To compute the number of 12 letter combinations of the 26 letters in the alphabet, we can use the formula for combinations, which is:
nCr = n! / r!(n-r)!
where n is the total number of items (26 letters in this case), r is the number of items to choose (12 letters in this case), and ! means factorial (the product of all positive integers up to that number).
Using this formula, we can plug in the numbers:
26C12 = 26! / 12!(26-12)!
= (26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15) / (12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
= 9,675,700
Therefore, there are 9,675,700 possible 12 letter combinations of the 26 letters in the alphabet.
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Distance Formula Assignment \[ \sqrt{\longrightarrow} d-\sqrt{\left(x_{1}-x_{1}\right)^{2}+\left(x_{1}-x_{1}\right)^{2}} \] Express your answex in exact form and approximate form. Round approximate an
The approximate distance between the points P and Q is 5.4 units. In the given distance formula assignment, we have two points P(x₁,y₁) and Q(x₂,y₂). The distance between these points is calculated using the formula:
d = square root of [(x₂ - x₁) squared + (y₂ - y₁) squared]
For the specific values x₁ = 2, y₁ = 3, x₂ = -3, y₂ = 5, the distance is computed as follows:
d = square root of [(-3 - 2) squared + (5 - 3) squared]
= square root of [(-5) squared + (2) squared]
= square root of [25 + 4]
= square root of 29
Hence, the exact distance between the points P and Q is the square root of 29 units. To approximate the value, rounding the square root of 29 to the nearest tenth gives 5.4.
Therefore, the approximate distance between the points P and Q is 5.4 units.
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Determine whether the equation represents a direct variation. If it does, find the constant of variation.
6y=5x-1
yes
Step-by-step explanation:
yes
Answer:
6y = 5x - 1
y = 5/6x - 1/6
From the equation we can see that,
y is directly proportional to x
in the form
y = mx + c
where, m is the slope and c is the constant
Constant of the given variation is -1/6.
Suppose we have a square with vertices at $0,$ $-6 13i,$ $-19 7i,$ and $-13-6i.$ Suppose that we want to multiply these points by a single complex number $a bi$ to get a square with vertices $0,$ $8 2i,$ $6 10i,$ and $-2 8i.$ What is $(a,b)
The number we're looking for, a + bi, is such that
(-6 + 13i) (a + bi) = 8 + 2i
which means
a + bi = (8 + 2i) / (-6 + 13i)
Simplify the right side :
a + bi = (8 + 2i) / (-6 + 13i) • (-6 - 13i) / (-6 - 13i)
… = -((8 + 2i) (6 + 13i)) / ((-6)² - (13i)²)
… = - (48 + 12i + 104i + 26i²) / (36 - 169i²)
… = - (48 - 26 + 116i) / (36 + 169)
… = - (22 + 116i) / 205
Then (a, b) = (-22/205, -116/205).
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Determine whether the statement is true or false. The equation y' = x + y + 1 is separable.
The equation y' = x + y + 1 is not seperable. Therefore the statement is false.
What do you mean by an ordinary differential equation?In mathematics, an ordinary differential equation (also known as an ODE) is an equation made up of one or more functions of a single independent variable and its derivatives. A function having one or more derivatives is a component of a differential equation.
Where are ordinary differential equations used?Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.
If you can express a differential equation as y′=f(x)g(y), where f(x) is only a function of x and g(y) is only a function of y, then the problem is separable. Here, it is not the situation.
But we are not limited to solving separable differential equations. We frequently use integrating factors to solve linear first-order differential equations, such as this one. Using the product rule, multiply your differential equation by an integrating factor—in this example, e—and you get (eyy)′=eyy+eyy′=eyx,
which you may integrate to get your differential equation's solution. Finding integrating factors for generic linear first-order differential equations of the type y′+p(x)y=q may be done in a general way (x).
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Find the vertex of the parabola f(x)=(x-2)^2+1
The vertex of the parabola f(x) = (x-2)^2 + 1 is at (2,1), and it represents the lowest point of the parabola.
The vertex of a parabola in standard form, f(x) = a(x-h)^2 + k, is given by the coordinates (h,k).
Comparing the given equation, f(x) = (x-2)^2 + 1, with the standard form, we can see that h = 2 and k = 1.
Therefore, the vertex of the parabola is located at the point (2,1). The vertex represents the minimum point of the parabola, since the coefficient a (which is positive in this case) determines whether the parabola opens upwards or downwards.
In summary, the vertex of the parabola f(x) = (x-2)^2 + 1 is at (2,1), and it represents the lowest point of the parabola.
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One day a store sold 28 sweatshirts. White ones cost $9.95 and yellow ones cost $13.50. In all, $321.20 worth of sweatshirts were sold. How many of each color were sold?
Answer:
white sold = 16
yellow sold = 12
Step-by-step explanation:
w = # of white sold
y = # of yellow sold
w + y = 28 solve this for w
w = 28 - y
9.95w + 13.5y = 321.20 substitute w = 28-y into this expression and solve for y
9.95(28-y) + 13.5y = 321.20
278.60 - 9.95y + 13.50y = 321.20
278.60 + 3.55y = 321.20
3.55y = 321.20 - 278.60 = 42.60
y = 42.60/3.55 = 12 substitute this into w = 28 - y and solve for w
w = 28 - 12 = 16
An investment adviser has determined that ABCD stock would be an appropriate investment for his client, but only if the price falls from the current level of $50 per share to $35 per share. What MUST the adviser do prior to placing an order to buy ABCD stock for the client's account
Prior to placing an order to buy ABCD stock at a lower price, the investment adviser must conduct thorough research and analysis, set a target price, and determine an appropriate entry point for the purchase.
The investment adviser's primary responsibility is to act in the best interest of their client and make informed investment decisions. In this case, where the adviser believes ABCD stock is appropriate only if the price falls to $35 per share, several steps need to be taken before placing an order.
Firstly, the adviser should conduct comprehensive research on ABCD stock to understand its historical performance, financial health, industry trends, and any relevant news or events that might impact its future prospects. This research will help validate the adviser's belief that the stock is worth considering at a lower price.
Secondly, the adviser should establish a target price of $35 per share based on their analysis and the client's investment objectives. This target price serves as a reference point and provides a clear criterion for initiating the purchase.
Lastly, the adviser needs to identify an appropriate entry point for the purchase. This involves monitoring the stock's price movements and market conditions closely. The adviser may choose to set a limit order at $35 per share or implement a strategy to take advantage of potential price declines, such as dollar-cost averaging.
By following these steps, the investment adviser ensures that they have thoroughly evaluated the investment opportunity and have a plan in place before placing an order to buy ABCD stock for the client's account.
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The table below provides the values of the functions f(x) and g(x) for several values of x. g(x) f(x) -1 ņ -2 1 Īonno 1 1 m-oilo 1 2 3 no - 12 Which of the following is a solution to the equation f(x) = g(x)?
Answer: x= -1
Step-by-step explanation: good luck on the mid terms baddies purrr
Answer:
X= -1
Midterm
You throw three number cubes that are numbers 1-6 all at the same time. What is the probability that you would get a triple 3 on the first throw?
Answer:
3/18 but if you have to simplify it, it would be 1/6
Answer:
1/27Step-by-step explanation:
For each cube the probabilty of number 3 is 1/6 since it is one option out of 6 possible numbers.
The probability of same number on all three cubes is:
P(3,3,3) = 1/3*1/3*1/3 = 1/27can anyone solve this please asap
Answer:
= 1.268Step-by-step explanation:
= (3 + √3) (2 - √3)
= 6 - 3√3 + 2√3 - 3
= 3 - 3√3 + 2√3
= 3 - √3 (3 - 2)
= 3 - √3
= 3 - 1.732 ...... (√3 = 1.732)
= 1.268
The height, s of a ball (in feet) thrown with an initial velocity of 80 feet per second from an initial height of 6 feet is given as a function of the time t (in seconds) by s(t)=-16t^2 +80t+6. Explain in detail how you could find the maximum height of the ball. Now, explain, in detail, a second method of finding the maximum height. Using one of these two methods, determine the time at which height is a maximum and find that maximum height. Be sure to use units in your answer and explain your methods thoroughly.
What is the product of (2i) and (5+3i)?
Group of answer choices
-6 + 10i
10 + 6i
16i
10 - 6i
-6 + 10i
Step-by-step explanation:
Greetings !
Write the expression in product form
\(2i \times (5 + 3i)\)
Apply distributive law a(b+c)=ab+ac
\(2i5 + 2i3i\)
Multiply the numbers
2.5=10=10iMultiply the numbers
2.3=6Apply exponent rule aa=a²
\(ii = i {}^{2} \\ = 6i {}^{2} \)
Apply imaginary number rule i²=-1
=6(-1)=-6
\( = 10i - 6\)
Rewrite in standard complex form:
\( - 6 + 10i\)
Hope it helps!
What does negative 2 over 3 > −1 indicate about the positions of negative 2 over 3 and −1 on the number line?
negative 2 over 3 is located to the right of −1
negative 2 over 3 is located on the left of −1
negative 2 over 3 is located on the right of 0, and −1 is located on the left of 0
negative 2 over 3 is located on the left of 0, and −1 is located on the right of 0
Answer:
2 to the 3rd of the queation would be around 17
Step-by-step explanation:
Answer:
-2 over 3 is located to the left of -1
Step-by-step explanation:
Carmen can type 18 words in 27 seconds. How many words can she type in 60 seconds?
Answer:
40words
Step-by-step explanation:
Answer: 40
Step-by-step explanation: I Took The Test
Which of these expressions is equivalent to – 4(5 – 2x)?
Answer:
-20+8x
Step-by-step explanation:
Answer:
-20 + 8x
Step-by-step explanation:
\(-4(5-2x)\\\\-20+8x\\\\\left \{ {{-4 * 5 = 20} \atop {-4 * -2x = 8x}} \right.\)
Hope this helps.
PLEASE HELP
percent to the nearest inwalreden of a pertent? 11.969.39 9804011 \( 511,61+32 \) ?
Rounding a percentage to the nearest whole number can be done by considering the decimal part of the percentage. For the percentages provided, 11.969 would round to 12%, 39.9804 would round to 40%, and 11.61+32 would equal 43.
To round a percentage to the nearest whole number, we examine the decimal part. If the decimal is 0.5 or greater, we round up to the next whole number. If the decimal is less than 0.5, we round down to the previous whole number. In the given examples, 11.969 has a decimal of 0.969, which is closer to 1 than to 0, so it rounds up to 12. Similarly, 39.9804 has a decimal of 0.9804, which is closer to 1, resulting in rounding up to 40. Lastly, the expression 11.61 + 32 equals 43, as it is a straightforward addition calculation.
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If triangle ABC has sides of lengths 6, 10, and x + 3, between which two numbers must the value of x lie?
Answer:
Step-by-step explanation:jhbhbhjvjhvkhvmvghv
It costs $0.50 to buy 1/3 lb of pears. What is the unit rate for the cost per pound.
The unit cost of pears is $1.50 per pound.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Cost for 1/3 lb of pears = $0.50
Since, 1 lb = 1 pound
Implies that,
Cost of 1/3 pounds of pears = $0.50
To find the cost of one pound of pears,
Use ratio property,
1/3 pound costs = 0.50
1 pound costs = 0.50 x 3 = $1.50
The cost of one pound of pear is $1,.50.
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What is the relation between scale factor and sensitivity of a transducer 1 point?
The relationship between scale factor and sensitivity of a transducer is scale factor is the inverse of the sensitivity
The scale factor is defined as the ratio between the original measurement and the new measurement.
If the scale factor is greater than 1, then the we are enlarging the measurement. If the scale factor is between 0 and 1, then we are shrinking the measurement
The sensitivity of the transducer is the output obtained per unit changes in the input. The higher sensitivity and lower sensitivity will lead to error. So the sensitivity should be moderate
Here the scale factor is inverse of the sensitivity, when the scale factor increases the sensitivity decreases
Therefore, the scale factor is the inverse of the sensitivity
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PLEASE PLEASE HELP ME!!!
how do you identify a perfect square trinomial? give an example
Answer:
Any time you take a binomial and multiply it to itself, you end up with a perfect square trinomial. For example, take the binomial (x + 2) and multiply it by itself (x + 2). The result is a perfect square trinomial.
If Julio earns $31617 for the first year at his job, and he receives a 7% raise each year, how
much will jullo have earned after 4 years in his position? Round the answer to the nearest
dollar.
A) $37617
B $38182
C) $39875
D) $140378
E) $139378
Answer:
$31,617(1 + 1.07 + 1.07^2 + 1.07^3) =
$140,378
D is the correct answer.
6. What is the value of −3 • (7 + (-3)²) ÷ 3? (1 point)
O13
0-2
O-16
O-48ہے
Answer:
\(-16\)
Step-by-step explanation:
\(-3 \cdot (7+(-3)^2) \div 3\)
To simplify this expression, use the order of operations (PEMDAS):
P arentheses
E xponents
M ultiplication
D ivision
A ddition
S ubtraction
First, simplify what is in the parentheses.
\(7 + (-3)^2\)
Remember that any number squared ( \(\Box ^2\) ) is positive, so:
\((-3)^2 = 9\)
Therefore,
\(7 + (-3)^2\)
\(= 7 + 9\)
\(= 16\)
We can now replace the parentheses in the original expression with 16.
\(-3 \cdot (7+(-3)^2) \div 3\)
\(= -3(16) \div 3\)
Finally, simplify by multiplying and dividing.
\(-3(16) \div 3\)
\(= -48 \div 3\)
\(= -16\)
Degrees of freedom for ANOVA is the same as for independent samples t-test
Question 1 options:
True
False
Question 2 (3 points)
In ANOVA, sum of squares is very similar to variance except Question 2 options:
it uses standard error instead
it is not scaled to sample size
it squares the quantity as a final step
it is an omnibus test
Question 3 (3 points)
You are interested in determining if there is a mean difference between people from Canada, Zimbabwe, and Germany. Which of the following would be the best to run?
Question 3 options:
ANOVA
t-test
confidence interval
Correlation
Question 4 (3 points)
You are interested in seeing if there is a mean difference between number off hours spent watching baseball for Yankees fans and Red Sox fans. You would most likely want to run which test?
Question 4 options:
ANOVA
Dependent (paired) samples t-test
Independent samples t-test
Correlation
Question 5 (3 points)
ANOVA is an omnibus test
Question 5 options:
True
False
Question 6 (4 points)
As sample size increases, t-tests are more likely to be....
Question 6 options:
It doesn't influence the statistic
Significant
Nonsignificant
Effective
Question 7 (4 points)
t-test 1: mean difference = 12
t-test 2: mean difference = 20
t-test 2 could be nonsignificant while t-test 1 could be significant
Question 7 options:
True
False
Question 8 (4 points)
The larger the t-statistic, the less likely it is to be significant
Question 8 options:
True
False
Question 9 (3 points)
If our sample size is _____, we often turn to the t-distribution
Question 9 options:
large
unknown
skewed
Small
Question 1: Degrees of freedom differ (False) Question 3: Best test for mean difference (ANOVA) Question 4: Yankees vs Red Sox (Independent t-test) Question 5: ANOVA is an omnibus test (True) Question 6: Larger sample, more significant (Significant) Question 7: T-test results can differ (True) Question 8: Larger t, more likely significant (False) Question 9: Small sample, use t-distribution (Small)
Question 1: The statement is False. The degrees of freedom for ANOVA and independent samples t-test are not the same. In ANOVA, the degrees of freedom are calculated differently than in an independent samples t-test.
Question 3: The best test to determine if there is a mean difference between people from Canada, Zimbabwe, and Germany would be ANOVA. ANOVA is used to compare the means of more than two groups.
Question 4: To determine if there is a mean difference between the number of hours spent watching baseball for Yankees fans and Red Sox fans, you would most likely want to run an Independent samples t-test. This test compares the means of two independent groups.
Question 5: The statement is True. ANOVA is an omnibus test because it examines whether there are any differences among the means of multiple groups.
Question 6: As sample size increases, t-tests are more likely to be significant. With a larger sample size, there is more power to detect small differences between means.
Question 7: The statement is True. It is possible for t-test 2 to be nonsignificant while t-test 1 is significant. This could occur if the mean difference in t-test 2 is not statistically significant, but the mean difference in t-test 1 is.
Question 8: The statement is False. The larger the t-statistic, the more likely it is to be significant. A larger t-statistic indicates a larger difference between means, which is more likely to be statistically significant.
Question 9: If our sample size is small, we often turn to the t-distribution. The t-distribution is used when the sample size is small and the population standard deviation is unknown.
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list five perfect squares.
Perfect squares are numbers gotten by squaring whole numbers. Therefore, 5 exmaples of perfect squares are
4(2^2)
9(3^3)
16(4^4)
25(5^5)
49(7^7)
So 5 perfect squares are 4, 9, 16, 25, 49
for f(x) = 2x + 1 and g(x)=x^2 - 7, find (f - g)(x)
A. x^2 + 2x - 8
B. -x^2 + 2x + 8
C. 2x^2 - 15
D. -2x + 2x - 6
Answer: B
Step-by-step explanation:
\((f-g)(x)=f(x)-g(x)=(2x+1)-(x^{2}-7)=2x+1-x^{2}+7=\boxed{-x^{2}+2x+8}\)
. Lucy orders books from an online bookstore. She pays $12 per book and $8.95 for shipping and handling. How much does she pay in all for 13 books?
Answer:
If the shipping is for all books then the total cost is 164.95
A fan is marked up 40% on the original price. The original price was $20. What is the new price of the fan before sales tax
can someone please help me with this question
What is the range of the function f(x)=3x+1 when the domain is {0, 1, 2}?
a.{2, 4, 10}
b.{1, 4, 7}
c.{3, 4, 5}
d.{2, 6, 18}
Answer:
B) [1, 4, 7]
Step-by-step explanation:
Substitute 0 in
f(0) = 3(0) + 1
Multiple
f(0) = 0 + 1
f(0) = 1
Substitute 1 in
f(1) = 3(1) + 1
f(1) = 3 + 1
f(1) = 4
Substitute 2 in
f(2) = 3(2) + 1
2 = 6 + 1
f(2) = 7
Using the equation y = 3x – 5, what would the output be for an input of 4
Answer:
output(y)=7
Step-by-step explanation:
y=3(4)-5
<=> y= 12-5
<=> y= 7