Bill sold 140 bottles of cherry soda and 70 bottles of grape soda.
Let's assume that x is the number of bottles of cherry soda sold and y is the number of bottles of grape soda sold. We can set up a system of equations to represent the given information:
x + y = 210 (equation 1: the total number of bottles sold is 210)
1.15x + 0.99y = 230.30 (equation 2: the total cost of the sodas is $230.30)
We can use the first equation to solve for y in terms of x:
y = 210 - x
Substituting this expression for y into the second equation, we get:
1.15x + 0.99(210 - x) = 230.30
Simplifying and solving for x, we get:
1.15x + 207.9 - 0.99x = 230.30
0.16x = 22.4
x = 140
So Bill sold 140 bottles of cherry soda. Substituting this value into equation 1, we get:
140 + y = 210
y = 70
Therefore, Bill sold 140 bottles of cherry soda and 70 bottles of grape soda.
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A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
He concludes that she is not running fast enough to exceed her fastest time.
What errors did the coach make? Check all that apply.
He used an incorrect time ratio converting hours to minutes.
His units do not cancel.
He used an incorrect distance ratio converting miles to feet.
He incorrectly concluded that she is not running fast enough.
He cannot determine her average rate in miles per hour after only 15 minutes.
In a case whereby A bike wheel is 26 inches in diameter the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters) the the diameter is 660.4mm
How can the diameter be calculated?Note; the bike man do not make any calculation, so we can not know mat be he make any mistake.
Since the bike wheel is 26 inches in diameter then we can calculate the diameter of the bike wheel through the multiplication of the two numbers.
Diameter in milimeters = ( 26.0 x 25.4)
Diameter in milimeters = 660.4 mm.
Hence diameter of the bike wheel in millimeters will be 660.4.
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In 2015, Connecticut had a population of about 3,600,000 million, New York had a population of about
1. 947
×
1
0
7
1. 947×10
7
, and Rhode Island had a population of about
1. 056
×
1
0
6
1. 056×10
6
. What is the total population of all three states combined? Write the total population in scientific notation
The total population of all three states combined is 24,126,000 or 2.4126 × 10⁷ in scientific notation.
To find the total population of all three states combined, we simply need to add up the population of each state. In this case, we are given the populations of Connecticut, New York, and Rhode Island, so we can simply add those numbers together to get the total population.
When working with numbers that are very large or very small, scientific notation can be a helpful way to express them. In scientific notation, a number is expressed as a coefficient multiplied by a power of 10. The coefficient is a number greater than or equal to 1 and less than 10, and the power of 10 indicates how many places the decimal point has been moved to create the coefficient.
In this problem, we are given the populations of the three states in scientific notation. Connecticut's population is given as 3.6 × 10⁶, which means that the coefficient is 3.6 and the power of 10 is 6. To convert this number to standard notation, we simply move the decimal point 6 places to the right to get 3,600,000. Similarly, New York's population is given as 1.947 × 10⁷, which means that the coefficient is 1.947 and the power of 10 is 7, and Rhode Island's population is given as 1.056 × 10⁶, which means that the coefficient is 1.056 and the power of 10 is 6.
To find the total population, we add the populations of the three states together:
Total population = Connecticut population + New York population + Rhode Island population
Total population = 3.6 × 10⁶ + 1.947 × 10⁷ + 1.056 × 10⁶
Total population = (3.6 + 19.47 + 1.056) × 10⁶
Total population = 24.126 × 10⁶
We can simplify this expression by multiplying the coefficient by 10⁶:
Total population = 24.126 × 10⁶ = 2.4126 × 10⁷
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Calculate the costs of these home improvement and maintenance costs.
Annual real estate taxes on a property are $2046. Insurance premiums total $1236. Required flood insurance protection premiums are $380 annually. The county assesses an annual special assessment landfill fee of $125. Trash collection costs $65 quarterly. Annual homeowner's association is $720 for common area maintenance of the subdivision. The pool company charges $45 quarterly to maintain the pool. Ongoing termite and pest protection costs $39 monthly. How much should a buyer save each month to cover these fees?
Answer: To calculate the total amount a buyer should save each month to cover these fees, we need to add up all the costs and divide by 12 (the number of months in a year).
Annual real estate taxes = $2046
Insurance premiums = $1236
Flood insurance premiums = $380
Annual special assessment landfill fee = $125
Quarterly trash collection costs = $65 x 4 = $260
Annual homeowner's association fee = $720
Quarterly pool maintenance costs = $45 x 4 = $180
Monthly termite and pest protection costs = $39 x 12 = $468
Total annual costs = $2046 + $1236 + $380 + $125 + $260 + $720 + $180 + $468 = $5405
Total monthly costs = $5405 / 12 = $450.42
Therefore, a buyer should save $450.42 each month to cover these fees.
Step-by-step explanation:
1)You have a monthly income of $2,800 and you are looking for an apartment. What is the maximum
amount you should spend on rent?
2)You have a monthly income of $1,900 and you are looking for an apartment. What is the maximum
amount you should spend on rent?
3)An apartment you like rents for $820. What must your monthly income be to afford this apartment?
4)An apartment you like rents for $900. What must your monthly income be to afford this apartment?
5)An apartment rents for $665/month. To start renting, you need the first and last month's rent, and a
$650 security deposit.
Using Rule of thumb,
The maximum amount you should spend on rent for an income of $2,800 is $840 (30% of $2,800).The maximum amount you should spend on rent for an income of $1,900 is $570 (30% of $1,900).To afford an $820/month apartment, your monthly income must be at least $2,733.33 (30% of $2,733.33).To afford a $900/month apartment, your monthly income must be at least $3,000 (30% of $3,000).To start renting the apartment, you would need $1,980 for first and last month's rent plus a $650 security deposit.1) A common rule of thumb is to spend no more than 30% of your income on rent. Therefore, the maximum amount you should spend on rent is:
$2,800 x 0.3 = $840
2) Using the same rule of thumb, the maximum amount you should spend on rent is:
$1,900 x 0.3 = $570
3) To afford an $820/month apartment, you should aim to spend no more than 30% of your income on rent:
$820 = 0.3x
x = $2,733.33
So your monthly income must be at least $2,733.33 to afford the apartment.
4) Following the same reasoning, your monthly income must be at least:
$900 = 0.3x
x = $3,000
5) To start renting, you need to pay first and last month's rent, plus a $650 security deposit, for a total of:
$665 x 2 + $650 = $1,980
So you would need $1,980 to start renting the apartment.
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) On January 2, 2019, Helmkamp Company purchased a $30,000 machine. It had an estimated useful life of 5 years and a residual value of $3,000. What is the amount of depreciation expense for 2020, the second year of the asset's life, using the double declining-balance method? (Round intermediary calculations to two decimal places and your final answer to the nearest dollar. )
The required answer is the double declining-balance method is $9,840.
To calculate the depreciation expense for 2020 using the double declining-balance method, we first need to determine the asset's straight-line depreciation rate. This is calculated by subtracting the residual value from the cost of the asset and dividing by the asset's useful life:
Depreciation base = $30,000 - $3,000 = $27,000
Annual depreciation expense (straight-line) = Depreciation base / Useful life = $27,000 / 5 = $5,400
Next, we need to determine the double declining-balance rate, which is twice the straight-line rate. Therefore:
Double declining-balance rate = 2 x (1 / Useful life) = 2 x (1 / 5) = 0.40 or 40%
Now we can calculate the depreciation expense for 2020:
Depreciation expense (2020) = Book value (beginning of year) x Double declining-balance rate
The book value at the beginning of 2020 would be the cost of the asset minus accumulated depreciation for the first year:
Book value (beginning of 2020) = $30,000 - ($5,400 x 1) = $24,600
As a result, depreciation increases during the initial year of possession and decreases thereafter.
Therefore:
Depreciation expense (2020) = $24,600 x 0.40 = $9,840
So the amount of depreciation expense for 2020, the second year of the asset's life,
using the double declining-balance method is $9,840.
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A store sells four ears of sweetcorn for one dollar how much will nine ears cost
Nine ears of sweetcorn will cost $2.25 at this store.
To determine the cost of nine ears of sweetcorn, given that four ears cost one dollar, you can follow these steps:
1. Determine the cost of one ear of sweetcorn: Since four ears cost one dollar, we can calculate the cost per ear by dividing the total cost by the number of ears: $1 / 4 ears = $0.25 per ear.
2. Calculate the cost of nine ears: Multiply the cost of one ear by the number of ears desired: $0.25 per ear × 9 ears = $2.25.
So, nine ears of sweetcorn will cost $2.25 at this store.
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Mia crosses a river when she drives from her house to the beach. The function d(t)=40|t-1. 25| shows Mia's distance from the river, d, in miles after t hours. The domain of the function is 0
The domain of the function is given as 0<t<3, which means that the time elapsed is between 0 and 3 hours. Mia's distance from the river after 2 hours of driving is 30 miles.
The given function is:
d(t) = 40|t-1.25|
Here, t represents the time elapsed in hours and d represents the distance from the river in miles.
To find Mia's distance from the river, we need to plug in values of t into the function.
For example, if t=2, then:
d(2) = 40|2-1.25|
d(2) = 40|0.75|
d(2) = 30
So Mia's distance from the river after 2 hours of driving is 30 miles.
Similarly, we can find Mia's distance from the river at other points in time.
To graph the function, we can plot points by choosing different values of t and finding the corresponding values of d. We can then connect these points to get a graph of the function.
Graph of the function d(t) = 40|t-1.25|
The graph shows that Mia starts at a distance of 40 miles from the river and then approaches it until she reaches the other side of the river, where her distance from the river is again 40 miles. The graph is symmetric about t=1.25, which means that Mia spends the same amount of time on either side of the river.
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Write the standard form of the equation of the circle with the given characteristics. Endpoints of a diameter: (0, 0), (8, 6)
The standard form of the equation of the circle with the given characteristics is[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
To get the equation of the circle using the endpoints of a diameter, we have to use the standard form :
[tex](x - h) ^{2} + (y - k)^{2} = {r}^{2} [/tex]
In which (h, k) represents the middle point of the circle and r as the radius. so, we need to find the midpoint of the diameter using the endpoints (0, 0) and (8, 6).
Midpoint = ((0+8)/2, (0+6)/2) = (4, 3)
Next, we need to calculate the radius by using the distance formula to calculate the distance between the center and one of the diameter endpoints.
[tex] {r}^{2} = {(8 - 4)}^{2} + {(6 - 3)}^{2} = {4}^{2} + {3}^{2} = 16 + 9 = 25[/tex]
Now, substituting the values of (h, k) and
[tex] {r}^{2} [/tex] into the standard form equation to get the equation:
[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
Therefore, the standard form equation of the circle with the given characteristics is
[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
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The standard form of the given question is (x - 4)² + (y - 3)² = 25, under the condition endpoints of a diameter: (0, 0), (8, 6).
In order To write the standard form of the equation of a circle with endpoints of a diameter (0, 0), (8, 6), we first need to find the center and radius of the circle.
The diameter comprises the midpoints of the center of the circle. The midpoint of (0, 0) and (8, 6) is ((0+8)/2, (0+6)/2) = (4,3). Center point of the circle is (4,3).
Diameter = 2× radius
. The distance between (0, 0) and (8, 6) is √((8-0)² + (6-0)²)
= √(64+36)
= √100
= 10.
Then, the radius of the circle is 10/2 = 5.
Then,
(x - h)² + (y - k)² = r²
here
(h,k) = center of the circle
r = radius.
Staging in this equation
h=4,
k=3
r=5
(x - 4)²+ (y - 3)² = 25
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the scale is 1 inch=50 miles. 5 inches is what
Answer:
Step-by-step explanation:
you multiply 5 by 50 and that would equal 250
5 x 50 = 250
Explain me that excersice step by step please3x((2x3)^-1x1/2^3)^-1x(3x2^2)^-2
Answer:
Begin by simplifying the phrases within the brackets, beginning with the innermost brackets:
(2 x 3)^-1 = 1/6 (because 2 x 3 = 6, and the negative exponent flips the fraction)
1/2^3 = 1/8 (because 2^3 = 8)
So, (2x3)^-1x1/2^3 = 1/6 x 1/8 = 1/48
Next, simplify the expression outside the parentheses:
(3x2^2)^-2 = 1/(3x2^2)^2 = 1/(3^2 x 2^4) = 1/36 x 1/16 = 1/576
Now, substitute the simplified terms back into the original expression and simplify:
3x(1/48)x(1/576) = 1/768
So the final answer is 1/768.
A tired frog is jumping across a pond. Her first jump will be her longest. She travels 300 cm. Her second jump carries her another 270 cm. How far will the frog travel before she cannot jump anymore?
S= 1560cm
S= 570cm
S= 2700cm
S= 3000cm
The frog will travel a total distance of 1650 cm before she cannot jump anymore. None of the options given are correct.
To find the total distance the frog will travel, we need to add up the distances of all her jumps. Given that her first jump is her longest at 300 cm and her second jump is 270 cm, we can assume that each subsequent jump is shorter than the one before it.
The difference between the first jump and the second jump is 30 cm. So let's assume that the common difference between each jump is 30 cm. So the frog takes a total of 10 jumps before she cannot jump anymore.
The total distance the frog will travel is:
300 + 270 + (240 + 210 + 180 + 150 + 120 + 90 + 60 + 30) = 1650 cm
So here none of the options are correct.
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Given that f is continuous on [1, 5] and differentiable on the interval (1,5), with f'(x) ≤ 23, for all x, and f(1) = 4. Find the largest possible value for f(5).
We are given that f is continuous on [1, 5], differentiable on (1, 5), and f'(x) ≤ 23 for all x. We want to find the largest possible value for f(5). the largest possible value for f(5) is found to be 96.
We can apply the Mean Value Theorem (MVT) here, which states that if a function is continuous on [a, b] and differentiable on (a, b), there exists a number c in the interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a). In this case, a = 1, b = 5, and f(1) = 4.
Since f'(x) ≤ 23 for all x, we know that f'(c) ≤ 23. Plugging into the MVT equation, we have:
[tex]f'(c) = (f(5) - f(1))/(5 - 1) ≤ 23, f'(c) = (f(5) - 4)/4 ≤ 23[/tex]
To find the largest possible value for f(5), we assume f'(c) is equal to its maximum, 23: 23 = (f(5) - 4)/4. Solving for f(5), we get: f(5) = 4 + 4 * 23 = 4 + 92 = 96. So, the largest possible value for f(5) is 96.
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I need questions 3,4,5 with answers and explanations/work
The family with 8 pets cannot be used to represent the whole because it is an outlier
Bar chartCircle graphExplaining why the family with 8 pets cannot be used to represent the wholeGiven that we have
A dot plot that represents the display
On the dot plot, we have
Outlier = 8
This data value is considered an outlier because it is relatively far from other values
As a general rule, outliers cannot be used to represent the whole
The display that could be used to show trendHere, we have
Dot plotBar chartCircle graphOf the three displays, the bar chart is used to represent data such that users may readily recognize patterns or trends.
So, the bar chart is to be used
The display that could be used not to show trendHere, we have
Dot plotBar chartCircle graphOf the three displays, the circle graph does not show that users patterns or trends.
So, the circle graph is to be used
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HELP MARKING BRAINLEIST IF RIGHT ASAP
Answer:
{51
Step-by-step explanation:
10^2 - 7^2= 51
You can’t square 51 because no two same whole numbers multiplied creates 51
B= 51
Check answer
7^2 + 51= 100
{100 = 10^2
Anna ate 58of an orange and gave the other 38 to her brother. which equation can be used to find the difference between the amount anna ate and the amount she gave her brother?
The result of this equation will give us the numerical value representing the difference between the amounts Anna ate and the amount she gave to her brother. In this case, the difference would be 20.
To find the difference between the amount of orange Anna ate and the amount she gave to her brother, we can use the equation: 58 - 38 = x
Here, x represents the difference between the two amounts. We can solve for x by subtracting 38 from 58.
58 - 38 = 20
Therefore, the difference between the amount of orange Anna ate and the amount she gave her brother is 20. Anna ate 58 of an orange and gave 38 to her brother, so the remaining 20 must be the difference between the two amounts.
In summary, the equation that can be used to find the difference between the amount Anna ate and the amount she gave her brother is 58 - 38 = x, where x represents the difference. The answer is 20.
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B. It will be a curve.
C. It will be a line.
D. There is no way to tell.
The given equation on a graph can be described best as C. It will be a line.
Why would this be a line ?The given equation is a linear equation because it has the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation can be rewritten as:
y = 3x + 15 - 64
y = 3x - 49
Since it's a linear equation, it will represent a straight line on the graph that can be found by using the equation and some values of x, to find values of y and then plotting them.
In conclusion, the best answer is C. It will be a line.
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The full question is:
An equation is given to be 3x + 15 = 64
What will this be on a graph ?
A. It will be irregular
B. It will be a curve.
C. It will be a line.
D. There is no way to tell.
[ ( -28 )-( +42)]-(+3) CUAL ES EL RESULTADO
ME DICEN
POR FIS AYUDA
ES PARA HOY
First, solve the expression inside the parentheses: (-28) - (+42) = -70
Next, subtract 3 from -70: -70 - (+3) = -73
What is the result of: [(-28) - (+42)] - (+3)?The given expression can be simplified as follows:
[( -28 )-( +42)]-(+3) = -28 - 42 - 3 = -73
So, the answer to the given expression is -73.
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It is typical for the person who is most difficult to convince in an argument to say that everyone else is stubborn. group of answer choices displacement sublimation projection rationalization regression
"It is typical for the person who is most difficult to convince in an argument to say that everyone else is stubborn." refers projection (option c).
To understand projection in mathematical terms, we can think of it as a function f(x), where x represents the individual's own thoughts or emotions. The output of the function, f(x), represents the projection of these thoughts or emotions onto someone else.
In the case of arguments, the person who is most difficult to convince may have a high value of x, indicating that they are feeling stubborn. However, instead of accepting this feeling, they project it onto others, resulting in a high value of f(x) for those around them.
Projection is just one example of the many defense mechanisms that humans use to protect themselves from unpleasant thoughts or emotions. Understanding these mechanisms can help us to better navigate difficult situations, including arguments, and improve our communication skills.
Hence the correct option is (c).
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Chris bought 5 tacos and 2 burritos for $13. 25.
Brett bought 3 tacos and 2 burritos for $10. 75.
The price of one taco is $
The price of one burrito is $
Answer:
Let's start by assigning some variables to the unknowns:
Let's call the price of one taco "t".
Let's call the price of one burrito "b".
With these variables, we can write two equations based on the information given in the problem:
5t + 2b = 13.25 (equation 1)
3t + 2b = 10.75 (equation 2)
We now have two equations and two variables. We can use algebra to solve for t and b. One way to do this is to eliminate b by subtracting equation 2 from equation 1:
(5t + 2b) - (3t + 2b) = 13.25 - 10.75
Simplifying this equation, we get:
2t = 2.5
Dividing both sides by 2, we get:
t = 1.25
So the price of one taco is $1.25.
Now that we know the price of one taco, we can substitute this value into one of the equations to solve for b. Let's use equation 1:
5t + 2b = 13.25
Substituting t = 1.25, we get:
5(1.25) + 2b = 13.25
Simplifying this equation, we get:
6.25 + 2b = 13.25
Subtracting 6.25 from both sides, we get:
2b = 7
Dividing both sides by 2, we get:
b = 3.5
So the price of one burrito is $3.5.
Therefore, the price of one taco is $1.25 and the price of one burrito is $3.5.
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Find the measure of angle D.
The measure of angle D is 25°
What is exterior angle theorem?Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the opposite interior angles.
Angle D and angle C are the two opposite angles.
Therefore;
40+9x-2 = 20x +5
38+9x = 20x +5
38-5 = 20-9x
11x = 33
divide both sides by 11
x = 33/11
x = 3
Therefore since angle D = 9x-2
substitute 3 for x
D = 9(3) - 2
D = 27 -2
D = 25°
Therefore the measure of angle D is 25°
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You are shopping for a King & Queen size mattress, each of which are shaped like a rectangle. The Queen is 16 inches longer than it is wide. The King is 20 inches wider than the Queen, but has the same length. The area of the King-sized mattress is 1,600 in² larger than the Queen. Find the Area of both mattresses
The area of the King-sized mattress is 4,800 square inches and the area of the Queen-sized mattress is 3,200 square inches.
To find the dimensions of the Queen-sized mattress, let x be the width. Then, the length of the mattress is x + 16. The area of the Queen-sized mattress is x(x + 16) = x² + 16x.
Since the King-sized mattress has the same length as the Queen-sized mattress, its length is x + 16. Also, its width is 20 inches wider than the Queen-sized mattress, so its width is x + 16 + 20 = x + 36. Therefore, the area of the King-sized mattress is (x + 16)(x + 36) = x² + 52x + 576.
The area of the King-sized mattress is 1,600 square inches larger than the area of the Queen-sized mattress. So, we can set up the following equation:
x² + 52x + 576 - (x² + 16x) = 1600
Simplifying this equation, we get:
36x + 576 = 1600
36x = 1024
x = 28
Therefore, the width of the Queen-sized mattress is 28 inches and the length is 44 inches. So, its area is 3,200 square inches.
The width of the King-sized mattress is 28 + 36 = 64 inches and the length is 44 inches. So, its area is 4,800 square inches.
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What is the measure of angle A? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠A=° Right triangle A B C, with right angle C B A. Side A B is three centimeters, side B C is four centimeters, and side C A is five centimeters.
The measure of angle A is given as follows:
m < A = 53.13º.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.Angle A is opposite to a side of length 4 cm, while the hypotenuse is of 5 cm, hence it's measure is obtained as follows:
sin(A) = 4/5
m < A = arcsin(4/5)
m < A = 53.13º.
Missing InformationWe have a right triangle, in which the side length opposite to angle A is BC = 4, while the hypotenuse is CA = 5.
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Select the correct answer from each drop-down menu.
Based on the two triangles shown, what can be concluded?
An angle opposite the longest side of a triangle is the side
The two triangles shows that an angle opposite the longest side of a triangle is the largest angle
Making conclusions from the two triangles shownFrom the question, we have the following parameters that can be used in our computation:
The two triangles
From the triangles we have the largest angles to be
C = 117.3 and E = 93 degrees
The lennths opposite these sides aere
AB = 6 and DF = 11.94
These lengths are the longest segments on their respective triangles
This means that an angle opposite the longest side of a triangle is the largest angle
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Rewrite the expression using a single, positive exponent: 14^-3·14^12
Answer:
It's 14⁹.
Add the powers in the process of multiplying.
Which is -3 + 12 answer is 9.
Hope this helped!
A bead is formed by drilling a cylindrical hole, with a 2 mm diameter, through a sphere
with an 8 mm diameter. estimate the surface area of the bead. leave the answer in
terms of pi
The estimated surface area of the bead is 52π square millimeters.
To estimate the face area of the blob, we need to find the face area of the sphere and abate the face area of the spherical hole. The face area of a sphere is given by the formula A = 4πr2 where r is the compass of the sphere.
The radius of the sphere is: r = 8 mm / 2 = 4 mm.
The surface area of the sphere is: S_sphere = 4π[tex]r^{2}[/tex] = [tex]4π(4 mm)^{2}[/tex] =64 [tex]mm^{2}[/tex]
The radius of the cylinder is: r = 2 mm / 2 = 1 mm.
The height of the cylinder is: h = 8 mm - 2 mm = 6 mm.
The surface area of the cylinder is: S_cylinder = 2πrh = 2π(1 mm)(6 mm) = 12π [tex]mm^{2}[/tex]
The estimated surface area of the bead is: S_bead = S_sphere - S_cylinder = 64π [tex]mm^{2}[/tex] - 12π [tex]mm^{2}[/tex] = 52π [tex]mm^{2}[/tex]
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A surveyor at an intersection noticed that over the past 24 hours, 318 cars turned left, 557 turned right, and 390 went straight. Based on the activity of the past 24 hours, what fraction is closest to the probability that the next car will turn left?
probability that the next car will turn left, we need to divide the number of cars that turned left by the total number of cars that passed through the intersection in the past 24 hours. This will give us a fraction that represents the likelihood of a car turning left.
Using the numbers provided, the total number of cars that passed through the intersection in the past 24 hours is:
318 (cars turned left) + 557 (cars turned right) + 390 (cars went straight) = 1265
So, the probability of the next car turning left is:
318 (cars turned left) ÷ 1265 (total number of cars) = 0.251 (rounded to three decimal places)
This means that there is a 25.1% chance that the next car will turn left at the intersection.
As a surveyor, it is important to be able to analyze data and calculate probabilities to make informed decisions. Understanding the probability of different outcomes can help to plan for future events and anticipate potential issues.
In this case, knowing the probability of a car turning left can help to inform traffic flow and reduce congestion at the intersection.
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Find angle C
SinC/4=sin104/8
Answer:
C = 52
Step-by-step explanation:
sin(c/4) = sin(104/8)
sin(c/4) = 0.22495
c/4 = 13
c = 52
Explain why one-twelfth interest every month on an initial one pound will give you (1 + (1/12))¹² pounds at the end of the year
One-twelfth interest every month on an initial one pound will give (1 + (1/12))¹² pounds at the end of the year due to the compounding effect of interest.
How to find the formula for compound interest?The interest rate of investment of one-twelfth per month means that for every pound invested, one-twelfth of that amount will be added as interest at the end of the month. Therefore, at the end of the first month, the initial investment of one pound will earn an additional interest of (1/12) pound, making the total amount of money to be 1+(1/12) pounds.
At the end of the second month, the new amount of money will earn another one-twelfth of interest, which will be added to the previous total. Therefore, the new total amount of money will be (1+(1/12))+(1/12) = (1+(2/12)) pounds, which can be simplified to (1+(1/6)) pounds.
By the end of the twelfth month, the initial one pound investment will have earned twelve one-twelfth interests, which can be calculated as (1+(1/12)[tex])^12[/tex] pounds, using the formula for compound interest. This simplifies to (1+1/12[tex])^12[/tex] pounds or (1.0833[tex])^12[/tex] pounds, which is approximately equal to 2.613 pounds.
Therefore, an initial investment of one pound with a one-twelfth interest rate per month will earn a total of (1+(1/12)[tex])^12[/tex] pounds or approximately 2.613 pounds by the end of the year.
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topic 3 providing lines are parallel
21
21. in the figure, provided line n and line m are parallel the values of x and y are
x = 7
y = 24
How to find x and y21. When line m and line n are parallel then using corresponding angle theorem we have that:
7y - 23 + 8x - 21 = 180
7y - 8x = 180 + 23 - 21
7x - 8x = 182
Also
8x - 21 + 23x - 16 = 180
8x + 23x = 180 + 21 + 16
31x = 217
x = 217 / 31
x = 7
using vertical angle theorem we have:
7y - 23 = 23x - 16
plugging in the value of x
7y - 23 = 23 * 7 - 16
7y - 23 = 145
7y = 145 + 23
7y = 168
y = 24
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Find the derivative of the function f by using the rules of differentiation. f(x)=x^{0,9} f'(x) =
The derivative of the function f(x) = [tex]x^{0,9}[/tex] is f'(x) = [tex]0.9x^{-0.1}[/tex].
To find the derivative of f(x), we use the power rule of differentiation, which states that if f(x) = [tex]x^n[/tex], then f'(x) = [tex]nx^{(n-1)}[/tex].
In this case, we have f(x) = [tex]x^{0,9}[/tex]. Applying the power rule, we get:
f'(x) = [tex]0.9x^{0.9-1} = 0.9x^{-0.1}[/tex]
Note that [tex]x^{-0.1}[/tex] can be rewritten as [tex]1/x^{0.1}[/tex]. So we have:
f'(x) =[tex]0.9/x^{0.1}[/tex]
This expression tells us the slope of the tangent line to the curve of f(x) at any given point. For example, at x = 1, we have:
f'(1) = [tex]0.9/1^{0.1} = 0.9[/tex]
This means that the slope of the tangent line to the curve of f(x) at x = 1 is 0.9. As x increases or decreases from 1, the slope of the tangent line changes accordingly.
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