A football field is 150 meters long. Karl takes 30 seconds to run the entire length. How fast was Karl running?
Answer:
5 m/s
Step-by-step explanation:
Divide the distance by Karl's time to find the rate at which Karl was running:
150/30 = 5 meters per second
how many integers must you pick in order to be sure that at least two of them have the same remainder when divided by 11?
We need to start by choosing some 10 integers so that we can ensure that when they are divided by 11, at least two of the integers will give the same remainder.
The following is the explanation:
If you divide a number by 11, the answer will be a fraction. There are 11 remainders which might occur, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
If for example we choose one number and divide it by 11, there is a chance that the remainder may be any of the 11 (0 reminders 1). Therefore, if we choose 10 numbers, we will have the opportunity to pick 10 unique remainders, ranging from 0 to 10.
In conclusion, if we select one more integer, that is we pick 10 integers, then at least two of them would have the same remainder since there are only 10 remainders.
Because of this, we need to choose 10 numbers such that we can guarantee that at least two of them will provide the same remainder when they are divided by 11.
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please help meee!!!!
5. The constant of proportionality is $0.4 per pound
4. The constant of proportionality is is 3 ounces of almond per ounces of dark chocolate
Determining Constant of proportionalityFrom the question, we are to determine the constant of proportionality from the given table
From the given information, we have that
There is a proportional relationship between x and y
That is,
y ∝ x
Then,
y = kx
Where k is the constant of proportionality
From the table,
When x = 5 pounds, y = $2
Then,
2 = k × 5
k = $2/5pounds
k = $0.4/pound
k = $0.4 per pound
4.
x is proportional to y
Then,
y = cx
Where c is the constant of proportionality
From the table,
When x = 3 ounces of dark chocolate, y = 9 ounces of almond
Then,
9 = c × 3
c = 9/3
c = 3 ounces of almond / ounces of dark chocolate
c = 3 ounces of almond per ounces of dark chocolate
Hence, the proportionality constant is 3 ounces of almond per ounces of dark chocolate
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44 out of 60 as a persentage
Answer: 73.3%
Step-by-step explanation:
take 44 and divide it by 60
44/60 = 0.0733 repeating
move the decimal place to the right twice
0.0733 --> 73.3%
Helppp please I’m confused
Answer: 55%
the percent of the female participants is: [tex]\frac{121}{121+99}.100=\frac{121}{220}.100=55[/tex] (%)
Step-by-step explanation:
the null hypothesis claims that the proportion of community college students who work full-time is 0.45. the alternative hypothesis is that this proportion is greater than 0.45. which sample proportion will have the smallest p-value?
The sample proportion will have the smallest p-value is for Z=3 that can be calculated by taking comparisons between Z=1,2 and 3.
Null hypothesis H0= P=0.45
Alternative hypothesis H1= P>0.45
The null hypothesis assumes that any form of distinction among the selected traits which you see in a fixed of records is because of chance. For example, if the predicted income for the playing recreation are truely same to 0, then any distinction among the common income withinside the records and 0 is because of chance.
H=1000, x1=500, x2=600 and x3=700
P1= x1/h=500/1000=0.5
P2=x2/h=600/1000=0.6
P3=x3/h=700/1000=0.7
Z1=P1-P/(P(1-P)/h)61/2 = 0.5-0.45/(0.45*0.55/1000)^1/2 = 0.32
P-value for Z1=P(Z1>0.32)=0.37748
Z2=P2-P/(P(1-P)/h)61/2 = 0.6-0.45/(0.45*0.55/1000)^1/2 = 0.95
P-value for Z2=P(Z2>0.95)=0.17106
Z3=P3-P/(P(1-P)/h)61/2 = 0.7-0.45/(0.45*0.55/1000)^1/2 = 1.59
P-value for Z3=P(Z3>0.95)=0.055917
Thus, the smallest P-value will be for Z3.
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Help me out please !!!!!!!!
Answer: 3 boxes
Step-by-step explanation:
she has 3 stuffed animals left and its not manditory to fill a box so you would put the threee remaining into one box
A, B and C are interior angles of a triangle ABC. Show that
(i) sin (B+C/2) = cos (A/2)
(ii) if angle A= 90°, then find the value of tan (B+C/2)
Answer:
ok i can do it if u want then see my m.s.g
The required solutions to the given triangle ABC below as:
(i) sin (B+C/2) = cos (A/2)
(ii) if angle A= 90°, then the value of tan (B+C/2) is is undefined.
What are Interior Angles?Interior angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles.
Given that A, B, and C are interior angles of a triangle ABC.
To solve the question, we would consider trigonometric ratios of complementary angles.
sin (90° - θ) = cosθ
We know that for ΔABC,
∠A + ∠B + ∠C = 180° (Angle sum property of triangle)
∠B + ∠C = 180° - ∠A
On dividing both sides by 2, we get,
(∠B + ∠C)/2 = (180° - ∠A)/2
(∠B + ∠C)/2 = 90° - ∠A/2
Applying sine angles on both sides:
sin {(∠B + ∠C)/2} = sin (90° - ∠A/2)
Since, sin (90° - θ) = cos θ, we get
sin (∠B + ∠C)/2 = cos A/2
(ii) if angle A= 90°, then find the value of tan (B+C/2)
If cos A/2 = 0 so ∠A = 90°
sin (∠B + ∠C)/2 = cos A/2 = 0
tan (B+C/2) = ∞
Thus, the value of tan (B+C/2) is undefined.
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Which of the following statement(s) is/are correct for congruent triangles?
A
Congruent triangles have same shape but different size.
B
Congruent triangles have both same shape and same size.
C
Corresponding angles and corresponding sides of congruent triangles are equal.
D
Congruent triangles have same size but different shape.
Answer:
B. Congruent triangles have both same shape and same size.
C. Corresponding angles and corresponding sides of congruent triangles are equal.
Dilate the line segment by a scale factor of 2 with a center of dilation at the origin. Draw the dilated segment on the provided graph.
Click on a fool to begin drawing.
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Une Segment
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10
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Please find attached the drawing of the image of the segment following a dilation by a scale factor of 2 with the center at the origin, created with MS Word.
What is a dilation transformation?A dilation transformation is one in which the size of the object is increased (or decreases) proportionately by a factor known as the scale factor of dilation.
The center of dilation is the origin, which is the point (0, 0)
The coordinates of points on the line segment are; (5, 5) and (0, 0)
Therefore, the line segment to be dilated passes through the center of dilation
The image of the segment to be dilated also will pass through the center of dilation, which is the origin or the point (0, 0)
The dilation of the segment by a scale factor of 2 has a point at the origin (0, 0), the second point is therefor at the point (2× 5, 2 × 5) = (10, 10)
The coordinates of the image of the segment following a dilation are therefore; (0, 0), and (10, 10)
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A company began construction of a new manufacturing plant. The plant was completed on october 31, 2024. Expenditures on the project were as follows ($ in millions): on july 1, 2023, the company obtained a $76 million construction loan with a 9% interest rate. The loan was outstanding through the end of october, 2024. The company's only other interest-bearing debt was a long-term note for $100 million with an interest rate of 11%. This note was outstanding during all of 2023 and 2024. The company's fiscal year-end is december 31
The interest amount that will be capitalized is $4.04 million.
What is the interest amount that will be capitalized?The entire cost to purchase a good or service is referred to as an expense. A $30 million piece of equipment with a six-year useful life, for instance, is considered a capital expenditure. An expense is something that calls for the transfer of funds, or fortune in general, from one person or group to another as payment for a good, service, or other type of cost. Rent is a cost to a tenant. Tuition is a cost to parents or students.
The following can be deduced from the information:
Average Expenditure for 2023
= 78 million* 6/6 month + 46 million ** 3/6 month
= 101 million
Amount of interest that should capitalized in 2023 using a specific interest method
= Average expenditure for 2023 * interest rate *6/12 month
= $101 million * 8% * 6/12
= $4.04 million
The interest amount is $4.04 million.
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1 2/5m-3/5(2/3m+1) please help me
Answer:
m - 3/5 or m - 0.6-----------------------------------------
Simplify the expression:
1 2/5m - 3/5(2/3m + 1) = Convert mixed number to fraction 7/5m - 3/5(2/3)m - 3/5 = Distribute 7/5m - 2/5m - 3/5 = Simplify(7 - 2)/5m - 3/5 = Collect terms with m5/5m - 3/5 = Simplifym - 3/5 AnswerTakeo ha two different boxe left to pack before hi move. Box 1 ha a volume of 2,166 cubic centimeter. Box 2 ha a volume of 1,260 cubic centimeter. What i the total volume of pace, in cubic centimeter, that Takeo ha available to pack?
Box 1 has a volume of 2,166 cubic centimeters and Box 2 has a volume of 1,260 cubic centimeters.The total volume of space available to Takeo is 3,426 cubic centimeters.
To find the total volume of space available to Takeo, first we take the volume of Box 1, which is 2,166 cubic centimeters. Then we take the volume of Box 2, which is 1,260 cubic centimeters. Finally, we add these two volumes together to get the total volume of 3,426 cubic centimeters.Takeo is in the process of packing before his move. He has two boxes to pack and each box has a different volume. Box 1 has a volume of 2,166 cubic centimeters and Box 2 has a volume of 1,260 cubic centimeters. By adding these two volumes together, Takeo has a total volume of 3,426 cubic centimeters of space available to pack before his move.
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Please help me with this
a) The equation is y = 4/x².
b) The value of x is 2/9 when y = 25.
What is relationship?
The relation in mathematics is the connection between two or more sets of values. Assume that there are two sets of ordered pairs, x and y. If set x and set y are related, then the values of set x are referred to as the domain while the values of set y are referred to as the range.
Given table is
x 1 2 3 4
y 4 1 4/9 1/4.
Given that y is inversely proportional to the square of x.
y∝ 1/x²
y = k/x² where k is proportional constant.
Putting x = 1 and y = 4 in equation y = k/x²:
4 = k/1²
k = 4
Putting x = 2 and y = 1 in equation y = k/x²:
1 = k/2²
k = 4
Putting k = 4 in y = k/x²:
y = 4/x²
Putting y = 25 in y = 4/x²
25 = 4/x²
25x² = 4
Divide both sides by 25:
x² = 4/25
Take square root on both sides:
x = 2/5
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Find the tables with unit rates greater than the unit rate in the graph. Then arrange these tables in order from least to greatest unit rate. x y 7 13 14 26 x y 5 9 10 18 x y 9 17 18 34 x y 11 21 22 42 x y 10 19 20 38 x y 13 25 26 50 x y 12 23 24 4
Except table 2, all tables have greater unit rate than the graph.
The required arrangements of tables is Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < table 7 < Table 6
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the given graph it is clear that the line passes through the points (0,0) and (11,20). So, unit rate of graph is
m=20-0/11=20/11=1.818
Similarly, we need to calculate the unit rate for each table.
m1=26-13/14-7=1.81
m2=18-9/10-5=9/5=1.81
m3=34-7/18-9=1.88
m4=42-21/22-11=21/11=1.90
m5=38-19/20-10=1.9
m6=50-25/26-13=25/13=1.923
m7=46-23/24-12=23/12=1.9166
Hence, Except table 2, all tables have greater unit rate than the graph.
The required arrangement of tables is Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < Table 7 < Table 6
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The temperature at 4pm is 43 degrees. Throughout the night it steadily falls 6 degrees.
What is the rate of change in this situation?
Answer:
The rate of change in this situation is 6 degrees per hour.
Step-by-step explanation:
The rate of change in this situation is -6 degrees per hour. To find this, we need to divide the change in temperature by the amount of time over which the change occurs. In this case, the temperature falls from 43 degrees to 43-6=<<43-6=37>>37 degrees, so the change in temperature is 43-37=<<43-37=6>>6 degrees. Since the temperature falls over the course of one night, the rate of change is 6 degrees / 1 night = -6 degrees per hour.
ASAP ANSWER PLEASE
ABC was rotated 90° clockwise around the origin to form A'B'C'. A'B'C' was dilated using a scale factor of 1/2 with a center of dilation at the origin. The result is A''B''C'', shown in the coordinate plane. What are the coordinates of ABC? Show your work.
The coordinates of ABC are A = (-2, -1) B = (-2, -10) C" = (-14, -1)
How to determine the coordinates of ABC?The coordinates of the triangle A"B"C" are given as
A" = (0.5, -1) B" = (5, -1) C" = (0.5, -7)
The transformation is given as
Rotation of 90° clockwise around the originDilation by 1/2 with a center of dilation at the originWhen these transformations are combined, we have
(x, y) ⇒ (-y/2, x/2)
So, we have
A" = (0.5, -1) B" = (5, -1) C" = (0.5, -7)
This gives
A = (-2, -1) B = (-2, -10) C" = (-14, -1)
Hence, the coordinates are A = (-2, -1) B = (-2, -10) C" = (-14, -1)
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A preschool has 100 feet of fencing to enclose 3 sides of a rectangular playground. The fourth side is formed by a wall of the school. The function A(x) = 100x − 2x2 represents the possible area of the playground with side length x feet. Which range is appropriate for this situation?
Answer:
This answer assumes that the function is A(x) = 100x − 2x^2. The function as written is A(x) = 100x - (4 or 4x)
The domain is 0 - 50 feet.
Step-by-step explanation:
The area function is a polynomial with a vertex (hghest area possible) at (25,1250). This is telling us that for a side length of 25 feet, the area is at a maximum of 1250 ft^2. This is actually not totally correct. We only need 3 sides of fencing since the school wall will make up the fourth. The given equation does not seem to allow for this caveat, since it uses 100 feet for all four sides.
Given the equation, the domain for the function A(x) is positive for all values between 0 and 50 feet. The domain is 0 - 50 feet.
Angles 4 and 8 are what type of angles?
A. Alternate exterior angles
B. Same side interior angles
C. Alternate interior angles
D. Corresponding angles
Answer:
D. Corresponding angles
Step-by-step explanation:
Corresponding angles are angles located on the same side, the intersection of transversal and two or more straight lines. So, answer is D
Use the drawing tools to graph the line that represents the equation 2y = -4x + 6.
Drawing Tools
Select
Point
Click on the Graph to
place a Point.
Line
Show Instructions
-8
4
-6
-4
-2
4-
2-
-2-
-4-
-6
2
4
6
8
If it is a line that does go through 0,0 then it is NOT PROPORTIONAL
What is the domain of this function?
Answer:
all real numbers
Step-by-step explanation:
the graph continues to the left and to the right because there are arrows
what is the probability that if 7 letters are typed, no letters are repeated? write your answer in decimal form, rounded to the nearest thousandth. the probability that no letters are repeated is .
The probability that no letters are repeated is 0.0015, rounded to the nearest thousandth.
The probability that no letters are repeated is calculated using the formula P = n! / (r^n * (n-r)!)
, where n is the total number of letters and r is the number of each letter.
The numbers here are n = 7 and r = 1.
This means the probability of no letters being repeated is 7! / (1^7 * 6!) = 0.0015.
This can be rounded to the nearest thousandth, giving the answer of 0.0015.
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0.442÷26.7812 pleaseeeeeeeeeeeeeeeee
Answer: The correct answer is 0.0165041148268188
Step-by-step explanation:
Complete division (no rounding precision):
0.442 ÷ 26.7812 = 0.0165041148268188
Please helppp I’m giving brainlyest
Answer:
B
Step-by-step explanation:
the shape will reflect b
sinxcosx = 1/2cosx
Solve for x.
Answer:
[tex]x=\dfrac{1}{2} \pi + 2\pi n[/tex]
[tex]x=\dfrac{3}{2}\pi +2 \pi n[/tex]
[tex]x=\dfrac{1}{6}\pi+2 \pi n[/tex]
[tex]x=\dfrac{5}{6}\pi+2 \pi n[/tex]
Step-by-step explanation:
Given trigonometric equation:
[tex]\sin x \cos x &= \dfrac{1}{2} \cos x[/tex]
Rearrange the equation so that it equals zero:
[tex]\begin{aligned}\sin x \cos x &= \dfrac{1}{2} \cos x\\2 \sin x \cos x &= \cos x\\2 \sin x \cos x - \cos x &=0\\ \cos x (2 \sin x - 1)&=0\end{aligned}[/tex]
Apply the zero-product property.
Case 1
[tex]\begin{aligned}\cos x &=0\\x&=\cos^{-1}(0)\\x&=\dfrac{1}{2} \pi +2\pi n, \; \dfrac{3}{2}\pi +2 \pi n\end{aligned}[/tex]
Case 2
[tex]\begin{aligned}2\sin x - 1& = 0\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\x&=\sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{1}{6} \pi+2 \pi n, \; \dfrac{5}{6} \pi +2 \pi n\end{aligned}[/tex]
Julie is given the data point (6, 7) as a point on the profit equation that she must create. Her boss mentioned that the last equation that
they used was y = 2x+3. If Julie wants to write the new equation that is parallel to the old equation, what would her new equation look
like?
y=6x+7
y=2x-5
y=2x+7. In order to create an equation that is parallel to the old equation, Julie must make sure that her new equation has the same slope as the old equation. The slope of the old equation is 2, so Julie's new equation should also have a slope of 2. Additionally, she must make sure that the y-intercept of her new equation is the same as the given data point, which is (6, 7). Therefore, the new equation should be in the form y = 2x + b, where b is the y-intercept. Plugging in the values from the given data point, we get y = 2x + 7. This equation is parallel to the old equation and passes through the given data point, so it is the correct answer.
Answer:
The answer to the question is that the new equation that is parallel to the old equation and passes through the point (6, 7) is y = 2x - 5.
Step-by-step explanation:
To create an equation that is parallel to the old equation, you need to use the same slope. This means that your new equation should be y = 2x + b, where b is a constant. Since the point (6, 7) is on the new equation, you can plug those values into the equation to find b.
simplfy y2 when y = -9
The solution to the expression y² is 81 when y = -9
How to simplify the expression at the given valueFrom the question, we have the following parameters that can be used in our computation:
y = -9
Also, from the question, we have
y2
Express the exponents in the above expression properly
So, we have the following representation
y²
Substitute the known values in the above equation, so, we have the following representation
y² = (-9)²
Remove the bracket in the expression
'This gives
y² = 9²
Evaluate the exponent
So, we have the following representation
y² = 81
Hence, the solution is 81
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Would you rather receive a 3% raise followed by a 9% raise or a 9% followed by a 3%
It is better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.
What is the percentage increase?
The concept of percent increase is basically the amount of increase from the original number to the final number in terms of 100 parts of the original.
It is generally better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.
This is because the percentage raise you receive is applied to your current salary. If you receive a 3% raise first, your salary will be higher when you receive the 9% raise, so the 9% raise will be applied to a higher base salary. This means that you will receive a larger increase in salary overall if you receive the 9% raise first.
For example, let's say you are currently making $50,000 per year. If you receive a 3% raise followed by a 9% raise, your salary would increase to $51,500 after the first raise and then to $56,365 after the second raise, for a total increase of $6,365.
On the other hand, if you receive a 9% raise followed by a 3% raise, your salary would increase to $54,500 after the first raise and then to $56,365 after the second raise, for a total increase of $5,865.
In this example, you would receive a larger increase in salary overall if you received the 9% raise first. This is because the 9% raise is applied to a lower base salary, resulting in a larger increase in salary overall.
Of course, the actual amount of the raise will depend on your current salary and the percentage of the raise. In general, though, it is usually better to receive a larger percentage raise first, followed by a smaller percentage raise.
Hence, It is better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.
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What’s the solution to 2x-2y=6 and 4x+4y=28
Answer
x=5 y=2
Step-by-step explanation:
As Venus revolves around the sun, it travels at a speed of approximately 22 miles per second. Convert this speed to miles per minute. At this speed, how many miles will Venus travel in 6 minutes?
Answer: In 6 minutes, Venus will travel 1320 * 6 = 7920 miles.
Step-by-step explanation: To convert the speed from miles per second to miles per minute, we multiply the speed by the number of seconds per minute. There are 60 seconds per minute, so Venus travels 22 * 60 = 1320 miles per minute.
In 6 minutes, Venus will travel 1320 * 6 = 7920 miles.