Answer:
20.65
Step-by-step explanation:
In a set of three lines, a pair of parallel lines is intersected by a transversal. The intersection forms eight special angles. Two of the special angles, ∠A and ∠B, are corresponding angles.
For the set of parallel lines intersected by a transversal,A = 4x andB = 2(x+14).
Use an equation to represent the corresponding angle relationship betweenA and B.
Use the equation to find the measures ofA andB.
We can solve this equation by using corresponding angle relationship between A and B , to get A= 56° and B=56°
What is corresponding angle ?
In geometry, when two lines are intersected by a transversal, the angles formed at each intersection point are called the corresponding angles. Corresponding angles are angles that occupy the same relative position at each intersection point where the transversal intersects two parallel lines.
What is equation?
In mathematics, an equation is a statement that shows the equality between two mathematical expressions using an equals sign (=). An equation can contain variables (represented by letters) and constants (fixed values).
In the given question,
The corresponding angle relationship between angle A and angle B can be represented by the equation:
angle A = angle B
Substituting the given values of angle A and B we get
4x = 2(x+14)
4x = 2x + 28
2x = 28
x = 14
Therefore angle A = 4x = 4(14) = 56°
Therefore angle B = 2(x+14) = 2(14+14) = 56°
So both angle A and B have a measure of 56°.
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the probability of a breakdown on assembly line a is 12%. the probability of a breakdown on assembly line b is 16%. the probability that both assembly lines break down is 2%. what is the probability that assembly line a or assembly line b break down?
If the probability of a breakdown on assembly line 'a' is 12% and probability of a breakdown on assembly line 'b' is 16%, then the probability that assembly line 'a' or assembly line 'b' break down is equals to the 26%, i.e., 0.26.
We have the probability of a breakdown on assembly line 'a' = 12% = 0.12
The probability of a breakdown on assembly line 'b' = 16% = 0.16
The probability that both assembly lines break down = 2% = 0.02
Let's two events a breakdown on assembly line 'a' and a breakdown on assembly line 'b' be 'X' and 'Y' respectively. That is P(X) = 0.12, P(Y) = 0.16,
P(X and Y) = P(X∩Y) = 0.02
we have to calculate the probability that assembly line 'a' or assembly line 'b' break down, P( X or Y) = P(X∪Y). Using addition rule of probability, the probability that event A or event B occurs is equal to the probability that A occurs plus the probability that B occurs minus the probability that both occur. So, P( X or Y) = P(X) + P(Y) - P( X∩Y)
= 0.12 + 0.16 - 0.02
= 0.26
Hence, required probability is 0.26.
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what is the future value of 6000 earning 18% interest, compounded monthly for 8 years
Answer:
To calculate the future value of an investment earning compound interest, we can use the formula:
FV = P(1 + r/n)^(nt)
where:
FV is the future value
P is the principal (starting amount)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, we have:
P = 6000
r = 0.18 (18% annual interest rate)
n = 12 (compounded monthly)
t = 8
Substituting these values into the formula, we get:
FV = 6000(1 + 0.18/12)^(12*8)
FV = 6000(1.015)^96
FV = 6000(3.045)
FV = 18270
Therefore, the future value of $6000 earning 18% interest, compounded monthly for 8 years, is $18,270.
I need some help! Giving brainliest
Answer:
Choice B: distance from home to library is length of HL
HL = 75 see calculations below
Step-by-step explanation:
use points (0,0) and (2.1, 7.2) to find HL:
HL = √(2.1 - 0)² + (7.2 - 0)² = √4.4 + 51.8 = √56.25 = 7.5
Sin^2(45+A)+sin^2(45-A)=1
Prove it
Answer:
Step-by-step explanation:
Setting A=45, we see that it is not true. However, you might find the following revealing:
sin2(45+A)=(sin45cosA+cos45sinA)2=12(1+2cosAsinA)
sin2(45−A)=(sin45cosA−cos45sinA)2=12(1−2cosAsinA)
Now, stare.
A store sells 3 T-shirts for $15
What is the cost per T-shirt?
Answer: $5
Step-by-step explanation:
If you sell 3 shirts for $15 you would then just divide the 3 shirts into how much all together to get the price for each shirt for $5.
mrs. jacobson is an inpatient in your hospital. her prescriber just ordered metformin 1,000 mg every 12 hours. how many metformin 500 mg tablets will you put in mrs. jacobson's med cart drawer for a 24-hour fill?
500 mg tablets will you put in mrs. jacobson's med cart drawer for a 24-hour fill.
Since the prescribed dose of metformin is 1,000 mg every 12 hours, Mrs. Jacobson needs to take metformin twice a day. Therefore, for a 24-hour fill, she needs a total of 2,000 mg of metformin.
Since the available strength of metformin is 500 mg, we can divide 2,000 mg by 500 mg to find out how many tablets Mrs. Jacobson needs to take.
2,000 mg ÷ 500 mg = 4 tablets
Therefore, you will put four metformin 500 mg tablets in Mrs. Jacobson's med cart drawer for a 24-hour fill.
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write the number 150 as a sum of three numbers so that the sum of the products taken two at a time is a maximum. (enter the three numbers as a comma-separated list.)
The three numbers are 50, 50, and 50, which give a maximum sum of products taken two at a time of 5000.
To find the sum of three numbers whose product is maximum, we need to distribute the numbers as equally as possible. Therefore, we divide 150 by 3, giving 50. This means that the sum of the three numbers is 150, and their product is maximized.
To check that this is indeed the case, we can calculate the sum of the products taken two at a time: 50x50 + 50x50 + 50x50 = 5000, which is the maximum possible sum.
Therefore, the three numbers are 50, 50, and 50.
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At a science exhibition, students learnt that it takes 5 hours for a block of ice to melt at 32° C.
Determine the time taken to melt a similar-sized block of ice at 20° C.
What is the simplest form of 8(5k+7)−10(6k−7)
The simplest form of the given expression is -20k + 126.
To find the simplest form of the expression 8(5k+7)−10(6k−7), follow these steps:
1. Distribute the numbers outside the parentheses to the terms inside the parentheses:
8 × 5k + 8 × 7 - 10 × 6k + 10 × 7
2. Perform the multiplication:
40k + 56 - 60k + 70
3. Combine like terms (terms with the same variable and exponent):
(40k - 60k) + (56 + 70)
4. Simplify the expression by performing the subtraction and addition:
-20k + 126
The simplest form of the given expression is -20k + 126.
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92 divided by 378 I need this rn pls!! If you can help!
Answer:
4 for up but of R it is 10
Step-by-step explanation:
378/92 equals 4 but 10 is the remainder
Isabella rents an apartment for $1,500 a month and has a year's lease. she owns a car that is worth $16,700. she has a savings account of $4,950 and a credit card balance of $925. what is her net worth?
Isabella's net worth is $2,725.
We know that the net worth is nothing but a measure of an individual's financial standing at a given point in time.
Here, to calculate the net worth, we need to add up all of the assets and subtract all of her liabilities:
We can see that,
Assets
Car worth: $16,700
Savings account: $4,950
So, the total assets worth:
$16,700 + $4,950 = $21,650
Now liabilities:
Credit card balance: $925
And the rent for the remainder of the lease:
$1,500 x 12 = $18,000 for year
So, the total liabilities would be:
$925 + $18,000 = $18,925
Hence her net worth would be:
21,650 - 18,925 = 2,725 dollars
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What’s 3.14 times six?
Answer:
18.84
Step-by-step explanation:
:)
The prisms are similar. What is the surface area of Prism B? Prism A is 10 m. Prism B is 6 m. Surface area = 880m2
Answer:
79.92m
Step-by-step explanation:
here you go hope this helps
30 points + marked as brain thing
The answer of the given question based on the Compound interest the answer is option a) Rounding to 2 decimal places gives D ≈ 824.50, so the closest option provided is a) 825. Therefore, the number that goes in box D is approximately 824.50, rounded to 2 decimal places.
What is Principal?In compound interest, term "principal" refers to the initial amount of money that is invested or borrowed. The principal is starting point for calculating interest that will be earned or paid over time.
When you invest money at compound interest rate, interest earned is added to principal amount, and resulting sum becomes new principal for next interest calculation.
Based on the information provided in the image, we can calculate the value in box D by multiplying the values in boxes B and C and then dividing by 100:
D = (B × C) ÷ 100
D = (850 × 97) ÷ 100
D = 824.5
Rounding to 2 decimal places gives D ≈ 824.50, so the closest option provided is a) 825. Therefore, the number that goes in box D is approximately 824.50, rounded to 2 decimal places.
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Total equity after adding the simple interest in the amount will be $825.
What is simple interest?
Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any interest that may have accumulated in previous periods.
In simple interest, the amount of interest earned or owed is calculated as a percentage of the principal amount, multiplied by the time period for which the interest is being calculated.
simple interest is found using
I = P * r * t
Where I is the amount of interest earned or owed, P is the principal amount, r is the annual interest rate as a decimal, and t is the time period in years.
Now,
Assuming that the return rate of 10% is a simple annual interest rate, the total equity after one year can be calculated using the formula for simple interest:
Total equity = Principal + Interest
where the interest is calculated as:
Interest = Principal x Rate x Time
In this case, the principal is $750, the rate is 10%, and the time is one year.
Then,
Interest = $750 x 0.10 x 1 = $75
Therefore, the total equity after one year would be:
Total equity = $750 + $75 = $825
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consider the differential equation given by[math equation]the goal of this problem is to solve this differential equation numerically, analytically and compare the solutions. find the exact solution (i.e. the analytical solution) use euler's method to solve the differential equation with a step size h=0,001; (this is the numerical solution)
The number of iterations increases. If there is a significant difference between the two solutions, we may need to investigate the numerical method used or check for errors in our analytical solution.
Step-by-step explanation:
The differential equation is missing in your question. However, I will give a general overview of how to solve a differential equation numerically using Euler's method and how to find an analytical solution.
Numerical Solution using Euler's Method:
Suppose we have a first-order differential equation of the form y' = f(x, y), where y' represents the derivative of y with respect to x. To solve this numerically using Euler's method, we need to start with an initial condition y(x0) = y0, and we want to find the value of y at some other point x1 = x0 + h.
The Euler's method involves approximating the derivative y' by the difference quotient (y1 - y0) / h, where y1 is the value of y at x1. Rearranging this equation, we get:
y1 = y0 + h * f(x0, y0)
Using this equation, we can iteratively compute the value of y at different points by using the previous value of y. For example, to find y2, we can use the equation:
y2 = y1 + h * f(x1, y1)
We continue this process until we reach the desired endpoint.
Analytical Solution:
An analytical solution to a differential equation is an explicit expression for y(x) that satisfies the differential equation for all values of x. To find an analytical solution, we may use techniques such as separation of variables, integrating factors, or other methods specific to the type of differential equation.
For example, if we have a differential equation of the form y' = k * y, where k is a constant, we can use separation of variables to obtain:
dy / y = k * dx
Integrating both sides, we get:
ln|y| = k * x + C
where C is an arbitrary constant of integration. Solving for y, we get:
y = Ce^(kx)
where C = ±e^C is a constant determined by the initial condition.
Comparison of Solutions:
Once we have the numerical and analytical solutions, we can compare them by plotting the graphs of y(x) for each method. If the numerical solution was computed with a small enough step size, it should converge to the analytical solution as the number of iterations increases. If there is a significant difference between the two solutions, we may need to investigate the numerical method used or check for errors in our analytical solution.
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6 Quincy bought a variety-pack that contained 20 game dice. He sorted the dice by color and found that 15% of the dice were red. How many red dice were in the pack?
Answer:
If 15% of the dice were red, then the proportion of red dice is 0.15.
To find out how many red dice are in the pack, we can multiply this proportion by the total number of dice:
0.15 x 20 = 3
Therefore, there are 3 red dice in the variety pack.
Step-by-step explanation:
If 15% of the dice in the variety-pack are red, then the proportion of red dice to total dice is 0.15.
Let's represent the number of red dice as "x".
We know that the total number of dice in the pack is 20. Therefore, the number of non-red dice must be 20 - x.
We can set up an equation using the proportion of red dice:
x/20 = 0.15
To solve for x, we can multiply both sides by 20:
x = 20 * 0.15
x = 3
Therefore, there are 3 red dice in the pack.
A number is 12 greater than a second number. The sum of the two numbers is 66. What is the the smaller number?
Answer:
Step-by-step explanation:
The smaller number would be 27. If the first number is 12 greater than the 2nd number and we have to make it equal to 66. Our smaller number would be 27 becuase if we add 12 to 27 that gives us 39. 39+27= 66. Hopefully that makes sense.
Some aliens on planet zenith leave their planet to explore other planets in the universe. 120 aliens have left planet zenith over the past 3 years. Write an expression to model the change in aliens per year on planet zenith. Evaluate your expression and give the answer in the context of the problem
Alien is an extraterrestrial species or a hypothetical species that lives beyond the planet Earth. They are beings from other planets that can travel in spacecraft. They are often depicted as having unique or supernatural powers that are beyond those of humans. The question given is about an alien species that leaves its planet to explore other planets. We are given the information that 120 aliens have left planet zenith over the past 3 years. We need to write an expression to model the change in aliens per year on planet zenith. We can write the following expression:Change in aliens per year = Total number of aliens left / Number of yearsThe total number of aliens left in the past 3 years is 120. Therefore,Total number of aliens left = 120Number of years = 3Substituting the values in the above expression, we get:Change in aliens per year = 120 / 3Change in aliens per year = 40 aliens per yearThe expression to model the change in aliens per year on planet zenith is 40 aliens per year. This means that 40 aliens are leaving planet zenith each year to explore other planets in the universe.
The average change in aliens per year can be calculated using the above expression. The change in aliens per year is 40 aliens. Hence, every year 40 aliens are leaving planet Zenith to explore other planets in the universe.
To model the change in aliens per year on planet Zenith, an expression can be formed from the given data. Let's look into the steps to model the change in aliens per year on planet zenith.
Step 1: We are given that 120 aliens have left planet zenith over the past 3 years.
Step 2: To find the change in aliens per year, we can divide the total number of aliens who left the planet over the past 3 years by the number of years.
Change in aliens per year = (120 aliens) / (3 years)
Step 3: Simplifying the above expression we get,Change in aliens per year = 40 aliens per year
Therefore, the expression to model the change in aliens per year on planet Zenith is 40 aliens per year. This implies that every year 40 aliens are leaving planet Zenith to explore other planets in the universe.
Evaluation: As per the given problem, 120 aliens have left planet Zenith over the past 3 years.
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emma buys a gift basket online for 30% off the list price. she has to pay $5.50 for shipping. the total charge is $45.20. what is the list price of the gift basket?
The list price of the gift basket is $65.20. This can be determined by taking the total charge of the gift basket ($45.20) and subtracting the shipping charge of $5.50. The remaining $39.70 is the discounted amount of the gift basket.
Since the gift basket was discounted by 30%, the original list price can be determined by dividing the discounted amount by 70%, which is 0.7. Then, the list price can be calculated by multiplying the discounted amount by 1.43 (the reciprocal of 0.7). Therefore, the list price of the gift basket is $65.20.
This method of calculating the list price of the gift basket is called reverse-discounting. The process of reverse-discounting involves subtracting the discounted amount from the total charge to get the original list price. This method is useful when the discount rate is known and the total charge is given. It allows for the original list price of the item to be determined quickly and accurately.
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Simplify open parentheses x to the 1 half power close parentheses to the 1 sixth power. X to the 1 third power
x to the 1 fourth power
x to the 1 twelfth power
x to the 2 thirds power
The simplification of the expression ( x^1/2)^1/6 × x^(1/3) is given by x to the 5 twelfth power.
Apply the rule of exponents representing raise a power to another power and product of the exponents with same base,
(a^m)^n= a^(mn)
( a^m ) × ( a^n ) = a^(m + n)
Here, x^(1/2) raised to the (1/6)th power.
Using the rule of exponents, we have,
x^((1/2) x (1/6))
Simplification of the product of the exponents, we get ,
= x^(1/12)
Now, multiply this by x^(1/3), so using the rule of product of exponents with same base we get,
x^(1/12) x x^(1/3)
Combining the like terms by adding the exponents, we have,
= x^((1/12) + (1/3))
Simplifying the sum of the exponents,
= x^(5/12)
Therefore, the simplification of the given expression is equal to x to the 5 twelfth power.
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The above question is incomplete, the complete question is:
Simplify open parentheses x to the 1 half power close parentheses to the 1 sixth power. X to the 1 third power
x to the 1 fourth power
x to the 1 twelfth power
x to the 2 thirds power
x to the 5 twelfth power
An isosceles right triangle is removed from
each corner of a square piece of paper, as
shown, to create a rectangle. If AB = 12 units,
what is the combined area of the four removed
triangles, in square units?
The combined area of the four removed triangles is 48 sq.units. Answer: 48
We need to find out the combined area of the four removed triangles, in square units. Given: AB = 12 units.
Let's consider the given square, and let's draw an altitude BD and also draw perpendiculars to BD from the three vertices A, C and D.
Let AB = x cm. Area of square = x² sq.cm.
Now, we are cutting a triangle with base x and height x, which is a right-angled triangle. Hence, area of each removed triangle = (1/2) * x * x = (x²/2) sq.cm.
Now, BD = x/√2. Area of rectangle = AB * BD = 12 * 12/√2 = 72√2 sq.cm.
Now, area of 4 triangles = (x²/2) + (x²/2) + (x²/2) + (x²/2) = 2x² sq.cm.
We know that, Area of rectangle = Area of 4 triangles + Area of square => 72√2 = 2x² + x² => 72√2 = 3x² => x² = 24√2 cm² => x = √(24 * 2) cm = √(48) cm = 4√3 * √2 cm.
Area of 4 triangles = 2x² sq.cm = 2 * 24 cm² = 48 sq.cm.
Hence, the combined area of the four removed triangles is 48 sq.units. Answer: 48.
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I’m stuck please help …
….
Step-by-step explanation:
If you take the sides you already have, 2, 7, 4, and 3, and add them together, you get 16. Lets take the portion of the perimeter you already have, and lets say this figure is a rectangle.
Divide 16 by 2 to give two sides of the rectangle a portion of the perimeter.
Since the area of a rectangle is width times height, lets create a formula:
8x = 44, 44 being the area, and 8x being the width times the variable of the height.
You get 5.5. for the height of the rectangle.
Add 8+8 to 5.5+5.5
you get 27
I need help with dis math
A line that includes the points (t,5) and (10, – 4) has a slope of – 9. What is the value of t? t
Answer:
The value of t is 9.
Step-by-step explanation:
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
In this case, we are given two points: (t, 5) and (10, -4), and the slope is given as -9. So we can set up the equation:
-9 = (-4 - 5) / (10 - t)
Simplifying, we get:
-9 = -9 / (10 - t)
Multiplying both sides by (10 - t), we get:
-9(10 - t) = -9
Expanding the left side, we get:
-90 + 9t = -9
Adding 90 to both sides, we get:
9t = 81
Dividing both sides by 9, we get:
t = 9
Therefore, the value of t is 9.
The number of cases of a disease
increases by the same factor each year, as
shown in the table below.
Write an expression for the number of
cases of the disease after n years.
Start
End of year 1
End of year 2
End of year 3
Number of cases
1400
2100
3150
4725
Answer:
N*r^n
Step-by-step explanation:
Let the initial number of cases at the start of year 1 be represented by N.
From the given information, we know that the number of cases increases by the same factor each year. Let this factor be represented by r.
Then, at the end of year 1, the number of cases would be N*r, since it has increased by a factor of r.
Similarly, at the end of year 2, the number of cases would be Nrr, or N*r^2.
At the end of year 3, the number of cases would be Nrrr, or Nr^3.
We can use this pattern to write a general expression for the number of cases after n years:
N * r^n
where N is the initial number of cases, r is the common factor by which the number of cases increases each year, and n is the number of years elapsed.
Eight avocados cost $4. How much is 1 avocaodo?
The cost of one avacado is equal to 0.5$ and it is found by the use of division method.
One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. an a person who knows what I mean by just calling it what they do when they just want to go to the store. Just call it what they call it, whatever ites. Really, whatever it is, these are the same people. It is a mathematical operation used for equal distribution and equal grouping.
One of the fundamental mathematical operations is division, which involves breaking a larger number into smaller groups with the same number of items.
We are given the cost of 8 avacados= $4.
The cost of 1 avacado= 1/8 * 4 = 1/2 = 0.5.
Hence, the cost of one avacado is equal to $0.5.
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use det() to calculate the determinant of n100. based on this information, do you think that n100 is invertible?
If det(n100) is equal to zero, then n100 is not invertible.
However, if det(n100) is non-zero, then n100 is invertible.
Given that the determinant of a matrix is a value associated with a square matrix, we can use det() to calculate the determinant of n100, as shown below: det(n100)
Based on this information, we cannot conclude whether or not n100 is invertible.
However, we can use the following statement to determine whether or not a matrix is invertible:
A matrix is invertible if and only if its determinant is non-zero.
If det(n100) is equal to zero, then n100 is not invertible.
However, if det(n100) is non-zero, then n100 is invertible.
Therefore, the determinant is an important tool that can help us determine whether or not a matrix is invertible.
Therefore, we must calculate det(n100) to determine if n100 is invertible or not.
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What is the greatest common factor of 9, 24, and 30
Answer: 3
Step-by-step explanation:
9/3=3
24/3= 8
30/3=10
assume there are juniors, seniors, and graduate students in your class and we want to know if their average gpa differ. what is the proper statistical test?
If the average GPA of juniors, seniors, and graduate students in your class differ, you should use a one-way ANOVA test. This is the proper statistical test used to compare the average GPAs of different groups.
ANOVA is used to test whether there are any significant differences between the means of three or more independent groups. In this case, we have three independent groups (juniors, seniors, and graduate students) and we want to determine whether their average GPAs differ significantly by proper statistical test.
If the ANOVA test indicates that there are significant differences between the means, we can use post-hoc tests (such as Tukey's test or Bonferroni's test) to determine which specific group means differ significantly.
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