The sections of each course it should offer are 3 finite maths, 2 applied calculus and 2 computer methods
How many sections of each course should it offer?Let's use the following variables to represent the unknowns:
x: number of sections of Finite Mathy: number of sections of Applied Calculusz: number of sections of Computer MethodsFrom the problem, we can write the following system of equations:
x + y + z = 7 (total number of sections)
40x + 40y + 10z = 220 (total number of students)
40000x + 60000y + 29000z = 298000 (total revenue)
Simplify
x + y + z = 7
4x + 4y + z = 220
40x + 60y + 29z = 298
We can solve this system of equations using substitution
So, we have
x = 7 - y - z
By substitution, we have
4(7 - y - z) + 4y + z = 22
This gives
28 - 4y - 4z + 4y + z = 22
So, we have
28 - 3z = 22
This gives
3z = 6
Divide
z = 2
Recall that
40x + 60y + 29z = 298
So, we have
40x + 60y + 29*2 = 298
40x + 60y + 58 = 298
This gives
40x + 60y = 240
Divide by 20
2x + 3y = 12
Also, recall that x = 7 - y - z
So, we have
2(7 - y - z) + 3y = 12
This gives
2(7 - y - 2) + 3y = 12
2(5 - y) + 3y = 12
Open brackets
10 - 2y + 3y = 12
Evaluating the like terms, we have
y = 2
Lastly. we have
x = 7 - y - z
x = 7 - 2 - 2
x = 3
Hence, the number of sections of Finite Math is 3
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brandon wants to start a lawn mowing service. He estimates it will take $300 to purchase equipment and that he will have $5 of expenses for each lawn he mows. how many lawns must he mow at $25 per lawn before he breaks even
Using arithmetic οperatiοns it is οbtained that Brandοn must mοw 15 lawns at $25 per lawn tο break even, meaning his revenue will cοver his cοsts.
What is arithmetic οperatiοn?A subject οf mathematics knοwn as arithmetic οperatiοns deals with the study and use οf numbers in all οther branches οf mathematics. Basic οperatiοns including additiοn, subtractiοn, multiplicatiοn, and divisiοn are included.
Let x be the number οf lawns Brandοn mοws.
Use the arithmetic οperatiοn οf multiplicatiοn.
His revenue frοm mοwing × lawns at $25 per lawn is -
Revenue = Price per lawn × Number οf lawns
Revenue = $25 × x
Revenue = $25x
Use the arithmetic οperatiοn οf additiοn.
His tοtal cοst includes the equipment cοst οf $300 and the variable cοst οf $5 per lawn, sο his tοtal cοst is -
Cοst = Equipment cοst + Variable cοst
Cοst = $300 + $5x
Tο break even, his revenue must be equal tο his cοst.
Use the arithmetic οperatiοn οf additiοn.
Sο we can set the revenue equal tο the cοst and sοlve fοr x -
Revenue = Cοst
$25x = $300 + $5x
$20x = $300
x = 15
Therefοre, Brandοn must mοw 15 lawns at $25 per lawn.
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6. 300 students were interviewed: 45 took PE, 45 took BIO, 45 took ENG, 12 took PE and BIO, 10 took PE and ENG, 8 took BIO and ENG, 4 took all three subjects. a) How many students took none of the three subjects? b) How many students took PE but not BIO or ENG? c) How many students took BIO and PE but not ENG
(a) The number of students who took none of the three subjects is 169.
(b) The number of students who took PE but not BIO or ENG is 19.
(c) The number of students who took BIO and PE but not ENG is 8.
What is the number of the students?To find the number of students who took none of the three subjects, we can add up the numbers in the "none" region of the diagram.
From the given information, we know that 45 students took PE, 45 took BIO, and 45 took ENG, so the total number of students who took at least one subject is:
45 + 45 + 45 = 135
We also know that 4 students took all three subjects, so we need to subtract them from the total to avoid double-counting:
135 - 4 = 131
Therefore, the number of students who took none of the three subjects is:
300 - 131 = 169
(b) To find the number of students who took PE but not BIO or ENG, we need to look at the region of the diagram that only includes PE.
This includes the 12 students who took both PE and BIO, the 10 students who took both PE and ENG, and the 4 students who took all three subjects.
Therefore, the number of students who took PE but not BIO or ENG is:
45 - 12 - 10 - 4 = 19
(c) To find the number of students who took BIO and PE but not ENG, we need to look at the region of the diagram where BIO and PE overlap, but ENG does not.
This includes the 12 students who took both PE and BIO, as well as the 4 students who took all three subjects.
Therefore, the number of students who took BIO and PE but not ENG is:
12 - 4 = 8
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Find the value of each variable provide proofs
The value of each variable in the triangle are:
x = 28 units
y = 7√6 units
z = 14√3 units
How to find the value of each variable?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Considering the upper triangle:
cos 45° = (14√2)/x
x = (14√2)/cos 45°
x = 28 units
hypotenuse =√((14√2)² + 28²) = 14√6 units
Considering the lower triangle:
The two triangles share the same hypotenuse.
Thus, hypotenuse = 14√6 units
sin 30° = y/hypotenuse
sin 30° = y/(14√6)
y = (14√6) * sin 30°
y = 7√6 units
cos 30° = z/hypotenuse
cos 30° = z/(14√6)
z = (14√6) * cos 45°
z = 14√3 units
Therefore, the value of each variable are x = 28 units, y = 7√6 units and z = 14√3 units.
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A stone outbuilding is 4.3 metres high, 3.5 metres wide and 2.2 metres deep. The slope of its roof is 2.6 m long, whilst its side walls are 2.5 metres high.
Calculate its volume to 2 decimal places.
m3
Calculate the total area of its slate roof to 2 decimal places.
m2
In response to the aforementioned query, we may say that The slate roof has a total area of 0.26 square metres.
What is area?An area can be used to describe a surface's area. Surface area, also known as planar region, refers to the area of a form or planar layer, whereas planar region refers to the area of an open surface or the border of a three-dimensional object. An object's area is the entire amount of space occupied by its planar (2-D) surface or form. Use a pencil to mark a square on the paper. an individual having two dimensions. A shape's area on paper is the amount of space it occupies. Think of the square as being made up of smaller unit squares.
Height, breadth, and depth together make up volume.
Volume: 4.3 x 3.5 x 2.2 metres
33.77 cubic metres is the volume (rounded to 2 decimal places)
The stone outbuilding has a volume of 33.77 cubic metres.
Area = base x height x half
Height: 2.5 to 2.6 metres
Height = 0.10 metres
Height = (-0.1 m) | (0.1 m)
determine the size of each triangle's face:
Area = base x height x half
Area: 0.6 x 2.6 x 0.1 metres
0.13 square metres is the area.
Total area Equals twice the area
= 2 x 0.13 square metres total area
0.26 square metres is the total area (rounded to 2 decimal places)
The slate roof has a total area of 0.26 square metres.
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4^2x+1 ×5^x-2 =6^1-x. find x
Find the product. List the units. 8 h x $9/h
By answering the above question, we may infer that Due to the fact that equation we are multiplying a unit of money by a unit of time, the units for this product are dollars.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
$9/hour multiplied by 8 hours results in:
$8 × $9/hour = $72
Due to the fact that we are multiplying a unit of money by a unit of time, the units for this product are dollars.
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What is the least common multiple of 34, 29, and 7?
Answer:
6902
Step-by-step explanation:
divide through by multiples of the given values
A student answered 86 problems on a test correctly and received a grade 98%. How many problems were on the test, if all the problems were worth the same number of points?
(Round to the nearest whole number)
Answer:
It should be 88 questions
Step-by-step explanation:
86/88 x 100 = 97.7 round to the nearest whole number and you get 98%
Simply the expression 2.5-3.4n-2n+8
Answer: 10.5 - 5.4n
Step-by-step explanation:
To simplify, we will combine like terms.
Given:
2.5 - 3.4n - 2n + 8
Add 2.5 + 8 and subtract -3.4n - 2n:
10.5 - 5.4n
Answer:
[tex]-5.4n + 10.5[/tex]
Step-by-step explanation:
[tex]2.5 + 3.4n -2n + 8\\(-3.4n - 2n) + (2.5 + 8)\\-5.4n + 10.5[/tex]
What is 90.0 - 0.026
Answer:
89.974
Step-by-step explanation:
QUESTION 11
Consider the following argument: If Huckleberry Finn uses offensive language, Huckleberry Finn should not be taught
high school. Huckleberry Finn uses offensive language. Thus, Huckleberry Finn should not be taught in high school. What
is the logical form of this argument?
O a. Modus Tollens
O b. Affirming a disjunct
O c. Denying the antecedent
O d. Modus Ponens
O e. Affirming the consequent
If Huckleberry Finn uses offensive language, Huckleberry Finn should not be taught high school. Huckleberry Finn uses offensive language. Thus, Huckleberry Finn should not be taught in high school. The logical form of this argument is known as denying the antecedent. The Option C is correct.
How is "denying the antecedent" a logical form in the statement?If we represent the argument in logical symbols, it would look like this:
P: Huckleberry Finn uses offensive language.
Q: Huckleberry Finn should not be taught in high school.
The argument can be summarized as follows:
If P, then Q.
Not P.
Therefore, not Q.
This is the form of denying the antecedent, where the argument asserts that if P is true, then Q must also be true. However, the argument then proceeds to deny the antecedent by claiming that P is not true, and therefore, Q must not be true either.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36 select two options
The equation of circles that have a diameter of 12 units and a center that lies on the y-axis is (x + 6)² + y² = 144
What is the equation of a circle?The equation of a circle with center (h, k) and radius r is given by
(x - h)² + (y - k)² = r²
To determine which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis, we must have that
for the circle to lie on the y - axis, k = 0 and r² = 144
So, comparing the equations that meet this criteria, we have
(x + 6)² + y² = 144
We cannot select the circle (x – 4)² + y² = 36. Although it lies on the y - axis, its radius is not equal to 12.
So, the circle is (x + 6)² + y² = 144
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solve; |7x+4|/8=3
(multiple choice)
-4
0.5
-2.3
-0.571
2.857
The answer of the given expression is -4.
What is expression ?
An expression is a combination of numbers, symbols, and operators that represents a mathematical quantity or relationship. It can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can be simple or complex and can be evaluated or simplified to a single value or another expression. Examples of expressions include 2x + 3, 4y - 7, (x + 5) / 2, and √(x² + y²).
We can solve the equation as follows:
|7x+4|/8 = 3
|7x+4| = 3*8
|7x+4| = 24
Now we have two cases to consider:
Case 1: 7x+4 is positive
|7x+4| = 7x+4
7x+4 = 24
7x = 20
x = 20/7
Case 2: 7x+4 is negative
|7x+4| = -(7x+4)
-7x-4 = 24
-7x = 28
x = -4
Therefore, the solutions are x = -4 and x = 20/7. However, we need to check if they satisfy the original equation:
For x = -4:
|7(-4)+4|/8 = 3
|-24|/8 = 3
3 = 3 (satisfied)
For x = 20/7:
|7(20/7)+4|/8 = 3
|24+4|/8 = 3
28/8 = 3.5 ≠ 3 (not satisfied)
So the only solution that satisfies the original equation is x = -4.
Therefore, the answer of the given expression is -4.
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need help now i have like so much questions that need to be done
The measure of angle ABC in the triangle inscribed in the circle is given as follows:
m < ABC = 84º.
How to obtain the angle measure?The sum of the measures of the interior angles of a triangle is of 180º.
The internal angles for the triangle are given as follows:
<A = 48º.<ABC.<C = 48º -> congruent to angle A, as segments AB and AC both represent the radius of the circle, as they are a segment connecting a point on the circumference of the circle to the center.Then the measure of angle ABC is obtained as follows:
m < ABC + 2 x 48 = 180
m < ABC = 180 - 96
m < ABC = 84º.
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EXERCISE 7B-1 Activity-Based Costing Product Costs for External Reports (LO7) answer
ABC is an important tool for companies to utilize when they need to accurately assess their product costs and make decisions based on that information. ABC can also be used to create external reports that show customers and other stakeholders the cost of a product.
What comes under external reports?External reports are documents that are created by outside organizations or individuals and contain information that is relevant to a particular company or industry. They are used to provide insight and data that can help an organization make informed decisions.
Activity-based costing (ABC) is a method of product costing that assigns costs to products based on the activities that go into producing them. It is used to decide how much it costs a company to make a product, and then the company can use this information to set prices and make pricing decisions. With ABC, companies track the costs associated with activities and assign those costs to the products that use the activities. This is different from traditional costing methods that allocate costs to products based on a single cost driver, such as machine hours or direct labor hours. ABC is a more accurate way of determining the cost of a product because it takes into account all of the activities that go into making it. ABC can also be used to create external reports that show customers and other stakeholders the cost of a product. These reports can help a company make decisions about pricing and production efficiency, and can also be used to compare products and services to competitors. ABC is an important tool for companies to utilize when they need to accurately assess their product costs and make decisions based on that information.
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ABC is an impοrtant tοοl fοr cοmpanies tο utilize when they need tο accurately assess their prοduct cοsts and make decisiοns based οn that infοrmatiοn. ABC can alsο be used tο create external repοrts that shοw custοmers and οther stakehοlders the cοst οf a prοduct.
What cοmes under external repοrts?External repοrts are dοcuments that are created by οutside οrganizatiοns οr individuals and cοntain infοrmatiοn that is relevant tο a particular cοmpany οr industry. They are used tο prοvide insight and data that can help an οrganizatiοn make infοrmed decisiοns.
Activity-based cοsting (ABC) is a methοd οf prοduct cοsting that assigns cοsts tο prοducts based οn the activities that gο intο prοducing them. It is used tο decide hοw much it cοsts a cοmpany tο make a prοduct, and then the cοmpany can use this infοrmatiοn tο set prices and make pricing decisiοns. With ABC, cοmpanies track the cοsts assοciated with activities and assign thοse cοsts tο the prοducts that use the activities. This is different frοm traditiοnal cοsting methοds that allοcate cοsts tο prοducts based οn a single cοst driver, such as machine hοurs οr direct labοr hοurs.
ABC is a mοre accurate way οf determining the cοst οf a prοduct because it takes intο accοunt all οf the activities that gο intο making it. ABC can alsο be used tο create external repοrts that shοw custοmers and οther stakehοlders the prοduct cοst . These repοrts can help a cοmpany make decisiοns abοut pricing and prοductiοn efficiency, and can alsο be used tο cοmpare prοducts and services tο cοmpetitοrs. ABC is an impοrtant tοοl fοr cοmpanies tο utilize when they need tο accurately assess their prοduct cοsts and make decisiοns based οn that infοrmatiοn.
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Complete question:
What Activity-Based Costing in Product Costs for External Reports?
Help Please!! Its Mathematics.
flip the 2/3 then multiply
5 x 3/2 = 15/2 = 7.5
Please help I really don’t understand
Answer:
Step-by-step explanation:
i dont undrestand either sorry
Multiplication Problem Solving
Questions:
1) 6x6= ?
2) 4x8= ?
3) 2x5= ?
4) 3x7= ?
5) 7x2= ?
6) 600 x 12,427= ?
Answer:
1 = 36
2. = 32
3 = 10
4.= 21
5. = 14
6 =7456200
Step-by-step explanation:
The table of ordered pairs (x, y) gives an exponential function.
Write an equation for the function.
X
-1
0
1
2
y
1
2
5
50
500
y = 5(10)ˣ is the equation for the exponential function
How to write the equation for the exponential function?The general form of the exponential function is y = abˣ
From the table, when x = 0, y = 5. Substitute the values into the function:
y = abˣ
5 = ab⁰ (Note: b⁰ = 1)
5 = a(1)
5= a
a = 5
Also, from the table, when x = 1, y = 50. Substitute the values into the function:
y = abˣ
50 = 5 × b¹
50 = 5b
5b = 50
b = 50/5 = 10
We can now write the equation for the exponential function:
y = abˣ
y = 5(10)ˣ
Therefore, the equation for the exponential function is y = 5(10)ˣ
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Avery earned $130.20 at her job when she worked for 6 hours. How. Much money did she earn each hour? I need helpppppp!!
Answer:
She got $21.70 an hour
Step-by-step explanation:
130.20/6= 21.7
What is the value of x?
9 is the equivalent value of x from the given triangle.
The triangular bisector theoremThe angle bisector theorem is concerned with the proportions of the two segments that a line that bisects the opposite angle divides a triangle's side into.
Applying the rule to solve the given question, we will have:
3x-7/12 = 3x +3/18
Cross multiply
12(3x+3) = 18(3x-7)36x + 36 = 54x - 126
Collect the like terms
36x-54x = -126 - 36
-18x = -162
x = 162/18
x = 9
Hence the value of x from the given figure is 9.
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The measures of the angles of a triangle are shown in the figure below. Solve for x. 83* 61* (4x+16)*
[tex]83 + 61 + (4x + 16) = 180[/tex]
[tex]144 + 4x + 16 = 180[/tex]
[tex]4x + 160 = 180[/tex]
[tex]4x = 180 - 160[/tex]
[tex]4x = 20[/tex]
[tex]x = 20:4 \implies \bf x = 5[/tex]
diameter of a circle is 21 cm. Find its area to the nearest whole number.\
Answer:346.5
Step-by-step explanation: At first,we have calculate the radius of the given circle,by using the following mathematical formula.
Radius = Diameter/2 = 21/2 = 10.5 cm
Now,we have to calculate the area of the circle by using the following mathematical formula,
Area of the circle = π×r² = 22/7 × 10.5 × 10.5 = 346.5 cm²
please lmk if this an option or answer for you.
Kyle used the Quantitative Reasoning Process to create a plan to pay off his student loans of $5,020. The interest rate on his loan is 1.5% annually and he plans to make monthly payments of $45.08 for 10 years. Complete months 1 and 2 of the amortization table below.
How much of Kyle's payment goes to Interest in Month 2?
Month Beginning Balance Payment: To Interest Payment: To Principal Ending Balance
1
2 ??
3
(Round your FINAL answer to the nearest cent.)
In response to the query, we can state that As a result, interest accounted for $6.23 of Kyle's payment in month 2.
what is interest ?By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The loan's interest is the name given to this percentage.
The yearly interest rate must be divided by 12 to obtain the monthly interest rate since it is given:
1.5% each month divided by 12 equals 0.125%.
initial balance is $5,020.
Amount paid: $45.08
Interest added equals 0.125% * $5,020 = $6.27
Principle paid equals $45.08 minus $6.27, or $38.81.
Final balance: $5,020 minus $38.81 equals $4,981.19
As a result, interest accounted for $6.27 of Kyle's payment in month 1.
Total starting balance: $4,981.19
Money received: $45.08; Interest owed: 0.125% * $4,981.19; Total: $6.23
Principal paid equals $45.08 minus $6.23, or $38.85.
Final balance: $4,981.19 minus $38.85 equals $4,942.34
As a result, interest accounted for $6.23 of Kyle's payment in month 2.
The amortisation table might look like this:
Month Starting Balance Payment: To Principal Ending Balance: To Interest Payment
[tex]1 $5,020.00 $6.27 $38.81 $4,981.19\s2 $4,981.19 $6.23 $38.85 $4,942.34\s3 $4,942.34 ...[/tex]
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at noon a weatherman recorded the temperature of each city in the area. What was the highest temperature?
The highest temperature on record belongs to California's Death Valley which, in 1913, reached a temperature of 134 degrees Fahrenheit, or 56.7 degrees Celsius, Al Jazeera reports.
What was the Highest temperature?The highest temperature in India is found in this city, situated at a height of 178 metres in Rajasthan, the country's biggest state. There, 50 degrees Celsius has been recorded as the greatest temperature to date. Extreme weather may be found in the city both in the summer and the winter.
However, according to the India Meteorological Department, the highest temperature ever recorded in India was 51°C (123.8°F) in the town of Phalodi, Rajasthan on May 19, 2016. It's important to note that temperatures can vary greatly depending on the location and time of year.
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The diagram shows the circle with equation x^2+y^2=20. Tangents touching the circle at points I and J pass through the point H (0,10). By letting the equation of a tangent be y=mx+10, find the two possible values of m.
On solving the provided question we can say that value equation is
y = mx => -7 = m * 4 => m = -7/4 and x² + y² = 13 => x² + (-7)² = 13 => x
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.
here, we have,
Squaring both sides and simplifying we get:
3m² + 56m + 36 = 0
The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.
y = mx => -7 = m * 4 => m = -7/4
x² + y² = 13 => x² + (-7)² = 13 => x
So the equation of the tangent line is y = m(x - 0) + 0,
where m = -(x+4)/(y-7)
Now we can substitute the coordinates of the center of the circle into the equation of the tangent line to get y = -(x+4)/(y-7) * x
Squaring both sides and simplifying we get:
3m² + 56m + 36 = 0
b) To find the coordinates of the points A and B, we can use the equation of the tangent line and the equation of the circle.
We know that the equation of the tangent line is y = -(x+4)/(y-7) * x and the equation of the circle is (x+4)² + (y-7)² = 13.
We can substitute y = -(x+4)/(y-7) * x into the equation of the circle and solve for x.
This equation simplifies to 3x² + 56x + 36 = 0, which factors to
(x+12)(x+3) = 0
y = -(-12+4)/(y-7) * -12 = 8/(y-7) * 12 = 96/(y-7)
y = 96 + 7 = 103 and y = -96 + 7 = -89
The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.
We know that the equation of the tangent line is y = mx and the equation of the circle is x² + y² = 13.
We can substitute the point (4, -7) for x and y in the equation of the tangent line and the equation of the circle and solve for m and x,y respectively.
y = mx => -7 = m * 4 => m = -7/4
x² + y² = 13 => x² + (-7)² = 13 => x
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$30,000 invested for 40 years at 10% compounded annually
The amount at the end of the 40 years calculated using compound interest at a rate of 10% is $1,357,777.67.
What is meant by compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. The interest charged on a loan or deposit is known as compound interest. That is the idea that we employ the most frequently on a daily basis. The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Given,
The principal amount P = $30,000
The time period t = 40 years
The rate of interest r = 10%
The number of times compounded in a year n = 1
The compound interest formula can be used to calculate the amount at the end of 40 years.
[tex]A = P(1 + \frac{r}{n})^{nt} = 30000(1 + \frac{0.1}{1})^{1*40}[/tex] = $1,357,777.67
Therefore the amount at the end of the 40 years calculated using compound interest at a rate of 10% is $1,357,777.67.
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In the figure below, point B is the corner of street ABC. If streetlights are to b
installed along one side of the street with equal distance between the lights, and a
treetlight must be installed at points A, B and C, at least how many streetlights
an be installed along the street?
A
1625 m
B
cli
1170 m
Therefore, at least 49 street lights can be installed along one side of the street with equal distance between the lights.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.
Here,
The distance between point A and B is AB, and the distance between point B and C is BC. Let's assume that the distance between each street light is "d".
Since there must be a street light at points A, B, and C, there will be a total of two gaps between these three street lights, which are AB and BC. Thus, the number of street lights required is equal to the sum of the lengths of AB and BC, divided by the distance "d" between the street lights, plus 1 for the street light at point B.
So, the total number of street lights required is
Number of street lights = (AB + BC) / d + 1
We know that AB = 1170 m and BC = 1625 m, and the distance between each street light should be equal. Therefore, we need to find the greatest common factor (GCF) of 1170 and 1625 to determine the distance between each street light.
1170 = 2 x 3 x 3 x 5 x 13
1625 = 5 x 5 x 13
The GCF of 1170 and 1625 is 65, which means the distance between each street light should be 65 meters.
Now we can calculate the total number of street lights required:
Number of street lights = (1170 + 1625) / 65 + 1
= 49
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Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data. What do the results tell us?
23 53 67 61 66 91 27 85 98 44 73
Question content area bottom
Part 1
Range= enter your response here (Round to one decimal place as needed.)
Part 2
Sample standard deviation= enter your response here (Round to one decimal place as needed.)
Part 3
Sample variance= enter your response here (Round to one decimal place as needed.)
Part 4
What do the results tell us?
A.
Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
B.
The sample standard deviation is too large in comparison to the range.
C.
Jersey numbers on a football team do not vary as much as expected.
D.
Jersey numbers on a football team vary much more than expected.
The range is 75, variance is 607.70 and standard deviation is 24.65
What is standard deviation?Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Given is a data set :- 23 53 67 61 66 91 27 85 98 44 73,
We need to find the range, variance, and standard deviation for the given sample data.
Range :-
Range = the difference between the highest and lowest numbers
Highest = 98
Lowest = 23
Range = 98 - 23 = 75
Mean :-
The mean of the data is calculated by the sum of all data is divided by the total number of data =
23+53+67+61+66+91+27+85+98+44+73 / 11 = 62.54
Variance :-
Variance is calculated by formula:
σ² = (xi-mean)² / n-1
σ² = (23-62.54)²+(53-62.54)²+(67-62.54)²+(61-62.54)²+(91-62.54)²+(66-62.54)²+(27-62.54)²+(85-62.54)²+(98-62.54)²+(44-62.54)²+(77-62.54)² / 10
= 1563.4+91.0116+19.9+2.37+809.98+11.97+1263.09+504.45+1257.41+343.73+209.09 / 10
σ² = 607.70
The standard deviation, we take the variance and get the square root of it :-
σ = √607.70
σ = 24.65
Hence, the range is 75, variance is 607.70 and standard deviation is 24.65
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What is the perimeter P of triangle ABC to the nearest whole number
The perimeter of triangle ABC is approximately 50.9 units.
What is perimeter of triangle ?The perimeter of a triangle is the total distance around the outside of the triangle. It is defined as the sum of the lengths of all three sides of the triangle.
According to given conditions:To find the perimeter of triangle ABC, we need to know the lengths of all three sides. We are given the measure of angle C (40 degrees), the length of side AC (13 units), and the measure of angle B (49 degrees).
To find the length of side BC, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. In other words:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides, and A, B, and C are the measures of the opposite angles.
Using this formula, we can write:
13/sin(40) = BC/sin(91)
Solving for BC, we get:
BC = (13 * sin(91)) / sin(40)
BC ≈ 21.12
To find the length of side AB, we can use the fact that the sum of the angles in a triangle is 180 degrees. We know the measures of angles B and C, so we can find the measure of angle A as follows:
A = 180 - B - C
A = 180 - 49 - 40
A = 91 degrees
Now we can use the law of sines again to find the length of side AB:
AB/sin(49) = 13/sin(91)
Solving for AB, we get:
AB = (13 * sin(49)) / sin(91)
AB ≈ 16.78
Finally, we can add up the lengths of all three sides to find the perimeter:
Perimeter = AB + AC + BC
Perimeter = 16.78 + 13 + 21.12
Perimeter ≈ 50.9 units
Therefore, the perimeter of triangle ABC is approximately 50.9 units.
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