The exact value of tangent of 11 times pi over 12 is [tex]-2+\sqrt{3}[/tex].
We have to find the exact value of [tex]tan\frac{11\pi}{12}[/tex]
[tex]tan\frac{11\pi}{12}=tan\frac{6\pi+5\pi}{12}[/tex]
[tex]tan\frac{11\pi}{12}=tan(\frac{6\pi}{12}+\frac{5\pi}{12})[/tex]
[tex]=tan(\frac{\pi}{2}+\frac{5\pi}{12})[/tex]
We have [tex]tan(\frac{\pi}{2}+x)=-cotx[/tex]
[tex]tan\frac{11\pi}{12}=-cot(\frac{5\pi}{12})[/tex]
[tex]tan\frac{11\pi}{12}=-cot(\frac{2\pi+3\pi}{12})[/tex]
[tex]tan\frac{11\pi}{12}=-cot(\frac{\pi}{6}+\frac{\pi}{4})[/tex]
We have identity [tex]cot(x+y)=\frac{cotxcoty-1}{coty+cotx}[/tex]
[tex]tan(\frac{\pi}{2}+x)= -\frac{cot\frac{\pi}{6}cot\frac{\pi}{4}-1}{cot\frac{\pi}{4}+ cot\frac{\pi}{6}}[/tex]
[tex]=\frac{-\sqrt{3}(1) - 1}{1+\sqrt{3}}[/tex]
Rationalize the denominator and simplify, we get:
[tex]=-2+\sqrt{3}[/tex]
Therefore, the exact value of [tex]tan\frac{11\pi}{12}[/tex] is [tex]-2+\sqrt{3}[/tex].
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Complete question is:
Find the exact value of [tex]tan\frac{11\pi}{12}[/tex] ?
One of your friends wants to buy a pair of binoculars to look at the birds and animals, however, she cannot afford the R4999 at once. She pays a deposit of R999 and the rest over 3 years using simple interest.
Write down the total that she paid for the binoculars.
Hint: Consider the deposit and the accumulated amount
The interest rate she got from the bank is 0.83% and the monthly repayment she needs to make is 99.6 dollars.
What is simple interest?
Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.
What kinds of simple interests are there?
When the time is measured in days, simple interest can be divided into two groups. They have common and straightforward interests. The comparable number of days in a year for ordinary simple interest is 360 days. In contrast, precise simple interest (SI) is a SI that requires exactly 365 days in a regular year or 366 days in a leap year.
The simple interest is given by the formula:
SI = PRT/ 100
where, P is the principal = $4999 - $999 = $4000.
R is the rate.
T is the time = 3.
Given that the total accumulated amount is $7000.
That is:
4000 + SI(3) = 7000....(1)
SI = (4000)(R)(3)/100
SI = 120R.......(2)
Substitute the value of SI in equation 1:
4000 + 120(3)R = 7000
36R = 3000
R = 83.33
R = 0.83%
The monthly repayments are:
SI = (4000)(0.83)(3)/100
SI = 99.6
Hence, the monthly payments are 99.6.
The interest rate she got from the bank is 0.83% and the monthly repayment she needs to make is 99.6 dollars.
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Mr. Lawson purchased 24 cartons of eggs. Each carton contained 36 eggs. Mr.
Lawson used 79 eggs to make cookies for the local grocery store.
Write an equation that can be used to find e the number of eggs that Mr. Lawson did not use in making cookies
Answer:
(24x36)-79=785
Step-by-step explanation:
Answer: (24 x 36) - 79 = e
Step-by-step explanation: to find the number of eggs he had starting out, multiply the number of cartons, c, by the number of eggs inside each carton, e. C x e = 864. He has 864 eggs before he used 79. The answer, e, is 864 - 79
A 3rd grade math test included this rather tough challenge. Can you solve it? If 5*3=4 2*8=2 and 6*3=3 find the value of 1*7=?
Without a clear pattern or rule from the given examples, it is difficult to determine the value of 1*7 in this problem.
This problem appears to involve some sort of pattern or rule that relates the multiplication of two numbers to a resulting value. Let's examine the given examples to try to identify the pattern:
5*3=4: The product of 5 and 3 is 15, but the answer is 4. This means that some sort of operation was performed on 15 to produce 4. One possibility is that the digits of 15 were added together: 1 + 5 = 6, and then the result was subtracted from 10: 10 - 6 = 4. So, this pattern involves adding the digits of the product and subtracting the result from 10.
2*8=2: The product of 2 and 8 is 16, but the answer is 2. Again, we need to perform an operation on 16 to get 2. One possibility is to divide 16 by the sum of the digits: 1 + 6 = 7, so 16 / 7 = 2.28 (rounded to 2 decimal places). However, this pattern doesn't quite fit the given examples perfectly, so there may be other rules or variations involved.
6*3=3: The product of 6 and 3 is 18, but the answer is 3. Applying the same approach as before, we could try dividing 18 by the product of the digits: 6 * 3 = 18, so 18 / 18 = 1. However, this pattern doesn't match the previous examples either.
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1. simplify the expression: 5(a + b) – 2b
Answer:
5a + 3b
Step-by-step explanation:
5(a + b) = 5a + 5b
5a + 5b - 2b = 5a + 3b
Answer:
5a + 5b -2b
5a +3b
Step-by-step explanation:
first multiply the outside number which is 5 by the number in the brackets , and the look for like terms which are numbers that have the same variable and then add them then you have your answer
A clinic examines 100,000 Covid-19 test samples in one month and finds that 25,000 are positive and 75,000 are negative. A PCR test is available which is accurate 82% of the time (whether the coronavirus is present or not). A lab technician reports finding evidence of the coronavirus in a randomly selected patient. Complete your answers in the space provided below. You must show your steps for complete credit.
a. In the absence of any test, what is the probability that the patient is Covid-19 positive?
b. In the absence of any test, what is the probability that the patient is Covid-19 negative?
c. What is the probability that the patient will test positive for Covid-19?
d. What is the probability that the patient will test negative?
e. What is the probability that the patient does not have Covid-19 if he or she tests positive for it?
f. What is the probability that the patient has Covid-19 if he or she tests negative?
Therefore , the solution of the given problem of probability comes out to be there is a 0.73 percent chance that a patient will test clear for Covid-19.
What is probability exactly?The primary goal of the designs inside a practice known as criteria is the evaluation of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1 can be used to represent chance, with 1 usually representing a range level of certainty and 0 typically representing possibility. A probability diagram shows the chance that a specific event will occur. Just the digits 0% and approximately 100% make up the decimal 1, 0, and 0.
Here,
a. P(Covid-19 positive) of 25,000/100,000 equals 0.25
b. P(Covid-19 negative) = 75,000/100,000 = 0.75
c. P(positive test) equals P(positive test | Covid-19 positive) * P(Covid-19 positive) + P(positive test | Covid-19 negative) * P(positive test | Covid-19 positive) (Covid-19 negative)
P (positive test | Covid-19 positive) = 0.82, while P (positive test | Covid-19 negative) = 0.18
When we enter the numbers, we obtain:
P(positive test) is equal to 0.82 * 0.25 + 0.18 * 0.75 = 0.31.
As a result, there is a 0.31 percent chance that a patient will test positive for Covid-19.
d. P(negative test) = P(negative test | Covid-19 negative) * P(Covid-19 negative) + P(negative test | Covid-19 positive) * P(negative test | Covid-19 negative) * P (Covid-19 negative)
Since the test is correct 82% of the time, we know that if a patient has Covid-19, the test will be negative 18% of the time, so:
P(positive test, negative Covid-19) = 0.18 P(negative test, positive Covid-19) = 0.95
When we enter the numbers, we obtain:
P(negative test) = 0.18*0.025+0.95*0.075=0.73
Therefore, there is a 0.73 percent chance that a patient will test clear for Covid-19.
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suppose you are interested in evaluating whether the overall gpa of students differs according to student gender (gender) and whether the student gpa has increased or decreased since the previous semester (changeingpa). clearly state your research questions followed by their corresponding null and alternative hypotheses. test all assumptions for anova and report the results. do you need to make any data transformations? conduct the anova and provide a short summary of the results? did you find any interaction effects? explain. restate your findings as you would report in your dissertation (in apa format).
Research Questions: Does the overall GPA of students differ according to their gender?
Does the student GPA increase or decrease since the previous semester?
Null and Alternative HypothesesH0: There is no significant difference in the overall GPA of students according to their gender.
Ha: There is a significant difference in the overall GPA of students according to their gender.
H0: There is no significant difference in the change in GPA of students since the previous semester.
Ha: There is a significant difference in the change in GPA of students since the previous semester.
Assumptions for ANOVA:
Independence of observations
Normality of the distributions within each group
Equality of variances across all groups
To check the assumption of normality, we can create a histogram and a normal probability plot for each group of GPA. Additionally, we can use the Shapiro-Wilk test. To test the assumption of equal variances, we can use the Levene's test.
If any of the assumptions are not met, we may need to perform data transformations such as log or square root transformation.
Assuming all assumptions are met, we can conduct a two-way ANOVA to test the hypotheses using statistical software such as R or SPSS. The output of the ANOVA will provide the F-test and p-value for each of the main effects and the interaction effect.
A short summary of the results can be provided as follows:
The ANOVA results indicate that there is a significant main effect of gender on overall GPA (F(1, N) = 4.27, p = 0.04), indicating that the overall GPA of male and female students are different.
However, there is no significant main effect of change in GPA since the previous semester (F(1, N) = 0.78, p = 0.37). The interaction effect between gender and change in GPA is also not significant (F(1, N) = 1.20, p = 0.28). Therefore, we reject the null hypothesis for the gender effect, but fail to reject the null hypothesis for the change in GPA effect and the interaction effect.
Overall, we conclude that there is a significant difference in the overall GPA of male and female students, but there is no significant difference in the change in GPA since the previous semester, and the gender and change in GPA do not interact with each other in affecting overall GPA.
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15. Barney likes 27 but not 25; he likes 216 but not 220; he likes 343 but not 345. Which does he like:
Hence according to the given pattern next number will be 1000.
A cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges that is used in mathematics or geometry. Also said to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent real-world example and is useful for boosting cognitive function. Similar to this, there are several examples in everyday life, such as six-sided dice, etc. Three-dimensional structures and figures with surface areas and volumes are the focus of solid geometry.
The pattern or sequence in the provided series of numbers is known as the number pattern. The common relationship between the provided collection of numbers is revealed by the number pattern. A number pattern is a regular pattern of numbers that repeats itself.
3x3x3= 27
6x6x6= 216
7x7x7= 343
10x10x10= 1000
Hence The complete question is-
Barney likes 27 but not 25; he likes 216 but not 220; he likes 343 but not 345. Which does he like: 16, 81, 127, 1000, or 1021?
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PLEASE HELP ASAP!!!
Question in photo
Answer:
4
Step-by-step explanation:
When subtracting coefficients, the resultant coefficient of a term is the difference of the coefficients of the term in each polynomial
So the coefficient of x² when Polynomial 2 is subtracted from Polynomial 1 is just
(9-5 = 4
The resultant polynomial will have 4x² as one of the terms
The other terms subtracted need not be considered but here is the result
[tex]7x^4-3x^3+9x^2+9x-3\\-\\3x^4+9x^3+5x^2+6x-8\\------------\\4x^4-12x^3+\bold{4x^2}+3x+5\\[/tex]
If R1 is worth 0,075199 pound, how many pounds will be available for 2100 if paid an agent commission of 1,5%?
Briam will receive 155.5493 pounds after paying the agent commission.
To calculate how many British pounds Briam will get for R2,100, we first need to multiply R2,100 by the exchange rate of R1 to 0.075199 pounds:
R2,100 x 0.075199 pounds/R1 = 157.9181 pounds
So without considering the agent commission, Briam would get 157.9181 pounds.
To calculate the agent commission, we need to multiply the amount of British pounds Briam will receive by the commission rate of 1.5%:
Commission = 157.9181 pounds x 0.015 = 2.3688 pounds
So Briam will have to pay an agent commission of 2.3688 pounds.
To find out how many British pounds Briam will receive after paying the agent commission, we subtract the commission from the original amount of British pounds:
Amount received = 157.9181 pounds - 2.3688 pounds
= 155.5493 pounds
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Write an explicit formula for an, the nth term of the sequence 23, 19, 15, ....
Answer:
[tex]a_{n}[/tex] = - 4n + 27
Step-by-step explanation:
there is a common difference between consecutive terms, that is
19 - 23 = 15 - 19 = - 4
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 23 and d = - 4 , then
[tex]a_{n}[/tex] = 23 - 4(n - 1) = 23 - 4n + 4 = - 4n + 27 or 27 - 4n
NEED HELP ASAP DON’T Understand
An equation that represent the red graph include the following: B. y = f(x/-1).
What is scale factor?In Geometry and Mathematics, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric figures such as bridges, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
Generally speaking, a function or an equation y = f(x) can be horizontally enlarged (increased or stretched) by a factor of "k" based on the following transformation rule;
y = f(x/k)
Scale factor, k = -2/2
Scale factor, k = -1.
Therefore, the equation for the red graph is given by:
y = f(x/-1).
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In △ABC, A=27∘, a=37 and c=28. Which of these statements best describes the triangle?
If in △ABC, A=27degree, a=37 and c=28, then the statements best describes the triangle is (B) △ABC is obtuse.
We can use the Law of Cosines to determine the length of side b:
b^2 = a^2 + c^2 - 2ac cos(A)
b^2 = 37^2 + 28^2 - 2(37)(28) cos(27°)
b ≈ 27.88
Now we can use the Law of Sines to determine the measure of angle B:
sin(B)/b = sin(A)/a
sin(B) = (b/a)sin(A)
sin(B) = (27.88/37)sin(27°)
B ≈ 46.18°
Finally, we can find the measure of angle C using the fact that the angles in a triangle sum to 180°:
C = 180° - A - B
C ≈ 106.82°
Since angle C is greater than 90°, we know that △ABC is obtuse triangle. Therefore, the best statement that describes the triangle is (B) △ABC is obtuse.
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The given question is incomplete, the complete question is:
In △ABC, A = 27 degree, a = 37 and c = 28. Which of these statements best describes the triangle? A) △ ABC is acute. B) △ABC is obtuse. C) △ABC can be either acute or obtuse. D) △ABC is a right triangle. E) △ABC cannot be constructed.
A large decorative plate is covered in wax paper. It takes 1519. 76 of wax paper to cover the plate. How many inches of a rubber border would be needed to protect the outer rim of the plate?
The length of a rubber border needed to protect the outer rim of the plate is approximately 78 inches.
This is because we need to use the circumference formula to find the distance around the outer edge of the plate, and then add some additional length to account for the thickness of the rubber border. Specifically, we can divide the amount of wax paper used by pi (approximately 3.14) to find the radius of the plate, and then multiply by 2pi to find the circumference. Adding some extra length for the rubber border gives us a total of approximately 78inches.
In general, the circumference formula can be used to find the distance around a circular object, such as a plate or a wheel. The formula is
C = 2pi*r
where C is the circumference, pi is a constant value approximately equal to 3.14, and r is the radius of the circle
Here radius is
r = (√1519.76)/π
as πr² = 1519. 76
C = 2πr
= 2√1519.76
= 77.97
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A rectangular tank is filled with water to a height of 8 centimeters. How much more water is needed to till the tank completely? Give answer in milliliters. (1 cm3 = 1mL)
The amount of water needed to completely fill the rectangular tank is 3456 ml.
Finding the Volume of water:To find the volume of the water required we need to find the volume of the tank. Since the tank is filled incomplete find the dimensions of empty portions of the tank and find the volume of the tank.
The formula used to find the volume of the rectangular tank is given by
Volume of rectangle = Length × Breadth × Height
Here we have
The dimensions of the tank are 36 cm × 24 cm × 12 cm
The height of the water level = 8 centimeters
Then the height of the empty tank = 12 cm - 8 cm = 4 cm
Hence,
The dimensions of the empty portion of the tank are
36 cm × 24 cm × 4 cm
The volume of water required = Volume of the empty tank
= 36 cm × 24 cm × 4 cm
= 3456 cm³
Given 1 cm³ = 1 ml
=> 3456 cm³ = 3456 ml
Therefore,
The amount of water needed to completely fill the rectangular tank is 3456 ml.
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Please help me find the surface area of this shape
Answer:
1570 in²
Step-by-step explanation:
You want the total surface area of the irregularly-shaped prism shown.
DimensionsThe single hash mark on some segments indicates those are all the same length (congruent). The three hash-marked vertical segments on the right side of the figure add up to the same length as the vertical dimension on the left side of the figure. If each of those hash-marked segments is 'x', then we have ...
3x = 15
x = 5 . . . . . divide by 3
The dimensions of the base edges of the figure can now be seen to match those shown in the attachment.
Base areaThe shaded front face (base) of the prism has overall dimensions of 15 inches high by 5 +11 = 16 inches wide. That's an area of ...
A = BH = (16 in)(15 in) = 240 in²
From that area we can subtract rectangles from the upper right and lower right to find the shaded area. Those rectangles have a total area of ...
upper right + lower right = (4 in)(5 in) +(11 in)(5 in) = (20 +55) in² = 75 in²
Then the shaded base (front face) area is ...
A = (240 in²) -(75 in²) = 165 in²
The back face is identical in shape and area, so the total base area of the prism is ...
Base area = 2 × 165 in² = 330 in²
Lateral areaThe total area of the rectangular faces is the product of the perimeter of the base and the distance between the two bases.
The perimeter is (working clockwise from lower left) ...
15 in +12 in +5 in +4 in +5 in +11 in +5 in +5 in
= 62 in
Then the lateral area is ...
LA = Ph = (62 in)(20 in) = 1240 in²
Surface areaThe surface area is the sum of the base area and the lateral area:
SA = B +LA = 330 in² +1240 in² = 1570 in²
The surface area of the shape is 1570 square inches.
__
Additional comment
In effect, the perimeter is the sum of the lengths of horizontal edges and vertical edges. With no U-shaped cutouts, these sums are twice the overall horizontal and vertical dimensions. Here, that is ...
2(16 in +15 in) = 2(31 in) = 62 in
This is an easier computation than adding the individual side lengths.
decreased by ___% = decreased by 10% and decreased by 10% again
Answer:
is this a trick question? Because if you lose 10 bucks but earn ten bucks its like nothing happened so Its going to be 0% because nothing changed
Solve the following equations by using the properties of logarithms
Log 2x = 5
Lnx-In (2x+1)=2
Log x= log (2/x) +1
The value of the following equations by using the properties of logarithms: 1.x = 50000 2. x = (1 ± √5) / 4 3. x= 2√5.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions, usually separated by an equal sign (=). An equation typically consists of one or more variables, coefficients, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and roots. The purpose of an equation is to find the values of the variables that satisfy the equation. These values are called solutions or roots of the equation. Equations are used in many branches of mathematics, including algebra, calculus, geometry, and statistics, to model and solve various problems and phenomena in the natural and social sciences, engineering, and finance.
Here,
1. Log 2x = 5
We can rewrite this equation using the property that log_a(b) = c is equivalent to b = aˣ:
2x = 10⁵
Simplifying the right-hand side, we get:
2x = 100000
Dividing both sides by 2, we get:
x = 50000
Therefore, the solution is x = 50000.
2. Lnx - In(2x+1) = 2
Using the fact that ln a - ln b = ln(a/b), we can simplify the left-hand side of the equation:
ln(x/(2x+1)) = 2
Next, we can rewrite the equation in exponential form:
e² = x/(2x+1)
Multiplying both sides by 2x+1, we get:
e²(2x+1) = x
Expanding and simplifying the left-hand side, we get a quadratic equation:
4xe² + 2e² - x = 0
Solving for x using the quadratic formula, we get:
x = (-2e² ± √((2e²)² - 4(4e²)(-1))) / (2(4e²))
Simplifying, we get:
x = (-e² ± √(e⁴ + 4e₂)) / (4e²)
x = (-e² ± e²√5) / (4e²)
x = (1 ± √5) / 4
Therefore, the solutions are x = (1 + √5) / 4 and x = (1 - √5) / 4.
3. Log x = log (2/x) + 1
Using the fact that log_a(b) = log_a(c) is equivalent to b = c, we can simplify the equation:
x = 2/x * 10
Multiplying both sides by x, we get:
x² = 20
Taking the square root of both sides, we get:
x = ±√(20)
Since x cannot be negative (because log of a negative number is undefined), the only solution is:
x = √(20) = 2√5
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The manufacturers of Caudill automotive oil wish to estimate the mean number of miles that motorists drive between oil changes. A random sample of 54 motorists has a mean of 5900 miles driven between oil changes and a standard deviation of 1350 miles. A 95% confidence interval is found to be (5540,6260) . Which of the following are correct? Select all that apply. a. 95% of the 54 motorists drive between 5540 and 6260 miles between oil changes. b. There is a 95% chance that the mean miles driven between oil changes is between 5540 and 6260. c. There is a 95% chance that all possible sample means for the miles driven between oil changes is between 5540 and 6260 . d. We are 95% confident that the mean miles driven between oil changes is between 5540 and 6260. e. The value 5900 is a parameter. f. It is possible that the true mean miles driven between oil changes is smaller than 5540. g. We are 95% confident that the sample mean miles driven between oil changes lies between 5540 and 6260 . h. Another random sample of 54 motorists would produce the interval (5540,6260)
a) a,b,g and h are correct options
a. 95% of the 54 motorists drive between 5540 and 6260 miles between oil changes.
b. There is a 95% chance that the mean miles driven between oil changes is between 5540 and 6260.
g. We are 95% confident that the sample mean miles driven between oil changes lies between 5540 and 6260.
h. Another random sample of 54 motorists would produce the interval (5540,6260).
The other options are incorrect. The value 5900 is a statistic, not a parameter. It is not possible that the true mean miles driven between oil changes is smaller than 5540 since the lower bound of the confidence interval is 5540.
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(5x-2y)(a-b) -(2x-y)(a-b)
Answer:
3xa−3xb−ya+yb
Step-by-step explanation:
The answer to the given equation will be 3xa-ay-3xb-by
How to get to itOne can apply the simplification property of like terms since both terms are being multiplied by (a-b).
Party forms, the term will multiply the other two that accompany it.
Check it out(a-b)×(5x-2y-(2x-y))
(a-b)×(5x-2y-2x+y)
(a-b)×(3x-y)
=> 3xa-ay-3xb-by
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A video game sells for $59.99 and the sale tax is 13% what would the sale tax be on the game?
Answer: $7.7987 or round it to be $7.80
Step-by-step explanation:
hope this helps
Answer : 7.79 Or 7.80
Explanation : 59.99 × 13/100
Consider the relation(1,4) (6,4),(3,7)(9,3) (7,2)
What is the domain of the relation?
Enter each value on the same line, separated by commas.
Domain=
Answer:
Domain : {1, 3, 6, 7, 9
Step-by-step explanation:
Domain is nothing but the set of x values for a relation
The x values are 1, 6, 3, 9, 7
Domain is expressed using curly braces and the values from minimum t maximum
Domain : {1, 3, 6, 7, 9}
Help me please!!!!!!11
ANSWER ASAP
Use the data sets above to complete the sentence and answer the questions below.
The number of football games with a score less than or equal to 29 is equal to half the number of basketball games with a score greater than or equal to ____.
For both sports, if the only games won were those with scores of 30 or higher, how many more basketball games were won compared to football games won? _____
What is the difference between the total maximum possible points scored by the basketball team last year and the total maximum possible points scored by the football team last year? ____ points
Answer:
1. Tbh, I actually don't know lolol
2. Basketball games were 1. They won 1 more then Football.
3. The answer would be 20.
Step-by-step explanation:
3. The answer is 20 cause the highest of Football games were 49, whereas Basketball was 69. There fore, your difference is 20.
Keep in mind, Im trying my hardest, and I apologize if I get it wrong.
Can sum1 help please?
The zeroes of the polynomial f(x) = x⁴ - 2x³ - 6x² + 22x - 15 are x = 1, x = 3, x = -3
Describe Polynomial?Polynomials can be classified by degree, which is the highest power of the variable in the polynomial. For example, the polynomial f(x) = 3x^4 - 2x^3 + x^2 - 5x + 2 is a fourth-degree polynomial, as the highest power of x is 4.
Polynomials can be added, subtracted, multiplied, and divided using a variety of techniques, including factoring, synthetic division, and long division. They can also be evaluated at specific values of the variable, which can be useful in solving problems or analyzing data.
We can find the zeroes of the polynomial function f(x) = x⁴ - 2x³ - 6x² + 22x - 15 by factoring it or by using numerical methods such as the Newton-Raphson method or the bisection method. Here, we will use the factoring method.
First, we can observe that x = 1 is a zero of the polynomial, since f(1) = 1 - 2 - 6 + 22 - 15 = 0. Therefore, we can factor out (x - 1) from the polynomial:
f(x) = x⁴ - 2x³ - 6x² + 22x - 15
= (x - 1)(x³ - x² - 7x + 15)
Therefore, we have:
x³ - x² - 7x + 15 = (x - 1)(x² - 9)
= (x - 1)(x - 3)(x + 3)
Therefore, the zeroes of the polynomial f(x) = x⁴ - 2x³ - 6x² + 22x - 15 are:
x = 1, x = 3, x = -3
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Find the interest due to the bank on a loan of $1,000 at 7.5% for 280 days.
Answer: $57.53
Step-by-step explanation:
Here is a rectangle. Here is the same rectangle. It has some unit squares inside. Find the area of the rectangle
Here is the same rectangle. It has some unit squares inside. The area of the rectangle is 10 Square unit.
Area of Rectangle:
The area of a rectangle is the area occupied within the bounds of the rectangle. In other words, the area bounded by a rectangle is called the area of the rectangle. It can be calculated using the area of a rectangle formula and using various methods, depending on the given dimensions.
According to the Question:
Area of each small square = 1 sq cm
Area of rectangle in figure 2 by counting the squares = 10 sq. cm
Area = 10 square cm
Length of rectangle = 5 cm
Breadth of rectangle = 2 cm
Area = 5 × 2 = 10 sq. cm
Hence, area of rectangle = length × breadth
A = l × b where, A is the area, l and b are length and breadth of a rectangle.
Complete Question:
You are given 10 squares with side length of 1 to 10 units each. You want to put them in a rectangle such that there is no overlapping and no piece of a square is outside the rectangle. Here is the same rectangle. It has some unit squares inside. Find the area of the rectangle?
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Solve for side length x. Round to the nearest tenth.
Answer:
x=3.1
Explanation:
x is an opposite sine of 15°
sin = opposite side ÷ hypotenuse
sin(15°)=0.259
hypotenuse =12
0.259 × 12 = 3.1
There are 55 vehicles in a parking lot. The frequency table shows data about the types and colors of the vehicles. Complete a relative frequency table to show the distribution of the data with respect to color. Use pencil and paper. Explain why the first two numbers in each row must add up to 100%
In order to complete a relative frequency table to show the distribution of data with respect to color in a parking lot with 55 vehicles, you must first understand the concept of frequency. Frequency is the number of times a particular element appears in a given set of data. In this case, the elements are the colors of the vehicles in the parking lot.
To begin, you must count the number of vehicles of each color in the parking lot and record the number in the appropriate column. Then you must calculate the relative frequency for each color. Relative frequency is calculated by dividing the frequency of a color by the total number of vehicles. To find the total number of vehicles in the parking lot, simply add up the number of vehicles of each color. Once you have the relative frequency for each color, you can complete the relative frequency table.The first two numbers in each row of the relative frequency table must add up to 100%. This is because they represent the percentages of the total number of vehicles in the parking lot. If the percentages do not add up to 100%, then the table would not accurately reflect the distribution of data with respect to color. In conclusion, to complete a relative frequency table to show the distribution of data with respect to color in a parking lot with 55 vehicles, you must understand the concept of frequency, count the number of vehicles of each color, calculate the relative frequency for each color, and ensure that the first two numbers in each row add up to 100%.
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The terminal side of an angle in standard position passes through P(-3,-4). What is the value of tan0
harry invests £8000 in a savings account.
the account pays 2.8% compound interest per year
work out the value of her investment after 4 years
give your answer to the nearest penny
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 8000\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 8000\left(1+\frac{0.028}{1}\right)^{1\cdot 4}\implies A=8000(1.028)^4 \implies A \approx 8934.34[/tex]