0.0002
The required probability can be calculated as follows:Explanation:There are 7 different songs from 7 different artists, thus there are 7! ways of shuffling these songs. In other words, there are 7! = 5040 different playlists in which these songs can be shuffled.We need to calculate the probability of Adam Rickitt's song being played first and Phil Collins' song being played second. This can be done in two steps.Step 1: We place Adam Rickitt's song at the beginning of the playlist. There is only one way to do this. After Adam Rickitt's song has been placed, we are left with 6 remaining songs that can be shuffled. Thus, there are 6! = 720 different playlists.Step 2: We place Phil Collins' song as the second song on the playlist. There is only one way to do this as well.Therefore, the probability that Adam Rickitt's song is played first and Phil Collins' song is played second is given by the product of the probabilities of the two steps as follows:P = 1/5040 × 1 = 1/5040 = 0.000198 rounded to 4 decimal places. Thus, the probability is approximately 0.0002. Therefore, the probability that the first song is by Adam Rickitt and the second song is by Phil Collins is 0.0002.
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Find the values of the variables and the measures of the indicated angles. (help)
Answer:
x = 30
Step-by-step explanation:
You want the measure of the acute angle where a tangent meets a chord that intercepts an arc of 300°.
Inscribed angleAn angle inscribed in a circle has half the measure of the arc it intercepts.
If one leg of that inscribed angle degenerates in length to zero, then the "inscribed" angle becomes the angle between the remaining chord and the tangent to one end of that chord.
In other words, the measure of the angle marked x° is half the measure of the arc it intercepts.
x° = 1/2(360° -300°) = 1/2(60°)
x° = 30°
The value of the variable x is 30.
Jam World Amusement Park sells special multi-day passes for guests who want to visit the park for more than one day. Their most popular passes are the 3-day pass, which costs $207, and the 7-day pass, which costs $364. How much more does the 3-day pass cost per day than the 7-day pass?
Answer: 17
Step-by-step explanation:
To find much each pass earns per day is to divide the two numbers. $207 divided by 3 is 69 and $364 divided by 7 is 52. Then you subtract 69 and 52 which is 17!
The Ratio of cargo cars to passenger cars in the rail yard is 9:15 if the total numbers of cars is 72 how many cargo cars are there
Answer:
27
Step-by-step explanation:
9+15=24
72/24=3 so 1=3 and there are 9 cargo cars so 9*3=27
you can also check by doing 3*15=45 and 45+27=72 so this is correct
Brookfield Street and Bloomington Avenue intersect. If Brookfield Street is 5 meters wide and Bloomington Avenue is 6 meters wide, what is the distance between two opposite corners of the intersection? If necessary, round to the nearest tenth.
Please respond
Thank you!
Answer:7.8
Step-by-step explanation:
[tex]\sqrt{6^2+5^2}[/tex]
evaluate the equation / expression
7.81025
Round 7.81025 to the required place
7.8
Answer:
7.8m
Step-by-step explanation:
To find:-
The distance between opposite corners of intersection.Answer:-
From the given data i made a figure to represent the given situation. To find the distance between the opposite corners we would have to use Pythagoras theorem, .
The distance between the corners represents the hypotenuse of the right angled triangle and another two sides are represented by 5m and 6m .
According to Pythagoras theorem,
[tex]\rm\implies a^2+b^2 = h^2 \\[/tex]
Here a is 5m and b is 6cm .
[tex]\rm\implies (5m)^3+(6m)^2 = h^2 \\[/tex]
[tex]\rm\implies 25m^2+36m^2=h^2\\[/tex]
[tex]\rm\implies 61m^2=h^2\\[/tex]
[tex]\rm\implies h =\sqrt{61m^2} \\[/tex]
[tex]\rm\implies \red{ h = 7.8 \ m } \\[/tex]
Hence the distance between the opposite corners is 7.8 m
Are all of the diagonals of a regular polygon congruent?
Yes, a regular polygon's diagonals are all congruent.
In geometry, a shape's diagonals are its building blocks. In mathematics, a diagonal is a line that connects two solids or polygons whose vertices are not next to one another's edges. In general, a diagonal connects the vertices of a form via sloping or slanting lines. Shapes with lateral sides, edges, and corners are referred to as "diagonals" in this context. Diagonals can be found in curved objects like circles, spheres, cones, and so on.
The diagonals of a square are the segments of lines joining its opposite vertices. A square is made up of two diagonals. The two diagonals of the square are parallel to one another. The diagonals of a square divide one another in half. Each diagonal divides the square into two identical, isosceles right triangles.
Yes all of the diagonal of a regular polygon is congruent , because all sides of regular shape are congurent.
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Martin is x years old. Jennifer is 3 years younger than Martin. Connor is twice as old as Martin. Write an expression for Jennifer’s age.
Answer: x-3
Step-by-step explanation: if Martin's age is unknown and we have to use x for it, you could only plug in x-3 to figure out Jennifer's age. And if we have to write an expression for Connor's age it would be x*2
martin = x years
jennifer = x - 3
Elizabeth is mountain climbing with Frank and has just climbed a 16-meter vertical rock face. Frank is standing 30 meters away from the bottom of the cliff, looking up at Elizabeth. How far away are Elizabeth and Frank?
The Pythagorean theorem
‘I’m just not sure which equation to use.”
Answer: 34
Step-by-step explanation:
based on the given conditions , formulate
[tex]\sqrt{16^2+30^2}[/tex]
x= [tex]\sqrt{(16)^2f(30)^2}[/tex]
x= [tex]\sqrt{256+900}[/tex]
x= [tex]\sqrt{11 56}[/tex]
x= 34
CD =1/2AB In quadrilateral ABCD above, AD || BC and CD =1/2AB. What is the measure of angle B? A) 150° B) 135° C) 120° D) 90°
In quadrilateral ABCD abοve, AD || BC and CD =1/2AB. the measure οf angle is B 90°
What is a quadrilateral?A quadrilateral is a clοsed shape and a type οf pοlygοn that has fοur sides, fοur vertices and fοur angles. It is fοrmed by jοining fοur nοn-cοllinear pοints. The sum οf interiοr angles οf quadrilaterals is always equal tο 360 degrees.
Since AD is parallel tο BC, we have:
∠ABC + ∠BCD = 180° (interiοr angles οn the same side οf the transversal AD)We alsο knοw that CD = 1/2AB. Let's call the length οf AB "x". Then we have:
CD = 1/2AB
CD = 1/2x
Nοw, let's lοοk at triangle BCD. We knοw that the sum οf the angles in a triangle is 180°, sο we have:
∠BCD + ∠CBD + ∠BDC = 180°
We alsο knοw that ∠BCD = ∠ABC (because they are cοrrespοnding angles), sο we can substitute ∠ABC fοr ∠BCD:
∠ABC + ∠CBD + ∠BDC = 180°
Nοw, let's use the fact that CD = 1/2x tο find the length οf BD:
BD = AB - CD
BD = x - 1/2x
BD = 1/2x
Sο, BD is half the length οf AB. This means that triangle BCD is a 30-60-90 triangle, with ∠CBD = 60° and ∠BDC = 30°.
Substituting these values intο οur equatiοn abοve, we get:
∠ABC + 60° + 30° = 180°
Simplifying, we get:
∠ABC + 90° = 180°
Subtracting 90° frοm bοth sides, we get:
∠ABC = 90°
Therefοre, the measure οf angle B is 90°.
D) 90°.
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7 1/4 x 2^2+(8 1/2-2) divided by 3
Answer:
Step-by-step explanation:
First, we need to simplify the expression inside the parentheses:
8 1/2 - 2 = 8 + 1/2 - 2 = 6 1/2
Next, we need to evaluate the exponent:
2^2 = 2 x 2 = 4
Now, we can substitute the simplified values into the expression:
7 1/4 x 4 + (6 1/2) ÷ 3
Next, we need to evaluate the multiplication and division from left to right:
7 1/4 x 4 = 29 + (6 1/2) ÷ 3
6 1/2 ÷ 3 = 2 1/6
Substituting the simplified value:
29 + 2 1/6
Next, we need to add the two values:
29 + 2 1/6 = 31 1/6
Therefore, the final answer is 31 1/6.
21. Calculating Cash Flows Consider the following abbreviated financial statements for
Weston Enterprises:
WESTON ENTERPRISES
2015 and 2014 Partial Balance Sheets
Assets Liabilities and Owners’ Equity
2015 2014 2015 2014
Current assets $1,176 $ 964 Current liabilities $ 445 $ 401
Net fixed assets 5,104 4,384 Long-term debt 2,713 2,380
WESTON ENTERPRISES
2015 Income Statement
Sales $14,740
Costs 5,932
Depreciation 1,190
Interest paid 328
a. What is owners’ equity for 2014 and 2015?
b. What is the change in net working capital for 2015?
c. In 2015, Weston Enterprises purchased $2,350 in new fixed assets. How much in
fixed assets did Weston Enterprises sell? What is the cash flow from assets for the
year? (The tax rate is 40 percent. )
d. During 2015, Weston Enterprises raised $455 in new long-term debt. How much
long-term debt must Weston Enterprises have paid off during the year? What is the
cash flow to creditors
a. The owners' equity increased from $1,567 in 2014 to $3,122 in 2015.
b. The change in net working capital for 2015 is $168.
c. The amount of fixed assets did Weston Enterprises sold is $1630
d. Weston Enterprises must have paid off $2,253 in long-term debt during the year
Now, let's move on to the questions.
a. To find the owners' equity for 2014 and 2015, we need to subtract the total liabilities from the total assets. For 2014, the calculation would be,
Owners' equity 2014 = Total assets 2014 - Total liabilities 2014
Owners' equity 2014 = (Current assets 2014 + Net fixed assets 2014) - (Current liabilities 2014 + Long-term debt 2014)
Owners' equity 2014 = (964 + 4,384) - (401 + 2,380)
Owners' equity 2014 = $1,567
For 2015, the calculation would be:
Owners' equity 2015 = Total assets 2015 - Total liabilities 2015
Owners' equity 2015 = (Current assets 2015 + Net fixed assets 2015) - (Current liabilities 2015 + Long-term debt 2015)
Owners' equity 2015 = (1,176 + 5,104) - (445 + 2,713)
Owners' equity 2015 = $3,122
b. The change in net working capital for 2015 can be calculated by subtracting the net working capital for 2014 from the net working capital for 2015. Net working capital is the difference between current assets and current liabilities.
Net working capital 2014 = Current assets 2014 - Current liabilities 2014
Net working capital 2014 = 964 - 401
Net working capital 2014 = $563
Net working capital 2015 = Current assets 2015 - Current liabilities 2015
Net working capital 2015 = 1,176 - 445
Net working capital 2015 = $731
Change in net working capital = Net working capital 2015 - Net working capital 2014
Change in net working capital = 731 - 563
Change in net working capital = $168
c. To find out how much in fixed assets Weston Enterprises sold, we need to use the equation for the cash flow from assets,
Cash flow from assets = Cash flow to creditors + Cash flow to owners
Cash flow from assets = (Interest paid - Net new long-term debt) x (1 - Tax rate) + (Depreciation x Tax rate)
Cash flow from assets = (328 - (2,713 - 2,380)) x (1 - 0.4) + (1,190 x 0.4)
Cash flow from assets = (-$57) + $476
Cash flow from assets = $419
Net increase in fixed assets = Net fixed assets 2015 - Net fixed assets 2014
Net increase in fixed assets = 5,104 - 4,384
Net increase in fixed assets = $720
Amount of fixed assets sold = Net increase in fixed assets - New fixed assets purchased
Amount of fixed assets sold = $2,350 - $720
Amount of fixed assets sold = $1,630
d. To calculate the amount of long-term debt paid off during the year, we need to use the equation for the cash flow to creditors,
Cash flow to creditors = Interest paid - Net new long-term debt
Cash flow to creditors = $328 - ($455 - $2,380)
Cash flow to creditors = $2,253
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what is the rate at which a car's value will decrease as its mileage goes up between 20,000 miles and 40,000 miles?
y=value of car
x=mileage
The car's value will decrease at rate of 1/5.
What is the rate at which a car's value will decrease?
Rate refers to the ratio between two quantities with different units. For example, if you travel 100 miles in 2 hours, your rate of speed would be 50 miles per hour (mph).
From the graph, we have the following:
1: At mileage (x) = 20,000 miles, value of car (y) = $12000
2: At mileage (x) = 40,000 miles, value of car (y) = $8000
Rate = (y2 - y1)/(x2 - x1)
Rate = (8000 - 12000)/(40000 - 20000)
Rate = -1/5
Thus, the car's value will decrease at rate of 1/5.
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Complete Question
Check attached image
Please help! Parallel lines with Parallel Sequences question! Thanks
Given the above parallelogram,
1) ∠ABC = 90°
2) ∠BCD = 90°
3) ∠CDA = 90°
4) ∠DAB = 90°
To find the value of the angles, we need to first find x. Given that ∠ABC = (x+35)° on the basis of opposite angles in a parallelogram, and
∠CDA = (180-(3x-75)°
since ∠ABC and ∠CDA are opposite angles.
We can state that
(180-(3x-75)° = (x+35)° since opposite sides of a parallelogram are equal.
Simplifying the above, we can find x:
180 - (3x - 75) = 180 - 3x + 75 = 255 - 3x
Now we can substitute this expression into the original equation:
255 - 3x = x + 35
To solve for x, we want to isolate the variable on one side of the equation. Let's start by adding 3x to both sides:
255 = 4x + 35
Next, we can subtract 35 from both sides:
220 = 4x
Finally, we can divide both sides by 4 to get the value of x:
x = 55
Therefore, the solution to the equation is x = 55°.
Since x = 55°
∠ABC = (x+35)°
∠ABC = 55 + 35
∠ABC = 90°
Also, since:
∠CDA = (180-(3x-75)°)
∠CDA = 180- (165-75)
∠CDA = 90°
Since ∠DAB = (3x-75)° on the basis of alternate angles,
∠DAB = (3(55) -75)°
∠DAB = 165 -75
∠DAB = 90°
Since ∠DAB is opposite ∠BCD and Opposite angles of a parallelogram are equal, thus, ∠BCD is also 90°
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One card is drawn from a standard deck of 52 playing cards. Find the probability of each of the following events: 1. A spade is drawn. 2. A seven is drawn. 3. A spade or heart is drawn. 4. A black jack is drawn.
1. 25%
2. 7.69%
3. 50%
4. 0.46%
1. The probability of drawing a spade is 1/4, or 25%.
2. The probability of drawing a seven is 4/52, or 7.69%.
3. The probability of drawing a spade or heart is 1/2, or 50%.
4. The probability of drawing a black jack is 1/216, or 0.46%.
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If $87,495 is borrowed for 7 years at an annual simple interest
rate of 8.355%, what is the total amount that must be repaid?
Enter the answer in dollars and cents, and round to the nearest
cent, if needed. Do not include the dollar sign. For example, if
the answer is $0.61, only the number 0.61 should be entered.
The total amount that must be repaid is $139,076.12.
What is Annual Simple Interest?Annual simple interest is a type of interest that is calculated on the principal amount of a loan or investment for a one-year period. Simple interest is a fixed percentage of the principal amount, which is added to the principal at regular intervals. The interest is calculated only on the original principal amount and does not include any interest earned on the interest itself.
What is Compound interest?Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment, but also on the interest earned on that principal amount over time. In other words, compound interest is interest that is added to the principal amount, and then interest is calculated on the new total amount (principal + interest). This process is repeated at regular intervals, such as monthly or annually.
In the given question, The total amount that must be repaid can be found using the simple interest formula:
I = Prt
Where:
P = principal amount borrowed = $87,495
r = annual interest rate = 8.355%
t = time period in years = 7
So, substituting the values we get:
I = 87,495 * 0.08355 * 7 = 51,581.12
Therefore, the total amount that must be repaid is:
87,495 + 51,581.12 = 139,076.12
Rounding to the nearest cent, the answer is $139,076.12.
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The first number in a pattern is 1.95.
Each number in the pattern is formed by subtracting 0.15 from the previous number.
What is the third number in this pattern?
1.5 1.65 1.8 2.25
Answer:
1.65
Step-by-step explanation:
The first number is 1.95, to find the rest we must keep subtracting 0.15 from the previous.
1.95-0.15 = 1.8 (second number)
1.8-0.15 = 1.65 (third number)
Above, we find our answer with the 3rd number.
ASAP. Will give you the brainliest answer!!! Please show working out.
Answer:
1250 pigs------------------------------
Find the area using formula:
[tex]A=(b_1+b_2)h/2[/tex]Substitute values into formula to get:
[tex]A=(12*5^3+8*5^3)(2*5^3)/2=(20*5^3)(2*5^3)/2= (10*5^3)(2*5^3)[/tex]Since each pig gets 2*5³ m² of land, by dividing the area by this number, Daniel can put:
10*5³ = 10*125 = 1250 pigs in the field-9>2x what best describes the soltuion to this inequality
The correct option is D. Inequality. The expression -9 > 2x is an inequality, meaning it shows a relationship between two values that are not necessarily equal.
In this case, it indicates that -9 is greater than 2 times x. To solve the inequality, we would need to isolate x on one side of the inequality symbol. We can start by dividing both sides by 2, which gives us -4.5 > x. This means that any value of x that is less than -4.5 would satisfy the inequality. Therefore, the solution set for this inequality is all real numbers less than -4.5.
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Full question:
Which word BEST describes 9(2x+6y)
A Constant
B. Equation
c. Expression
D. Inequality
Write an equation in point-slope form of the line that passes through the point (2,−8) and has a slope of 4.
Answer:
y = 4x + -8
hope this helps <3
Please answer the both questions in the photos below ( will mark brainliest if available + 30p )
The classification of the system of linear equations 4x + y = 4 and y = -4x + 4 is: consistent and independent. The Option B is correct.
Why is the equation's classification consistent independent?We have a consistent independent equation when a system of linear equations has exactly one solution. When this occurs, the graphs of the system's lines cross at exactly one point.
For our question, we can start by rearranging the first equation to isolate y:
[tex]4x + y = 4\\y = -4x + 4[/tex]
We can see that the second equation is already in the form y = mx + b, where m is the slope and b is the y-intercept. So we can identify that the slope of the second equation is -4 and the y-intercept is 4.
Now we can compare the slopes and y-intercepts of the two equations to determine the classification of the system of equations:
If the slopes are the same and the y-intercepts are different, the system is inconsistent and there is no solution.If the slopes are different, the system is consistent and there is a unique solution.If the slopes are the same and the y-intercepts are the same, the system is consistent and there are infinitely many solutions.In this case, we can see that the slopes of the two equations are different (-4 and 0) and the y-intercepts are the same (4). Therefore, the system is consistent and there is a unique solution. So the classification of the system of linear equations 4x + y = 4 and y = -4x + 4 is: consistent and independent
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A grocery store charges $14 for 20 pounds of bananas. Write an equation that gives the cost, C, of x pounds of bananas
This equation tells us that the cost of x pounds of bananas is equal to the number of pounds of bananas, x, multiplied by the cost per pound
So equation becomes C = 0.70x
We can use proportional reasoning to set up an equation to represent the cost, C, of x pounds of bananas.
We know that 20 pounds of bananas cost 14, so the cost per pound can be found by dividing the total cost by the total weight:
Cost per pound = Total cost / Total weight
Cost per pound = 14 / 20 pounds
Cost per pound = 0.70 per pound
Now, we can use this cost per pound to set up an equation:
C = cost of x pounds of bananas
x = number of pounds of bananas
Cost per pound = 0.70
So, we can write the equation as:
C = 0.70x
This equation tells us that the cost of x pounds of bananas is equal to the number of pounds of bananas, x, multiplied by the cost per pound, 0.70.
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Write the equation to solve for x and find x.
-A
4x + 23
78° 78°
Equation=
X=
10x-1
Given that two of the angles in this triangle are equal and have a measure of 78 degrees and sides 4x + 23, 10x-1 the solution x = -1.15 is a valid solution.
What is the inequality equation?
A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.
In a triangle, the sum of the measures of the angles is always 180 degrees. Since we are given that two of the angles in this triangle are equal and have a measure of 78 degrees each, the third angle must have a measure of:
180 - 78 - 78 = 24 degrees
Now we can use the Law of Cosines to set up an equation to solve for x. The Law of Cosines states that:
c² = a² + b² - 2abcos(C)
where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.
We can choose any of the sides to be the side opposite the 24-degree angle, but let's use side 2, which has a length of 10x - 1. Then we have:
(10x - 1)² = (4x + 23)² + (side 3)² - 2(side 3)(4x + 23)cos(78)
Simplifying and solving for side 3, we get:
(side 3)² = (10x - 1)² - (4x + 23)² + 2(10x - 1)(4x + 23)cos(78)
(side 3)² = 36x² + 360x + 840
Taking the square root of both sides, we get:
side 3 = √(36x² + 360x + 840)
Now we can use the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we have:
side 1 + side 2 > side 3
4x + 23 + 10x - 1 > √(36x² + 360x + 840)
14x + 22 > √(36x² + 360x + 840)
Squaring both sides, we get:
196x² + 616x + 484 > 36x² + 360x + 840
Simplifying and rearranging, we get:
160x² + 256x - 356 < 0
We can solve this inequality using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 160, b = 256, and c = -356.
Plugging in these values, we get:
x = (-256 ± √(256² - 4(160)(-356))) / 2(160)
x = (-256 ± √(124160)) / 320
x = (-256 ± 352) / 320
x = 0.30 or x = -1.15
However, we need to check that these values satisfy the inequality we found earlier:
14x + 22 > √(36x² + 360x + 840)
For x = 0.30, we get:
14(0.30) + 22 > √(36(0.30)² + 360(0.30) + 840)
25.2 > 25.2
This is not true, so x = 0.30 does not work.
For x = -1.15, we get:
14(-1.15) + 22 > √(36(-1.15)² + 360(-1.15) + 840)
3.3 > 3.3
This is true, so x = -1.15 is a valid solution.
Therefore, the solution x = -1.15 is a valid solution.
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The scatter plot shows the average monthly temperature, , and a family's monthly heating cost, , for different months.
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.
(b) Using your equation from part (a), predict the monthly heating cost for a month with an average temperature of .
Note that you can use the graphing tools to help you approximate the line.
y102030405060708090100x1020304050607080901000
(a) Write an approximate equation of the line of best fit.
(b) Using your equation from part (a), predict the monthly heating cost for a month with an average temperature of .
Answer:
need brainly point
Step-by-step explanation:
I need to find if it's a solution or not
Based on the information, we can infer that the graph would be as shown in the attached image.
How to graph the equations?To graph the equations we must identify the values of the coordinates of each of the equations. In this case it would be:
Equation 1:
(-2.5), (0.2), (2,-1), (4, -4.75).Equation 2:
(-6.0), (-4, -0.75), (-2, -1.25), (0, -2).According to the above, the lines would look as shown in the graph. In the case of the first equation, it would be represented by the red line and the second equation would be represented by the blue line.
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niesa has a texting plan for her phone that charged her a fixed $20 fee each month and then a charge of $0.08 each text that she sends. Last month she spent $53.84 for the plan
Niesa sent apprοximately 423 texts last mοnth.
What is equatiοn ?In mathematics, an equatiοn is a fοrmula that expresses the equality οf twο expressiοns, by cοnnecting them with the equals sign =.
The wοrd equatiοn and its cοgnates in οther languages may have subtly different meanings; fοr example, in French an équatiοn is defined as cοntaining οne οr mοre variables, while in English, any well-fοrmed fοrmula cοnsisting οf twο expressiοns related with an equals sign is an equatiοn.
Let T be the number οf texts that Niesa sent last mοnth.
We can set up the equatiοn:
Tοtal cοst = fixed fee + (cοst per text x number οf texts)
$53.84 = $20 + ($0.08 x T)
Sοlving fοr T, we can subtract $20 frοm bοth sides:
$33.84 = $0.08 x T
Then, we can divide bοth sides by $0.08:
T = $33.84 / $0.08
T ≈ 423
Therefοre, Niesa sent apprοximately 423 texts last mοnth.
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This is for highschool geometry
Answer:
i dont
Step-by-step explanation:
never mind sorry for bothering you! :(
12. Find the work done in moving an object 30 feet horizontally if pulled with a force of 70 pounds with an angle of elevation of 30 degrees.
The work done in moving an object 30 feet horizontally if pulled with a force of 70 pounds with an angle of elevation of 30 degrees is $1582.07\text{ ft-lbs}$.
Given that an object is moved 30 feet horizontally if pulled with a force of 70 pounds with an angle of elevation of 30 degrees.To find the work done in moving an object, we know thatWork done = Force * Distance * cos(θ)Where θ is the angle between the force applied and the displacement of the object.Here, force applied = 70 poundsDistance = 30 feetAnd θ = 30 degreesWe know that the force is applied at an angle of 30 degrees to the horizontal, thus the horizontal component of the force is given by:Horizontal component of force = Force × cos (θ)So, the horizontal component of the force applied is:Horizontal component of force = 70 cos 30°= 60.62 pounds (approx)Therefore, the work done in moving the object 30 feet horizontally is:Work done = force × distance × cos (θ)= 60.62 × 30 × cos 0.5= 60.62 × 30 × 0.87= $1582.07 \text{ ft-lbs}$Therefore, the work done in moving an object 30 feet horizontally if pulled with a force of 70 pounds with an angle of elevation of 30 degrees is $1582.07\text{ ft-lbs}$.
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What is the value of x?
The value of x in the triangle is 2√3
What are right trianglesRight triangles are triangles with one angle measuring 90 degrees.
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
The triangle
From the triangle, we have the following equation
x/2 = 6/x
Cross multiiply the equation
So, we have the following representation
x^2 = 12
Take the square roots of both sides
So, the equation becomes
x = 2√3
Hence, the value of x is 2√3
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Jacob is putting carpet in his house. He wants to carpet the living room, which measures 15 ft x 12 1/3 ft. He also wants to carpet the dining room, which is 10 1/4 ft x 10 1/3 ft
Jacob needs 290.92 ft² of carpet in total to cover both the living room and the dining room.
To find out how much carpet Jacob needs to cover his living room, we can multiply the length and width of the room:
15 ft x 12 1/3 ft = 15 ft x (37/3) ft = 555/3 ft²
To simplify this fraction, we can divide both the numerator and denominator by 3:
555/3 ft² = 185 ft²
So the living room requires 185 square feet of carpet.
To find out how much carpet Jacob needs to cover his dining room, we can multiply the length and width of that room:
10 1/4 ft x 10 1/3 ft = (41/4) ft x (31/3) ft = 1271/12 ft²
To simplify this fraction, we can divide both the numerator and denominator by 1:
1271/12 ft² = 105.92 ft² (rounded to two decimal places)
So the dining room requires 105.92 square feet of carpet.
To find out how much carpet Jacob needs in total, we can add the amount of carpet required for each room:
185 ft² + 105.92 ft² = 290.92 ft²
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fsA glass contains 320 cm³ of apple juice. The mass of the juice is 350 g. Calculate the density of the juice in kilograms per cubic metre (kg/m³). Give your answer to the nearest integer.
The density of the apple juice is approximately 1094 kg/m³.
What is the density of the juice?Density is expressed mathematically as;
p = m / v
Where m is mass and v is volume.
Given that;
Volume of apple juice v = 320 cm³Mass m = 350 gDensity p = ?To calculate the density of the apple juice in kilograms per cubic metre (kg/m³), we need to convert the volume from cubic centimeters (cm³) to cubic meters (m³) and the mass from grams to kilograms.
1 cm³ = (1/100)^3 m³ = 10^-6 m³ (conversion factor from cm³ to m³)
1 g = (1/1000) kg (conversion factor from g to kg)
So, the volume of the apple juice in cubic meters is:
320 cm³ × (10^-6 m³/cm³) = 0.00032 m³
And the mass of the apple juice in kilograms is:
350 g × (1/1000) kg/g = 0.35 kg
Now, we can calculate the density using the above formula:
p = m / v
p = 0.35 kg / 0.00032 m³
p = 1093.75 kg/m³
p = 1094 kg/m³
Therefore, the density is 1094 kg/m³.
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Set up a system of equations and then solve using inverse matrics.
A manufacturer of portable tools has three sets, Basic, Homeowner, and Pro, which must be painted, assembled, and packaged for shipping. The following table gives the number of hours required for each operation for each set.
Basic Homeowner Pro
Painting 1. 4 1. 7 3
Assembly 1 1. 5 1. 6
Packaging 1 1 1. 4
If the manufacturer has 75. 7 hours for painting per day, 57. 9 hours for assembly per day, and 46. 6 hours for packaging per day. How many sets of each type can be produced each day?
The manufacturer can produce
Basic sets,
Homeowner sets and
Pro sets per day
The system of equations for this problem is:
Basic: 1x + 1.5y + z = 75.7
Homeowner: 4x + 1.7y + 1.6z = 57.9
Pro: 3x + 1.5y + 1.4z = 46.6
To solve this problem using inverse matrices, we first need to create the matrices of coefficients and constants:
Coefficient Matrix:
[[1, 1.5, 1],
[4, 1.7, 1.6],
[3, 1.5, 1.4]]
Constant Matrix:
[[75.7],
[57.9],
[46.6]]
Next, we can use inverse matrices to find the solution:
Inverse of Coefficient Matrix =
[[-9.38, 7.81, 3.2],
[4.69, -3.81, -1.6],
[3.46, -2.81, -0.8]]
Solution =
[[-9.38*75.7 + 7.81*57.9 + 3.2*46.6],
[4.69*75.7 - 3.81*57.9 - 1.6*46.6],
[3.46*75.7 - 2.81*57.9 - 0.8*46.6]]
Therefore, the manufacturer can produce
Basic sets,
Homeowner sets and
Pro sets per day
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