The value of inequality : x≤-9
Given,
Inequality 4(x-3) + 4 ≤ 10+ 6x
Firstly,
The distributive property: 4x-12 + 4 ≤ 10+ 6x
Then,
Combine like terms: 4x -8 ≤ 10+ 6x
Then,
The addition property of inequality: 4x ≤ 18 + 6x
Then,
The subtraction property of inequality: -2x ≤ 18
Then,
The division property of inequality:
Divide both sides of inequality by 2,
So,
x≤-9
Hence after last step the value of x is less than or equal to -9 .
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Ravi has two and one-fourth meters of rope. He gives ninety-three centimeters of the rope to his brother. How many centimeters of rope does Ravi have left?
If he gives ninety-three centimeters of the rope to his brother, Ravi has 132 centimeters of rope left.
Two and one-fourth meters of rope can be written as 2.25 meters. Since 1 meter is equal to 100 centimeters, we can convert 2.25 meters to centimeters by multiplying it by 100, giving us 225 centimeters.
If Ravi gives 93 centimeters of the rope to his brother, we can subtract it from the original length to find how much rope he has left.
225 cm - 93 cm = 132 cm
In general, to convert between meters and centimeters, you can multiply the number of meters by 100 to get the length in centimeters. To convert between centimeters and meters, you can divide the number of centimeters by 100 to get the length in meters.
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graph the function
X+6, X ≤-2
f(x)= x², -2≤ x ≤ 1.
-2x, x > 1
Answer:
Step-by-step explanation:
To graph the function, we'll break it down into three parts based on the given conditions.
For x ≤ -2:
The function f(x) = x + 6 is valid in this range. We'll plot a straight line with a slope of 1 and a y-intercept of 6. Since x ≤ -2, we'll extend the line towards the left indefinitely.
For -2 ≤ x ≤ 1:
The function f(x) = x² is valid in this range. We'll plot a curve representing a quadratic function. The graph starts at the point (-2, 4), curves upward, and ends at the point (1, 1).
For x > 1:
The function f(x) = -2x is valid in this range. We'll plot a straight line with a negative slope of -2. Since x > 1, we'll extend the line towards the right indefinitely.
Combining these three parts, we get the graph of the function as follows:
23(2+2+3+372+27272+"
Using the given scale 1:50, calculate the actual length of the wall if it is measured to be 15cm.
Y varies directly as x, and y=9 when x = 27
If y varies directly as x, when x = 15, the value of y is equal to 5.
If y varies directly as x, we can express this relationship using the formula y = kx, where k is the constant of proportionality.
Given that y = 9 when x = 27, we can substitute these values into the equation:
9 = k x 27
To solve for k, we divide both sides of the equation by 27:
k = 9 / 27
k = 1/3
Now that we know the value of k, we can use it to find y for any other value of x.
Let's find y when x = 15:
y = (1/3) x 15
y = 5
Therefore, when x = 15, y is equal to 5.
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The complete question:
Y varies directly as x, and y=9 when x = 27.
Find the value of y, when x =15.
ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
A scale has a percent error of 5%. The actual mass of a rock is 30 g.
The scale is likely to show the mass as either;
A: 25 g. or 30 g.
B: 25.5 g. or 30.5 g.
C: 28 g or 31.5 g.
D: 28.5 g. or 31.5 g.
Answer:
ans d
Step-by-step explanation:
5 percent of 30 is 1.5 so d
a) Work out the area of the whole rectangle shown below. b) Use your answer to part a) to help you work out the area of the dotted, purple triangle. 4 cm 7 cm
a) Area of rectangle = 28 cm²
b) Area of triangle = 14 cm²
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
Length of rectangle = 4 cm
Width of rectangle = 7 cm
Since, WE know that;
Area of rectangle = Lenght x Width
Hence, We get;
Area of rectangle = 4 x 7
Area of rectangle = 28 cm²
And, By figure,
Heigh of triangle = 4 cm
Base of triangle = 7 cm
Hence,
Area of triangle = 1/2 x 4 x 7
Area of triangle = 14 cm²
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An equilateral triangle has a perimeter of 36 inches. What is the height of the triangle? Express your answer as a simplified radical.
Answer: the height of the equilateral triangle is 6√3 inches.
Step-by-step explanation:
To find the height of an equilateral triangle, we can use the formula:
height = (√3/2) * side
In this case, we are given the perimeter of the triangle, which is 36 inches.
Since an equilateral triangle has three equal sides, each side would be 36 inches divided by 3, which is 12 inches.
Now we can substitute the side length into the formula:
height = (√3/2) * 12
Simplifying:
height = (√3/2) * 12
height = (√3 * 12)/2
height = (12√3)/2
height = 6√3
Therefore, the height of the equilateral triangle is 6√3 inches.
Answer:
RG
Step-by-step explanation:
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The measure,
⇒∠s = 124 degree
In the given figure of kite,
PQRS,
Measure of angle p = 22 degree
And angle R is a right angle
Therefore,
∠R = 90 degree
Now we know that for a kite PQRS
Angle Q and Angle S are equal
Now consider,
Angle s is equal to x degree
Therefore,
∠S = ∠ Q = x degree
We know that,
For a kite the sum of interior angle is equal to 360 degree.
Therefore,
⇒ ∠P + ∠Q + ∠R + ∠S = 360
⇒ 22 + x + 90 + x = 360
⇒ 22 + x + 90 + x = 360
⇒ 2x = 248
⇒ x = 124 degree.
Thus,
Measure of angle s = 124 degree.
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Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
All the equations which are equivalents are,
⇒ 2 + x = 5
⇒ x + 1 = 4
⇒ Negative 5 + x = negative 2
We have to given that;
All expressions are,
2 + x = 5
x + 1 = 4
9 + x = 6
x + (-4) = 7
-5 + x = -2
Now, We can simplify all the expressions as;
⇒ 2 + x = 5
⇒ x = 5 - 2
⇒ x = 3
⇒ x + 1 = 4
⇒ x = 4 - 1
⇒ x = 3
⇒ 9 + x = 6
⇒ x = 6 - 9
⇒ x = - 3
⇒ x + (-4) = 7
⇒ x = 7 + 4
⇒ x = 11
⇒ -5 + x = -2
⇒x = - 2 + 5
⇒ x = 3
Thus, All the equations which are equivalents are,
⇒ 2 + x = 5
⇒ x + 1 = 4
⇒ Negative 5 + x = negative 2
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Solve (540x45) +(540x 55) using suitable property. And mention the name of the
property used
Answer:
the answer is 54,000
Step-by-step explanation:
(540 × 45) + (540 × 55)
=24300 + 27700
=54000
What is the length of Arc LM? Use 3.14 as pi and round your answer to the nearest tenth. please show work, will mark brainliest.
To find the length of arc LM, we need to use the formula for the circumference of a circle:
C = 2πr
In this case, the arc LM is a portion of the circumference of the circle. To find the length of the arc, we need to determine the angle at the center of the circle that corresponds to the arc.
Looking at the image you provided, we can see that angle LOM is a right angle (90 degrees). The angle at the center of the circle, LOCM, is half of the right angle, which is 45 degrees.
To calculate the length of arc LM, we need to find the fraction of the total circumference represented by the central angle LOCM. The fraction is given by:
Fraction of circumference = Angle at center / 360 degrees
Fraction of circumference = 45 degrees / 360 degrees
Fraction of circumference = 1/8
Now, we can calculate the length of arc LM:
Length of arc LM = Fraction of circumference * Circumference
Length of arc LM = (1/8) * (2πr)
Since the radius (r) is not given in the image, we cannot calculate the exact length of arc LM. However, we can provide the formula for the length of arc LM in terms of the radius:
Length of arc LM = (1/8) * (2πr) = πr/4
So, the length of arc LM is πr/4, where r is the radius of the circle.
If you have the value of the radius, you can substitute it into the formula to find the specific length of arc LM.
Will give brainliest if correct
Explain your answer please!
The correct option is A, the relative frequency is 0.03
How to find the relative frequency?To find the relative frequency for a given outcome, we need to take the quotient between the number of times that we got that outcome, and the total number of times that the experiment is done.
Here the outcome is "wants fruit smooties"
And for the total "number of times that the experiment is done" we need to count the number of students
We know:
Total number = 500
Number of 8th grades who want a fruit smoothies = 17
Relative frquency = 17/500 = 0.03
The correct option is the first one.
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What are the side lengths of triangle Graph shows a triangle plotted on a coordinate plane. The triangle is at A(minus 7, 3), B(minus 3, 6), and C(5, 0). Type the correct answer in each box. If necessary, round any decimal to the nearest tenth. units units units
With the coordinate provided, the lengths of the triangle are Side AB = 5 units, Side BC = 10 units and Side CA = 12.4 units.
How do we find the sides of triangles using coordinates?To find the side lengths of the triangle using the coordinates provided, we use the distance formul.
The distance between two points (x1, y1) and (x2, y2) is given by √((x2-x1)² + (y2-y1)²).
Side AB: Distance between A(-7, 3) and B(-3, 6)
= √((-3 - -7)² + (6 - 3)²)
= √((4)² + (3)²)
= √(16 + 9)
= √25
= 5 units
Side BC: Distance between B(-3, 6) and C(5, 0)
= √((5 - -3)² + (0 - 6)²)
= √((8)² + (-6)²)
= √(64 + 36)
= √100
= 10 units
Side CA: Distance between C(5, 0) and A(-7, 3)
= √((-7 - 5)² + (3 - 0)²)
= √((-12)² + 3²)
= √(144 + 9)
= √153
= 12.4 units
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Read instructions and do this on a separate piece of paper and draw all lines with a ruler or any straightedge. I will mark you brainliest.
The required angles (corresponding, vertical and alternate) in relation to the Parallel lines are attached accordingly.
What is a parallel line?Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space.
When two parallel lines cross by any other line (i.e. the transversal), corresponding angles are generated in matching corners or corresponding corners with the transversal.
When two parallel lines are sliced by a transversal, the resulting alternate exterior angles are congruent, according to the Alternate Exterior Angles Theorem.
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you will get 10 points for each question and help
The probability is very high and the event is very likely to occur.
option B.
What is the explanation for the probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
If the probability of a rolling a number greater than 1 on a six sided cube die is 5/6, it implies that the chances of obtaining a number greater than 1 is very high.
We will convert 5/6 to percentage to see the actual value of 5/6.
5/6 x 100%
= 83.33 %
So the value of this probability is very high and the event is very likely to occur.
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Is 34.05 greater than 34.59
No, 34.05 is not greater than 34.59.
When comparing two numbers, we look at their digits from left to right.
In this case, both numbers start with 34, which means they have the same value in the tens place.
However, when we move to the decimal part, 0.05 is smaller than 0.59.
Therefore, 34.05 is smaller than 34.59.
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Mr. Gupta gave his students a quiz with three questions on it. Let
�
XX represent the number of questions that a randomly chosen student answered correctly. Here is the probability distribution of
�
XX along with summary statistics:
�
=
# correct
X=# correctX, equals, start text, \#, space, c, o, r, r, e, c, t, end text
0
00
1
11
2
22
3
33
�
(
�
)
P(X)P, left parenthesis, X, right parenthesis
0.05
0.050, point, 05
0.20
0.200, point, 20
0.50
0.500, point, 50
0.25
0.250, point, 25
Mean:
�
�
=
1.95
μ
X
=1.95mu, start subscript, X, end subscript, equals, 1, point, 95
Standard deviation:
�
�
≈
0.8
σ
X
≈0.8sigma, start subscript, X, end subscript, approximately equals, 0, point, 8
Mr. Gupta decides to score the tests by giving
10
1010 points for each correct question. He also plans to give every student
5
55 additional bonus points. Let
�
YY represent a random student's score.
What are the mean and standard deviation of
�
YY?
The mean score of a random student (YY) is 574.5. the standard deviation of the random student's score (YY) is 8.
How to answer the aforementioned questionGiven:
- Each correct question is worth 10 points.
- Every student receives an additional 555 bonus points.
Let's calculate the mean and standard deviation of YY:
Mean of YY:
The mean score, denoted as μY, can be calculated using the mean of XX (μX) and the scoring scheme:
μY = μX * 10 + 555
Substituting the value of μX from the given information:
μY = 1.95 * 10 + 555
μY = 19.5 + 555
μY = 574.5
Therefore, the mean score of a random student (YY) is 574.5.
Standard Deviation of YY:
The standard deviation of YY, denoted as σY, can be calculated using the standard deviation of XX (σX) and the scoring scheme:
σY = σX * 10
Substituting the value of σX from the given information:
σY = 0.8 * 10
σY = 8
Therefore, the standard deviation of the random student's score (YY) is 8.
Complete question: Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions
that a randomly chosen student answered correctly. Here is the probability distribution of X along with
summary statistics:
0
1
2
2.
3
X = # correct
P(X)
0.05
0.20
0.50
0.25
Mean: Hex = 1.95
Standard deviation: Ox 0.8
Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give
every student 5 additional bonus points. Let Y represent a random student's score.
What are the mean and standard deviation of Y?
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13. Find mzYZU.
(10x +9)
(6x-13)
34°
Right angle
Pls help ASAP
Given is a circle with center Z, we need to find the measure of the angle YZU,
We know that,
In a circle, the length of an arc and the length of the corresponding central angle are inextricably linked and equal.
Also,
The whole circle measures 360°.
So,
arc YU + arc UV + arc VX + arc YX = 360°.
10x+9 + 90° + 34° + 6x-13 = 360°
16x = 240°
x = 15
So, arc YU = 10(15) + 9
arc YU = 159°
Since arc YU = ∠ YZU
Therefore the measure of the angle YZU is 159°
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Test Prep What fraction is represented by the point on the number line?
The fraction represented by the point between 1 and 2 on the number line is 5/3.
If the point is between 1 and 2 on the number line, we can determine the fraction it represents by considering the distance between the point and the two adjacent integers.
The point A lies between the numbers 1 and 2, which indicates that the whole number part of the fraction is 1.
Also note that the segment between 1 and 2 is divided into 3 equal parts. A lies on the 2nd part, which implies that the fractional part is 2/3.
2
Thus, the point A corresponds to the mixed fraction 1 -
3
2 5
1 - = (1*3)+2 / 3 = -
3 3
So, the fraction represented by the point between 1 and 2 on the number line is 5/3.
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BTS-2 has coordinates (-8,6) and the edge connecting vertices P and Q has the equation y = 4.
(b) Write down the coordinates of BTS-4.
a. Jason will receive the strongest signal from BTS-4 because he is located in the Voronoi cell of BTS-4.
b. The coordinates of BTS-4 are (−8,4).
How to explain the informationa. Jason will receive the strongest signal from BTS-4 because he is located in the Voronoi cell of BTS-4. A Voronoi cell is a region of space that is closer to a given point than any other point. In this case, the given point is BTS-4. The Voronoi diagram is a partitioning of the plane into Voronoi cells, one for each point.
b. The edge connecting vertices P and Q has the equation y=4, which means that it is a horizontal line that intersects the y-axis at 4. The coordinates of BTS-2 are (−8,6), which means that it is located 8 units to the left of the origin and 6 units above the origin. Therefore, BTS-4 must be located 8 units to the left of the origin and 4 units above the origin, which gives it the coordinates (−8,4).
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Help Me please!!!!!!!!!!!
The triangles are similar and
Yes , ΔPSQ ≅ ΔRST because ∠S ≅ ∠S and PS / RS = QS / TS . Thus the triangles are similar by the SAS theorem
Given data ,
Let the first triangle be ΔPSQ
Let the second triangle be ΔRST
Now , the corresponding sides are
PS / RS = QS / TS
where the corresponding sides of similar triangles are in the same ratio
And , the common angle to both the triangles is m∠S
So , ∠S ≅ ∠S and PS / RS = QS / TS
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Hence , the triangles are similar
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Can someone answer and provide an explanation for these problems? Find the midpoint of the line segment with the given endpoints.
52) The midpoint of the line segment is (-0.5, 9).
53) The midpoint of the line segment is (3, -8.5).
52) To find the midpoint of the line segment with endpoints (8,9) and (-9,9), we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (x, y) are the average of the corresponding coordinates of the endpoints.
For the x-coordinate:
(x₁ + x₂) / 2 = (8 + (-9)) / 2 = (-1) / 2 = -0.5
For the y-coordinate:
(y₁ + y₂) / 2 = (9 + 9) / 2 = 18 / 2 = 9
Therefore, the midpoint of the line segment is (-0.5, 9).
53) To find the midpoint of the line segment with endpoints (8,-10) and (-2,-7), we apply the same process using the midpoint formula.
For the x-coordinate:
(x₁ + x₂) / 2 = (8 + (-2)) / 2 = 6 / 2 = 3
For the y-coordinate:
(y₁ + y₂) / 2 = (-10 + (-7)) / 2 = -17 / 2 = -8.5
Hence, the midpoint of the line segment is (3, -8.5).
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PLS HELP! In the figure below, m angle SUT=123 and m arc PR= 124 . Find m arc ST.
The measure of the arc of the circle is mST = 122°
Given data ,
Let the circle be represented as C
where the two chords of the circle are RT and PS
And the chords RT and PS intersect at the point U
Now , when two chords intersect inside a circle, four angles are formed. At the point of intersection, two sets of congruent vertical angles are formed in the corners of the X that appears.
On simplifying , we get
m∠SUT = ( 1/2 ) ( mPR + mST )
123° = ( 1/2 ) ( 124° + mST )
On solving for mST , we get
( 124° + mST ) = 246°
Subtracting 124° on both sides , we get
mST = 122°
Hence , the measure of arc mST = 122°
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The following table represents the highest educational attainment of all adult residents in a certain town. If an adult is chosen randomly from the town, what is the probability that they have a high school degree or some college, but have no college degree? Round your answer to the nearest thousandth.
The probability that a random adult has a high school degree or some college, but has no college degree is 53. 50 % .
How to find the probability ?The number of adults with some high school degree or some college would be :
= 3, 561 + 6, 058
= 9, 619 people
The probability that a random adult would have high school degree or some college is therefore :
= Adults with high school degree or some college / Total adults in the town
= 9, 619 / 17, 981
= 53. 50 %
In conclusion, the probability is 53. 50%.
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Need an answer quick!!
What is the volume of the shape on the next page?
Answer:
6 in³
Step-by-step explanation:
volume = width X length X height
= 3 X 1 X 2
= 6 in³
Question 5 Joy is a 52-year-old nurse who earns a salary of R286 500 per annum. She contributes 7% of her annua salary to a pension fund. She only has her 2 daughters listed as a dependents on her medical aid. Sh is concerned that the R4000 monthly income tax deduction is too much.
Determine Joy's annual income tax liability. If the amount is significantly different from the R4000 monthly deduction, she may need to consult a tax advisor to ensure accurate tax planning.
To assess whether the monthly income tax deduction of R4000 is too much for Joy, we need to calculate her annual income tax liability and compare it to the deduction.
First, let's calculate the amount Joy contributes to her pension fund annually:
Pension fund contribution = 7% of annual salary
Pension fund contribution = 7/100 * R286,500
Pension fund contribution = R20,055
Next, we need to determine Joy's taxable income by subtracting her pension fund contribution from her annual salary:
Taxable income = Annual salary - Pension fund contribution
Taxable income = R286,500 - R20,055
Taxable income = R266,445
Now, we can calculate the income tax liability based on the South African income tax brackets for the 2023 tax year. Please note that tax brackets are subject to change, so it's essential to verify with the latest tax regulations.
According to the current tax brackets, the tax rates for the 2023 tax year are as follows:
18% on the first R216,200 of taxable income
26% on the portion of taxable income between R216,201 and R337,800
31% on the portion of taxable income between R337,801 and R467,500
36% on the portion of taxable income between R467,501 and R613,600
39% on the portion of taxable income above R613,601
Using these tax rates, we can calculate the income tax liability:
Tax liability = (18% * amount within first bracket) + (26% * amount within second bracket) + (31% * amount within third bracket) + (36% * amount within fourth bracket) + (39% * amount within fifth bracket)
First, let's calculate the amounts within each tax bracket:
Amount within first bracket = min(Taxable income, R216,200)
Amount within second bracket = min(max(Taxable income - R216,200, 0), R337,800 - R216,201)
Amount within third bracket = min(max(Taxable income - R337,800, 0), R467,500 - R337,801)
Amount within fourth bracket = min(max(Taxable income - R467,500, 0), R613,600 - R467,501)
Amount within fifth bracket = max(Taxable income - R613,600, 0)
Now, let's substitute the values and calculate the income tax liability:
Tax liability = (18% * min(Taxable income, R216,200)) + (26% * min(max(Taxable income - R216,200, 0), R337,800 - R216,201)) + (31% * min(max(Taxable income - R337,800, 0), R467,500 - R337,801)) + (36% * min(max(Taxable income - R467,500, 0), R613,600 - R467,501)) + (39% * max(Taxable income - R613,600, 0))
By calculating this equation, you can determine Joy's annual income tax liability. If the amount is significantly different from the R4000 monthly deduction, she may need to consult a tax advisor to ensure accurate tax planning.
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La siguiente gráfica muestra las calificaciones de un grupo de 40 alumnos que van desde el mínimo 7 hasta el máximo 10 de calificación. ¿Cuántos alumnos sacaron 9?
The specific data points or the Frequency distribution of grades for the 40 students.
The specific information from the graph , the exact number of students who received a grade of 9.
If the graph represents the distribution of grades of 40 students on a scale from 7 to 10, we can estimate the number of students who received a grade of 9 by considering the shape of the graph.
the graph is a normal distribution or bell curve, with the majority of students clustered around the mean (which is likely to be around 8.5 or 9), we can expect a significant number of students to have received a grade of 9. In a typical bell curve distribution, the highest density of scores is around the mean.
without additional information about the shape of the graph or the specific values represented on the x-axis, it is difficult to provide an accurate estimation of the number of students who received a grade of 9. The graph may represent a variety of distributions, such as skewed, bimodal, or uniform.
the exact number of students who received a grade of 9, the specific data points or the frequency distribution of grades for the 40 students.
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Based on the information given regard to the graph, there are 6 students who got 9.
How to explain the valueA graph is a diagram such as a series of one or more points, lines, line segments, curves, or areas which represents the variation of a variable in comparison with that of one or more other variables.
The collection of all points whose coordinates satisfy a given relation such as a function.
The graph shows that there are 4 students who got 7, 8 students who got 8, and 12 students who got 10. This leaves:
40 - 4 - 8 - 12
= 6 students who got 9.
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Please help me :(
What is the measure of p in the following diagram?
PS: Its in a Chapter 11 Go math book! Maybe... can you help me pls?
The measure of p in the diagram is,
m∠P = 45°
We have to given that;
PM is perpendicular to MO.
Now, If m ∠P = m∠2
then it's an isosceles triangle.
And, m ∠M = 90°, therefore it's an isosceles right triangle.
We know that,
the sum of measures of angles in a triangle is equal 180°.
Therefore we have the equation:
m∠P + m∠2 + m∠M = 180°
Substitute m∠M = 90° and m∠P = m∠2 = x:
x + x + 90° = 180°
substract 90° from both sides
2x = 90°
divide both sides by 2
x = 45°
m∠P = 45°
Thus, The measure of p in the diagram is,
m∠P = 45°
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Nadeen bought a 91-day T-bill that has an interest rate of
4.30% p.a. and a face value of $5,000.
a) How much did she pay for the T-Bill?
b) After 40 days, Barbara sold the T-bill to her friend when the interest rate for this T-bill in the market increased to 5.30% p.a. What was her selling price?
The 91-day T-bill that Nadeen bought at an interest rate of 4.30% p.a. and face value of $5,000 indicates;
a) Nadeen paid about $4,946.24 for the T-bill
b) Barbara's selling price for the T-bill is about $4,962.74
What is a T-bill?A Treasury bill (T-bill), is a short-term obligation that is issued by the U.S. Department of Treasury and which is backed by the United States government, and has a maturity of less than a year. T-bills are low risk investment as they are backed by the credit and full faith of the U.S. government.
The formula for the price of the T-bill can be calculated with the formula;
Price = Face Value/(1 + (Interest Rate × Days to Maturity/360))
Plugging in the value from the question, we get;
Price = 5000/(1 + (0.043 × 91/360)) ≈ 4946.24
Therefore, Nadeen paid $4,946.24 for the T-billb) The formula for the selling price can be presented as follows;
Selling Price = Face Value/(1 + (Interest Rate × Remaining Days to Maturity/360))
Plugging in the known values, we get;
Selling Price = 5,000/(1 + (0.053 × (91 - 40)/360)) ≈ $4,962.74
Therefore, Barbara sold the T-bill to her friend for $4,962.74
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Question: 4/8
Mr. Oswald, the head of human resources, has
been in the company for 24 years, which
corresponds to three times as many as the
number of years Mrs. Bright, the finance
director, is also employed there.
Considering neither of them leaves their jobs,
how many years will Mr. Oswald have worked for
the company when that corresponds to twice as
many as Mrs. Bright's number of years there?
Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than Twice the number of years Mrs. Bright has worked.
The number of years Mrs. Bright has worked for the company. We know that Mr. Oswald has been in the company for 24 years, which is three times the number of years Mrs. Bright has worked.
So, Mrs. Bright has worked for 24 / 3 = 8 years in the company.
Now, let's find the number of years Mr. Oswald needs to work for the company to make it twice the number of years Mrs. Bright has worked.
Twice the number of years Mrs. Bright has worked is 2 * 8 = 16 years.
Since Mr. Oswald is already employed for 24 years, we need to find the additional years he needs to work to reach 16 more years.
16 more years - 24 years = -8 years.
The result of -8 years indicates that Mr. Oswald has already worked for more than twice the number of years Mrs. Bright has worked. Therefore, it is not possible for Mr. Oswald to work for more years in order to make it twice the number of years Mrs. Bright has worked.
Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than twice the number of years Mrs. Bright has worked.
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