what is the distance between the points (7,-5) and (7,6)

Answer:

67.50

Step-by-step explanation:

The equation which can be used to find the original price of the headphones is x = 71.80 + 17.95 and the original price is $89.75.

Given that:

The amount which is being discounted for a pair of wireless headphones is $17.95.

The amount which is paid after the discount for the headphones is $71.80.

It is required to find the equation to find the original price of the headphones.

Let x represent the original price of the headphones.

Original price = Amount paid after the discount + Amount which is being discounted.

Substituting the given values,

x = 71.80 + 17.95

x = $89.75

Hence, the original price is $89.75.

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The marble is equally likely to be green, red, or blue as it is to be yellow.

Answer:

There would have been, 20 bottles collected, 25 pieces of paper collected, and 10 cardboard boxes. Theses three therefore show 55/100, of the total amount collected.

Step-by-step explanation:

Answer: There would have been, 20 bottles collected, 25 pieces of paper collected, and 10 cardboard boxes. Theses three therefore show 55/100, of the total amount collected.

Step-by-step explanation:

a. True. The product of two 2 x 2 matrices A and B is given by the formula AB = [a1*b1 + a2*b3, a1*b2 + a2*b4; a3*b1 + a4*b3, a3*b2 + a4*b4], where a1, a2, a3, and a4 are the elements of A and b1, b2, b3, and b4 are the elements of B.

In this case, the columns of A are ay and az, and the columns of B are bI and ba. So, the product AB is given by [ay*bI + az*ba, ay*ba + az*bb], which is equivalent to [a,b ab].

b. True. Each column of AB is a linear combination of the columns of B using weights from the corresponding column of A. This is because the elements of each column of AB are obtained by multiplying the elements of the corresponding column of A with the elements of the corresponding row of B and summing the products.

c. True. The sum of two matrices is obtained by adding the corresponding elements of the matrices.

So, AB+ AC = [a1*b1 + a2*b3 + a1*c1 + a2*c3, a1*b2 + a2*b4 + a1*c2 + a2*c4; a3*b1 + a4*b3 + a3*c1 + a4*c3, a3*b2 + a4*b4 + a3*c2 + a4*c4] = [a1*(b1+c1) + a2*(b3+c3), a1*(b2+c2) + a2*(b4+c4); a3*(b1+c1) + a4*(b3+c3), a3*(b2+c2) + a4*(b4+c4)] = A(B+C).

d. True. The transpose of a matrix is obtained by flipping the matrix along its main diagonal. So, AT + BT = [a1, a3; a2, a4] + [b1, b3; b2, b4] = [a1+b1, a3+b3; a2+b2, a4+b4] = (A + B)T.

e. False. The transpose of a product of matrices equals the product of their transposes in the reverse order. So, if A and B are two matrices, then (AB)T = BT*AT.

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The correct options are:-

Option B: Translation of 1 unit right

Option F: Vertical stretch by a factor of 2

Translation is a type of transformation in mathematics that involves moving a shape or object without changing its size, shape or orientation.

This is done by sliding the object along a straight line in a particular direction, such as up, down, left or right.

Based on the given information, the transformations that were applied to the red graph to obtain the blue graph are:

A translation of 1 unit right (Option B).

A vertical stretch by a factor of 2 (Option F).

Therefore, the correct options are:

Translation of 1 unit right?

Vertical stretch by a factor of 2.

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The required system of inequalities is given as x > 8y ≥ 4850x + 1300y ≤ 16000 which means that Nadia has a budget of $16,000 dollars to spend and she can spend it in any way, but not exceeding the budget.

To write the system of inequalities for the given situation of Nadia's budget of $16,000 dollars to spend on tracking devices to study grizzly bears, a radio tracker costs $850, and a GPS tracker costs $1300 and Nadia wants to buy more than 8 radio trackers and at least 4 GPS trackers, the following system of inequalities are used:

x > 8

y ≥ 4

850x + 1300y ≤ 16000

This system of inequalities represents the given situation where x is the number of radio trackers and y is the number of GPS trackers. The inequalities describe the following:

1. x > 8: Nadia wants to buy more than 8 radio trackers

2. y ≥ 4: Nadia wants to buy at least 4 GPS trackers

3. 850x + 1300y ≤ 16000:

Nadia has a budget of $16,000 dollars to spend and she can spend it in any way, but not exceeding the budget.

Thus, the required system of inequalities is given as:x > 8y ≥ 4850x + 1300y ≤ 16000.

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Answer:

√36 = 6

a^2 + b^2 = c^2

6^2 + 6^2 = c^2

36 + 36 = c^2

72 = c^2

√72 = c

2 36

2 18

2 9

3 3

6√2 = c

6√2 = (estimate rounded up, 8.49)

48000 is your awnserrrr

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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the given series ∑n=1∞ \((-1)^n(n^3)/(5^n)\) converges.

To determine whether the series ∑n=1∞ \((-1)^n(n^3)/(5^n)\) converges or diverges, we can apply the ratio test.

The ratio test states that for a series ∑aₙ, if the limit of the absolute value of the ratio of consecutive terms is less than 1 as n approaches infinity, then the series converges. Mathematically, it can be represented as:

lim (n→∞) |aₙ₊₁ / aₙ| < 1

Let's apply the ratio test to the given series:

aₙ = (-1)^n(n^3)/(5^n)

aₙ₊₁ =\((-1)^{(n+1)}((n+1)^3)/(5^{(n+1)})\)

Now, let's calculate the limit:

lim (n→∞)\(|(-1)^{(n+1)}((n+1)^3)/(5^{(n+1)}) / (-1)^n(n^3)/(5^n)|\)

Simplifying the expression:

lim (n→∞)\(|(-1)((n+1)^3)/(5) / (n^3)/(5^n)|\)

Since the negative signs cancel out, we have:

lim (n→∞) \(|(n+1)^3/(n^3 * 5)|\)

Expanding \((n+1)^3\):

lim (n→∞) \(|(n^3 + 3n^2 + 3n + 1)/(n^3 * 5)|\)

Now, let's simplify the expression:

lim (n→∞) \(|1 + 3/n + 3/n^2 + 1/n^3)/(5)|\)

As n approaches infinity, the terms with \(3/n, 3/n^2, and 1/n^3\) approach zero.

Therefore, the limit simplifies to:

lim (n→∞) |1/5|

The absolute value of 1/5 is less than 1.

Therefore, the series converges according to the ratio test.

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The complementary function for the differential equation is ye(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\). The particular solution for the differential equation is \(Yp(x) = -7e^(^6^x^)\). The general solution for the differential equation is y(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\) -\(7e^(^6^x^)\).

To find the complementary function for the given differential equation, we assume a solution of the form \(ye(x) = e^(^r^x^)\), where r is a constant to be determined. Plugging this into the differential equation, we get:

\(r^2e^(^r^x^) + 6e^(^r^x^) = 0\)

Factoring out \(e^(^r^x^)\), we obtain:

\(e^(^r^x^)(r^2 + 6) = 0\)

For a nontrivial solution, the term in the parentheses must equal zero:

\(r^2 + 6 = 0\)

Solving this quadratic equation gives us r = ±√(-6) = ±i√6. Hence, the complementary function is of the form:

ye(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\)

Next, we need to find the particular solution Yp(x) for the differential equation. The particular solution is assumed to have a similar form to the forcing term \(-294x^2^e^(^6^x^).\)

Since this term is a polynomial multiplied by an exponential function, we assume a particular solution of the form:

\(Yp(x) = (A + Bx + Cx^2)e^(^6^x^)\)

Differentiating this expression twice and substituting it into the differential equation, we find:

12C + 12C + 6(A + Bx + Cx^2) = \(-294x^2^e^(^6^x^)\)

Simplifying and equating coefficients of like terms, we get:

12C = 0 (from the constant term)

12C + 6A = 0 (from the linear term)

6A + 6B = 0 (from the quadratic term)

Solving this system of equations, we find A = -7, B = 0, and C = 0. Therefore, the particular solution is:

\(Yp(x) = -7e^(^6^x^)\)

Finally, the general solution for the differential equation is given by the sum of the complementary function and the particular solution:

y(x) = ye(x) + Yp(x)

y(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\) - \(7e^(^6^x^)\)

This is the general solution to the given differential equation.

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Answer:

Fractions

Step-by-step explanation:

the first step would be to conveery 50 into 100. put 40/50 in a fraction and mutiply by two.

\(\frac{40}{50}\) x \(\frac{2}{2}\) = \(\frac{80}{100}\). convert this to a percent. therefore, mark's average in english is an 80%. do the same with his math .

The probability is 5/12 or about 0.4167

What is Probability?

Probability is a branch of mathematics concerned with numerical descriptions of how likely an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates a certainty.

To determine the probability that the sum of the numbers on two dice is greater than 4, we must count the favorable outcomes and divide them by the total number of possible outcomes.

Let's consider all the possible outcomes of rolling two dice:

Cube 1: {1, 2, 3, 4, 5, 6}

Dice 2: {1, 2, 3, 4, 5, 6}

To find favorable results, we need to determine all combinations where the sum of the numbers is greater than 4.

Favorable results:

{2, 3, 4, 5, 6} (1:1 dice, 2:1 dice)

{3, 4, 5, 6} (1:1 dice, 2:2 dice)

{4, 5, 6} (1:1 dice, 2:3 dice)

{5, 6} (1:1 dice, 2:4 dice)

{6} (1:1 dice, 2:5 dice)

{5, 6} (1:2 dice, 2:1 dice)

{4, 5, 6} (1:2 dice, 2:2 dice)

{3, 4, 5, 6} (1:2 dice, 2:3 dice)

{2, 3, 4, 5, 6} (1:2 dice, 2:4 dice)

{2, 3, 4, 5, 6} (1:3 dice, 2:1 dice)

{3, 4, 5, 6} (1:3 dice, 2:2 dice)

{4, 5, 6} (1:3 dice, 2:3 dice)

{5, 6} (1:4 dice, 2:1 dice)

{4, 5, 6} (1:4 dice, 2:2 dice)

{5, 6} (1:5 dice, 2:1 dice)

{6} (1:6 dice, 2:1 dice)

There are 15 favorable outcomes out of a total of 36 possible outcomes (6 choices for die 1 multiplied by 6 choices for die 2).

The probability of getting a sum greater than 4 when rolling two dice is:

P(sum > 4) = favorable results / total results

= 15/36

= 5/12

So the probability is 5/12 or about 0.4167.

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Answer:

As per the question, Peter can finish twice as much work as finished by Tom in a given duration of time. of their one day work will be completed by Tom. So, Tom will take 48 days to complete the task

Step-by-step explanation:

Let Tom alone take 2x days

Peter alone will take x days

Together in 1 day they do 1/x + 1/2x = 1/16

3/2x = 1/16

2x = 48

ANSWER Tom takes 48 days and Peter takes 24 days

CHECK

1/48+1/24 = 3/48= 1/16

Sally's conclusion that high school GPA is an excellent and useful predictor of performance ratings at work is not entirely supported by the correlation coefficient of 0.09 with a significance level of p<.01.

Although a significant correlation suggests a positive association between high school GPA and performance ratings, the strength of the relationship is weak. The practical significance of such a weak correlation may be limited in real-world scenarios where multiple factors can influence job performance.

It is also important to note that correlation does not imply causation.

Therefore, even if high school GPA is significantly correlated with performance ratings at work, it does not necessarily mean that high school GPA is a causative factor in better job performance. Other variables such as work experience, motivation, and personality may also contribute to predicting job performance, and their effects should also be taken into account when assessing the usefulness of high school GPA as a predictor.

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 Total volume of the salt shaker is 56.52+706.5=763.02 cm³

The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr²h.

Given here: The volume of a salt shaker  

The radius of the salt shaker which is 5 cm

Thus the volume of the cylinderical salt shaker is = π×3²×5²

                                                                                  =706.5 cm³

and the volume of the hemisphere at the top is=  (2/3)πr³

                                                                               =56.52 cm³

Hence, Total volume of the salt shaker is 56.52+706.5=763.02 cm³

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The complete question is Which is a better estimate for the volume of a salt shaker? where radius =3 cm and height =5 cm

Answer:

|279|

Step-by-step explanation:

so when ur doing absolute value you js need distance so lets work with the problem, if ur 279 feet below water u would need to get to zero feet below sea level (ground lvl) to do so how many feet towards ground lvl would u go? (279 clearly) so the distance from how many feet under u are to the ground lvl is ur absolute value.

Tbh in school they over complicate it if u need an absolute number from a negative number like -279 (as it is in the problem) you would js make it a positive (if its positive 279 u js say the absolute value is 279)

(also the absolute value is the distance between the number and zero so yh u can put that)

Answer:

1. 25

2. 24

equations below

Step-by-step explanation:

Order of operations is: PEMDAS = parentheses, exponents, multiplication, division, addition, subtraction

1. 5 x (20/4)

normally we multiply before we divide, but in this case, the division is in parentheses, so we start there

= 5 x 5

then multiply

= 25

------------------------

2. The lovely land of exponents

6^2 (the only way I can type 6 squared, or 6 to the power of 2, where the 2 is up as a superscript)

6^2 - 2 x 6

PEMDAS has us do the exponents before multiplication or subtraction:

6^2 = 6 x 6 = 36

= 36 - 2 x 6

then multiply:

= 36 - 12

then subtract:

= 24

Answer:

Step-by-step explanation:

Note that:

Two angles are Complementary when they add up to 90 degrees

Two angles are supplementary when they add up to 180 degrees

Let the angle = x

If the complement of an angle is equal to the supplement of four times the angle, then find the measure of the angle.

90 - x = 180 - 4x

The y-intercept, which represents the point the graph crosses the y-axis, is the point where x = 0, or the usual start of a time based function

The true statements about the y-intercept are;

B. The y-intercept is 10

D. The y-intercept tells me that they paid the babysitter $10 to buy her lunch

Reasons:

The points on the graph are;

\(\begin{array}{|c|cc|} \mathbf{Time }&&\mathbf{Cost}\\0&&10\\1&&20\\2&&30\\3&&40\\4&&50\\5&&60\end{array}\right]\)

The slope of the graph is therefore; \(\dfrac{60 - 50}{5 - 4} = 10\)

The equation of the graph is y - 60 = 10·(x - 5)

y = 10·x - 50 + 60 = 10·x + 10

The y-intercept is give by the point where the x-value is zero

At the start when x = 0, the amount paid to the baby sitter is y = 10×0 + 10 = 10

Therefore, the y-intercept which is $10, represent the amount the family

paid to the babysitter at the start for her lunch

The correct statements are therefore;

Option B; The y-intercept = 10

Option D; The y-intercept indicates the amount given to the babysitter for

her lunch

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Answer:

d and b i did the quiz

Step-by-step explanation:

The limit definition of a derivative is a mathematical method used to calculate the instant rate of change of a characteristic at a particular point. it is based at the idea of the limit of a function because the input techniques a certain cost.

The limit definition of a derivative is expressed as follows:

\(f'(x) = lim (h → 0) [f(x + h) - f(x)] /h\)

Wherein f'(x) represents the derivative of the function f(x) at a particular factor x. The expression \(( f(x + h) - f(x)) / h\) represents the common price of alternate of the characteristic over a small interval of size h, focused at x. The limit of this expression as h approaches 0 represents the instant fee of change of the characteristic at x, or the slope of the tangent line to the function at that factor.

The limit definition of a derivative is a fundamental concept in calculus and is used to calculate the slopes of tangent lines, to find maximum and minimum factors, and to clear up optimization issues in a huge variety of packages.

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The value of x at equilibrium can be found by setting the price-demand equation equal to the price-supply equation and solving for x.

To find the equilibrium level, we set the price-demand equation \(\( D(x) = 72 - 0.1x \)\) equal to the price-supply equation \(\( S(x) = 15 + 0.09x \)\). This represents the point where the quantity demanded equals the quantity supplied.

Setting the equations equal, we have:

\(\( 72 - 0.1x = 15 + 0.09x \)\)

Simplifying the equation, we get:

\(\( 0.19x = 57 \)\)

Dividing both sides by 0.19, we find:

\(\( x = \frac{57}{0.19} \approx 300 \)\)

Therefore, the value of x at equilibrium is approximately 300.

To find the consumers' surplus and producers' surplus at the equilibrium level, we need to determine the area between the price-demand and price-supply curves.

The consumers' surplus is the area below the price-demand curve and above the equilibrium price, while the producers' surplus is the area below the equilibrium price and above the price-supply curve.

To calculate the consumers' surplus, we need to find the integral of the price-demand function from 0 to the equilibrium quantity (300):

\(\( \text{Consumers' Surplus} = \int_0^{300} (72 - 0.1x) dx \)\)

To calculate the producers' surplus, we need to find the integral of the price-supply function from 0 to the equilibrium quantity (300):

\(\( \text{Producers' Surplus} = \int_0^{300} (15 + 0.09x) dx \)\)

After evaluating these integrals, we can find the numerical values of the consumers' surplus and producers' surplus, rounding to the nearest integer.

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Answer:

Step-by-step explanation:

2x + 10 + 3x + 30 = 180

Add like terms

5x + 40 = 180

5x = 180 - 40

5x = 140

x = 140 / 5

x = 28

hope it helped

(2x + 3x )+(10 + 30)= 180

5x + 40 = 180

5x = 180 - 40

5x = 140

x = 28

Yes, when comparing more than 2 treatment means, it is generally recommended to use analysis of variance (ANOVA) instead of several t-tests.

ANOVA allows you to test the overall differences between groups while taking into account the variability within each group. This helps to reduce the likelihood of making a Type I error (false positive) compared to conducting multiple t-tests. By using ANOVA, you can determine if there is a significant difference among the means of the groups.

If the ANOVA indicates a significant difference, you can then perform post-hoc tests (e.g., Tukey's HSD or Bonferroni) to compare specific group means. Overall, ANOVA is a more efficient and statistically appropriate method when comparing multiple treatment means. Hope this explanation helps!

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Answer: 12.5

Step-by-step explanation:

For function f(x) = Ax² - 18x³ + Cx², with given values A=2 and C=1, we can determine the end behavior and intercepts, find the critical points and points of inflection, and determine the concavity.

a) To determine the end behavior of the function, we examine the highest power term, which is -18x³. Since the coefficient of this term is negative, as x approaches positive or negative infinity, the function will tend towards negative infinity.For intercepts, we set f(x) equal to zero and solve for x. This gives us the x-values where the function intersects the x-axis. In this case, we have f(x) = Ax² - 18x³ + Cx² = 0. However, we are not provided with specific values for A or C, so we cannot determine the exact intercepts without this information.
b) To find the critical points, we take the derivative of f(x) and set it equal to zero. The critical points occur where the derivative is either zero or undefined. Taking the derivative of f(x), we get f'(x) = 2Ax - 54x² + 2Cx. Setting f'(x) equal to zero, we can solve for x to find the critical points.To find the points of inflection, we take the second derivative of f(x). The points of inflection occur where the second derivative changes sign. Taking the second derivative of f(x), we get f''(x) = 2A - 108x + 2C. Setting f''(x) equal to zero and solving for x will give us the points of inflection.
c) The question seems to be incomplete, as the prompt ends abruptly after "c) Det." Please provide additional information or clarify the question so that I can provide a more complete answer.

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Answer

15

Step-by-step explain

6+9=15