Using strategy 1 (in your head), divide 60m by 10m to get 6, then multiply that number by one to get 6cm. the length on drawing is 6cm
Procedure 2 (proportions)
Create a proportion first.
We know that 1 cm equals 10 metres, so we place them on a fraction (the operation is unaffected by the denominator or numerator). However, we don't know how many cm equal 10m, so we make that into a variable, in this case x.
1cm x cm
——— ———
100m 60m
Go diagonally to where the variables have already been put in to solve a proportion. You are unable to calculate 60 metres and x centimetres because you are unsure of x. Yet you can travel 60m. Start by multiplying 1 by 30 to reach the number 60. The result of multiplying 60 by 10m is x. This will equal 6.
Thus, your response is 6.
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Tamara earns her living as a salary plus commission employee. Her annual salary is $48,000, and she earns 4% commission on all sales she makes. If Tamara wants to make a total of $6,000 this month, how much in sales does she need to have?
a.
$30,000
b.
$50,000
c.
$100,000
d.
$150,000
Please select the best answer from the choices provided
A
B
C
D
Answer:
B. $50,000
Explanation:
4%=.04
50,000 x .04=2000
48000/12=4000
She makes $4000 off of her salary each month. Then because she only gets 4% of her commissions you multiply the 50000 by .04 and you get 2000. So she gets $2000 in commissions and $4000 off of her salary.
5 less than a qoutient of a number and 3
Answer:
The solution to the equation is -7
Step-by-step explanation:
I hate these kinds of Questions but it all comes down to how you mathematically interpret it.
During a thunderstorm at a sports event, a detector goes off to let participants know there is lightning in the area so people can seek shelter. The accuracy of the lightning detector is summarized in the table.
Lightning detector activates Lightning detector does not activate Row Totals
Lightning in area 88% 2% 90%
No lightning in area 7% 3% 10%
Column Totals 95% 5% 100%
What is the ratio of false positives to false negatives in this scenario? Round your answer to one decimal place.
0.1
1.5
2.3
3.5
The ratio of false positives to false negatives in this scenario is 3.5.
3.5 is the correct answer. False positives are lightning detector activations when there is no lightning in the area. False negatives are lightning detector not activations when there is lightning in the area. To calculate the ratio of false positives to false negatives, divide the false positives (7%) by the false negatives (2%). 7/2 = 3.5. Therefore, the ratio of false positives to false negatives in this scenario is 3.5.
The ratio of false positives to false negatives in this scenario is 3.5.
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Answer:
i took the test :)
Step-by-step explanation:
3.5
if the cost of 2 tables and 3 chairs is rs 3200 and the cost of 10 chairs and 4 tables is the same, what will be the cost of 5 tables and 6 chairs
The cost of 5 tables and 6 chairs would be Rs. 1200.
Algebraic problemLet the cost of one table be x and the cost of one chair be y.
From the given information, we have the following two equations:
2x + 3y = 3200 ... equation (1)
4x + 10y = 3200 ... equation (2)
To solve for x and y, we can multiply equation (1) by 2 and subtract it from equation (2) to eliminate x:
4x + 10y = 3200
(4x + 6y = 6400)
4y = -3200
Solving for y, we get:
y = -800
Substituting y = -800 into equation (1), we get:
2x + 3(-800) = 3200
Simplifying and solving for x, we get:
2x - 2400 = 0
2x = 2400
x = 1200
Therefore, the cost of one table is Rs. 1200, and the cost of one chair is Rs. -800 (which means the cost of one chair is Rs. 800 with a negative sign indicating a decrease from the original cost of Rs. 1200).
To find the cost of 5 tables and 6 chairs, we can simply multiply the cost of one table by 5 and the cost of one chair by 6 and add them:
Cost of 5 tables = 5 * Rs. 1200 = Rs. 6000
Cost of 6 chairs = 6 * Rs. (-800) = Rs. -4800 (or Rs. 4800 with a negative sign indicating a decrease from the original cost of Rs. 800)
Total cost = Rs. 6000 + Rs. (-4800) = Rs. 1200
Therefore, the cost of 5 tables and 6 chairs is Rs. 1200.
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Paul gets $5 every week for doing his chores. He is saving his money to buy a skateboard that costs $85. He has already saved $25.
Which equation describes the number of weeks (w) that it will take Paul to save enough money to buy the skateboard?
Let x be the number of weeks it will take Paul to save enough money to buy the skateboard.
In one week, Paul earns $5, so in x weeks he will earn 5x dollars.
Since he already has $25 saved, the total amount of money he will have after x weeks is:
5x + 25
To be able to buy the skateboard that costs $85, Paul needs to save up an additional:
85 - 25 = 60
Therefore, we can set up the following equation to find the number of weeks it will take Paul to save up enough money:
5x + 25 = 60
Simplifying and solving for x:
5x = 35
x = 7
Therefore, it will take Paul 7 weeks to save up enough money to buy the skateboard.
The equation that describes the number of weeks (w) that it will take Paul to save enough money to buy the skateboard is:
5w + 25 = 85
Alex's porch has a length and width of 12 feet each. He wants to paint the porch with a
water sealant that costs $35 per square foot. However, his wife wants him to change
the length of the porch to 14 feet. What would the difference in cost of applying sealant
be if Alex does extend his porch length?
Answer: $1820
Step-by-step explanation:
Area = Length*Width
Forst we have to solve for the area.
A = 12 * 12
A = 144 ft^2
Next we have to multiply be the cost per square foot.
144 * 35
= $5040
Solve for the area.
A = 14 * 14
A = 196 ft^2
Multiply by the cost per square foot.
196 * 35
= $6860
Lastly subtract both costs:
6860 - 5040 = 1820
Therefore the difference in cost would be $1820.
Hope this helps :)
calculate (5)^-2+3 giving your answers to two decimal places
Answer: 3.04
Step-by-step explanation:
3.04
Identify the area of a regular pentagon with side length 21
in.
rounded to the nearest tenth.
The area of regular pentagon is 758.7 square in.(rounded to the nearest tenth.)
What is pentagon?A pentagon is a specific type of polygon with 5 sides and 5 angles. The word “pentagon” is constructed of two words, namely Penta and Gonia, which defines five angles. So in a simplified way it can be said that pentagon is a polygon having 5 sides.
Here is a regular pentagon with side length 21 in.
Area of regular pentagon (A)= [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} a^{2}[/tex]
Here a= 21 in
So Area = [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} (21)^{2}[/tex] square in.
= [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} 441[/tex] "
≈758.73053 square in
= 758.7 square in. ( rounded to the nearest tenth).
Hence the area of regular pentagon is 758.7 square in.
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The area of a rectangle is given by the function A(x) = 2x3 + 6x2 + 5x + 15. If the length is defined by x + 3, what is the width of the rectangle?
2x3 + 6x2 + 4x + 12
2x3 + 6x2 + 6x + 18
2x2 + 6x + 5
2x2 + 5
The width of the rectangle is given by the expression 2x² + 5. Then the correct option is D.
Given that:
Area, A(x) = 2x³ + 6x² + 5x + 15
Length, L = x + 3
The formula for the area of a rectangle is:
A = length x width
A(x) = (x + 3) · W
A(x) / (x + 3) = W
W = (2x³ + 6x² + 5x + 15) / (x + 3)
W = [2x²(x + 3) + 5x(x + 3)] / (x + 3)
W = [(2x² + 5)(x + 3)] / (x + 3)
W = 2x² + 5
Therefore, the width of the rectangle is given by the expression 2x² + 5. Then the correct option is D.
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Write the equation of a line perpendicular to y = x - 5 and passing through the point (-3,9).
1. y = -x + 6
2. y = -x + 9
3. y = -x + 12
4. y = x + 12
The equation of line perpendicular to y=x-5 passing through (-3,9) is y=-x+6.
What is a perpendicular line?Two distinct lines intersecting each other at 90 degrees or at a right angle are called perpendicular lines
Equation:To find the equation of a line perpendicular to y = x - 5, we need to first determine the slope of the original line. The slope of a line in slope-intercept form (y = mx + b) is the coefficient of x, so in this case, the slope of the original line is 1.
Since we want to find the equation of a line perpendicular to this line, we need to find the negative reciprocal of the slope, which is -1.
So, the slope of the perpendicular line is -1, and we also know that it passes through the point (-3,9).
We can use the point-slope form of a line to write the equation of the perpendicular line:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope of the line.
Substituting the values we know, we get:
y - 9 = -1(x - (-3))
Simplifying this expression, we get:
y - 9 = -x - 3
Adding 9 to both sides, we get:
y = -x + 6
Therefore, the equation of the line perpendicular to y = x - 5 and passing through the point (-3,9) is:
y = -x + 6
So the answer is option 1: y = -x + 6.
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someone help me with this
The gallons of gas that Aubrey would need to travel 111.54 miles is 7.8 gallons.
What is a direct proportion?In Mathematics, a direct proportion simply refers to a mathematical equation which is typically used to represent the equality of two (2) ratios.
By applying direct proportion to the given information, we have the following mathematical equation:
15 gallons of gasoline = 214.5 miles
X gallons of gasoline = 111.54 miles
By cross-multiplying, we have the following:
214.5x = 15 × 111.54
x = 1,673.1/214.5
x = 7.8 gallons of gasoline.
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Find the square of: 5i√3
Answer: We have:
(5i√3)² = (5i)²(√3)² = -25(3) = -75
Therefore, the square of 5i√3 is -75.
Step-by-step explanation:
The square of the complex number of 5i√3 is 75.
What is a complex number?A complex number is the sum of a real number and an imaginary number.
To find the square of the complex number, 5i√3, we use the following Steps below
Step1: Square the expression
(5i√3)²Step 2: use the law of surd to seperate each of the terms in the expression
[(5i)²(√3)²]Note: In complex number notation,
i×i = 1Therefore,
25(3)75Hence, square of 5i√3 is 75
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Please help to complete this chart pleaseeeeeee
The completed chart for a one-time investment made in the amount of $9,200 is attached below.
How to calculate interest rate and compounding periods?For Annually compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.06)¹⁵
A = $9,200 (1.06)¹⁵
A = $22,048.34
For Semi-Annually compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.03)³⁰
A = $9,200 (1.03)³⁰
A = $21,214.29
For Quarterly compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.015)⁶⁰
A = $9,200 (1.015)⁶⁰
A = $20,947.34
For Monthly compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.005)¹⁸⁰
A = $9,200 (1.005)¹⁸⁰
A = $20,812.09
For Weekly compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.0012)⁷⁸⁰
A = $9,200 (1.0012)⁷⁸⁰
A = $20,756.54
For Daily compounded interest:
A = P (1 + i)ⁿ
A = $9,200 (1 + 0.0002)⁵⁴⁷⁵
A = $9,200 (1.0002)⁵⁴⁷⁵
A = $20,726.55
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Image transcribed:
1. Fill in the chart for the following investment.
A one-time investment is made in the amount of $9,200 for 15 years at an APR of 6%.
Compound Interest: A = P (1 + i)", where A is the final amount, P is the principal invested, i is the interest rate per compounding period, and n is the number of compounding periods.
Which angle(s) below is/are supplementary?
A. X and Y
B. Z
C. V
D. W and U
Answer:
Only Z
Step-by-step explanation:
Supplementary angles are angles whose sum up to 180 degrees.
What is the hundredth digit of pi? This would include the 3 in the beginning.
the two plates of a capacitor hold 2500 μc and –2500 μc of charge, respectively, when the potential difference is 960 v. what is the capacitance?
2.6 * 10⁻⁶ F is the capacitance.
What is a capacitor short answer?
A capacitor is a component used in electrical circuits to hold charges. The idea behind how a capacitor functions is that when an earthed conductor is moved close to a conductor, its capacitance increases noticeably.
As a result, a capacitor contains two plates with equal and opposing charges that are spaced apart. Two conductors that are near to one another and are isolated from one another make up a capacitor, a device for storing electrical energy. The parallel-plate capacitor is a straightforward illustration of such a storage device.
We have realtion Q=CV
where Q is charge , C is capacitance and V is voltage.
C=Q/V
C=(2500 * 10⁻⁶)/960
C= 2.6 * 10⁻⁶ F
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please help with this question! thank you :))
Answer:
2x
Step-by-step explanation:
it is x+x or 2x, since if x>=0, the absolute value of x is just x, then we can say that it is x+x without the absolute value symbols. :)
If the vertex of the function is at the. 0, 0. 5 what is the recommended amount of mulch for a flower bed with a radius of 20 feet round to the nearest 10th if necessary
the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.
The given information about the vertex of the function does not appear to be relevant to the question about mulch for a flower bed. However, we can still solve the problem using the given radius of the flower bed.
The formula to find the recommended amount of mulch for a circular flower bed is:
Mulch = π * r^2 * d
Where r is the radius of the flower bed and d is the desired depth of the mulch.
Assuming a desired depth of 0.5 feet, we can plug in the given radius of 20 feet to the formula:
Mulch = π * (20 feet)^2 * 0.5 feet
Mulch = π * 400 square feet * 0.5 feet
Mulch = 200π cubic feet
To find the approximate value in decimal form, we can use the approximation π ≈ 3.14:
Mulch ≈ 200 * 3.14
Mulch ≈ 628 cubic feet
Rounding to the nearest tenth, we get:
Mulch ≈ 628.3 cubic feet
Therefore, the recommended amount of mulch for the flower bed with a radius of 20 feet and a desired depth of 0.5 feet is approximately 628.3 cubic feet.
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someone please help I'll give brain list (I'm failing)
Answer:
1) 3rd one down 1 7/12 ( the one you've selected well doneee)
2)pretty sure its also the 3rd one down ( don't come for me if its wrong)
Step-by-step explanation:
4 1/6 = 25/6
5 3/4= 23/4
25/6 x4= 100/24
23/4 x 6 = 138/24
138/24 - 100/24 = 38/24
divide by 2:
19/12= 1 7/12
Riley has 200 stamps.
35% are from Russia.
20% are from Australia.
10% are from Asia.
The rest are from North America. How many stamps are from North America?_
Riley has 200 stamps.
35% are from Russia.
20% are from Australia.
10% are from Asia.
The rest are from North America. How many stamps are from North America?
Answer:
70 stamps are from North America
Step-by-step explanation:
All I did was add the percentages together
35+20+10= 65
I then took 65% of 200 to get 70.
Naomi invested $920 in a account paying an interest rate of 4.7% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $2310
Answer:
We can use the continuous compound interest formula:
A = Pe^(rt)
where A is the final amount, P is the initial amount, r is the interest rate (as a decimal), and t is the time (in years). We can rearrange this formula to solve for t:
t = ln(A/P) / r
where ln is the natural logarithm function.
Using the given values, we have:
P = 920
A = 2310
r = 0.047
So,
t = ln(2310/920) / 0.047
t ≈ 18.8 years
Rounding to the nearest year, it would take about 19 years for the value of the account to reach $2310.
Answer:
19 years
Step-by-step explanation:
The sales tax in California is 7.25%. If you go to a store to buy a pair of jeans that has a price of $40, how much will you pay in sales tax
You will pay $2.90 in sales tax in California for a pair of jeans that costs $40.
What is sales tax?At the time of sale, a tax known as sales tax is applied to the cost of products or services. The state, county, or city where the transaction occurs determines the tax rate, which is often expressed as a percentage of the purchase price. The vendor is responsible for collecting sales tax and remitting it to the relevant government body. Sales taxes are levied in order to raise money for the government and pay for essential services like infrastructure, healthcare, and education. Because it is based on the quantity of goods or services consumed rather than income or wealth, sales tax is a sort of consumption tax.
Given that, sales tax in California is 7.25%.
Thus,
Sales tax = price of jeans x sales tax rate
Sales tax = $40 x 0.0725
Sales tax = $2.90
Therefore, you will pay $2.90 in sales tax in California for a pair of jeans that costs $40.
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How many flowers, spaced every 4 in. , are needed to surround a circular garden with a 100-ft radius? use 3. 14
Answer:the answer would be around 300 or 314
if you have 100ft in a circle and divided the space using the equation it what you get .
Step-by-step explanation:
the coc admissions department wants to see how many students would be in favor of using a new program to register for classes. they put a link on their website so that any students that want to try out the program can. the students can then take a survey and say how well they like the new system. this is what method of collecting data was used: group of answer choices convenience census cluster systematic voluntary response simple random sample (srs) stratified
The method of collecting data that was used in the given scenario is voluntary response.
A voluntary response method of data collection is a research technique that allows participants to decide whether or not they want to be included in the sample.
When participants are allowed to choose whether or not to participate, this is known as self-selection.
This method has a disadvantage in that it could lead to bias in the data because those who respond to the survey may not represent the entire population of interest.
In the given scenario, the COC admissions department put a link on their website so that any students that want to try out the program can. The students can then take a survey and say how well they like the new system. This means that the method of collecting data that was used is voluntary response.
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Will mark as brainliest
The expressions, when written as products , would be:
81a² + 6bc - 9b² - c² ⇒ (9a - c)(9a + c) + 6bcb²c² - 4bc - b² - c² + 1 ⇒ (b² - 1)(c² - 4c + 1)1 - 25x² + 10xy - y² ⇒ (1 - 5x + y)(1 + 5x + y)How to write as products?To factor this expression, let's first rearrange the terms:
(81a² - c²) + (6bc - 9b²)
Now, we can see that the first part is a difference of squares, which can be factored as:
(9a - c)(9a + c)
However, the second part (6bc - 9b²) cannot be factored further as a product of binomials. So the expression can be written as:
(9a - c)(9a + c) + 6bc
1 - 25x² + 10xy - y²
This expression remains:
(1 - 5x + y)(1 + 5x + y)
Using the same rule as above.
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The difference between the tens digit and ones digit of a two-digit number is 2. The number is 27 greater than the number created when the digits are reversed. What is the two-digit number?
Thus, the two digits are 9 and 11.
What is the Two-Variable Equations?
Two-variable equations are algebraic equations that involve two variables, typically x and y, and describe a relationship between them.
Let's call the tens digit "T" and the ones digit "O". Based on the problem, we know that:
T - O = 2 (the difference between the tens and ones digit is 2)10T + O = 10O + T + 27 (the number is 27 greater than the number created when the digits are reversed)T = 2 + O
Then substitute this equation in 10T + O = 10O + T + 27 i.e.
10T + O = 10O + T + 27
10T - T = 10O - O + 27
9T = 9O + 27
9(2 + O) = 8O + 27
9(2 + O) = 8O + 27
18 + 9O = 8O + 27
9O - 8O = 27 - 18
O = 9
Then,
T = 2 + 9
T = 2 + 9
T = 11
Thus, the two digits are 9 and 11.
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Obtain the volume of rectangular boxes with a, 2b and 3c as length, breadth and height respectively
Step-by-step explanation:
The volume of a rectangular box is given by the formula:
Volume = length x breadth x height
In this case, the length is a, the breadth is 2b, and the height is 3c. So, the volume can be calculated as:
Volume = a x 2b x 3c
= 6abc
Therefore, the volume of the rectangular box with a, 2b and 3c as length, breadth and height respectively is 6abc.
Simplify 5c - 8d - 4c + 3d
Simplify 6p - 2w + p + 5w
Answer:37c − 32d
2:7p+3w
Step-by-step explanation:
Answer:
1. c - 5d
2. 7p + 3w
Step-by-step explanation:
1.)
5c - 8d - 4c + 3d =
5c + -8d +-4c + 3d
Combine like terms:
(5c + -4c) +(-8d + 3d) =
c - 5d
2.)
6p - 2w + p + 5w =
6p + -2w + p + 5w
Combine like terms:
(6p + p) + (-2w + 5w) =
7p + 3w
How do you find the surface area for this? Anything helps! (will give brainliest)
Answer:
95.2 square yards
Step-by-step explanation:
8(3) + 2(1/2)(3)(7.2) + 2(1/2)(8)(6.2)
= 24 + 21.6 + 49.6 = 95.2 square yards
Adrienne earns $98 for working 8 hours. If she earned $453.25, How many hours did she work?
Answer:
37 hours
Step-by-step explanation:
First, we will find the amount of money that Adrienne makes per hour: 98/8, which equals $12.25.
Now, we can find the number of hours it takes to earn $453.25 by dividing it by $12.25:
$453.25 / $12.25 = 37 hours