Using trigonometric identities, the given expression, tan(x) × cos(x), simplified to a single trigonometry is sin(x)
Simplifying trigonometric identitiesFrom the question, we are to simplify the given trigonometric expression
From the given information
The given expression is
tan(x) × cos(x)
From trigonometric identities, we know that
tan(x) = sin(x) / cos(x)
Now,
Substituting this value in the given expression
tan(x) × cos(x)
We get
sin(x) / cos(x) × cos(x)
Simplifying further
sin(x) / cos(x) × cos(x) = sin(x)
Hence,
The simplified expression is sin(x)
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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 25 pounds each. The small boxes weigh 50 pounds each. There are 105 boxes in all. if the truck is carrying a total of 3,875 pounds in boxes, how many of each type of box is it carrying?
What is the radius of X?
The radius of the diameter X is 6cm. Option D
How to determine the radius
To determine the radius of the circle, we have;
It is important to that the formula for diameter
The formula for calculating the diameter is given as;
d = r/2
Such that the parameters are given as;
d is the diameter of the circle.r is the radius of the circle.From the information given, we have that;
Diameter, d = 12cm
Now, we have to substitute the values
Radius =diameter/2
Radius = 12/2
Radius = 6cm
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explicit formula for an, the nth term of the sequence 6, 0, -6, ....
Answer:
12 - 6n
Step-by-step explanation:
As this sequence decreases, rather than increases, this tell us that the nth term of this sequence will be minus. The difference from 6 and 0 is 6, telling us that the decrease is by 6 each time. So now we know the nth term of this sequence; -6n, but the sequence of -6n is -6,-12,-18 and so on. We need 6,0,-6. To find out the second part of the nth term find the difference from the sequence given and the sequence of -6n. The difference is 12 because the 6--6 = 12. So now we get the nth term of the sequence -6n + 12 which is written as 12-6n.
Drag and drop to complete the proof below:
Given: DE←→
is tangent to circle C, at point F
Prove: ∠FEC and ∠ECF are complementary
To complete the proof below, we have;
<EFC is right angle; definition of a right angle
m<EFC = 90 degrees; definition of a tangent line
m<EFC + m<FEC + m<ECF = 180; Triangle sum theorem
90° + m<FEC + m<ECF = 180; Substitution property of equality
m<FEC + m<ECF = 90; Subtraction property of equality
<FEC + <ECF are complementary angles; definition of complementary angles
How to match the statementsTo match the statement with their corresponding equations, we need to know the following;
The sum of the angles in a triangle is 180 degreesThe measure of the angle at right angle is 190 degreesComplementary angles are pair of angles that sum up to 90 degreesLearn more about angles at: https://brainly.com/question/25716982
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Graph the line with slope
3/4
passing through the point (-4,-1)
.
Answer:
check attachment
Step-by-step explanation:
First write in point-slope form:
y-y1=m(x-x1)
Now substitute:
y-(-1)=3/4(x-(-4))
And then just solve. You should get a y-intercept of 2.
The growth of a colony of bacteria is modeled by the function below, where t is the
is time in hours after the culture is begun and f(t) is the number of bacteria present.
After how many hours will there be 2000 bacteria in the colony? Round your answer
to the nearest hundredth (two decimal places).
f(t) = 500e^0.195t
namely, what is "t" when f(t) = 2000
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(t)}{2000}=500e^{0.195t}\implies \cfrac{2000}{500}=e^{0.195t}\implies 4=e^{0.195t} \\\\\\ \log_e(4)=\log_e\left( e^{0.195t}\right)\implies \log_e(4)=0.195t\implies \ln(4)=0.195t \\\\\\ \cfrac{\ln(4)}{0.195}=t\implies 7.11\approx t[/tex]
I need help with this problem
Answer:
0.375
Step-by-step explanation:
Problem 3
Draw the pictures to compute 1 ÷ 11 in a base ten system, and show the answer is 0.09.
The result of 1/11 in the base 10 system is given as is 0.09.
How to solveTo visualize the long division of 1 ÷ 11 in a base ten system:
Set up the long division: 11 outside and 1.00 inside the division bracket.
Place the decimal point in the quotient above the dividend's decimal point.
Bring down the first digit (0) and divide 11 into 10; it goes 0 times.
Subtract the product (0) from 10, leaving 10.
Bring down the next digit (0) and divide 11 into 100; it goes 9 times.
Subtract 99 from 100, leaving a remainder of 1.
The result is 0.09.
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Triangles ABC and DEF are mathematically similar. 9 Cm B The area of triangle ABC is 34 cm. Calculate the area of triangle DEF. F 13.5 cm
Answer:
Since the triangles are similar, their corresponding sides are in proportion. The ratio of sides AB to DE is 9:13.5, which simplifies to 2:3. Therefore, the ratio of their areas is the square of the ratio of their sides, which is 4:9.
If the area of triangle ABC is 34 cm, then the area of triangle DEF is:
Area of DEF = (Area of ABC) x (DE^2/AB^2) = 34 x (13.5^2/9^2) = 34 x 1.5^2 = 34 x 2.25 = 76.5 cm^2
Therefore, the area of triangle DEF is 76.5 cm^2.
Step-by-step explanation:
The volume of 1,000 drops of a liquid is 10 fluid ounces. What is the volume of 10 drops?
Answer:
0.1 oz
Step-by-step explanation:
1000=10 oz
10 drops
1000/100=10
10/100=O.1 oz
The price of 7 citrons and 9 fragrant wood apples is 135 units. The price of 9 citrons and 7 fragrant wood apples is 137 units. Find the price of a citron and the price of a wood apple.
The price of a citron is :
The price of a wood apple is :
Let's assume the price of a citron is "x" units and the price of a fragrant wood apple is "y" units.
From the given information, we can form two equations:
7x + 9y = 135 ...(1)
9x + 7y = 137 ...(2)
We can solve this system of equations using the elimination method. Multiplying equation (1) by 9 and equation (2) by 7, we get:
63x + 81y = 1215 ...(3)
63x + 49y = 959 ...(4)
Subtracting equation (4) from equation (3), we get:
32y = 256
y = 8
Substituting the value of y in equation (1), we get:
7x + 9(8) = 135
7x + 72 = 135
7x = 63
x = 9
Therefore, the price of a citron is 9 units and the price of a fragrant wood apple is 8 units.
You save $8,500.00. You place 40% in a savings account earning a 4.2% APR compounded annually and the rest in a stock plan. The stock plan decreases 3% in the first year and increases 7.5% in the second year.
A. What is the total gain at the end of the second year for both accounts combined?
B. If you had invested 60% in the savings account and the rest in the stock plan, what is the difference in the total gain compared to the original plan?
The total gain at the end of the second year for both accounts combined is $509.09.
We have,
Amount saved = $8500
40% of 8500 is saved in saving account = 0.4 x 8500 = $3400
Remainder amount in stock plan = 8500 - 3400 = 5100
Working for savings plan
A = P(1 + r/n[tex])^{nt[/tex]
A = 3400(1 + 0.042/1)²
A = $3691.60
So, we gain = 3691.6 - 3400 = $291.6
Working for stock plan:
The stock plan decreases 3% in the first year
= 5100 x 0.97
= $4947
and increases 7.5% in the second year.
= 4947 x 1.75
= $5318.03
So, we gain = 5318.03 - 5100 = $218.03
Thus, the total gain is
= 291.06 + 218.03
= $509.09
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The box plots display the scores that two different groups of students got on their last math quiz.
The correct option is A.
The interquartile range for Data Set A is 15 and the interquartile range for Data Set B is 10.
Given that, the box plots display the scores that two different groups of students got on their last math quiz.
We need to find the interquartile range of each data set.
So, the interquartile range of data set A = 80-65 = 15
the interquartile range of data set B = 90-80 = 10
Hence, the interquartile range for Data Set A is 15 and the interquartile range for Data Set B is 10.
The correct option A.
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Jacob biked 10 miles in 45 minutes at this rate how far would he bike in 4.5 hours in hours how many hours would it take him to hike 90 miles create a proportion to represent these situation and solve
Answer:60, 6.75
Step-by-step explanation:
To solve the first prompt, we must create an equality statement.
[tex]\frac{10}{45}=\frac{x}{270}[/tex] X being the distance he can go in 4.5 hours.
In order to have came up with 270, we needed to take 4.5 hours and turn it into a measure of minutes to correspond to the minute value of 45.
This is found by multiplying 4.5 by 60.
Now that we have this done, we can cross multiply the equality statement.
[tex]10\cdot270=45x[/tex]
Simplify the first side
[tex]2700=45x[/tex]
Divide both sides by 45
[tex]\frac{2700}{45}=\frac{45x}{45}[/tex]
[tex]60=x[/tex]
This means that Jacob can bike 60 miles in 4.5 hours.
For the second prompt, we need to find how long it would take for him to bike 90 miles given the amount of time it took for him to bike 10 miles.
We can use an equality statement like this:
[tex]\frac{45}{10}=\frac{x}{90}[/tex]
Now we cross multiply:
[tex]45\cdot90=10\cdot x[/tex]
Simplify:
[tex]4050=10x[/tex]
Now we can divide both sides by 10.
[tex]\frac{4050}{10}=\frac{10x}{10}[/tex]
[tex]405=x[/tex]
This means that it would take Jacob 405 MINUTES to bike 90 miles.
To turn this into a measure of hours, we need to divide 405 by 60, which comes out to 6.75.
It would take Jacob 6.75 hours to bike 90 miles.
nd the interest on the loan using the Banker's ru P = $4800, r= 8.8%, t = 105 days! The interest on the loan using the Banker's rule
The interest on the loan using the Banker's Rule is $139.20.
How to find the interest on the loan using the Banker's ruleThe formula for calculating interest using the Banker's Rule is:
Interest = Principal x Rate x Time / 360
where:
Principal is the amount of the loan
Rate is the interest rate as a decimal
Time is the time period in days
Using this formula, we can calculate the interest on the loan as:
Interest = 4800 x 0.088 x 105 / 360
Interest = 139.20
Therefore, the interest on the loan using the Banker's Rule is $139.20.
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Ana's lawn is shaped like a square with an area of 224.9 .
Which measurement is closest to the side length of his lawn in feet?
The graph of which equation passes through the
point
Answer:
The answer is A.
A graph passes through a point if its equation is equal to the coordinate of this point. In this exemple:
5x+4y=8
we replace the variables with 4 and -3 (x with 4 and y with -3):
5(4)+4(-3)=8
20-12=8
8=8 so it passes.
NOW , for the slope:
slope = - 5/4 ( the equation is 5x+4y=8 , the cartesian equation is 5x+4y-8=0. THE cartesian equation with variables is ax+by+c=0) NOW this is linked with the slope bcz the slope is linked to the director vector (-b;a) that gives (-4;5), this is the director vector's formula that we're going to call U. THEN with this formula you get the slope: Y of U / X of U = 5/-4 = - 5/4 (bcz you dont leave the denominator with a negative sign).
THAT'S it thats the answer.
Corellian Engineer needs to develop a new navigation system for its YT-1300 Freighter. They opened the process to competitive bids. The best bid gave the following numbers. (All numbers in millions).
Working -
Total cost estimate for thos project = Programming + Beta Testing + Installation + Final shake down.
= 5,000 + 3,500 + 2,000 + 7,000
= 17,500.
the total cost estimate for this project is $17,500.
What process did Corellian use for this estimate? Choose one.
1.Top down (Macro)
2.Balanced
3.Bottom up (Micro)
4.OMG, my head hurts
Corellian Engineer used the Bottom up (Micro) approach to estimate the total cost of developing a new navigation system for its YT-1300 Freighter. The total cost estimate of $17,500. So, the correct option is C).
The process that Corellian used for this estimate is the Bottom up (Micro) approach, which involves estimating costs for each component or task in the project and then summing them up to get the total cost estimate.
In this case, they estimated the costs for programming, beta testing, installation, and final shake down, and then added them up to get the total cost estimate of $17,500.
So, the correct answer is C).
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PLEASE HELP HURRY FAST PLEASE THANK YOU! please put answers as either a b c or d thank you and please help me on every single one ill give brainiest if completed thanks
4. Find the rational roots of x^4+5x^3+7x^2-3x-10=0
A. -2,1
B. 2,1
C. -2,-1
D. 2,-1
5. Find all the zeros of the equation 3x^2-4=-x^4
A. 1,2i
B. -1,-2i
C. 1,-1,2i,-2i,0
D. 1,-1,2i,-2i
6. What is a polynomial function in standard form with zeros 1,2,-2, and -3?
A. x^4+2x^3+7x^2-8x+12
B. x^4+2x^3-7x^2-8x+12
C. x^4+2x^3-7x^2+8x+12
D. x^4+2x^3+7x^2+8x+12
7. Which correctly describes the roots of the following cubic question.
x^3-3x^2+4x-12=0
A. three real roots, each with a different value
B. one real root and two complex roots
C. three real roots, two of which are equal in value
D. two real roots and one complex root
8. What is the solution of 5^3x=900. Round your answer to the nearest hundredth
A. 1.24
B. 1.41
C. 4.23
D. 0.69
9. x= 1,2,4,6,8,10,11 y= 0,-1,0,4,8,9,8 <--- Table is right here
Which of the following questions best represents the regression line for the data given in the table above.
A. y=x+2
B. y=2x-2
C. y=-x-2
D. y=x-2
10. Is the relationship between the variables in the table a direct variation, an inverse variation, both, or neither? If it is a direct or inverse variation, write a function to model it. ---> Table x= 2,5,12,20 y= 30,12,5,3
A. direct variation; y=15x
B. inverse variation; y=60/x
C. direct variation; y=2x+2
D. neither
11. A drama club is planning a bus trip to New York City to see a Broadway play. the cost per person for the bus rental varies inversely as the number of people going on the trip. It will cost $30 per person if 44 people go on the trip. How much will it cost per person if 55 people go on the trip. Round your answer to the nearest cent if necessary
A. $48.00
B. $12.50
C. $24.00
D. $33.00
12. What is the simpler form of the radical expression? 4sqrt2401x^12y^16
A. 49|x^9|y^16
B. 49x^9|y^16|
C. 7|x^3|y^4
D. 7x^3|y^4|
13. Simplify. 125^1/3
A. 125
B. 5
C. 25
D. sqrt125
14. Graph the function. y=sqrtx+3
15. An initial population of 293 quail increases at an annual rate of 6%. Write an exponential function to model the quail population. What will the approximate population be after 4 years?
A. f(x)=(293 x 1.06)^x; 930
B. f(x)=293(0.06)^x; 379
C. f(x)=293(1.06)^x; 370
D. f(x)=293(6)^x; 190
16. Evaluate the logarithm
log3 2187
A. 5
B. 6
C. 7
D. -7
17. Estimate the value of the logarithm to the nearest tenth
log4 22
A. 2.2
B. 0.4
C. -0.7
D. 3.2
18. Solve 1n 4 + 1n (3x)=2. Round your answer to the nearest hundredth
A. 1.13
B. 0.18
C. 1.41
D. 0.62
19. Write an equation for the translation of y= 4/x that has the asymptotes x=7 and y=6.
A. y= 4/x-6 +7
B. y= 4/x+7 +6
C. y= 4/x-7 +6
D. y= 4/x+6 +7
20. What is the graph of the rational function?
y=(x-5)(x-3)/(x+4)(x-4)
21. What are the points of discontinuity?
y=(x-3)/x^2-12x+27
A. x=4,x=9,x=1
B. x=-9,x=-3
C. x=-9,x=-3,x=-1
D. x=9,x=3
22. What is the quotient 6-x/x^2+2x-3/x^2-4x-12/x^2+4x+3 in simplified form? State any restrictions on the variable.
23. Simplify the complex fraction x+3/ 1/x+1/x+3
A. x^2/2x+3
B. x^2/2x
C. x^2/x+3
D. x^2+2x+3/2x+3
24. Simplify the difference
x^2-x-56/x^2+6x-7 - x^2+2x-15/x^2+9x+20
A. x-71/(x-1)(x+4)
B. 2x^2-8x-29/(x-1)(x+4)
C. -8x-35/(x-1)(x+4)
D. -35/(x-1)(x+4)
25. Solve the equation 1/x-3+1/x+5=1/3
A. x=1,x=7
B. x=3,x=-5
C. x=-3,x=1
D. x=-3,x=7
Answer:
Step-by-step explanation:
4. A. Im not sure but that seems like the most logical.
5. D.
6. B.
7. B.
8. I think it's A. maybe-
9.- id-k sorry-
10. i--dk..]
11. C
12. D
13. B.
15. C.
16. C
17. A.
18. D
19. C.
21. D.
22. -(x+1)/(x-1)(x+2) x does not equal -3, -2, 1, and 6
23. i d-ksorry
24.i-d-k sorry
25. D.
Hope this helped sorry i culdn't get them all-
The answers to all parts are shown below.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
1. x⁴ + 5x³ + 7x² -3x - 10 = 0
= (x-1)(x+2)(x² + 4x + 5)
Thus, the rational roots are 1 and -2.
2. 3x² -4 = - x⁴
x⁴ + 3x² -4 = 0
(x-1)(x+1)(x² + 4) =0
Thus, the zeroes are 1, -1, -2i, +2i.
3. We can write the zeroes as
p(x)=(x-1)(x-2)(x+2)(x+3).
So, p(x) = x⁴ + 2x³ -7x² -8x +12
4. x³ -3x² +4x- 12=0
(x-3)(x²+4) =0
x= 3, -2i, 3i
5. x= 1,2,4,6,8,10,11
y= 0,-1,0,4,8,9,8
So, equation of line
(y- 0) = (-1-0)/(2-1)(x-1)
y = -1(x-1)
y + x +1=0
6. x= 2,5,12,20 and y= 30,12,5,3
k = 30/2
k = 15
So, the relationship is y= 15x.
7. cn = constant(k)
n= 44
then, c= 30/44 = 0.68
and, k = 44 x 0.68
k = 30
So, c = 1.5 dollars per person.
8. 125¹/³
= (5³)¹/³
= 5
9. y = 293(1.06)⁴ = 370
10. log₃ 2187
= log₃ 3⁷
= 7
11. log₄ 22
= 2.29
12 . y= 4/x
The new equation is y = 4/(x - 7) + 6.
13. (6-x)/ (x² + 2x - 3) / (x² -4x- 12)/ (²x² + 4x + 3)
= - (x+1)/ (x+1)(x+2)
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Find the volume of the composite solid. Round your answer to the nearest hundredth.
6 ft
-12 ft
The volume is about
cubic feet.
Problem 5:
Find the missing side using
trigonometry:
52
18 H
AWO
Drag&Drop the correct trig function:
Cos
Tan
Rati
Circle which shortcut you use.
Multiply
Round your answer to the nearest tenth:
Give Feedback to Micrones
Sin
%
or
IN
Divide
Ans
Ans
The missing length is 11.0818 unit.
We have,
Angle = 52 degree
H = 18
Using Trigonometry
cos 52 = B/H
cos 52 = x / 18
0.615661 = x /18
x = 11.0818 unit
Thus, the missing length is 11.0818 unit.
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The base of a parallelogram has a length of 10xm what is the height?
The height of this parallelogram include the following: B. 12 cm.
How to calculate the area of this parallelogram?In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = b × h
Where:
b represents the base area of a parallelogram.h represents the height of a parallelogram.By substituting the given parameters into the formula for the area of a parallelogram, we have the following;
Area of a parallelogram = 10 × 12
Area of a parallelogram = 120 cm².
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Convert 135° from degrees to radians.
Answer:
Answer:Radians = Degrees × 3.14/180
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174135×0.0174
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174135×0.0174 = 2.355
Help please on this one i need help
∠ AFE is supplementary to ∠ AFB and the measure of ∠ AFE = 102⁰.
option A.
What is a supplementary?Supplementary angles are the two angles that sum up to 180 degrees.
That is, if the sum of two angles is equal to 180 degrees, then the two angles are supplementary.
From the given diagram we can form the following equation;
∠ AFE + ∠ AFB = 180 (sum of angles on a straight line is equal to 180⁰ )
∠ AFE = 180 - ∠ AFB
∠ AFE = 180 - 78
∠ AFE = 102⁰.
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please help me choose which one it is
The correct statement regarding the relations in this problem is given as follows:
Only relation A could represent a linear relationship.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.From the first bullet point, we have that what classifies a linear relation is a constant rate of change.
For relation K, we have that it is not linear, as:
From x = -7 to x = -4, the rate of change is of 5/3.From x = -4 to x = -2, the rate of change is of 1/2. -> different to 5/3.For relation R, we have that it is linear, as it has a constant rate of change.
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A normal distribution has a mean of 85.5 and a standard deviation of 4.8 to find the data value corresponding to the value of the given
The data value corresponding to z = 0.55 is approximately 87.6075.
How to solve for the data valueTo find the data value corresponding to a given z-score, we need to use the formula:
z = (x - μ) / σ
where z is the standard score, x is the data value, μ is the mean, and σ is the standard deviation.
Rearranging this formula, we get:
x = z * σ + μ
Substituting the given values, we get:
x = 0.55 * 4.85 + 85.3
x = 87.6075
Therefore, the data value corresponding to z = 0.55 is approximately 87.6075.
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A normal distribution has a mean of 85.3 and a standard deviation of 4.85. Find the data value corresponding to the value of z given. (Enter your answer to four decimal places.) z = 0.55
b) The Median and Mode of the following wage distribution are known to be $33.5 and $34 respectively. Three frequency values from the table are, however, missing. Find the missing values. Wages (in $) 0-10 10 - 20 20 - 30 30 - 40 40 - 50 50-60 60-70 Frequencies (f) 10 10 ? ? ? 6 230 repsectively
The missing values are 60, 100 and 40 if the Median and Mode of the wage distribution are known to be $33.5 and $34 respectively
Wages (in Rs)_freq____ CF
0-10________4___________4
10-20_______16________20
20-30_______x________20+x
30-40______y_________20+x+y
40-50______z________20+x+y+z
50-60______6_______26+x+y+z
60-70______4______30+x+y+z
Since total 230
So, 30+x+y+z=230
x+y+z=200
Mode =34
Median = 33.5
By solving the equations we get x=60, y=100 and z=40
Hence, the missing values are 60, 100 and 40
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A beaker is shaped like a cylinder with a radius of 1.8 inches and a height of 4.6 inches. It is filled to the top with a solution. Caleb wants to pour it into a different beaker with a radius of 1.25 inches. What is the minimum height the second beaker must be so it does not overflow? Round to the nearest tenth.
The minimum height the second beaker must be so it does not overflow is 9.55 inches.
Given that a beaker has a radius of 1.8 inches and height of 4.6 inches. we need to find the height of another beaker which has the radius of 1.25 in and has same volume,
Volume of a cylinder = π × radius² × height
= 3.14 × 1.8² × 4.6
= 46.8 in³
Now, the second beaker =
46.8 = 3.14 × 1.25² × h
h = 46.8 / 3.14 × 1.25²
h = 9.55
Hence, the minimum height the second beaker must be so it does not overflow is 9.55 inches.
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Examine the equation below used for determining the capital gain made on a stock.((900)(12.55)-(900)(12.55)(.01))-(900)(8.14)+25)=3,831.05
This capital gain problem that can be modelled using this equation is one that relates to the price of a stock or share.
How can the problem be crafted?It can be writen as follows.....
Suppose that one purchased 900 shares of a stock at a price of $ 12.55 per share .
After a year, the stock price rose to $ 13.25 per share, but you sold the shares at a price of $8. 14 per share due to financial difficulties.
You also incurred a transaction cost of $25.
What is the capital gain or loss made on the stock?
given the above question, if we solved for for the problem, we would get....
Solving for x, we get:
((900 )(x )-(900 )(x)(.01))-(900) (x-4) +25)
= 15,740
Simplifying this expression, we get:
(0.99900x) - (36 x 900) + 25
= 15,740
0.99900 x = 15,655
x = 17.39
Therefore, the current stock price is $17.39
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Full Question:
1. Examine the equation below used for determining the capital gain made on a stock. Look through this chapter and your notes to help you write a problem that could be modeled by this equation.
.((900)(12.55)-(900)(12.55)(.01))-(900)(8.14)+25)=3,831.05
The line plot represents the afterschool activities at 15 middle schools.
A horizontal number line starting at 0 and increasing by units of two up to 30. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The title is Afterschool Activities, and the number line is labeled Number of Activities.
Which statement best describes the spread and distribution of the data?
The data is symmetric with an approximate range of 24. The most frequent number of activities was 16, which might mean about half of each class participated.
The data is skewed with an approximate range of 24. The most frequent number of activities was 10, which might mean there are 10 different sports and clubs for middle school students that are the most popular.
The data is bimodal with an approximate range of 24. The most frequent number of activities was either 16 or 28, which might show that the entire class needed to choose an activity.
The data is symmetric with an approximate range of 24. The most frequent number of activities was less than 10, which might mean that the schools do not have funding for the activities.
According to the line plot, the statement that best describes the spread and distribution of the data is "The data is bimodal with an approximate range of 24. The most frequent number of activities was either 16 or 28, which might show that the entire class needed to choose an activity.". (option c).
The horizontal number line starts at 0 and increases by units of two up to 30. The dots above the numbers represent the number of schools that offer a certain number of activities. For instance, there is one dot above 4, 6, 14, and 28, which means that only one school offers four activities, one school offers six activities, one school offers 14 activities, and one school offers 28 activities.
Based on this line plot, we can conclude that the data is not symmetric because there is not an equal number of dots on either side of the plot. Therefore, we can rule out the first and fourth options.
We can observe that there are more dots on the left-hand side of the plot, indicating that there are more schools that offer fewer activities. Additionally, the most frequent number of activities is 16, which means that about half of the schools offer this number of activities.
Furthermore, we can estimate the range of the data to be approximately 24, as the number line goes up to 30, and the highest number of activities offered by any school is 28.
Hence the correct option is (c).
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