Answer:
46/273
Step-by-step explanation:
To add fractions, they must have a common denominator. To set one, find a common multiple of both denominators. Simply multiply them together if it proves difficult.
7 x 39 = 253
Now set the denominators to this number and multiply the numerators by the opposite fraction's denominator.
39/259 + 7/253 = 46/253
This simplifies to 2/11
So, 1/3 + 1/39 = 2/11
Order these numbers from least to greatest 5.96 5 2/9 5.961 21/4
The numbers from least to greatest is arranged as 5 2/9 < 21/4 < 5.96 < 5.961
Arranging the Number in Ascending OrderTo solve this problem, we have to arrange the numbers in an ascending order from the least to the greatest. To do this, we can convert all numbers to whole numbers or fractions to decimal form to make it easier.
convert 5 2/9 to decimal = 5.222
convert 21/4 = 5.25
Let's arrange the number in ascending order
5.22 < 5. 25 < 5.96 < 5.961
The numbers can be arranged from least to greatest using a number line.
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find m help pls worth alot of points :)
Answer:
m∠C = 50 degrees
Step-by-step explanation:
∠CAQ is a straight angle (180) so ∠CAB is supplementary to ∠QAB
∠CAQ = ∠QAB + ∠CAB
180 = 110 + ∠CAB
180 - 110 = ∠CAB
70 = ∠CAB
The total angle measurement in all triangles is 180 degrees, knowing this, we can set up the equation:
180 = ∠CBA + ∠BCA + ∠CAB
180 = 2 + 29x + 24x + 2 + 70
180 = 74 + 53x
180 - 74 = 53x
106 = 53x
2 = x
Knowing x = 2, we can solve for m∠C
24(2) + 2 = ∠C
48 + 2 = ∠C
50 = ∠C
A line goes through the points (−8,−5) and (−10,−6). Find its slope. Enter your answer as a simplified improper fraction, if necessary. Do not include "m=" in your answer.
Answer:
4/3 i think
Step-by-step explanation:
C Apply Your Knowledge (See Ex. 7)
10 A factory produces lemon-scented widgets. Each widget is
cheaper, the more that are produced, but costs will go up if
too many widgets are produced, due to storage requirements.
The accountant for the factory says that the costs for
producing x thousands of units a day can be approximated by
the formula C = 0.04x² -8.504x + 25302. Find the daily
production level that will minimize the costs. Be sure to
show your work and include units of measurement.
The daily production level that will minimize the costs is 106300 units.
Given,
In the question:
The accountant for the factory says that the costs for producing x thousands of units a day can be approximated by the formula
C = 0.04x² -8.504x + 25302.
To find the daily production level that will minimize the costs.
Now, According to the question:
From the information, the function is given as
C = 0.04x² - 8.504x + 25302.
C = cost
From the function, the following can be deduced:
a = 0.04
b = 8.504
c = 25302
Then, -b/(2a) will be:
= -8.504 / (2 × 0.04)
= 106.300
Note that production level will minimize the cost in thousands.
The production level will now be:
= 106.300 × 1000
= 106300 units
Hence, The daily production level that will minimize the costs is 106300 units.
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Which of the following statements is true for the quadratic equation x² – 16x + 64 = 0?
It's impossible to determine how many solutions the equation has.
The equation has no solutions.
The equation has two solutions.
The equation has one solution.
Since the discriminant of the quadratic equation Δ is equals to 0, the given quadratic equation has one solution. Thus, the fourth option is correct.
We know that for a quadratic equation [tex]ax^{2} +bx+c =0[/tex], there exists a discriminant, Δ = [tex]b^{2}-4ac[/tex]. This discriminant gives us the nature of roots that a quadratic equation can have.
If Δ > 0, the quadratic equation has two real rootsIf Δ = 0, the quadratic equation has single solution as two double rootsIf Δ < 0, the quadratic equation has no real rootsHere, we have the given quadratic equation as -
[tex]x^{2} -16x+64=0[/tex]
Comparing this to the general expression of a quadratic equation, we have
a = 1
b = -16
c = 64
So, now we have to find the discriminant of the given quadratic equation.
Δ = [tex]b^{2}-4ac[/tex]
[tex]= (-16)^{2} -4*1*64\\= 256-256 = 0[/tex]
We see that the discriminant, Δ = 0. This implies that the given quadratic equation has one solution. Thus, the fourth option is correct.
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Let (7, -4) be a point on the terminal side of 0. Find the exact values of sin0, escO, and cott.
The exact values of the trigonometric functions of the ordered pair are listed below:
sin θ = - 4√65 / 65 sec θ = √65 / 7 cot θ = - 7 / 4What are the exact values of three trigonometric functions associated with an ordered pair?In this problem we find an ordered pair in rectangular form (x, y) that the represents the terminal side of angle θ and from which we must determine the exact values of the sine, secant and cotangent. The definitions for each of the three functions are:
sin θ = y / √(x² + y²)
sec θ = √(x² + y²) / x
cot θ = x / y
If we know that x = 7 and y = - 4, then the exact values of the trigonometric functions are, respectively:
sin θ = (- 4) / √[7² + (- 4)²]
sin θ = - 4√65 / 65
sec θ = √[7² + (- 4)²] / 7
sec θ = √65 / 7
cot θ = 7 / (- 4)
cot θ = - 7 / 4
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A burst pipe fills a basement with 37 in. of water. A pump empties the water at a rate of 1.5 in./hr. The water level h, in inches, after t hours is represented by h = 37 - 1.5t. How long until the water is drained from the basement?
The time until the water is drained from the basement is 24.67 hours.
How to calculate the time?From the information, it was stated that the burst pipe fills a basement with 37 in. of water and a pump empties the water at a rate of 1.5 in./hr.
Also, the water level h, in inches, after t hours is represented by h = 37 - 1.5t. In this case, for the water to be drained, it'll be at zero. This will be illustrated as:
37 - 1.5t = 0
1.5t = -37
Divide.
t = 37 / 1.5
t = 24.67 hours.
The time is 24.67 hours.
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NO LINKS!! Use the diagram below to answer the following questions Part 5
Answer:
1a. BF, CG, DH.
1b. (1) ABF and DCG.
(2) ADH and BCG.
1c. AD, AE, BC, BF, CE, DF.
2a. OP.
2b. JO, KP, LQ, MR.
2c. OPQ.
2d. JK, JN, KL, MN.
Step-by-step explanation:
A prism is a polyhedron that has:
Two bases that are congruent and parallel to each other.Lateral sides that are parallelograms and link the two bases.Height that is the distance between the two bases.Lines
Parallel lines are lines on a plane that never meet and are the same distance apart.Intersecting lines cross each other in a plane and share a common point called the point of intersection.Skew lines are a pair of non-coplanar lines that do not intersect, and are not parallel to each other.Planes
A plane is a flat, two-dimensional surface that extends into infinity.
A plane can be named by the letters naming three non-collinear points in the plane.
Parallel planes are planes that never intersect. Intersecting planes are not parallel and always intersect along a line. Question 1From inspection of the give diagram, the figure appears to be a rectangular prism with bases ABCD and EFGH.
1a. All segments that are parallel to AE are:
BF, CG and DH.1b. Two examples of parallel planes:
(1) ABC and EFG.(2) ADH and BCG.1c. All segments that are skew to GH:
AD, AE, BC, BF, CE and DF.Question 2From inspection of the give diagram, the figure appears to be a pentagonal prism with bases JKLMN and OPQRS.
2a. All segments that are parallel to JK:
OP.2b. All segments that are parallel to NS:
JO, KP, LQ and MR.2c. A plane that is parallel to plane JKL:
OPQ.2d. Four segments that are skew to RQ:
JK, JN, KL and MN.U = 2, 3, 4, 5, 7
C= 2, 4
D= 2, 7
(a) (CnD)’=
(b) C’uD=
Answer:
U={2,3,4,5,7}
C={2,4}
D={2,7}
Now,
a.) CUD
= {2,4}U{2,7}
= {2,4,7}.
again,
b.) CnD
= {2,4}n{2,7}
= {2}.ans
Step-by-step explanation:
U(union) means all of the numbers but not similar one…
n(intersection) means common factors.
Hope it really helps you
please mark me as brainalist...
A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 1700 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?
Complete the statements below with the process used to achieve steps 1-4. Select the correct answer from each drop-down menu. Consider the equation below. -2(5x+8)=14+6x The equation was solved using the following steps.
The complete statements for solving the equation in the steps are:
1. Distribute -2 to 5x and 8
2. Subtract both sides by 6x
3. Add both sides by 16
4. Divide both sides by -16
How to Solve an Equation?Solving an equation involves finding the value of the variable in the equation that would make the it true. This is done by isolating the variable to one side of the expression to determine its value.
Given the equation, -2(5x + 8) = 14 + 6x, the following steps are taken to find the value of x in the expression:
Step 1: Distribute -2 to 5x and 8
10x + 16 = 14 + 6x
Step 2: Subtract both sides by 6x
-16x + 16 = 14
Step 3: Add both sides by 16
-16x = 30
Step 4: Divide both sides by -16
x = 30/-16
Simplify
x = -15/8
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Find the area of the shaded region in the figure below, if the diameter of the circle is 12 and the height of the rectangle is 11. Use 3.14 for pi and round to the nearest hundredth.
The area of the shaded region is 75.48 rounded to the nearest hundredth, considering the areas of the circle and rectangle
How to calculate for the area of the shaded regionWe have to first calculate for the area of the rectangle, and then calculate for the area of half the circle and then subtract it from the area of the rectangle to get the area of the shaded region.
Area of rectangle = Length × breadth
Area of rectangle = 12 × 11(diameter of the circle is also the length of the rectangle)
Area of rectangle = 132.
Area of circle = πr²
Area of the circle = 3.14 × 6² (6 is the radius given that the diameter = 12)
Area of the circle = 3.14 × 36
Area of the circle = 113.04
Half the area of the circle = 113.04/2
Half the area of the circle = 56.52
Area of the shaded region = 132 - 56.52
Area of the shaded region = 75.48
Therefore, by calculating for areas of the circle and rectangle, we are able to derive the area of the shaded region to be 75.48
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Use matrices A and B. compute B-a, if you can. A=[-5 4 -8 -2] B=[-2 7 -3 1 -6 0]
The subtraction of matrices B and A cannot be computed, as the matrices have different dimensions, hence we cannot calculate the matrix B - A.
How to subtract matrices?Matrices are subtracted subtracting the terms at the same position in each matrix.
Hence, two matrices can only be subtracted if they have the same dimensions.
Matrix A in this problem is defined as follows:
A = [-5 4]
[-8 -2]
Hence it's dimensions are 2 x 2, as it has 2 rows and 2 columns.
Matrix B in this problem is defined as follows:
B = [-2 7 -3]
[1 -6 0]
Hence it's dimensions are 2 x 3, as it has 2 rows and 3 columns.
The matrices A and B have different dimensions, a different number of columns in this case, and hence their subtraction cannot be computed.
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if you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long, how much string do you still have?
If you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long, Then 16.875 is the remaining string.
What is Fraction?A fraction represents a part of a whole.
1 foot =12 inches
2 foot=24 inches.
Given,
if you have a 2 foot piece of string and cut off and use a piece 4 3/4 inches long and a piece 2 3/8 inches long.
Then how much string do you still have
We have to subtract the used strings from 24 inches string.
4 3/4 inches=19/4
2 3/8 inches=19/8
Now we have to subtract 19/4 and 19/8 from 24 inches.
24-19/4-19/8
24-4.75-2.375
16.875
Hence 16.875 is the string left with us.
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Solve one sixth times quantity x plus 24 end quantity equals negative 6.
The value of one sixth times quantity x plus 24 end quantity equals negative 6 is -180.
Whet is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, the expression given will be illustrated as:
1/6x + 24 = -6
Collect like terms
x / 6 = -6 - 24
x/6 = -30
Cross multiply
x = -30 × 6
x = -180
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Answer:
Answer: (D) x= 12
Step-by-step explanation:
First you would distribute 1/6 into everything. 1/6 is equal to .16, so you can do that if you would like. you would get .16x + 4
Next, divide .16 on both sides. It should look like this
.16x/.16 + 4/.16.
Your answer should be x+ 25 = -6, or x = 12.
I hope this helps, as I could be wrong. Good luck!
P.S. The guy above me just put the question into AI and just copy pasted it. Not worrying if it was right or not.
Graph the absolute value equation that represents the given situation, d = 1/5|8-250| - 50.
-
Then mark the points that represent the horizontal distance from the left shore where the
river bottom is 20 feet below the surface.
For the given graph of absolute value equation d = (1/5)|s-250| -50 , the point that represents the horizontal distance from the given left shore when river bottom is 20 feet below the given surface is equal to 400 feet or 100 feet.
As given in the question,
Given absolute value equation is:
d = (1/5)|s-250| -50
Simplify it for the river bottom d =-20 feet below the given surface
-20 = (1/5)|s-250| -50
⇒-20(5) = | s- 250| - 250
⇒ 250 -100 = |s-250|
⇒ 150 = | s- 250|
⇒ s - 250 = 150 or s -250 = -150
⇒ s= 400 feet or s = 100 feet
Graph of the equation is attached.
Therefore, for the given graph of absolute value equation d = (1/5)|s-250| -50 , the point that represents the horizontal distance from the given left shore when river bottom is 20 feet below the given surface is equal to 400 feet or 100 feet.
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Think about
A model of a house was built using the scale 5 in:25 ft. If a window in the
model is 1.5 in. wide, how wide is the actual window?
If a window in the model is 1.5 in. wide, then the actual window is 7.5 feet wide.
What is meant by unit ratio?A two-term ratio expressed with a second term of one is referred to as a unit ratio. A unit ratio can be created from any ratio. Example. An illustration of a set of marbles is shown below. The set has eight blue marbles and two red marbles.
Having a denominator of 1, a unit rate is a ratio between two separate units. Divide the numerator by the denominator to obtain the unit rate. The unit rate is the decimal number that results. The price of a good or service is the numerator of a ratio called the unit price, and the quantity is the denominator.
Given,
The scale of the Model =5 in: 25 ft.
Dividing both sides by 5 we get,
[tex]\frac{5in}{5}[/tex] :[tex]\frac{25ft}{5}[/tex]
1 inch:5 feet
If a window on the model is 1.5 inch wide, then from the unit ratio we get,
1 inch × 1.5 : 5 feet × 1.5 feet
1.5 Inch : 7.5 feet
As a result, a window that is 1.5 inches wide in the model will actually be 7.5 feet wide.
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Watch help video
What is the discriminant of the quadratic equation-2a2- 5x+7=0?
0-81
O 81
0-31
O 31
Submit Answer
The discriminant of the quadratic equation -2x²-5x+7=0 is 81 units when formula of discriminant is (b²-4ac).
What is the discriminant of the quadratic equation?Keeping in mind that a, b, and c are the coefficients of your quadratic in standard form, the discriminant is calculated using the formula b squared minus 4ac. It reveals how many possible answers there are to a quadratic equation. There are two solutions if the discriminant is greater than zero. The square root's argument (i.e., its contents), which is the expression b²-4ac, is known as the "discriminant" because using its value, you can "discriminate" between (i.e., be able to distinguish between) the different solution types.
Here,
-2x²-5x+7=0
discriminant=(b²-4ac)
=(-5)²-(4*-2*7)
=25+56
=81 units
When the discriminant formula is (b²-4ac), the discriminant of the quadratic equation (-2x²-5x+7=0) is 81 units.
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h(x) = -4x + 2 x+7 3x - 5 x < -5 −5 < x < 5 x>5 Given the piecewise function shown, find the value of h(-6).
Answer:
answer in image
Step-by-step explanation:
Crane Company owns equipment that cost $78,000 when purchased on
January 1, 2019. It has been depreciated using the straight-line method
based on an estimated salvage value of $18,000 and an estimated useful lifeof 5 years.
Prepare Crane Company's journal entries to record the sale of the
equipment in these four independent situations. (Credit account titles areautomatically indented when amount is entered. Do not indent
manually. If no entry is required, select "No Entry" for the account
titles and enter O for the amounts.)
(a.) Sold for $44,000 on January 1, 2022.
(b.) Sold for $44,000 on May 1, 2022.
(c.) Sold for $20,000 on January 1, 2022.
(d.) Sold for $20.000 on October 1. 2022.
The journal entries to record the sale of the equipment by Crane Company are as follows:
a) Sold for $44,000 on January 1, 2022:
Debit Cash $44,000
Credit Sales of Equipment $44,000
Debit Sale of Equipment $78,000
Credit Equipment $78,000
Debit Accumulated Depreciation $36,000
Credit Sale of Equipment $36,000
Debit Sale of Equipment $2,000
Credit Profit from Sale of Equipment $2,000
b) Sold for $44,000 on May 1, 2022:
Debit Cash $44,000
Credit Sales of Equipment $44,000
Debit Sale of Equipment $78,000
Credit Equipment $78,000
Debit Accumulated Depreciation $40,000
Credit Sale of Equipment $40,000
Debit Sale of Equipment $6,000
Credit Profit from Sale of Equipment $6,000
c) Sold for $20,000 on January 1, 2022:
Debit Cash $20,000
Credit Sales of Equipment $20,000
Debit Sale of Equipment $78,000
Credit Equipment $78,000
Debit Accumulated Depreciation $36,000
Credit Sale of Equipment $36,000
Debit Loss from Sale of Equipment $22,000
Credit Sale of Equipment $22,000
d) Sold for $20.000 on October 1. 2022:
Debit Cash $20,000
Credit Sales of Equipment $20,000
Debit Sale of Equipment $78,000
Credit Equipment $78,000
Debit Accumulated Depreciation $45,000
Credit Sale of Equipment $45,000
Debit Loss from Sale of Equipment $13,000
Credit Sale of Equipment $13,000
Cost of equipment = $78,000
Salvage value = $18,000
Depreciable amount = $60,000 ($78,000 - $18,000)
Purchase date = January 1, 2019
Estimated useful life = 5 years
Annual depreciation expense = $12,000 ($60,000/5)
Sales Situations:a) Accumulated Depreciation to January 1, 2022 = $36,000 ($12,000 x 3)
Book value of equipment = $42,000 ($78,000 - $36,000)
Transaction Analysis:Cash $44,000 Sales of Equipment $44,000
Sale of Equipment $78,000 Equipment $78,000
Accumulated Depreciation $36,000 Sale of Equipment $36,000
Sale of Equipment $2,000 Profit from Sale of Equipment $2,000
b) Accumulated Depreciation to May 1, 2022 = $40,000 ($12,000 x 3.333)
Book value of equipment = $38,000 ($78,000 - $40,000)
Transaction Analysis:Cash $44,000 Sales of Equipment $44,000
Sale of Equipment $78,000 Equipment $78,000
Accumulated Depreciation $40,000 Sale of Equipment $40,000
Sale of Equipment $6,000 Profit from Sale of Equipment $6,000
c) Accumulated Depreciation to January 1, 2022 = $36,000 ($12,000 x 3)
Book value of equipment = $42,000 ($78,000 - $36,000)
Transaction Analysis:Cash $20,000 Sales of Equipment $20,000
Sale of Equipment $78,000 Equipment $78,000
Accumulated Depreciation $36,000 Sale of Equipment $36,000
Loss from Sale of Equipment $22,000 Sale of Equipment $22,000
d) Accumulated Depreciation to January 1, 2022 = $45,000 ($12,000 x 3.75)
Book value of equipment = $33,000 ($78,000 - $45,000)
Transaction Analysis:Cash $20,000 Sales of Equipment $20,000
Sale of Equipment $78,000 Equipment $78,000
Accumulated Depreciation $45,000 Sale of Equipment $45,000
Loss from Sale of Equipment $13,000 Sale of Equipment $13,000
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$
Amount Due at Maturity
6,000.00
Discount Rate
3.50%
1. Calculate the bank discount:
2. Calculate the proceeds:
Time
160
Ordinary Interest
360
Required:
Using the information above please answer the following:
Note: Use cells A2 to D3 from the given information to complete this question.
The bank discount is $93.33 and the proceeds are $5,906.67.
What is the discount?
Discount causes the product's selling price to drop, which increases its allure for the consumer. A price reduction has a psychological effect on the buyer, influencing them to make the purchase. The two types of discounts offered are trade discounts and cash discounts.
We have,
Amount Due at Maturity = $6,000
Discount rate = 3.5%
Time = 160 days
Bank Discount = $6,000*3.5%*160/360=$93.33
Proceeds = Maturity value - Bank Discount
= $6,000 - $93.33
= $5,906.67
Therefore, the bank discount is $93.33 and the proceeds are $5,906.67.
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Catherine needs to sell boxes of cookies as a fundraiser for a team. She starts with 135 boxes and begins selling at constant rate of
15 boxes each day.
Use the Segment tool to plot a graph representing the number of boxes of cookies Catherine has left to sell from the time she begins
selling until the cookies are gone.
Answer: The equation that represents this situation is y = -15x + 135
A linear equation is given by:
y = mx + b;
where y, x are variables, m is the rate of change and b is the y intercept.
Let y represent the amount of boxes remaining after x days.
She starts with 135 boxes, hence b = 135. She sells at a constant rate of 15 boxes each day, hence m = -15. The equation becomes:
y = -15x + 135
The first point should be plotted at (9,0) then the next at (0,135). Just plot multiples of 15 on the chart until you get to the 9th multiple
Step-by-step explanation:
A producer wishes to determine the equilibrium price and quantity of his good in the market. He estimated the market demand and supply function as follows demand :P=q^2+13/2q+64 and supply: P= 10q^2-45/2q-164
The equilibium price is 163.39 and the supply quantity is 150
He estimated the market demand and supply function as follows demand :P=q²+13/2q+64 and supply: P= 10q²-45/2q-164
We need to find the equilibium price
The equilibrium price (EP) is the price where the demand for a product or service balances its supply. .
At equilibium price
Demand function = supply function
q²+13/2q+64 = 10q²-45/2q-164
(10 - 1)q² - (45/2 + 13/2)q - (164 + 64) = 0
9q² - 29q - 228
q = 6.895 = 6.9
The equilibium price = 6.9² + (13/2)6.9 + 64
= 163.36
similarly putting the value of q in supply function we get supply quantity ie 149.95 = 150
Therefore, the equilibium price is 163.39 and the supply quantity is 149.95 = 150
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29. According to the weather reports, the probability of rain on a certain day is
70% in Yellow Falls and 50% in Copper Creek. What is the probability that it
will rain in both cities? State if Dependent or Independent
The probability that it will rain in both cities is 0.35. It is independent.
What is probability?Probability is the likelihood that a particular event will occur.
In this case, the probability of rain on a certain day is 70% in Yellow Falls and 50% in Copper Creek.
The probability that it will rain will be:
= P(Yellow Falls) × P(Copper Creek)
= 0.7 × 0.5
= 0.35
This is independent.
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Use the Distributive property to express 18+24
The distributive property allows the expression 18 + 24 to be expressed as 6(3 + 4).
What is a distributive property?Most algebraic structures that include two operations, addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields, are defined in terms of this fundamental feature of numbers. The distributive property of binary operations generalizes the equality-proclaiming distributive law in mathematics. One of the axioms for rings and fields is that of the distributive laws. Boolean algebras like the algebra of sets or the switching algebra are examples of structures with two operations that are each distributive over the other.
We do the following to express using the distributive property:
Find the biggest common factor between the numbers 18 and 24.
18 = 1, 2, 3, 6, 9, 18
24 = 1, 2, 3, 4, 6, 8, 12, 24
6 is the most common value between the numbers 18 and 24, making it the most common factor
The values should be divided by 6 and expressed in the form a(b + c):
b = 18 /6 = 3
c = 24 / 6 = 4
6(3 + 4)
Consequently, the necessary expression is 6(3 + 4).
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Let y = tan(3x + 8). Find the differential dy when x = 4 and dx = 0.1 cbc homepage Find the differential dy when x = 4 and dx = 0.2
The value of differential dy when x = 4 and dx = 0.2 is 0.68 .
In the question ,
it is given that ,
the equation is y = tan(3x + 8) ,
we need to find the differential dy , when x = 4 and dx = 0.2
So , differentiating y = tan(3x + 8) with respect to "x" ,
we get
dy/dx = sec²(3x + 8) *3
dy/dx = 3*sec²(3x + 8)
Substituting the values of x = 4 and dx = 0.2 ,
we get ,
dy/(0.2) = 3*sec²(3(4) + 8)
dy/0.2 = 3*sec²(20)
dy/0.2 = 3*1.1324
dy/0.2 = 3.3972
dy = 0.2 * 3.3972
dy = 0.67944
dy ≈ 0.68
Therefore , The value of differential dy when x = 4 and dx = 0.2 is 0.68 .
The given question is incomplete , the complete question is
Let y = tan(3x + 8). Find the differential dy when x = 4 and dx = 0.2 ?
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Alisha and Emily are making t-shirts for the Math team. they need a total of 21 shirts. Alisha has made 13 shirts and Emily made p shirts . Write a formula to model this
The formula to model the given situation is 13 + p = 21 .
In the question ,
it is given that ,
Alisha and Emily are making T- Shirts for the Math's team .
total number of T- Shirts required = 21 shirts .
number of shirts made by Alisha = 13 shirts
number of shirts made by Emily = p shirts
So , the equation that represents the given situation is
13 + p = 21
Solving further , we get
p = 21 - 13
p = 8
So , Emily made 8 T - Shirts .
Therefore , The formula to model the given situation is 13 + p = 21 .
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[tex]\sqrt{2x+3} = 5\\[/tex]
x= 11.
Step-by-step explanation:1. Write the expression.[tex]\sqrt{2x+3}=5[/tex]
2. Square both sides of the equation.[tex]\sqrt{2x+3} ^{2} =5^{2} \\ \\2x+3=25[/tex]
3. Subtract 3 from both sides of the equation.[tex]2x+3-3=25-3\\ \\2x=22[/tex]
4. Divide both sides by 2.[tex]\frac{2x}{2} =\frac{22}{2} \\ \\x=11[/tex]
5. Verify your answer.[tex]\sqrt{2(11)+3}=5\\ \\\sqrt{22+3}=5\\ \\\sqrt{25}=5\\ \\5=5.[/tex]
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A decagon has 10 sides. One angle of a regular decagon measures (8w + 17)°. Determine the value of w. Round to the nearest whole number. w = 144 w = 23 w = 16 w = 8
Answer:
I think the answer is 144
The value of w to the nearest whole number is 16°
What a regular polygon?If a polygon has equal sides and angles, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a square is a regular quadrilateral.
Given:
Decagon has 10 sides.
As, sum of interior angles of a polygon = ( n - 2) x 180
where n = number of sides of polygon
Here n = 10
sum of interior angle = ( 10 - 2) x 180 which is 1440°
If a regular polygon has equal angles and each angle is (8w + 17)
10( 8w + 17) = 1440
8w + 17 = 144
8w = 144 - 17
8w = 127
w = 127/8
w = 15.875
Thus, the value of w = 16°
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Nakeisha is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Nakeisha's songs were played on 2 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $760. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Nakeisha's songs were played. Define the variables that you use to write the system. Please help this is due tonight!!!
Solving a system of equations we will see that the song was used on 5 movies and 7 commercials
How to determine the numbers of commercials and movies?The variables we will use are:
x = number of commercial.y = number of movies.We know that:
x = y + 2
and:
x*$30 + y*$110 = $760
So the system of equations is:
x = y + 2
x*$30 + y*$110 = $760
Replacing the first equation in the second one:
(y + 2)*$30 + y*$110 = $760
$60 + y*$30 + y*$110 = $760
y*$140 = $760 - $60
y*$140 = $700
y = $700/$140 = 5
Then the value of x is:
x = y + 2 = 5 + 2 = 7
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