1) The future value of $460 in 8 months, with an annual interest rate of 12% is $496.10.
2) The present value that must be deposited now so that its value will be $3,500 after 9 months is $3,350.34.
3a) The total amount to be repaid, including accumulated interest, for Zach's purchase of furniture worth $2,800 with a $400 down payment, is $2,552.87.
3b) The monthly payment is $106.37.
How the future value, present value, and monthly payments are determined:An online finance calculator can be used to determine the future value, present value, and monthly payments for 1), 2), and 3).
The future value is the present value compounded into the future at an interest rate.
The present value is the future value discounted to the present period at an interest rate.
1) Future Value:N (# of periods) = 0.6667 years (8/12 months)
I/Y (Interest per year) = 12%
PV (Present Value) = $460
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $496.10
Total Interest = $36.10
2) Present Value:N (# of periods) = 0.75 years (9/12 years)
I/Y (Interest per year) = 6%
PMT (Periodic Payment) = $0
FV (Future Value) = $3,500
Results:
Present Value (PV) = $3,350.34
Total Interest = $149.66
3) Down Payment:The cost of furniture bought by Zach = $2,800
Down payment = $400
Loan amount - $2,400 ($2,800 - $400)
Interest rate = 6%
Loan period = 2 years.
N (# of periods) = 24 months (2 years x 12)
I/Y (Interest per year) = %6
PV (Present Value) = $2,400
FV (Future Value) = $0
Results:
Monthly Payment (PMT) = $106.37
Sum of all periodic payments = $2,552.87
Total Interest = $152.87
The total amount to be repaid = Loan amount + Accumulated Interest
= $2,552.87
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Find the value of x in the figure. Assume segments are tangent
Answer:
9
Step-by-step explanation:
You want the radius of a circle that has a tangent of length 12 meeting an external segment of length 6.
Pythagorean theoremThe given triangle is a right triangle with legs x and 12, and hypotenuse (x+6). The Pythagorean theorem tells you the relationship is ...
(x+6)² = x² +12²
x² +12x +36 = x² +144
12x = 108 . . . . . . . . . . . . subtract (x²+36)
x = 9 . . . . . . . . . . . . . divide by 12
The value of x in the figure is 9.
__
Additional comment
You can also consider what you know about Pythagorean triples. Two that might be applicable to a side length of 12 are {3, 4, 5} and {5, 12, 13}.
If the triple used here were {5, 12, 13}, that would make x=5 and the external segment 13-5=8 instead of 6.
If the triple used here were {3, 4, 5}, it would have a scale factor of 3 to become {9, 12, 15}. Then x=9 and the external segment is 15-9 = 6. This is the solution.
Another way to solve this is using the secant/tangent relation. For this, you need to extend the line 6+x across the circle. Then the relation is ...
12² = 6(6+2x) . . . . tangent² = (segment to near)·(segment to far)
12 = 3 +x . . . . . divide by 12
x = 9
Circle 1 has center (−6, 2) and a radius of 8 cm. Circle 2 has center (−1, −4) and a radius 6 cm.
What transformations can be applied to Circle 1 to prove that the circles are similar?
Enter the scale factor as a fraction in simplest form.
The circles are similar because the transformation rule (_ , _) can be applied to Circle 1 and then dilate it using a scale factor of (_/_)
Answer
its scale factor is 4/3 and 0.75
Step-by-step explanation:
Nicks lunch cost $14.75 tax was 1.03 and he left a tip of 2.50 how much did he pay for his lunch
Answer:
$18.28
Step-by-step explanation:
To complete this problem is a straightforward answer:
First, you add 14.75 + 1.03 which equals $15.78 then, you'll want to add 2.50 to 15.78 and there you have your answer!!
During summer vacation, Alexa read, on average, 10 pages per night. Now that she has returned to school, she is averaging 80% fewer. How many pages per night is Alexa averaging now?
During summer vacation, Alexa read, on average, 10 pages per night. The number of pages per night Alexa averaging now is 2 pages.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
By calculating the percentage of the original Wesley is now reading, we can make the inquiry a little simpler. He is reading 20% of what he used to read rather than 80% less, for example.
Now we need to set up a proportion to solve the problem.
20% of the 10
20/100 = x/10
Cross multiply
20 x 10 = 200
200/100 = 2
He is currently reading 2 pages per night
Thus, the number of pages is 2.
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what is the answer to this question?
Therefore, a point c satisfying the conclusion of the Mean Value Theorem for f(x) = x⁻³ on the interval [1, 8] is approximately x = 2.3608.
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function is often represented as an equation or a graph. It is a fundamental concept in mathematics and plays a crucial role in many areas, including calculus, algebra, and geometry. Functions are used to model real-world phenomena and solve problems in various fields, such as physics, engineering, economics, and more.
Here,
By the Mean Value Theorem, there exists a point c in the open interval (1, 8) such that:
f'(c) = [f(8) - f(1)] / (8 - 1)
where f'(x) is the derivative of f(x).
First, let's find the derivative of f(x):
f(x) = x⁻³
f'(x) = -3x⁻⁴
Now, substitute the values into the Mean Value Theorem equation:
-3c⁻⁴ = [8⁻³ - 1⁻³] / (8 - 1)
Simplify the right-hand side:
-3c⁻⁴ = (1/512) - (1/1)
-3c⁻⁴ = -511/512
Solve for c:
c⁻⁴ = (511/512) / 3
c⁻⁴ = 511/1536
c = [tex](511/1536)^{\frac{1}{4} }[/tex]
c ≈ 2.3608
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5(u+6)-8u=33 what is the simplest answer
Answer:
u = -1
Step-by-step explanation:
5(u + 6) - 8u = 33
5u + 30 - 8u = 33
5u - 8u + 30 = 33
-3u + 30 = 33
-30 = -30
-3u = 3
u = -1
help please - In what kind of an event does a choice made for one decision affect the choices available for the other decisions?
dependent
independent
singular
horizon
There are two red, one blue and one green ball in the box on the left. There are two blue, one red
and one green ball in the box on the right.
Payouts:
• $0 if the balls are different colors,
• $0.50 if they are both red,
• $1 if they are both blue, and
• $16 if they are both green.
Question:
If the game costs $1 to play, would you expect to gain or lose money on average? And how
much?
In your solution, you must show:
• How you compute the probability that payout is $0.
• How you compute the probability that payout is $0.50.
• How you compute the probability that payout is $1.
• How you compute the probability that payout is $16.
• Summarize the data into a probability table.
• Compute the expected value.
• Remember to account for the $1 you pay to play the game.
• Your conclusion.
Each game should cost us roughly 8 cents.This game's expected value is negative, thus playing it is not a good idea because you will most likely lose money in the long run.
How to calculate the expected value?Chance that the reward will be $0:Given problem describes that there can be 4 unique ball colour combinations as :
red and greenred and blueblue and greengreen and blueProvided that each colour contains two balls in the respective boxes, each combination has a probability of happening of 2/4 * 1/3 = 1/6. The likelihood that the payoff will be zero is thus 4 * 1/6 = 2/3.
Chance that the reward will be $0.50:Red balls make two different combinations as: (red, red) in left box and (red, red) in right box. Due to the fact that each box contains just one red ball, each combination has a probability of happening of 1/4 * 1/3 = 1/12. The likelihood that the dividend will be $0.50 is thus 2 * 1/12, or 1/6
Chance that the reward will be $1:Blue balls makes two different combinations as: blue and blue in the left box and (blue, blue) in the right box. Due to the fact that each box contains just one blue ball, each combination has a probability of happening of 1/4 * 1/3 = 1/12. Hence, the likelihood that the payoff will be $1 is 2 * 1/12, or 1/6.
Chance that the reward will be $16:In the left box, there is only one conceivable pair of balls that are both green: (green, green). Given that there is only one green ball in the left box, this combination has a probability of happening of 1/4 * 1/3, or 1/12. Hence, there is a 1/12 chance that the payment will be $16.
Probability table:[tex]Payout\; |\;Probability\\ \ $0 \qquad \qquad 2/3\\$0.50 \quad \qquad 1/6\\$1 \qquad \qquad 1/6\\$16 \qquad \qquad 1/12[/tex]
Expected value:By multiplying each payout by the associated probability and adding them together, the anticipated value is determined. The predicted outcome in this situation is:
[tex]\$ 0 * 2/3 + \$0.50 * 1/6 + \$1 * 1/6 + \$16 * 1/12 - \$1 = -\$0.0833[/tex]
Conclusion:The anticipated value of playing this game, according to the revised figures above, is [tex]-\$0.0833[/tex], which indicates that you should anticipate losing on average roughly $0.08 every game. Thus, it is unprofitable game to play if played on regular basis.
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A quadratic function, f(x), has the -intercepts (-5,0) and (9,0). The point (-2,11) lies on f(x). Complete the statements. The value of is [DROP DOWN 1] and the equation of f(x) in factored form is [DROP DOWN 2].
The quadratic function in factored form can be written as:
f(x) = a(x + 5)(x - 9)
The value of a is -1/3, and the equation of f(x) in factored form is -(1/3)(x + 5)(x - 9).
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.
The -intercepts of a quadratic function correspond to the zeros of the function, which means that the roots of the quadratic equation are -5 and 9.
Therefore, the quadratic function in factored form can be written as:
f(x) = a(x + 5)(x - 9)
where a is a constant. We can find the value of a by using the point (-2,11) that lies on f(x). Substituting x=-2 and y=11 into the function, we get:
11 = a(-2 + 5)(-2 - 9)
11 = a(3)(-11)
11 = -33a
Solving for a, we get:
a = -1/3
Therefore, the equation of f(x) in factored form is:
f(x) = -(1/3)(x + 5)(x - 9)
Completing the statements:
The value of a is -1/3, and the equation of f(x) in factored form is -(1/3)(x + 5)(x - 9).
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brian and leo are flying to their grandmother's house on an airplane where 50 out of 150 seats are window seats and passengers are randomly assigned seats on the plane for each flight. the probability that both brian and leo are both assigned window seats on the way to their grandmother's house (from drop down menu, 1/3, 1/6, 1/9), which is (from drop down menu, the same as, less than, great than), the probability that brian is assigned a window seat on the flight to t his grandmother's house and the flight home from his grandmother's house.
The probability that both Brian and Leo are both assigned window seats on the way to their grandmother's house is the product of the probabilities of each event occurring independently.
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
The probability of an event can be determined by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if a coin is tossed, there are two possible outcomes: heads or tails.
In the given question,
The probability that Brian is assigned a window seat on any one flight is 50/150, which simplifies to 1/3. Since there are two flights involved (one to his grandmother's house and one back), we can think of this as two independent events.
The probability that both Brian and Leo are both assigned window seats on the way to their grandmother's house is the product of the probabilities of each event occurring independently.
P(both assigned window seats on the way there) = P(Brian gets window seat) x P(Leo gets window seat) = (1/3) x (1/3) = 1/9.
The probability that Brian is assigned a window seat on the flight to his grandmother's house and the flight home from his grandmother's house is the probability of the intersection of two events: Brian getting a window seat on the flight there and Brian getting a window seat on the flight back.
Since these are two independent events, we can multiply their probabilities:
P(Brian gets window seat on flight there and back) = P(Brian gets window seat on flight there) x P(Brian gets window seat on flight back) = (1/3) x (1/3) = 1/9.
Comparing the two probabilities, we can see that they are the same:
P(both assigned window seats on the way there) = P(Brian gets window seat on flight there and back) = 1/9.
Therefore, the answer to the second part of the question is "the same as".The probability that both Brian and Leo are both assigned window seats on the way to their grandmother's house is the product of the probabilities of each event occurring independently.
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At a tennis event, 10% of a player's score is based on serves, 40% on return balls, and 50% on wins.
Kyle makes 85% of his serves, returns 70% of the balls, and wins 75% of his games.
What is Kyle's score at the tennis event?
Enter your answer in the box.
Therefore, Kyle's score at the tennis event is 0.74, or 74%.
What is percent?Percent, denoted by the symbol %, is a way of expressing a number as a fraction of 100. Percentages can be used to compare two or more values or to express a change in a quantity over time. Percentages are commonly used to represent proportions, rates, or changes over time, and they are widely used in many fields, such as finance, statistics, and science. To calculate a percentage, we can multiply the given value by the percentage as a decimal or fraction.
Here,
To calculate Kyle's score at the tennis event, we need to use the given percentages for each category and apply them to the weight of each category. First, let's calculate Kyle's score for serves:
Kyle's serves score = 10% of 85%
= 0.1 * 0.85
= 0.085
Next, let's calculate Kyle's score for return balls:
Kyle's return balls score = 40% of 70%
= 0.4 * 0.7
= 0.28
Finally, let's calculate Kyle's score for wins:
Kyle's wins score = 50% of 75%
= 0.5 * 0.75
= 0.375
Now, we can add up all of Kyle's scores to get his overall score:
Kyle's score = Kyle's serves score + Kyle's return balls score + Kyle's wins score
= 0.085 + 0.28 + 0.375
= 0.74
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Find the area of the trapezoid.
( The answer is not 12 )
Answer:
48 units squared
Step-by-step explanation:
The area of a trapezoid is 1/2(base1+base2)*height. By counting, Base 1 is 4 units, base 2 is 8 units, and the height is 8 units. (Just count the squares each side takes and multiply by 2). So we can plug in these values into the formula above, to get 1/2(4+8)*8. Solving this , we get 1/2(12)*8=6*8=48.
Answer:
48 sq units
Your mistake was probably thinking each square unit on the graph was 1 unit, but if you look closely each one is 2, this is proven by the 6 covering 3 boxes.
Step-by-step explanation:
This is the formula for the area of a trap:
A = (a + b)/2 * h
A is the area
a is one of the bases
b is the other base
h is the height
A = (4+8)/2 * 8
A = (12)/2 * 8
A = 6 * 8
A = 48 sq units
Given: Right ∆ABM and right ∆CDM; M is the midpoint of BC-.
Prove: ∆ABM ≅ ∆DCM
Proof: • ∆AMB ≅ ∆CMD ________
BM = √(x₂ − x₁₂)² + (x₂ - y₂)²
= √(4-1)²+(3-3)²
=√3² + (0)²
=√3²=3
CM = √(x₂ − x₁₂)² + (x₂ - y₂)²
= √(7-4)²+(3-3)²
=√3² + (0)²
=√3²=3
• BM- ≅ CM- ____
• Therefore: ∆ABM ≅ ∆DCM; the triangles are congruent by ____
Under the HL criteria, the triangles are congruent. The proof is so finished.
Since M is the midpoint of BC, we have BM = CM.
AM = DM (Given that ∆ABM and ∆CDM are right triangles and M is the midpoint of BC).AB = CD (Given that the triangles are right and ∠AMB = ∠DMC = 90°).Therefore, by Hypotenuse-Leg (HL) congruence criterion, we have:
∆ABM ≅ ∆DCM.BM- = CM- (since BM = CM).Therefore, ∆ABM ≅ ∆DCM; the triangles are congruent by HL criterion.
Hence, the proof is complete.
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graph the following quadratic expression and state the following key features
The answer of the given question based on the quadratic expression is Vertex: (3, -1) , Axis of symmetry: x = 3 , y-intercept: (0, 8) , x-intercepts: (2, 0) and (4, 0) , Shape: upward-opening parabola.
What is Quadratic expression?A quadratic expression is a mathematical expression that can be written in the form ax² + bx + c, where a, b, and c are constants (numbers) and x is a variable. The term "quadratic" comes from the Latin word "quadratus," which means "square."
To graph the quadratic function f(x) = x² - 6x + 8, we can first find the vertex of the parabola by using the formula x = -b/2a. In this case, a = 1 and b = -6, so the x-coordinate of the vertex is x = -(-6)/(2*1) = 3.
To find the y-coordinate of the vertex, we can substitute x = 3 into the expression for f(x):
f(3) = (3)² - 6(3) + 8 = -1
Therefore, the vertex of the parabola is (3, -1).
we can find y-intercept by setting x = 0:
f(0) = (0)² - 6(0) + 8 = 8
So the y-intercept is (0, 8).
To find the x-intercepts, we can set f(x) = 0 and solve for x:
x² - 6x + 8 = 0
(x - 4)(x - 2) = 0
x = 2 or x = 4
So the x-intercepts are (2, 0) and (4, 0).
Finally, we can see that the leading coefficient of the quadratic expression is positive (a = 1), so the parabola opens upward.
Therefore, the key features of the graph of f(x) = x² - 6x + 8 are:
Vertex: (3, -1)
Axis of symmetry: x = 3
y-intercept: (0, 8)
x-intercepts: (2, 0) and (4, 0)
Shape: upward-opening parabola.
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3. A one-tailed hypothesis test with the t statistic
Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for remorse, superficial charm, thrill seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions.
Suppose you have a sample of 40 12-year-old children with antisocial tendencies and you are particularly interested in the emotion of surprise. The average 12-year-old has a score on the emotion recognition scale of 11.80. (The higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion recognition scale are normally distributed.
You believe that children with antisocial tendencies will have a harder time recognizing the emotion of surprise (in other words, they will have higher scores on the emotion recognition test).
What is your null hypothesis stated using symbols?
What is your alternative hypothesis stated using symbols?
This is a tailed test. Given what you know, you will evaluate this hypothesis using a statistic.
Using the Distributions tool, locate the critical region for α = 0.05.
In order to use the t distribution, you will first need to determine the degrees of freedom (df) for α = 0.05. The degrees of freedom (df) is . The critical value of t is .
Your sample of 12-year-old children with antisocial tendencies has an average score of 12.55 with a standard deviation of 3.28.
Calculate the t statistic. To do this, you will first have to calculate the estimated standard error. The estimated standard error is . The t statistic is . (Hint: For the most precise results, retain four significant figures from your calculation of the standard error to calculate the t statistic. Round your final answer to four decimal places, and then round it again to two decimal places for your answer selection.)
The t statistic lie in the critical region. Therefore, you reject the null hypothesis.
Based on the results of this test, there enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies.
Based on the results of this test, there is not enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies.
Is there is enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies?The null hypothesis stated using symbols is: H0: μ ≤ 11.80 (where μ represents the population mean score on the emotion recognition scale for 12-year-old children with antisocial tendencies)
The alternative hypothesis stated using symbols is: H1: μ > 11.80
This is a one-tailed test, as the alternative hypothesis is only looking for an increase in the population mean score for recognizing the emotion of surprise among children with antisocial tendencies.
Using the Distributions tool with a one-tailed test and α = 0.05, the critical region is in the right tail of the distribution and the critical value of t is 1.684.
The degrees of freedom (df) for α = 0.05 and n = 40-1 = 39 is 39.
The estimated standard error is the standard deviation of the sample divided by the square root of the sample size, which is 3.28/√40 = 0.518. The t statistic is (12.55 - 11.80) / 0.518 = 1.45 (rounded to four decimal places), which is not greater than the critical value of t. Therefore, we fail to reject the null hypothesis.
Based on the results of this test, there is not enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies.
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I need help with this please and thanks you. Giving brainiest.
The slope of the line is -3, which means that Scott's delivery time decreased by 3 minutes per day on average.
What is the equation of the line in point-slope form and in slope-intercept form?(a) To find the equation of the line, we can use the point-slope form of the equation, which is:
y - y₁ = m(x - x₁)where m is the slope of the line, and (x₁, y₁) is a point on the line. We can use the two intercepts given in the question as two points on the line.
The y-intercept is (0, 30), and the x-intercept is (10, 0). So, we have:
y - 30 = m(x - 0)
and
y - 0 = m(x - 10)
Simplifying the first equation, we get:
y - 30 = mx
Simplifying the second equation, we get:
y = mx + 0.
We can see that both equations are equivalent and represent the same line.
Therefore, the equation of the line in slope-intercept form is:
y = mx + 30
To find the value of m, we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)where (x₁, y₁) and (x₂, y₂) are any two points on the line. We can use the intercepts given in the question:
m = (0 - 30) / (10 - 0)
m = -3
Therefore, the equation of the line in point-slope form is:
y - 30 = -3(x - 0)
Simplifying, we get:
y - 30 = -3x
(b) The y-intercept of the line is 30, which represents the delivery time on day 0. So, initially, it took Scott 30 minutes to deliver his packages.
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If a player throws two darts 80 times, how many times do you predict each of the
Following sums would occur? 8? 10? 14?
The predictions for the number of times that the following sums would occur are as follows:
8 ; 160 * (3/400) = 1210 ; 160 * (3/400) = 1214 ; 160 * (2/400) = 8How to make the predictionsTo make accurate predictions, we need to follow the binomial distribution rule that assumes the darts to be independent each of other. By this rule, the number of possibilities of the darts being thrown is 2 * 80 which equals 160.
Next, there are three possible ways to achieve the sum of 8 which are (1, 7), (2, 6), or (3, 5). The probabilities are: 1/20) * (1/20) = 1/400. Now we multiply these by the number of possibilities to arrive at:
160 * (3/400) = 12
For the sum of 10, there are also three possible ways, namely: (1, 9), (2, 8), or (3, 7). The probability of getting a sum of 10 on any given throw is 3/400. When we express this, we arrive at:
160 * (3/400) = 12
For the sum of 14, there are two possible ways, namely: (5, 9) or (6, 8). Given the probability of 1/400, the probability of getting a sum of 14 on any given throw is 2/400. When we express this with the binomial distribution, we will arrive at 160 * (2/400) = 8
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Graph the parabola y=(x+5)^2-2
Answer: Use the steps that are easiest to draw a parabola!
Step-by-step explanation:
I used Desmos, here are the key points.
Vertex: (-5,-2)
Extra points to graph:
(-3, -2), (-7,2) (-2, 7), (-8,7) (-1, 14), (-9, 14)Hope this helps!
Find the slant height of the cone.
15 m
11 m
17 m
13 m
An elementary school in Washington gets its school supplies from the district office, 2 miles
away. On a map of the district, this distance is represented by 8 inches. What scale does the
map use?
The scale of the map is that 4 inches on the drawing represents 1 mile in real life
Calculating the scale of the mapWe can use the scale formula:
scale = distance on map / actual distance
In this case, the distance on the map is 8 inches, and the actual distance is 2 miles.
Now we can plug in the values:
scale = 8 inches / 2 miles
scale = 4 inches /1 mile
Therefore, the scale of the map is 4 inches represents 1 mile
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The figure below is a net for a right rectangular prism.
10 in
13 in
10 in
5 in
10 in
10 in
What is the surface area of the right rectangular prism, in square inches?
The surface area of a rectangular prism is 490 in² by the area of each face and then add them up.
Why is it named a rectangular prism ?We refer to the prism as a rectangular prism since each face is shaped like a rectangle. A cuboid, which has six rectangular faces, and each opposite rectangular face is equal to and parallel to another rectangular face is known to have a similar shape.
To find the surface area of the right rectangular prism, we need to find the area of each face and then add them up.
Looking at the net, we can see that there are 6 faces, each with its own dimensions:
The top and bottom faces are both rectangles with dimensions 10 in by 13 in, so each has an area of 10 in × 13 in = 130 in².
The front and back faces are both rectangles with dimensions 10 in by 5 in, so each has an area of 10 in × 5 in = 50 in².
The left and right faces are both rectangles with dimensions 13 in by 5 in, so each has an area of 13 in × 5 in = 65 in².
Therefore, the total surface area of the right rectangular prism is:
2(130 in²) + 2(50 in²) + 2(65 in²) = 260 in² + 100 in² + 130 in² = 490 in²
So, the surface area of the right rectangular prism is 490 square inches.
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How can I integrate this please?
The antiderivative of cos(sin x) is 1/2 (sin⁻¹(sin x) + 1/2 sin(2 sin⁻¹(sin x))) + C.
Describe Integration?Integration is a mathematical technique that involves finding the integral of a function. The integral of a function is the area under the curve of the function, and it is represented by a symbol ∫. Integration is the inverse of differentiation, which is a technique for finding the derivative of a function.
There are two main types of integrals: definite integrals and indefinite integrals. A definite integral is the integral of a function over a specific interval, while an indefinite integral is the integral of a function without specifying the interval. Definite integrals are used to find the area under the curve of a function between two points, while indefinite integrals are used to find a family of functions that differ by a constant.
Let u = sin x, then du/dx = cos x and dx = du/cos x. Substituting these expressions into the integral, we get:
∫ cos(sin x) dx = ∫ cos(u) du/cos x
= ∫ cos(u) du / √(1 - u²)
We can now use a trigonometric substitution to evaluate this integral. Let u = sin θ, then du/dθ = cos θ and:
cos² θ + sin² θ = 1
cos² θ = 1 - sin² θ = 1 - u²
Substituting these expressions into the integral, we get:
∫ cos(u) du / √(1 - u²) = ∫ cos(θ) cos θ dθ
= ∫ cos² θ dθ
= ∫ (1 + cos(2θ))/2 dθ
= 1/2 ∫ dθ + 1/2 ∫ cos(2θ) dθ
= 1/2 (θ + 1/2 sin(2θ)) + C
Substituting back u = sin x and θ = sin⁻¹(u), we get:
∫ cos(sin x) dx = 1/2 (sin⁻¹(sin x) + 1/2 sin(2 sin⁻¹(sin x))) + C
Therefore, this is the antiderivative of cos(sin x).
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This partial circle has a radius of 11 inches.
What is the area of this figure?
Use 3.14 pi.
Enter your answer as a decimal in the box. Round your answer
to the nearest hundredth.
Answer:
284.96
Step-by-step explanation:
Hope it helps:)
Select the correct answer. Which statement correctly describes this expression? 2 m 3 − 11 A. the difference of twice a number and 11 cubed B. twice the cube of a number subtracted from 11 C. the difference of twice the cube of a number and 11 D. the cube of twice a number decreased by 11
The expression "2[tex]m^{3}[/tex]- 11" represents the difference of twice the cube of a number (2[tex]m^{3}[/tex]) and 11, which is option C.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division. It represents a quantity or a relationship between quantities, and it can be simplified or evaluated by performing the indicated operations.
The expression "2[tex]m^{3}[/tex]- 11" can be broken down into two parts: "2[tex]m^{3}[/tex]" and "-11". The first part, "2[tex]m^{3}[/tex]", represents twice the cube of a number (in this case, the number is "m"). To obtain the cube of a number, you multiply the number by itself three times, so "[tex]m^{3}[/tex]" means "m x m x m". Multiplying this by 2 gives "2m x m x m" which can be written as "2[tex]m^{3}[/tex]".
The second part, "-11", simply represents the number 11 decreased by 11. Therefore, the difference between "2[tex]m^{3}[/tex]" ad "-11" is "2[tex]m^{3}[/tex] - 11".
Therefore, the expression "2[tex]m^{3}[/tex] - 11" represents the difference of twice the cube of a number (2[tex]m^{3}[/tex]) and 11, which is option C.
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If I was getting food stamps and I needed three months proof of income and I had to have a gross of 2495 and net of 1920 what would I need to put for the three months income amount?
▸
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the perimeter of the right triangle shown.
-7-6-5-4-3-2-1
5 units
13 units
26 units
30 units
10
5
4
32
2
-1
2
-3
7 7 9 9
-4
-5
-6
2
4 5 6 7
ҳ
Answer:
The perimeter is 5 + 12 + 13 = 26 units.
What is the area of an equilateral triangle with perimeter of 9 ft
[tex]3.9ft^{2}[/tex]
**9) A tree breaks and falls a shown. How tall was the tree before it broke?
Bubble in your answer on the grid. Be sure to use the correct place value.
Hence by using Pythagoras the height of tree before it break is 47.02m
Describe Pythagoras.
The Ionian Greek philosopher and mathematician Pythagoras is credited with creating Pythagoreanism. He was born in 570 BCE in Samos, Ionia (Greece), and passed away at Metapontum, Lucania, between 500 and 490 BCE. (Italy). The three sides of a right-angled triangle are the subject of Pythagoras' most famous theorem, which is now referred as as Pythagoras' theorem.
Let A'CB represent the tree before it broke at point C, and let A' be the point at which the tree's top contacts the earth after it broke. Then, at B, ABC is a right triangle.
AB=20 m and BC=15 m
Using Pythagoras theorem, H² = P²+ B²
In ΔABC
(AC) ²
=(AB)² +(BC) ²
(AC) ²
=(20) ²+15)²
(AC) ² =400+625
(AC) ²=1025
AC= 32.02
Hence total height is 32.02+15 =47.02m
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Find out how much a retirement account based on a principal of $100509 compounded 5% quarterly after 29 years is worth?
Round your answer to 2 decimal places.
The retirement account is worth $424647.577 after 29 years. Rounded to two decimal places, the answer is $424647.577
What is the capital amount with an example?
Capital is the amount you owe at any one time. This is exactly your loan amount if you just took the loan. As you pay EMIs, the principal is reduced and when it reaches zero, your loan is closed.
To calculate the future value of a pension account, we can use the formula:
FV =[tex]FV = P(1 + r/n)^(nt)[/tex]
where:
FV = Future Value
P = capital (initial amount)
r = annual interest (as a decimal)
n = number of times the interest rate is increased per year
t = time (in years)
In this case, the principal is $100,509, the annual interest is 5%, and the interest is compounded quarterly (4 times a year). The period is 29 years.
So we can plug these values into the formula and get:
FV =[tex]100509(1 + 0.05/4)^(4*29)[/tex]
FV = 100509(1.0125)^116
FV = 100509 (4.22497)
FV = $424647.577
Therefore, the value of the retirement account after 29 years is $ $424647.577 Rounded to two decimal places, the answer is $424647.577
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See image !!!!!!!!!!!!!!!!!!!!!
The income elasticity and types of goods, based on the change in demand as a result of a rise in income is:
Tokens = 1. 15 = Normal goodHearts = - 0.38 = Inferior goodClubs = 2. 62 = Normal goodClubs are most likely to be classified as a luxury good.
How to find the income elasticity?To compute the income elasticity of demand for each good, we use the formula:
Income Elasticity of Demand (E) = (% Change in Quantity Demanded) / (% Change in Income)
Tokens:
E = (15% increase in quantity demanded) / (13% increase in income)
E = 15 / 13
E = 1.15
Hearts:
E = (5% decrease in quantity demanded) / (13% increase in income)
E = -5 / 13
E = -0.38
Clubs:
E = (34% increase in quantity demanded) / (13% increase in income)
E = 34 / 13
E = 2.62
A luxury good is a type of normal good with a high income elasticity of demand (E > 1). In this case, clubs have the highest income elasticity of demand (E = 2.62). Therefore, clubs are most likely to be classified as a luxury good.
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