A. In this instance, the research hypothesis may be that the new workout is successful in lowering the incidence of heart attacks.
What is p-value?A p-value is a statistical indicator that, under the null hypothesis, shows the likelihood of receiving a test statistic that is as extreme to or more extreme than the one seen in the sample data. Depending on the degree of statistical significance the researcher selects, it is employed in hypothesis testing to determine whether to reject or fail to reject the null hypothesis. The null hypothesis is rejected in favour of the alternative hypothesis if the p-value is less than or equal to the selected level of significance (typically 0.05). The null hypothesis is not rejected if the p-value is higher than the selected level of significance.
A. In this instance, the research hypothesis may be that the new workout is successful in lowering the incidence of heart attacks.
B. The alternative hypothesis may be that the additional exercise has no impact on the frequency of heart attacks.
C. Depending on the study's specific design and the outcome measure used to gauge the prevalence of heart attacks, the comparison distribution would vary.
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3.27 Underage drinking, Part 2: we learned in Exercise 3.25 that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty 18-20 years old. What is the probability that 45 or more people in this sample have consumed alcoholic beverages? Answer is 0.0006
In conclusion, the probability that 45 or more people in a sample of fifty 18-20 year olds have consumed alcoholic beverages is 0.0006. This can be calculated by using the binomial distribution formula or by visually representing the data in a probability tree diagram.
The probability that 45 or more people in a sample of fifty 18-20 year olds have consumed alcoholic beverages is 0.0006. This can be determined by using the binomial distribution formula. The formula states that the probability of getting x successes in n trials is equal to nCr x (p)x (1-p)n-x, where n is the number of trials (in this case, 50), p is the probability of success (69.7%), and x is the number of successes (45). By plugging these values into the formula, we obtain a probability of 0.0006.
In addition to the binomial distribution formula, we can also use a visual representation such as a probability tree diagram to represent the given data. The probability tree diagram can be used to show the number of ways a certain outcome can occur. In this case, it would be the probability of 45 or more people in the sample of fifty 18-20 year olds consuming alcoholic beverages. The probability tree diagram consists of a trunk which branches off into multiple possible outcomes. At the end of each branch, there is a probability that corresponds to the probability of the given outcome occurring.
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GIVING BRAINLIEST! IF TWO OR MORE PEOPLE ANSWER!
Answer:
a. Goron 224
b. Smith 96
Fishman 256
Step-by-step explanation:
a. For Goron: 640 x 0.35 = 224
b. For Smith: 640 x 0.15 = 96
For Fishman: 640 x 0.40 = 256
the city cafe is known for their vegetable plate lunch special that comes with four vegetables, cornbread, and sweet tea. if the four vegetables can be selected from a list of ten vegetables, what formula should be used to determine how many different vegetable plates are there? assume no vegetable is selected more than once
From the given list of vegetables, the number of different ways in which these vegetables can be selected from a list of vegetables such that no vegetable is selected more than once given here by the formula of Combination, which is: [tex]^nC_k[/tex] = n!/[k!(n-k)!].
What is the formula for vegetable plates?The city café is known for its vegetable plate lunch special that comes with four vegetables, cornbread, and sweet tea. If the four vegetables can be selected from a list of ten vegetables, the formula to determine how many different vegetable plates there are would be a combination of 10 vegetables taken 4 at a time.
The number of different ways that four vegetables can be selected from a list of ten vegetables is given by the formula of Combination, which is:
[tex]^nC_k[/tex] = n!/[k!(n-k)!]
where, n = number of elements in the set = 10 vegetables
k = number of elements chosen = 4 vegetables
n - k = number of elements not chosen = 10 - 4 = 6 vegetables
Therefore, the number of different vegetable plates is:
[tex]^nC_k[/tex] = 10!/ [4!(10-4)!]
[tex]^nC_k[/tex] = (10×9×8×7)/ (4×3×2×1) = 210
Hence, there are 210 different vegetable plates.
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Let Y be a binomial random variable with n trials and probability of success given by p. Use the method of moment-generating functions to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p.
Let Y be a binomial random variable with n trials and probability of success given by p. We are to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p.
Binomial random variables are a type of discrete random variables which have the following properties:Each trial is independent, with two possible outcomes called success and failureThe probability of success p is the same for each trial. The binomial random variable X is the number of successes that occur in n trials.
The probability distribution of X is given by:P(X = x) = ( n choose x ) p^x(1 - p)^(n - x)for x = 0, 1, 2, ... , nThe moment-generating function of X is given by:M(t) = E(e^(tX)) = sum_(x=0)^n [ (n choose x) p^x(1-p)^(n-x) e^(tx)]We are to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p.
Since Y is a binomial random variable, it has the following moment-generating function:M_Y(t) = E(e^(tY)) = sum_(y=0)^n [ (n choose y) p^y(1-p)^(n-y) e^(ty)]Note that U = n - Y, so that n - u = y or u = n - y. Then the moment-generating function of U is given by:M_U(t) = E(e^(tU)) = E(e^(t(n - Y))) = E(e^(nt) e^(-tY)) = e^(nt) E(e^(-tY)) = e^(nt) M_Y(-t).
Thus the moment-generating function of U is the product of a term that is independent of y and the moment-generating function of a binomial random variable with n trials and probability of success 1-p. Therefore, U is a binomial random variable with n trials and probability of success 1-p.
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A blueprint shows an apartment with
an area of 15 square inches. If
the blueprint's scale is
1 inch : 8 feet, what will the actual
square footage of the apartment be?
The actual area of the apartment will
be
square feet.
A blueprint shows an apartment with an area of 15 square inches. If the blueprint's scale is 1 inch : 8 feet. The actual area of the apartment will be 960 square feet.
Dilation:
Inflation is the process of increasing the size of an item without affecting its shape. Depending on the scale factor, the size of the object can increase or decrease. Dilation is a transformation used to change the size of an object. Dilation is used to make objects larger or smaller. This transformation produces an image of the same shape as the original.
The dilation should either stretch or contract the original shape. This transformation is referred to as the "scaling factor".
When zooming in produces a larger image, it is called zooming in.
If dilation produces a smaller image, this is called downscaling.
There is no effect of dilation on the angle.
A blueprint shows an apartment with an area of 15 square inches.
If the blueprint's scale is 1 inch : 8 feet.
Then the scale factor will be 8/1 feet per inch.
Then the actual area square footage of the apartment will be
Actual area = 15 x (scale factor)²
Then the actual area of the footage will be
⇒ Actual area = 15 x (8/1)²
⇒ Actual area = 15 x 64
⇒ Actual area = 960 square feet
Thus, the actual area of the apartment will be 960 square feet.
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Two cars are driving away from an intersection in perpendicular directions. The first cars velocity isms 7 meters per second and the second cars velocity is 3 meters per second. At a certain instant, the first car is 5 meters from the intersection and the second car is 12 meters from the intersection. What is the rate of change of the distance between the cars at that instant?
The rate of change of the distance between the cars at that instant is 5.46 meters/ second.
The first car's velocity = 7 meters per second
The second car's velocity = 3 meters per second.
Distance from the intersection of first car = 5m
Distance from the intersection of second car = 12m
The rate of change is used to numerically quantify the percentage change in value over a predetermined period of time. It is a measure of a variable's velocity.
Calculating the distance between both cars at the instant
= √(12² + 5²)
= √ 144 + 25
= √169
= 13
Calculating the rate of change of distance -
2d/dt
= d(x² + y²)/dt
= 2x dx/dt + 2ydy/dt
= 2×5×7 + 2×12×3
= 70 + 72
= 142
Therefore, total distance -
dd/dt
= 142/26
= 5.46
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Please help me with this question thank you
Answer:
∠DCB = 32
Step-by-step explanation:
∠A + ∠B = 90
∠B = 90 - ∠A = 90 - 32 = 58
∠DCB + ∠B = 90
∠DCB = 90 - ∠B = 90 - 58 - 32
matching question match the sets on the left with a true statement about the cartesian product of those sets on the right. {1, 2} x {3, 4} = {1, 2, 3, 4} x {3, 4, 5, 6} = {4, 5, 6, 7} x {4, 5, 6, 7} = {a, e, i, o, u} x {b, g, t, d} =
{1, 2, 3} x {1, 2, 4} =
Choose:
(5, 5) is a member.
its cardinality is 4. (2, 2) is a member. its cardinality is 20.
(4, 3) is a member.
The correct answer is: (4, 3) is a member. Its cardinality is 4.
Matching the sets on the left with a true statement about the Cartesian product of those sets on the right:{1, 2} × {3, 4} = {(1, 3), (1, 4), (2, 3), (2, 4)}{1, 2, 3, 4} × {3, 4, 5, 6} = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), (4, 3), (4, 4), (4, 5), (4, 6)}{4, 5, 6, 7} × {4, 5, 6, 7} = {(4, 4), (4, 5), (4, 6), (4, 7), (5, 4), (5, 5), (5, 6), (5, 7), (6, 4), (6, 5), (6, 6), (6, 7), (7, 4), (7, 5), (7, 6), (7, 7)}{a, e, i, o, u} × {b, g, t, d} = {(a, b), (a, g), (a, t), (a, d), (e, b), (e, g), (e, t), (e, d), (i, b), (i, g), (i, t), (i, d), (o, b), (o, g), (o, t), (o, d), (u, b), (u, g), (u, t), (u, d)}{1, 2, 3} × {1, 2, 4} = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (2, 4), (3, 1), (3, 2), (3, 4)}The following are true statements about the Cartesian product of these sets:its cardinality is 4. (4, 3) is a member.
Therefore, the correct answer is: (4, 3) is a member. Its cardinality is 4.
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1/sinx+cosx + 1/sinx-cosx = 2sinx/sin^4x-cos^4x
The simplified expression is 2cos²(x) + sinx - 1 = 0
The expression we will be simplifying is
=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.
To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:
(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)
Simplifying this expression using the distributive property, we get:
(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)
Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:
1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1
Similarly, for the second fraction, we can use the same identity to obtain:
1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1
Substituting these values back into the original expression, we get:
1 + 1 = 2sinx/(sin⁴x - cos⁴x)
Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:
sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ
Substituting this back into the expression, we get:
2 = 2sinx/(sin²ˣ - cos²ˣ)
Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):
2 = -2sinx/cos(2x)
Multiplying both sides by -cos(2x), we get:
-2cos(2x) = 2sinx
Dividing both sides by 2, we get:
-cos(2x) = sinx
Using the double-angle formula for cosine, we get:
-2cos²(x) + 1 = sinx
Simplifying this expression, we get:
2cos²(x) + sinx - 1 = 0
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Anita borrowed ₹6000 from a bank at 15% interest rate per annum. Find the interest and
amount to be paid at the end of 3 years.
Answer: The interest and amount to be paid at the end of 3 years is Rs.8700
Step-by-step explanation:
let P ,R, T be the Principle amount , Rate of interest and Time
Given that ,P= 6000rs
R= 15%
T=3 years
Interest= PRT÷ 100=6000rs×15r×3t÷100
=2700rs
value to be paid after 3 years = 6000rs+2700rs= 8700rs
Suppose a tank of water is a cylinder. The tank has a diameter of 14 inches and is filled
to a height of 9 inches. A fish tank decoration is placed in the tank and the water rises
by 2 inches with the decoration being completely covered by water. Find the volume of
the decoration to the nearest tenth of a cubic inch.
The decoration's volume, to the closest tenth of an inch cubic, is: 308.9 cubic inches make up V.
what is volume ?The quantity of space that an object or substance occupies is measured by its volume. Usually, it is expressed in cubic measures like cubic metres, cubic feet, or cubic inches. By multiplying an object's length, width, and height, or by applying a formula unique to the shape of the object, one can determine the volume of the object.
given
The cylinder's radius is equal to half of its diameter, or 14/2, or 7 inches. The new water level is 9 + 2 = 11 inches because the initial water level was 9 inches and the decoration raised the water level by 2 inches.
The decoration's volume is equivalent to the volume of water it removed from the area.
We can determine the volume of the ornamentation by using the following formula: V = r2h.
V = (72/2), which equals 98 cubic inches.
The decoration's volume, to the closest tenth of an inch cubic, is: 308.9 cubic inches make up V.
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NEED HELP
5. Find the value of the variables of t and s
In given triangle, the value of t is 3.75 and the value of s is 10.4.
What are the 3 sides of a triangle?In a right triangle, the hypotenuse is the longest side, a "opposite" side is the one across from a given angle, and a "adjacent" side is close to a given angle. We use unique terminology to describe the sides of right triangles.
We can set up the following ratios because the two triangles in the illustration are comparable to one another:
t / 5 = 6 / 8 (using the smaller triangle)
s / 13 = 8 / 10 (using the larger triangle)
Simplifying these ratios, we get:
t / 5 = 3 / 4
s / 13 = 4 / 5
We may cross-multiply and simplify to find t and s:
t = 5(3/4) = 15/4 = 3.75
s = 13(4/5) = 10.4
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Find X
Picture Below
Step-by-step explanation:
From CalcWorkshop:
" Intersecting Chords Theorem. If two chords or secants intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord "
6 * 4 = 8 * x
x = 3
why can't we use mean when a data set has one or two values that are much higher than all of the others
The reason we can't use the mean when a data set has one or two values that are much higher than all of the others is that it skews the average, making it not representative of the rest of the data.
What is the mean?The mean is a numerical measure of the central tendency of a data set. It is calculated by dividing the sum of all the values in a data set by the number of data points.
A data set is a collection of observations or measurements that are analyzed to obtain information. It can be represented graphically, in tabular form, or in any other format. The data set may be a sample or the entire population.
If a data set has one or two extremely high or low values, it can significantly impact the mean. These values are known as outliers. The outliers can cause the mean to be higher or lower than the actual middle value of the data.
Hence, in such cases, the median is a better choice for finding the central tendency of the data. The median is the middle value of the data set, and it is less affected by outliers than the mean. The mode, which is the value that occurs most frequently in the data set, is also a measure of central tendency that is less sensitive to outliers than the mean.
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Create a Dataset Give a positive integer less than 100 as the last data value in each of the following datasets so that the resulting dataset satisfies the given condition (a) The mean of the numbers is substantially less than the median 51,52,53,54 (b) The mean of the numbers is substantially more than the median 2,3,4,5, (c) The mean and the median are equal. 2,3,4,5
(a) Dataset with mean substantially less than median:
9, 10, 11, 12, 90
The mean of this dataset is (9+10+11+12+90)/5 = 26.4, while the median is 11, which is substantially greater than the mean. The last data value is 90, which is a positive integer less than 100.
(b) Dataset with mean substantially more than median:
98, 99, 100, 101, 200
The mean of this dataset is (98+99+100+101+200)/5 = 119.6, while the median is 100, which is substantially less than the mean. The last data value is 200, which is a positive integer less than 100.
(c) Dataset with mean equal to median:
2, 3, 4, 4, 5
The mean of this dataset is (2+3+4+4+5)/5 = 3.6, which is equal to the median (the middle value of the dataset). The last data value is 5, which is a positive integer less than 100.
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Find the slope of the tangent line to the ellipse x^(2)/16 +y^(2)/4=1 at the point (x,y). slope =?
Are there any points where the slope is not defined? (Enter them as comma-separated ordered-pairs, e.g., (1,3), (-2,5). Enter none if there are no such points.) slope is undefined at ?
The slope of the tangent line at the point (x,y) is -x/(2y). The ellipse's slope is not defined at the coordinates (4, 0), (-4, 0).
What is slope of a tangent?The rate of change of a curve at a certain position is represented by the slope of a tangent line to the curve at that location. In other words, it indicates whether the curve is steep or shallow at that particular location. Calculating the derivative of a function in calculus also requires estimating the slope of a tangent line, which is a crucial step. We may determine the slope of the tangent line and subsequently the derivative of the function at a location by determining the limit of the slope of a secant line as the two points on the line approach closer and closer together.
The equation of the ellipse is x²)/16 +y²/4=1.
We take the derivative of the equation with respect to xto find the slope:
x²/16 + y²/4 = 1
(x²/16)' + (y²/4)' = 1'
2x/16 + 2y/4 * dy/dx = 0
dy/dx = -x/(2y)
When the denominator of 2y equals 0, there are some locations where the slope is not specified. The ellipse's slope is not defined at the coordinates (4, 0), (-4, 0), and all locations on the x-axis between these two points when y = 0, which occurs.
Hence, the slope of the tangent line at the point (x,y) is -x/(2y). The ellipse's slope is not defined at the coordinates (4, 0), (-4, 0).
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Education Planning For the past 15 years, an employee of a large corporation has been investing in an employee sponsored educational savings plan. The employee has invested $8,000 dollars per year. Treat the investment as a continuous stream with interest paid at a rate of 4.2% compounded continuously.
a. What is the present value of the investment?
b. How much money would have had to be invested 15 years ago and compounded at 4.2% compounded continuously to grow to the amount found in part a?
The amount that would have had to be invested 15 years ago and compounded at 4.2% compounded continuously to grow to the present value is $37,537.19.
The investment can be treated as a continuous stream with the interest paid at a rate of 4.2% compounded continuously.The present value of the investment can be calculated using the formula:P = C/e^(rt)Where,P = Present ValueC = Cash Flowsr = Interest Rate Per Periodt = Number of Periodse = Euler’s numberThe given values are as follows:C = $8,000 per yearr = 4.2% compounded continuously for 15 years.
C = $8,000e = 2.71828t = 15 yearsNow, we need to calculate the present value using the above formula.P = 8000/e^(0.042 x 15) = $82,273.24.The formula to calculate the amount that would have been invested 15 years ago is:A = P x e^(rt)Where,A = Future Value of the investmentP = Present Value of the investmentr = Rate of Interest Per Periodt = Number of Periodse = Euler’s numberThe present value of the investment is $82,273.24.
The rate of interest is 4.2% compounded continuously.t = 15 yearsNow, we need to calculate the amount that would have been invested 15 years ago.A = 82,273.24 x e^(0.042 x 15) = $37,537.19
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I don't really understand how to do reference angles. I only need the last one, -60 degrees, does anyone know how to figure out it's reference angle?
Answer: 60?
Step-by-step explanation:
The reference angle is the acute angle formed between the terminal side of an angle in standard position and the x-axis. To find the reference angle of an angle, you can follow these steps:
Determine the quadrant in which the angle terminates. For -60 degrees, this would be the fourth quadrant.
Determine the corresponding angle in the first quadrant by finding the angle formed between the terminal side and the x-axis. In the fourth quadrant, this angle is equal to 360 degrees minus the original angle. So for -60 degrees, the corresponding angle in the first quadrant is 360 - 60 = 300 degrees.
Subtract this angle from 360 degrees to find the reference angle. For -60 degrees, the reference angle is 360 - 300 = 60 degrees.
Therefore, the reference angle of -60 degrees is 60 degrees.
Part A: Graph the system of equations {−2x+y=6x−y=1
Part B: Determine the solution from Part A.
Answer:
Step-by-step explanation:
An important math tool is graphing. It can be a straightforward method for introducing more general concepts like most and least, greater than, or less than. It can also be a great way to get your child interested in math and get them excited about it. Using graphs and charts, you can break down a lot of information into easy-to-understand formats that quickly and clearly convey key points.
Given equation 2x + y = 6 we can drive from this equation that at x = 0 y will be 6 and y =0 x will be 3 hence we have two points of the line (0,6) and (3,0)
From the Given equation (2) 6X + 3Y = 12 we can drive from this equation that at x = 0 y will be 4 and y =0 x will be 2 hence we have two points of the line (0,4) and (2,0).
For every seven dogs at the vet there are 10 cats if there is a total of 102 dogs and cats how many cats were at the vet
The total number of cats at the vet is approximately 61.
What is a proportion?A percentage is an equation proving the equality of two ratios. A ratio is a fractional comparison of two numbers or quantities. Proportions are used in mathematics to solve issues that involve comparing two numbers or discovering an unknown value. For instance, proportions can be used to determine equivalent fractions, compute percentages, and solve issues requiring rates and ratios. In a proportion, the numerator of one ratio is the same as the numerator of the other ratio, and vice versa for the denominator. Simplifying and cross multiplying can be used to address proportional problems.
Let the total number of dogs =x.
Let the total number of cats = y.
Given that, for every seven dogs at the vet there are 10 cats.
Thus, using proportions we have:
7 dogs / 10 cats = x / y
Using cross multiplication:
7 dogs x y = 10 cats (x)
y = (10/7) (x)
Now, x +y = 102
x = 102 - y
Substituting the value:
y = 10/7 (102 - y)
y = 145.71 - 1.4y
y + 1.4y = 145.71
2.4y = 145.71
y = 60.71
Hence, the total number of cats at the vet is approximately 61.
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Francis has an unpaid balance of $480 on his credit card. The annual percentage rate is 12%. What is the finance charge on his next monthly statement?
Answer:
$4.80
Step-by-step explanation:
You want to know the finance charge on a balance of $480 if the APR is 12%.
Finance chargeThe monthly finance charge is the product of the monthly interest rate and the balance. The monthly interest rate is 1/12 of the annual rate.
finance charge = (1/12 · 12%) · $480 = 0.01 · $480 = $4.80
The finance charge on the next monthly statement is $4.80.
For her phone service, Leila pays a monthly fee of $27, and she spends an additional $0.06 per minute of use. The least she has been charged in a month is $102.90.
What are the possible numbers of minutes she has used her phone in a month?
Use m for the number of minutes, and solve your inequality for m.
Answer:
Step-by-step explanation:
First Of all, Say the N-word, Now if she said the N-word, shell be given 27 dollars,Now I need to do my Homework, if i made you laugh, mark me the Brainliest
What is the scale factor of the following pair of similar polygons ?
The scale factor of the following pair of similar polygons after the dilation is 0.7
Calculating the scale factor of the similar polygonsGiven
The pair of similar polygons
From the pair of similar polygons, we have the following corresponding side lengths
Pre-image of the polygon = 30
Image of the polygon = 21
The scale factor of the similar polygons is then calculated as
Scale factor = 21/30
Evaluate the quotient
Scale factor = 0.7
Hence, the scale factor is 0.7
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4. A polygon with area 10 square units is dilated by a scale factor of k. Find
the area of the image for each value of k. (Lesson 5-4)
a. k = 4
b. k = 1.5
c. k = 1
d. k = 1/3
Answer:
If a polygon is dilated by a scale factor of k, then its area is multiplied by k².
a. When k = 4, the area of the image is 10 × 4² = 160 square units.
b. When k = 1.5, the area of the image is 10 × 1.5² = 22.5 square units.
c. When k = 1, the area of the image is 10 × 1² = 10 square units. (The image is the same size as the original.)
d. When k = 1/3, the area of the image is 10 × (1/3)² = 10/9 square units.
Step-by-step explanation:
cos(-180").tan 8.cos 690 sin (8-180) cos² (6-90) (5)
cos(-180°) = -1
tan 8° = 0.1425
cos 690° = 0
sin (8-180°) = - sin 172° = - 0.9997
cos² (6-90°) = cos(-84°) = 0.4997
Therefore, the answer to the expression is -0.4997.
Can someone help me with this please?
To solve the question asked, you can say: So, the other angle of the figure is 49 degree.
what are angles?In Euclidean geometry, an angle is a shape consisting of two rays, known as sides of the angle, that meet at a central point called the vertex of the angle. Two rays can be combined to form an angle in the plane in which they are placed. Angles also occur when two planes collide. These are called dihedral angles. An angle in planar geometry is a possible configuration of two rays or lines that share a common endpoint. The English word "angle" comes from the Latin word "angulus" which means "horn". A vertex is a point where two rays meet, also called a corner edge.
here the given angles are as -
107 + (180-156) + x = 180
as total angle sum of a triangle is 180
so,
x = 180 - 131
x = 49
So, the other angle of the figure is 49 degree.
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you have spent $2,500 on liquor for your bar. your bar sales have been $12,890. what is your cost of sales for liquor, expressed as a percentage?
The cost of sales for liquor, expressed as a percentage is 19.39%.
What is the cost of sales for liquor in percentage?To compute for the cost of sales for liquor, expressed as a percentage given that you have spent $2,500 on liquor for your bar and your bar sales have been $12,890, you can use the formula:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
where, Cost of Goods Sold (COGS) = Beginning Inventory + Purchases - Ending Inventory (or the total cost of goods sold during the period)
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
Let's compute for the COGS first:
COGS = Beginning Inventory + Purchases - Ending Inventory
= $0 + $2,500 - $0
= $2,500
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
= $12,890 - $0 - $0
= $12,890
Cost of sales is obtained as follows:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
= ($2,500 / $12,890) × 100
= 19.39%.
Therefore, the cost of sales for liquor, expressed as a percentage is 19.39%.
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Answer?
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The nth term of a sequence is n²+ a.
The 6th term of the sequence is 29
Find the sum of the first 4 terms.
Answer:
2
Step-by-step explanation:
Seq. nth term, sum
The nth term of a sequence is n^2+ a
The 6th term of the sequence is 29
Find the sum of the first 4 terms
We are given that the nth term of the sequence is n^2 + a.
To find the value of 'a', we can use the fact that the 6th term of the sequence is 29.
Substituting n = 6 in the expression for the nth term, we get:
6^2 + a = 29
Simplifying this equation, we get:
a = 29 - 6^2
a = -7
So, the expression for the nth term of the sequence is:
n^2 - 7
Now, we need to find the sum of the first 4 terms of the sequence.
The first term of the sequence is given by substituting n = 1 in the expression for the nth term:
1^2 - 7 = -6
The second term of the sequence is given by substituting n = 2:
2^2 - 7 = -3
The third term of the sequence is given by substituting n = 3:
3^2 - 7 = 2
The fourth term of the sequence is given by substituting n = 4:
4^2 - 7 = 9
Therefore, the sum of the first 4 terms of the sequence is:
-6 + (-3) + 2 + 9 = 2
25 POINTS
1. Explain the process of verifying a trigonometric identity.
2. What is a similarity and difference between verifying a trigonometric identity and solving an equation?
3. How do you find the value of cos120° using the sum or difference formula?
4. How do you decide whether to use a positive or negative sign in the half- angle formula for sine and cosine?
5. When solving a trigonometric equation, what is the difference between finding all solutions and finding all solutions within a specific interval?
The process of verifying trigonometric identity involves the use of Pythagorean theorem, double angle formula etc. The similarity between verifying a trigonometric identity and solving an equation is that it both involves mathematical expressions.
What is the process of verifying a trigonometric identity?1. The process of verifying a trigonometric identity involves using various trigonometric identities and properties to manipulate one side of the equation until it is simplified to the other side. This typically involves using algebraic manipulations, such as factoring and combining like terms, as well as trigonometric identities such as the Pythagorean identity, double angle formula, or sum and difference formula.
2. One similarity between verifying a trigonometric identity and solving an equation is that both processes involve manipulating mathematical expressions. However, a key difference is that verifying a trigonometric identity requires proving that the identity holds for all values of the variables involved, whereas solving an equation involves finding the specific values of the variables that make the equation true.
3. To find the value of cos120° using the sum or difference formula, we can use the fact that 120° is equal to 60° + 60°. We can then use the cosine sum formula, which states that cos(x+y) = cos(x)cos(y) - sin(x)sin(y), with x = y = 60°. This gives us:
[tex]cos(120\°) = cos(60\° + 60\°) = cos(60\°)cos(60\°) - sin(60\°)sin(60\°) = \frac{1}{2}*\frac{1}{2} - (\sqrt(3)/2)(\sqrt(3)/2) = -1/2[/tex]
Therefore, cos120° = -1/2.
4. The sign to use in the half-angle formula for sine and cosine depends on the quadrant in which the angle lies. If the angle is in the first or second quadrant, we use the positive sign. If the angle is in the third or fourth quadrant, we use the negative sign. For example, if we want to find sin(x/2) and x lies in the third quadrant (i.e., between 180° and 270°), we use the negative sign in the formula sin(x/2) = -√((1-cos(x))/2).
5. When solving a trigonometric equation, finding all solutions means determining all possible values of the variable that make the equation true, regardless of the range of values allowed for the variable. Finding all solutions within a specific interval, on the other hand, means restricting the values of the variable to a certain range and finding all possible solutions within that range. This is important because trigonometric functions are periodic and have infinitely many solutions, so it is often necessary to specify a range of values in order to obtain a finite set of solutions.
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4/7+1/8+1/3 prime number
According to the solution, the Given number is not prime (7/8 or 0.875). This doesn't qualify as a prime number.
What does a prime number mean in mathematics?Prime numbers are those that have just two elements, one and themselves. For instance, the first five prime numbers are 2, 3, 5, 7, and 11. Comparatively, composite numbers are defined as having more than two elements.
How are prime numbers taught in schools?Try to divide the number by all the smaller numbers to see if your child can determine whether it is prime. It is a prime number if it can only be divided by itself and by one.
According to the given information.= 4/7+1/8+1/3
= 7/8 or 0.875
This is not a prime number.
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