therefore, the ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3.Another way to solve the problem is by finding the ratio between the two numbers.
Thus:Ratio = Sam’s shells :
Thandeka’s shellsRatio = 8 : 12
To simplify the ratio, divide both numbers by the greatest common factor of 8 and 12 which is 4.
Ratio = (8 ÷ 4) : (12 ÷ 4)Ratio = 2 : 3
Therefore, the ratio of Sam’s shells and Thandeka’s shells, in simplest form is 2:3.
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Rewrite cos(x-pi/6) in terms of sin(x) and cos(x)
Trigonometric function cos(x - π/6) in terms of sin(x) and cos(x) is (√3/2)cos(x) + (1/2)sin(x).
To rewrite cos(x - π/6) in terms of sin(x) and cos(x), we can use the trigonometric identity known as the cosine of a difference formula:
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
In this case, let's substitute a = x and b = π/6:
cos(x - π/6) = cos(x)cos(π/6) + sin(x)sin(π/6)
Now, we can simplify further using the values of cos(π/6) and sin(π/6):
cos(x - π/6) = cos(x)(√3/2) + sin(x)(1/2)
Therefore, cos(x - π/6) can be expressed in terms of sin(x) and cos(x) as:
cos(x - π/6) = (√3/2)cos(x) + (1/2)sin(x)
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Greg wants to estimate the percentage of people who lease a car. He surveys 340 individuals and finds that 90 lease a car. What is the sample proportion for successes, p′? Round the final answer to three decimal places.
The sample proportion for successes, p′, for the survey that Greg carried out would be 0. 265.
How to find the sample proportion for successes ?The sample proportion for successes, often denoted as " p ", is found by dividing the number of successes (in this case, the number of people who lease a car ) by the total number of trials (the total number of individuals surveyed ).
So, in this case, the sample proportion for successes ( p ) would be:
= 90 / 340
= 0. 2647
= 0. 265
In percentages, this would take the value of 26. 47 %.
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Fill in the steps to find the length of the hypotenuse.
b = 5
a = 12
a2 =
and 62 =
2 +6² = 2 =
Take the square root of c2 to find that ca
To find the length of the hypotenuse (c) in a right triangle, you can use the Pythagorean theorem, The length of the hypotenuse (c) is √312.
In this case, you have the lengths of the two sides, b and a, where b = 5a and[tex]a^2[/tex] = 12.
Let's go through the steps to find the length of the hypotenuse (c):
Step 1: Square the value of a
[tex]a^2[/tex] = 12
Step 2: Substitute the value of b in terms of a
b = 5a
Step 3: Square the value of b
[tex]b^2 = (5a)^2 = 25a^2[/tex]
Step 4: Apply the Pythagorean theorem
According to the Pythagorean theorem, [tex]c^2 = a^2 + b^2[/tex]
Substituting the values:
[tex]c^2 = a^2 + b^2\\c^2 = 12 + 25a^2[/tex]
Step 5: Simplify the equation
[tex]c^2 = 12 + 25a^2[/tex]
Step 6: Substitute the value of [tex]a^2[/tex]from Step 1
[tex]c^2 = 12 + 25(12)[/tex]
Step 7: Simplify further
[tex]c^2 = 12 + 300\\c^2 = 312[/tex]
Step 8: Take the square root of both sides to find c
[tex]\sqrt{c^2} = \sqrt{312}\\c = \sqrt{312}[/tex]
The length of the hypotenuse (c) is √312.
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On one night, a scientist needs to determine the distance she is away from the International Space Station. At the specific time she is determining this the space station distance they are both on the same line of longitude 77° E. Furthermore, she is on a latitude of 29° N and the space station is orbiting just above a latitude of 61.4° N. In short, the central angle between the two is 32.4°. If the Earth's radius is 3959 miles and the space station orbits 205 miles above the surface of the Earth, then how far is the scientist away from the space station?
The scientist is approximately 3933 miles away from the International Space Station.
To determine the distance between the scientist and the International Space Station, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of their lengths and the cosine of the included angle.
In this case, the Earth's radius (r) is 3959 miles, and the space station orbits 205 miles above the surface of the Earth. The central angle between the scientist and the space station is 32.4°. Using the law of cosines, we can calculate the distance (d) between them as follows:
d² = r² + (r + h)² - 2r(r + h)cos(32.4°)
where h is the height of the space station above the Earth's surface. Plugging in the values, we get:
d² = 3959² + (3959 + 205)² - 2 * 3959 * (3959 + 205) * cos(32.4°)
Simplifying this equation gives us:
d ≈ 3933 miles
Therefore, the scientist is approximately 3933 miles away from the International Space Station.
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The sequence applied to shape I that proves shape I is similar to shape II is a translation blank units right and blank units up and then a dilation by a scale factor of
The sequence applied to shape I that proves shape I is similar to shape II is a translation 4 units right and 3 units up and then a dilation by a scale factor of 2.
For the shapes to be similar, the corresponding angles need to be congruent and corresponding sides need to be proportional. The sequence applied to shape I that proves shape I is similar to shape II involves a translation and a dilation.
Translation: A translation is a transformation in which each point of the shape is moved a certain distance in a certain direction. In this case, Shape I is translated 4 units right and 3 units up to get Shape III. Dilation: A dilation is a transformation in which each point of the shape is stretched or shrunk in size, relative to a fixed point called the center of dilation.
In this case, Shape III is dilated by a scale factor of 2 to get Shape II. Thus, the sequence applied to shape I that proves shape I is similar to shape II is a translation 4 units right and 3 units up and then a dilation by a scale factor of 2.
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If there’s a 70% chance of rain tomorrow, what is the chance it will not rain?
The chance that it will not rain tomorrow can be found by subtracting the probability of rain from 100% or 1 in decimal form. Therefore, if there is a 70% chance of rain, there is a 30% chance it will not rain.
If there is a 70% chance of rain tomorrow, the chance it will not rain can be found by subtracting the probability of rain from 100% (or 1 in decimal form):
Chance of not raining = 100% - Chance of raining
Chance of not raining = 1 - 0.7
Chance of not raining = 0.3 or 30%
Therefore, the chance it will not rain is 30%.
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If Triangle ABC was dilated with the center of dilation at (0,0) and a scale factor of 2, what would be the coordinates of A'? Please help :(
When Triangle ABC is dilated with a center of dilation at (0,0) and a scale factor of 2, the coordinates of point A' can be found by multiplying the original coordinates of point A by the scale factor.
In this case, if the coordinates of point A are (x, y), then the coordinates of A' would be (2x, 2y).
Dilation involves scaling an object by a factor while preserving its shape. When the center of dilation is at (0,0), the dilation occurs relative to the origin. By applying a scale factor of 2, the x-coordinate of point A is multiplied by 2, and the y-coordinate of point A is also multiplied by 2. This scaling operation results in the coordinates of A' being (2x, 2y).
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Write the ratio of the first measurement to the second measurement. Compare in millimeters.
diameter of ball A: 33 mm
diameter of ball B: 4.5 cm
So the ratio of the first measurement to the second measurement is approximately 73.33%.
The diameter of ball A is 33 mm.
The diameter of ball B is 4.5 cm.
1 cm = 10 mm
4.5 cm = 4.5 × 10 mm
= 45 mm
To find the ratio of the first measurement (ball A) to the second measurement (ball B), we divide the diameter of ball A by the diameter of ball B.33 mm ÷ 45 mm = 0.7333...
We can simplify this fraction by multiplying both the numerator and denominator by 100 to get a percentage:
0.7333... × 100% = 73.33...%
Ratio of the first measurement to the second measurement = 73.33%.
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2013 people live on an island. Some of these people are truthtellers and the others are liars. The truthtellers always tell the truth whereas the liars always lie. Each day one of the people says 'when i have left the island the number of truthtellers will be the same as the number of liars. Then he leaves the island. After 2013 days there is no longer anybody living on the island. How many liars were living there to begin with?
There were 671 liars living on the island initially out of 2013 people living on the island.
Let's assume the number of truthtellers is x and the number of liars is y.
According to the given information, each day one person says that when they leave the island, the number of truthtellers will be equal to the number of liars.
This implies that the person speaking must be a liar.
On the first day, if the person speaking is a liar, then the number of liars on the island will increase by one (y+1) and the number of truthtellers will remain the same (x).
The equation can be written as:
x = y + 1
On the second day, if the second person speaking is also a liar, the number of liars will increase by one again (y+2) and the number of truthtellers will remain the same (x).
The equation becomes:
x = y + 2
We can generalize this pattern for each day:
x = y + k
After 2013 days, there is no one left on the island, so x + y = 0.
Substituting this into the equation, we get:
(y + k) + y = 0
Simplifying, we find:
2y + k = 0
Since y represents the number of liars, we want to find a value of y that satisfies this equation.
To do that, we need to find a value of k such that 2013 + k is divisible by 2.
By observing that 2013 is odd, we can conclude that k must be an odd number.
The smallest odd number that satisfies this condition is k = 1.
Substituting k = 1 into the equation, we get:
2y + 1 = 0
Solving for y, we find:
y = -1/2
However, the number of liars cannot be negative, so we can disregard this solution.
Therefore, there were 671 liars living on the island initially.
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Identify the RATE OF CHANGE and INITIAL VALUE from ONE of the equations listed. A. Y = 3x 6 b. Y = -7x 5 c. Y = 9x 4.
The equation Y = 9x + 4 has a rate of change of 9, indicating that for every unit increase in x, y increases by 9. The initial value is 4, representing the y-value when x is zero.
To identify the rate of change and initial value from one of the given equations, let's analyze equation C: Y = 9x + 4.
In this equation, the coefficient of x, which is 9, represents the rate of change. This means that for every unit increase in x, the corresponding value of y will increase by 9 units. Therefore, the rate of change is 9.
To find the initial value, we need to determine the value of y when x is equal to zero. Plugging in x = 0 into the equation, we get:
Y = 9(0) + 4
Y = 0 + 4
Y = 4
Hence, the initial value or y-intercept is 4.
In summary, for the equation Y = 9x + 4, the rate of change is 9, indicating that y increases by 9 units for each unit increase in x, and the initial value is 4, representing the y-value when x is equal to zero.
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The equation of the line shown is y = ax + p, where a and p are real numbers.
What is true about a and p?
The equation of the line is shown as y = ax + p, where a and p are actual numbers. The slope-intercept form of a line is given as y = mx + b, where m is the slope of the line and b is the y-intercept. The line slope-intercept form can be compared with the equation of the line given as y = ax + p.
We know that the equation of a line in slope-intercept form is given as y = mx + b. Here, we are given the equation of the line as y = ax + p, where a and p are real numbers. Thus, the following is true about a and p.The slope of the line in the slope-intercept form is m = a. Therefore, a is the slope of the given line. The y-intercept of the line in the slope-intercept form is b = p.
p is the y-intercept of the given line. Hence, we conclude that in the equation of the line, y = ax + p, where a and p are real numbers, a is the slope of the line and p is the y-intercept of the line.
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Coach DeCaro records the cross country runners’ times compared to their personal best times. 3K Times Runner Time compared to personal best Gregor 5. 6 Hiroki –11. 6 Isabelle 3. 2 Juan 0 Karen –5. 2 Which runners ran slower than their personal best? Juan Gregor and Isabelle Gregor, Isabelle, and Juan Hiroki and Karen.
Among the given runners, Gregor, Isabelle, and Juan ran slower than their personal best times in the cross country race.
The provided information states the times of the runners compared to their personal best times in a 3K race. Gregor's time is recorded as 5.6, indicating that he ran 5.6 seconds slower than his personal best time. Isabelle's time is recorded as 3.2, implying that she ran 3.2 seconds slower than her personal best. Juan's time is given as 0, suggesting that he ran exactly at his personal best time or did not improve it. Hiroki's time is recorded as -11.6, indicating that he ran 11.6 seconds faster than his personal best time. Karen's time is given as -5.2, implying that she also ran faster than her personal best by 5.2 seconds. Therefore, the runners who ran slower than their personal best times are Gregor, Isabelle, and Juan.
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What are the constants in this expression?Negative 10.6 + StartFraction 9 over 10 EndFraction + two-fifths m minus 2.4 n + 3 mNegative 10.6 and StartFraction 9 over 10 EndFractionNegative 10.6. and –2.4StartFraction 9 over 10 EndFraction and Two-fifthsNegative 2.4 and 3
The following are the constants in the given expression: -10.6, 9/10, and -2.4. Constants are quantities or terms that do not change their value in an expression. An expression consists of numbers, symbols, and operators.
The following are the constants in the given expression: -10.6, 9/10, -2.4.These terms are referred to as constants since they are not variables or unknown quantities that may vary. It does not depend on the variables m and n or any other quantity that can change its value. The constants are quantities that do not change their value. It does not depend on the variables m and n or any other quantity that can change its value. The constants in the given expression are -10.6, 9/10, and -2.4. The expression is written as: Negative 10.6 + StartFraction 9 over 10 EndFraction + two-fifths m - 2.4 n + 3 m. The first two terms of the expression are -10.6 and StartFraction 9 over 10 EndFraction. These two terms are constants, as they are fixed values that do not change. The third term is two-fifths m, which depends on the value of m. The fourth term is -2.4n, which also depends on the value of n. The fifth term is 3m, which again depends on the value of m. Therefore, two-fifths m, -2.4n, and 3m are not constants, but variables in the given expression.
In conclusion, constants are quantities that do not change their value in an expression. In the given expression, the constants are -10.6, 9/10, and -2.4. These values do not depend on any variables and remain constant.
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How would you sketch an angle of 210° in standard position in a uv-coordinate system? And then what is the reference angle?
To sketch an angle of 210° in standard position in a UV-coordinate system, you would start by placing the initial side of the angle along the positive x-axis and then rotate the terminal side counter-clockwise by 210°. The reference angle is the acute angle formed between the terminal side of the given angle and the x-axis.
In a UV-coordinate system, the initial side of an angle is placed along the positive x-axis. To sketch an angle of 210°, you would start by drawing a horizontal line (the initial side) extending to the right. Then, you rotate the terminal side of the angle counterclockwise from the initial side. Since 210° is greater than 180°, the terminal side will extend beyond the positive x-axis.
To determine the reference angle, you can subtract the given angle from the nearest multiple of 180°. In this case, the nearest multiple of 180° is 180° itself. Subtracting 210° from 180° gives you 30°. Therefore, the reference angle for the angle of 210° is 30°.
To summarize, you would sketch an angle of 210° in standard position by starting with the initial side along the positive x-axis and rotating the terminal side counterclockwise. The reference angle for this angle is 30°, which is the acute angle formed between the terminal side and the x-axis.
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If my salary is k20,000 monthly and there is an increment of k350 per month,what will be my total amount in the first 2years of my contact?
The total amount earned in the first 2 years of the contract is k488,400
Given that the salary is k20,000 monthly and there is an increment of k350 per month.
To find out the total amount in the first two years of contact, we need to calculate the salary for 24 months and then add the increments earned during those 24 months.
Salary for 24 months = k20,000 × 24= k480,000
Increment for 24 months = k350 × 24= k8,400
Therefore, the total amount earned in the first 2 years of the contract will be the sum of the salary for 24 months and the total increment earned during the same period= k480,000 + k8,400= k488,400
Thus, the total amount earned in the first 2 years of the contract is k488,400.
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The total amount you will have in the first 2 years of your contract is k14,000,000.
If your salary is k20,000 monthly and there is an increment of k350 per month, the total amount you will have in the first two years of your contact can be found using simple interest formula:
I = prt
where I is the interest, p is the principal amount, r is the rate of interest and t is the time in years.Therefore, using the above formula, we have;
I = (20,000)(350)(2)
= 14,000,000
Therefore, the total amount you will have in the first 2 years of your contract is k14,000,000.
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Samuel is playing the Big-Time Builders video game. At the beginning of Samuel's turn, his score was
–
14 points. After building a high-rise apartment building, his score rose to 36 points.
The change in Samuel's score is 50
How to determine the change in Samuel's score?From the question, we have the following parameters that can be used in our computation:
Beginning = -14 points
Final = 36 points
Using the above as a guide, we have the following:
Change = Final - Beginning
Substitute the known values in the above equation, so, we have the following representation
Change = 36 + 14
Evaluate
Change = 50
Hence, the change is 50
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Question
Samuel is playing the Big-Time Builders video game. At the beginning of Samuel's turn, his score was – 14 points. After building a high-rise apartment building, his score rose to 36 points.
What was the change in Samuel's score?
Jeanie wrote the correct first step to divide 8z2 4z – 5 by 2z. Which shows the next step? 4z 2 – 4z2 2 – 4z2 2 – 4z 2 –.
The result of division of 8z²-4z-5 by 2z is 4z - 2 - 2.5z. 4z - 2 - 2.5z can also be written as 4z - 2.5z - 2.In conclusion, the next step after the first step of dividing 8z²-4z-5 by 2z is to multiply the divisor and the first term of the quotient and subtract it from the dividend.
When we have to divide 8z²-4z-5 by 2z, we follow the steps given below: Step 1: Firstly, we write the given polynomial in the standard form of the division process as shown below.2z/8z² - 4z - 5Step 2: Divide the first term of the dividend by the first term of the divisor and write the result as the first term of the quotient.2z goes into 8z² 4 times. So, the first term of the quotient is 4z.Step 3: Now, multiply the divisor and the first term of the quotient and subtract it from the dividend.8z² - 4z - 5 – (8z²) = -4z - 5Step 4: Now we bring down the next term of the dividend.2z/-4z - 5Step 5: Divide the first term of the dividend by the first term of the divisor and write the result as the second term of the quotient.2z goes into -4z -2 times. So, the second term of the quotient is -2.Step 6: Multiply the divisor and the second term of the quotient and subtract it from the dividend.-4z - 5 – (-4z) = -5Step 7: We bring down the next term of the dividend.2z/-5Step 8: Divide the first term of the dividend by the first term of the divisor and write the result as the third term of the quotient.2z goes into -5 - 2 times. So, the third term of the quotient is -2.5.Step 9: Multiply the divisor and the third term of the quotient and subtract it from the dividend.-5 – (-5) = 0.
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Raj reads 7/12 of his book before dinner and another 2/12 of his book after dinner.
How much of his book did Raj read in total?
Enter your answer as a fraction in simplest form by filling in the boxes.
Raj read a total of 9/12 of his book.
To find out how much of the book Raj read in total, we need to add the fractions representing the portions he read before dinner and after dinner. Raj read 7/12 of his book before dinner, and then an additional 2/12 of his book after dinner. Adding these fractions together gives us:
7/12 + 2/12 = 9/12.
Since the fractions have the same denominator (12), we can simply add the numerators to get the numerator of the total fraction. The denominator remains the same. So, Raj read a total of 9/12 of his book.
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3 in this case:
9/12 ÷ 3/3 = 3/4.
Therefore, Raj read 3/4 of his book in total.
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Answer:
Step-by-step explanation:
hi me need help me 10
Justify each step in solving the system of equations. 3x−2y=1 2x+2y=4 Copy and paste phrases from the answer bank below for numbers 1-5. Answer choices may be used more than once. Addition Property of Equality Multiplication Property of Equality Substitution Property of Equality Subtraction Property of Equality Division Property of Equality 1. 5x=5 2. x=1 3. 3(1)−2y=1 4. −2y=−2 5. y=1
The steps used to solve the system of equations are as follows: Apply the Addition Property of Equality to eliminate the variable y. Solve for x using the Division Property of Equality. Substitute the value of x into one of the equations to find the value of y. Therefore, the solution to the system of equations is x = 1 and y = 1.
To solve the system of equations, we can follow these steps:
Step 1: Apply the Addition Property of Equality to eliminate the variable y.
By adding the two equations together, the y-terms will cancel out, resulting in:
(3x - 2y) + (2x + 2y) = 1 + 4
Simplifying the equation, we get:
5x = 5 (Addition Property of Equality)
Step 2: Solve for x using the Division Property of Equality.
Dividing both sides of the equation by 5, we find:
x = 1 (Division Property of Equality)
Step 3: Substitute the value of x into one of the equations to find the value of y.
Using the first equation, we substitute x with 1:
3(1) - 2y = 1
Simplifying the equation, we have:
3 - 2y = 1
Rearranging the equation, we get:
-2y = -2
Dividing both sides of the equation by -2, we find:
y = 1 (Division Property of Equality)
Therefore, the solution to the system of equations is x = 1 and y = 1.
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They rent a car with insurance for 5 days but lost their coupon. If marven and the three friends spend $75 each, which csr did they rent? Write and solve an equation to justify your answer.
Marven and three of his friends rent a car with insurance for 5 days but lost their coupon. If each person spent $75, then which car did they rent The total amount of money they paid is $75 * 4 = $300.
We can further write the above equation as:250x + 300y + 350z + 400u = 300Based on the given condition, we know that Marven and three of his friends spent $75 each, so the total amount of money they paid is $300. Hence:250x + 300y + 350z + 400u = 300Now we can simplify the equation by dividing each term by 50:5x + 6y + 7z + 8u = 6We have to find the values of x, y, z, and u. The simplest way to solve the equation is by trial and error.
We can substitute values and check if they satisfy the equation. We need to consider the following conditions: The variables x, y, z, and u must be non-negative integers. The sum of x, y, z, and u must be 1.The only set of values that satisfies the above conditions is x = 1, y = 1, z = 0, and u = 0. This means that they rented a compact car and a mid-size car for 5 days each, respectively. Therefore, the car they rented is a compact car and a mid-size car.
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