Suppose a certain company sells regular keyboards for $83 and wireless keyboards for $115. Last week the store sold three times as many regular keyboards as wireless. If total keyboard sales were $5,824, how many of each types were sold?

Answer:

Sorting

Step-by-step explanation:

When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

Answer:

2×2= 4

5×5= 25

6+5+5=16

10000000000+2= 10000000002

Step-by-step explanation:

Step-by-step explanation:

2×2 = 4

5×5 = 25

6+5+5 = 16

10000000000+2= 10000000002

\(R^2\) measures the proportion of the variance in the dependent variable (wage) that can be explained by the independent variables (exper and \(exper^2\)) in the regression model.

In this case, the given \(R^2\) value is 0.011, which means that approximately 1.1% of the variance in wages can be explained by the years of experience (exper) and its squared term (\(exper^2\)) included in the regression model.

\(R^2\) ranges between 0 and 1, where 0 indicates that none of the variance in the dependent variable is explained by the independent variables, and 1 indicates that all the variance is explained. A low \(R^2\) value suggests that the independent variables have limited explanatory power in predicting the wages of individuals.

In conclusion, the given \(R^2\) value of 0.011 indicates that only a small proportion of the variation in wages can be attributed to the years of experience and its squared term in the regression model.

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I got 9 7/9 by using a calculator

Answer:

3332 green beads

Step-by-step explanation:

There are 1428 more green beads than red beads.

There are 3,332 greed beads in the box

Given :

A box contains red, purple and green beads in the ratio 4:6:7

From the given ratio,

number of red beads = 4x

number of purple beads= 6x

number of green beads= 7x

There are 1428 more green beads than red beads.

green  beads =1428 + red beads

\(7x=1428+4x\\3x=1428\\x=476\)

we know that number of green beads= 7x

number of green beads= \(7(476)=3332\)

There are 3,332 greed beads in the box

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The value of α that satisfies the given conditions is between -√5 and √5.

We are given the initial value problem:

y′′+y −6y=0,y(0)=α,y (0)=5

We need to find the value of α so that the solution to the initial value problem approaches zero as x→∞

Solution:The characteristic equation for the given differential equation is given by:

m² + 1 - 6 = 0

This can be simplified to:

m² - 5 = 0⇒ m₁ = -√5 and m₂ = √5

Therefore, the general solution of the differential equation is given by:

y(x) = C₁e⁻√5x + C₂e⁺√5x

To find the values of C₁ and C₂, we can use the initial conditions:

y(0) = α, y'(0) = 5

On substituting the given values in the above equation, we get:

α = C₁ + C₂     ........(i)

and5 = -√5C₁ + √5C₂      ........(ii)

On solving equations (i) and (ii), we get:

C₁ = (α - 5/√5)e⁺√5x/2 + (α + 5/√5)e⁻√5x/2

andC₂ = (α + 5/√5)e⁺√5x/2 - (α - 5/√5)e⁻√5x/2

Therefore, the solution of the differential equation is:

y(x) = (α - 5/√5)e⁺√5x/2 + (α + 5/√5)e⁻√5x/2

Since the value of √5 is positive, the second term approaches zero as x→∞ when α > -5/√5.

To ensure that the entire solution approaches zero as x→∞, we need to have both terms approach zero.

Therefore, we need to choose the smallest possible value of α that satisfies the condition α > -5/√5.

The smallest possible value of α is given by:-5/√5 < α < 5/√5

Simplifying this inequality, we get:-√5 < α < √5

Therefore, the value of α that satisfies the given conditions is between -√5 and √5.

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In the above problem, the system of linear inequalities to represent Jackson's workout is: 6.9x + 10.4x ≥ 400; x ≤ 45.

Let x be the number of minutes Jackson uses the stair stepper.

The calories burned during x minutes of light effort on the stair stepper are 6.9x.

The calories burned during x minutes of vigorous effort on the stair stepper are 10.4x.

To burn at least 400 calories, we can write the inequality:

6.9x + 10.4x ≥ 400

To ensure that Jackson has at most 45 minutes to exercise, we can write the inequality:

x ≤ 45

Therefore, the system of linear inequalities to represent Jackson's workout is:

6.9x + 10.4x ≥ 400

x ≤ 45

where x is the number of minutes Jackson uses the stair stepper.

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To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.

To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.

This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.

Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.

Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.

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FALSE. The number of dots in a dotplot of a bootstrap distribution is equal to the size of the bootstrap sample, not the original sample.

In a bootstrap analysis, multiple samples of the same size are drawn from the original sample with replacement, creating a distribution of sample statistics. The dotplot of this distribution represents the frequency of the sample statistics and can help us understand the variability of the original sample.

The number of dots in the dotplot reflects the number of bootstrap samples, which can be much larger than the original sample size. Therefore, the number of dots in the bootstrap distribution can be different from the size of the original sample.

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The fraction of Cos L is 23/25

First, let's understand what a fraction is. A fraction represents a part of a whole. It has two parts: the numerator and the denominator. The numerator represents the part we are interested in, and the denominator represents the whole.

Now, let's look at our problem. We have a right triangle with sides KL and JL, and we need to find cos L. Cosine is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. So, to find cos L, we need to identify the adjacent and hypotenuse sides.

From the given information, we know that KL is adjacent to angle L, and JL is the hypotenuse. So, we can write:

cos L = KL/JL

Now, we need to simplify this fraction. To simplify a fraction, we need to divide both the numerator and the denominator by their greatest common factor (GCF). The GCF of 23 and 25 is 1, so we cannot simplify the fraction any further.

Therefore, the final answer is:

cos L = KL/JL = 23/25

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Answer:

mean is when you add all the numbers up and divide by how many numbers there are.

ok just saw your other comment for help, hope this isn't too late but the answer would be 35.2

Rounded: 35

hope it helped :)

If there is a correlation between the number of employees and customer satisfaction in two different Buffalo Wild Wings stores, we need to perform a Pearson's correlation coefficient analysis.

To run stats testing on sales data from two different Buffalo Wild Wings stores, we need to use a correlation analysis. Specifically, we need to use Pearson's correlation coefficient to determine if there is a relationship between the number of employees and customer satisfaction. The Pearson's correlation coefficient ranges from -1 to +1, with -1 indicating a perfect negative correlation and +1 indicating a perfect positive correlation. If the coefficient is close to zero, it indicates that there is no correlation.
The data we need to collect includes the number of employees in each store and the sales data for a specific period. We also need to gather customer satisfaction data, which can be collected through surveys or other feedback mechanisms. Once we have the data, we can use a statistical software program like SPSS or Excel to perform the correlation analysis.
If the correlation coefficient is positive and statistically significant, it means that there is a relationship between the number of employees and customer satisfaction. This could mean that more employees lead to better customer service, which in turn leads to higher customer satisfaction and sales. However, if the correlation is negative or not statistically significant, it means that there is no relationship between the two variables.
In conclusion, to determine if there is a correlation between the number of employees and customer satisfaction in two different Buffalo Wild Wings stores, we need to perform a Pearson's correlation coefficient analysis. Gathering accurate data and using statistical software will allow us to determine if there is a significant relationship between the variables.

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The correct inequality that describes the problem is 4x ≥ 40. Thus, the correct answer is A.

The answer is A because Ms. Wells is ordering 4 large cheese pizzas, and she expects to spend at least $40 on the pizzas. The inequality 4x ≥ 40 represents the total cost of the pizzas, which is 4 times the cost of each pizza (4x) and should be greater than or equal to $40. This inequality tells us that the total cost of the pizzas is at least $40, which is what Ms. Wells expects.

Option B, 4x > 40x, is incorrect because it doesn't make sense mathematically. The right side of the inequality is 40x, which is not related to the problem, and it also doesn't make sense that each pizza will cost 40 dollars.

Option C, 4x ≤ 40, is incorrect because it represents the total cost of the pizzas as less than or equal to $40, which doesn't match with Ms. Wells' expectation that she expects to spend at least $40 on the pizzas.

This question should be provided with answer choices, which are:

The correct answer is A.

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Answer:

17) m = 35; n = 110

18) b = 90; c = 80; d = 100

Step-by-step explanation:

17)

2m = 70

m = 35

n + 70 + 70 + n = 360

2n + 140 = 360

2n = 220

n = 110

18)

b - 10 + b + 10 = 180

2b = 180

b = 90

b - 10 = c

90 - 10 = c

c = 80

b + 10 = d

90 + 10 = d

d = 100

Answer:

30a^2

the number gets multiplied with the number and the letter with the letter

Answer:

A rectangular football field is 64 meters wide and 100 meters long. A player runs from one corner of the firmed in a diagonal line to the opposite corner. ... How much shorter is it to run across the field than around it ( nearest tenth)? ... Substitute the length of the sides (7 in, 25in n) into the Pythagorean theorem.

Step-by-step explanation:

im srry if it is wrong but i tried

Answer:

$2.39, hope this helps,

Step-by-step explanation:

1.50+0.89=2.39

Answer: $2.39

Step-by-step explanation: 0.89 + 1.50

0.8 + 1.5 = 2.3

89 + 50 = 139

2.39

Answer:

it depend on the question but if it is asking if they have the same answer then it is true

Step-by-step explanation:

Answer: false

Step-by-step explanation: 4+5=9 5+4=-9

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent Josh's rate of travel in miles per hour. After 2 hours, his distance is ...

  distance = speed · time

  distance = x · 2 = 2x

Then 2x is Greg's rate of travel After 5 hours, his distance is ...

  distance = speed · time

  distance = (2x) · 5 = 10x

The distance they are apart is ...

  10x -2x = 256

  8x = 256

  x = 32

__

Josh's rate: 32 miles per hour; Josh's distance = (2 h)(32 mi/h) = 64 miles.

Greg's rate: (32 mi/h)·2 = 64 mi/h; Greg's distance = (5 h)(64 mi/h) = 320 miles.

__

Check: 320 miles - 64 miles = 256 miles . . . . correct separation

Answer: is it 208 or not i'm doing the same test

Step-by-step explanation:

Answer:

$2766.67

Step-by-step explanation:

415/.15 = 2766.666666666666667

Answer:

4x-20

Step-by-step explanation:

(x-5) + (x-5) + (x-5) + (x-5) = 4x-20

or

(4)(x-5) = 4x-20

The expression x² - 10x + 25 will represent the a square with side (x-5) units.

A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.

Area of square = Side²

The perimeter of square = 4× side

Length of diagonal of square = √(2) × side

Given,

Side of square = (x - 5)

The area of a square is given by = Side²

So,

Area = (x - 5)²

Area = x² - 10x + 25

Hence,The expression x² - 10x + 25 will represent the a square with side (x-5) units.

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Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

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

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer:

Below

Step-by-step explanation:

There is only ONE step

g/16 = 16      multiply both sides of the equation by 16

g = 256    Done.

A congruent rectangle is a rectangle that has the same size and shape as another rectangle. In other words, two rectangles are congruent if they have the same length and width.

Since the rectangle is 4 inches by 7 inches, one of the dimensions represents the length and the other represents the width. The length and the width can be interchanged to form a different rectangle with the same area.

Since the rectangle is congruent to the 4-inch by 7-inch rectangle, the length and width of the rectangle are either 4 inches or 7 inches. Therefore, the length of segment JM can be either 4 inches or 7 inches.

So, there are two possible values for the length of segment JM: 4 inches and 7 inches.

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The true statements from the options provided are:

A. The product Ax is defined as a linear combination of columns of A with the corresponding entries of x as weights.

D. The product Ax is a vector in \(R^n\).

E. Ax is a vector whose ith entry is the sum of the products of the corresponding entries from row i of A and the vector x.

A linear combination in mathematics is an expression created from a group of terms by multiplying each component by a constant and combining the results (for example, an expression of the form axe + by, where a and b are constants, would be a linear combination of x and y).

The true statements from the options provided are:

A. The product Ax is defined as a linear combination of columns of A with the corresponding entries of x as weights.

D. The product Ax is a vector in \(R^n\).

E. Ax is a vector whose ith entry is the sum of the products of the corresponding entries from row i of A and the vector x.

These statements accurately describe properties and definitions related to matrix-vector multiplication. The product Ax is obtained by taking a linear combination of the columns of A, where the entries of x act as weights. The resulting product Ax is a vector in \(R^n\), and its entries are calculated by summing the products of the corresponding entries from row i of A and the vector x.

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Finite-state machines for given inputs: (a) 0s multiple of 3: 3-state machine. (b) At least four 1s: 4-state machine. (c) Exactly one 1: 2-state machine. (d) Begins with 000: 3-state machine. (e) Second is 0, fourth is 1: 4-state machine. (f) 01 pairs or 2 1s + 0s: 3-state machine. (g) Ends in 110: 3-state machine.

To construct finite-state machines that act as recognizers for the given inputs, we can follow these guidelines:

(a) For the set of all strings where the number of 0s is a multiple of 3, we can use a finite-state machine with three states. Start with the initial state, and transition to the next state whenever a 0 is encountered. After three transitions, go back to the initial state. If the machine ends in the accepting state, output 1.
(b) For the set of all strings containing at least four 1s, we can use a finite-state machine with four states. Start with the initial state, and transition to the next state whenever a 1 is encountered. If the machine enters the final state after four transitions, output 1.

(c) For the set of all strings containing exactly one 1, we can use a finite-state machine with two states. Start with the initial state and transition to the final state when the first 1 is encountered. Output 1 only if the final state is reached.

(d) For the set of all strings beginning with 000, we can use a finite-state machine with three states. Start with the initial state and transition to the next state whenever a 0 is encountered. If the machine reaches the final state after three transitions, output 1.

(e) For the set of all strings where the second input is 0 and the fourth input is 1, we can use a finite-state machine with four states. Start with the initial state and transition to the next state based on the inputs. Output 1 only if the machine reaches the final state.

(f) For the set of all strings consisting entirely of any number (including none) of 01 pairs or consisting entirely of two 1s followed by any number (including none) of 0s, we can use a finite-state machine with three states. Start with the initial state and transition based on the inputs. Output 1 only if the final state is reached.

(g) For the set of all strings ending in 110, we can use a finite-state machine with three states. Start with the initial state and transition based on the inputs. Output 1 only if the final state is reached.

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Finite-state machines (FSMs) can be constructed to act as recognizers for specific patterns in input strings. These are examples of how to construct FSMs as recognizers for different patterns in input strings. Each FSM is designed to produce an output of 1 when the input received matches the description provided.

Let's consider the given cases and construct FSMs for each one.

(a) The set of all strings where the number of Os is a multiple of 3:
To construct an FSM for this, we can keep track of the number of Os encountered so far. Initially, set the count to zero. When an O is encountered, increment the count by one. If the count becomes a multiple of 3, the FSM outputs 1; otherwise, it outputs 0. Reset the count to zero whenever a 1 is encountered.

(b) The set of all strings containing at least four 1s:
To create an FSM for this, we can keep track of the number of 1s encountered so far. Initially, set the count to zero. When a 1 is encountered, increment the count by one. If the count becomes equal to or greater than four, the FSM outputs 1; otherwise, it outputs 0.

(c) The set of all strings containing exactly one 1:
To build an FSM for this, we can have two states: a "no 1 encountered" state and a "1 encountered" state. Initially, start in the "no 1 encountered" state. Whenever a 1 is encountered, transition to the "1 encountered" state. If another 1 is encountered in the "1 encountered" state, transition to a third "more than one 1 encountered" state. In this case, the FSM outputs 0. Otherwise, if no additional 1s are encountered, the FSM outputs 1.

(d) The set of all strings beginning with 000:
To create an FSM for this, start in an initial state. When a 0 is encountered, transition to a second state. If two consecutive 0s are encountered in the second state, transition to a third state. Finally, if a third 0 is encountered in the third state, the FSM outputs 1; otherwise, it outputs 0.

(e) The set of all strings where the second input is 0 and the fourth input is 1:
To construct an FSM for this, start in an initial state. When the first input is read, transition to a second state. In the second state, transition to a third state if the second input is 0. In the third state, transition to a fourth state if the third input is not 0. Finally, in the fourth state, if the fourth input is 1, the FSM outputs 1; otherwise, it outputs 0.

(f) The set of all strings consisting entirely of any number (including none) of 01 pairs or consisting entirely of two Is followed by any number (including none) of Os:
To create an FSM for this, we can have multiple states to represent different scenarios. We start in an initial state and transition to a second state when a 0 is encountered. In the second state, transition back to the initial state if a 1 is encountered. If a 1 is encountered in the initial state, transition to a third state. In the third state, transition to a fourth state if an O is encountered. Finally, if an O is encountered in the fourth state, the FSM outputs 1; otherwise, it outputs 0.

(g) The set of all strings ending in 110:
To construct an FSM for this, start in an initial state. Transition to a second state if a 1 is encountered. In the second state, transition to a third state if a 1 is encountered again. Finally, if a 0 is encountered in the third state, the FSM outputs 1; otherwise, it outputs 0.

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Sure! Here's the 99.5% confidence interval for the true population mean textbook weight: (49.433, 60.567) ounces.

To construct a confidence interval for the true population mean textbook weight, we can use the formula:

Confidence Interval = (sample mean) ± (critical value) * (standard deviation / √(sample size))

Given the information provided:

- Sample mean = 55 ounces

- Population standard deviation = 11.4 ounces

- Sample size = 32 textbooks

First, we need to find the critical value corresponding to a 99.5% confidence level. Since the sample size is relatively small (32 textbooks), we can use a t-distribution instead of a normal distribution.

The degrees of freedom for a t-distribution are given by (sample size - 1). In this case, the degrees of freedom will be (32 - 1) = 31.

Using a t-table or a statistical calculator, we find the critical value for a 99.5% confidence level and 31 degrees of freedom is approximately 2.750.

Now, we can calculate the confidence interval:

Confidence Interval = 55 ± 2.750 * (11.4 / √32)

Confidence Interval = 55 ± 2.750 * (11.4 / 5.657)

Confidence Interval = 55 ± 5.567

Therefore, the 99.5% confidence interval for the true population mean textbook weight is approximately (49.433, 60.567) ounces.

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