You need to solve a system of equations. You decide to use the elimination method.which of these is not allowed? 2x-3y=12 equation 1 and -x+2y=13 equation 2

Note that the above is solved using a Truth Table. The truth table is attached accordingly. Note that the argument is invalid

A truth table is a table that displays all possible combinations of truth values for the propositional variables in a logical expression and the resulting truth value of the expression.

It is an important tool in logic as it enables us to determine the validity of arguments, identify tautologies and contradictions, and simplify complex expressions. Truth tables provide a systematic and rigorous method of evaluating logical expressions and reasoning about their truth values.

With respect to the table, since there is at least one row where all premises are true but the conclusion is false (the fifth row in this case), the argument is invalid

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In a case whereby teacher gave a reading test to a class of 5th grade students and computed the mean, median, and mode for the test scores. the statements that cannot be an accurate description of the scores is b. The majority of the students had scores above the median.

A data set's mean is its average. The most frequent value in a data set is called the mode. The centre of the group of numbers is known as the median, which implies that the since there could majority of the students had scores above the mode, but ion the case of median, since it is value in the middle of a data set then majority of the the students  can not scores above the median.

The midway number in a set of data is known as the median. The data should first be arranged and ranked from smallest to greatest. Divide the total number of observations by two to get the midway value. The value in that location is the median if there are an odd number of observations; otherwise, round the number up.

Therefore, option B is correct.

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So, we can express matrix B as a linear combination of matrices A1 and A2 as shown above.

An arrangement of integers into rows and columns is called a rectangular matrix. Every single number in a matrix is referred to as a "matrix element" or "entry." The example matrix, designated as A, has two rows and three columns.

To express matrix B as a linear combination of matrices A1, A2, and A3, we need to find coefficients x, y, and z such that:

B = xA1 + yA2 + z*A3

Substituting the matrices B, A1, A2, and A3 into this equation, we get the following system of linear equations:

x + z = 1

x - y + z = 1

-3x + y + z = 0

x + y + z = 1

Solving this system of equations, we get:

x = 1/2

y = 1/2

z = 0

Therefore, we have:

B = (1/2)*A1 + (1/2)A2 + 0A3

Substituting the values of A1, A2, and A3, we get:

B = (1/2)[1 0] + (1/2)[0 1] + 0*[1 -1]

= [1/2 1/2]

So, we can express matrix B as a linear combination of matrices A1 and A2 as shown above.

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We can write B as a linear cοmbinatiοn οf A1, A2, and A3 as:

B = 2 A2 + A3

In linear algebra, a linear cοmbinatiοn οf matrices is a sum οf scalar multiples οf thοse matrices. That is, given matrices A1, A2, ..., An and scalars c1, c2, ..., cn, their linear cοmbinatiοn is defined as:

c1A1 + c2A2 + ... + cnAn

Tο write B as a linear cοmbinatiοn οf A1, A2, and A3, we need tο sοlve the system οf linear equatiοns:

x1 A1 + x2 A2 + x3 A3 = B

where x1, x2, and x3 are the cοefficients οf the linear cοmbinatiοn.

Rewriting the matrix equatiοn, we get:

x1 + x3 = 1

x1 - x3 = 1

-3x1 + x2 + x3 = -3

x2 + x3 = 1

Sοlving this system οf equatiοns, we get:

x1 = 0

x2 = 2

x3 = 1

Therefοre, we can write B as a linear cοmbinatiοn οf A1, A2, and A3 as:

B = 2 A2 + A3

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The proportion of items in each bin is given by the:

a. relative frequency.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The concept of probability was presented because it is the same concept of relative frequency, which gives the proportion of items in each bin.

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Answer:

y- intercept = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (4, - 1 ) into the partial equation

- 1 = - 2(4) + c = - 8 + c ( add 8 to both sides )

7 = c

that is the y- intercept = 7

The tens digit is 8, and the units digit is 9 (since y = x + 1). Therefore, the original number is 89.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation contains one or more variables, which are unknown values that can vary or change. The variables are usually represented by letters such as x, y, or z. The expressions on either side of the equals sign can be constants, variables, or functions of variables.

The simplest form of an equation is a linear equation, which can be represented as ax + b = c, where a, b, and c are constants and x is a variable. To solve a linear equation, we need to find the value of the variable that makes the equation true. This is done by performing arithmetic operations on both sides of the equals sign to isolate the variable.

Equations can also be more complex, involving multiple variables, powers, and functions. In such cases, algebraic techniques such as factoring, substitution, and solving systems of equations may be required to find the solution.

Equations are used to describe relationships between variables in many fields of study, including physics, chemistry, economics, and engineering. They are also used in everyday life, such as in calculating the cost of a purchase after applying a discount, or determining the amount of time it takes to travel a certain distance

Let's represent the tens and units digits with x and y, respectively. According to the problem statement, we have two equations:

y = x + 1 (the units digit is one more than the tens digit)

10x + y + 10y + x = 187 (the sum of the original number and the reversed number is 187)

Simplifying the second equation, we get:

11x + 11y = 187

x + y = 17 (dividing both sides by 11)

Substituting y = x + 1 into the second equation, we get:

x + (x + 1) = 17

2x + 1 = 17

2x = 16

x = 8

So the tens digit is 8, and the units digit is 9 (since y = x + 1). Therefore, the original number is 89.

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We can write tan(− 0.9) as -

tan(− 0.9) = -1.26.

Tangent function is defined as the ratio of perpendicular and base. Mathematically, we can write -

tan(Ф) = p/b

tan(Ф) = perpendicular/base

Given is to find the value of tan(− 0.9).

We know -

1 radian = 57.2958 degrees

0.9 radian = 57.3 x 0.9 = 51.57 degrees

0.9 radian = 51.57 degrees                           ... { 1 }

So, we can write -

tan(− 0.9) = tan( - 51.57°) = - 1.26

Therefore, we can write tan(− 0.9) as -1.26.

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Answer:

A scale factor of a famous statue uses a scale factor of 210:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?

The actual height of the statue is 252 feet (1.2 x 210).

Answer:

252

Step-by-step explanation:

The mean absolute deviation of the set of numbers 2, 3, 3, 6, and 1 is 1.2.

What is the mean absolute deviation?

Mean absolute deviation (MAD) is a measure of the average absolute distance between each data value and the mean of a data set. Similar to standard deviation, MAD is a parameter or statistic that measures the spread, or variation, in your data.

To find the mean absolute deviation of a set of numbers, we first need to find the mean of the set. The mean is the sum of the numbers divided by the total number of numbers. For the set of numbers 2, 3, 3, 6, 1, the mean is:

mean = (2 + 3 + 3 + 6 + 1) / 5

= 15 / 5

= 3

Next, we need to find the absolute deviation of each number in the set from the mean. The absolute deviation is the absolute value of the difference between the number and the mean. For each number in the set, we calculate the absolute deviation as follows:

|2 - 3| = 1

|3 - 3| = 0

|3 - 3| = 0

|6 - 3| = 3

|1 - 3| = 2

To find the mean absolute deviation, we take the average of the absolute deviations. We add up the absolute deviations and divide by the total number of numbers in the set:

mean absolute deviation = (1 + 0 + 0 + 3 + 2) / 5

= 6 / 5

= 1.2

Therefore, the mean absolute deviation of the set of numbers 2, 3, 3, 6, and 1 is 1.2.

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Answer: The cost for the total trips is $14. The amount of trips that Wanda can make is a maximum of 7 to equal the amount.

Step-by-step explanation:

First, make the amount of trips, x

Step 1. $32 = $18 + $2x

Step 2. ($32 - $18) = ($18 - $18) + $2x

Step 3. $14 = $2x

Step 4. $14 / $2 = $2x / $2

Step 5. $7 = x

Step 6. $32 = $18 + ($2 * 7)

Step 7. $32 = $18 + $14

Step 8. Check for the equation. $32 = $32

(correct me if im wrong)

Answer:

66.67

Step-by-step explanation:

8 people stayed home, 8/12=2/3=66.67(approx)

Answer:

See Screenshot

Step-by-step explanation:

The first and second lengths are not possible lengths of triangle.

The third and fourth lengths are possible lengths of triangle.

For the first case; 3 ft, 5 ft, 9 ft: Not possible. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. However, in this case, 3 ft + 5 ft = 8 ft, which is less than 9 ft.

For the second case 11 cm, 6 cm, 17 cm: Not possible. Using the same reasoning as above, we see that 6 cm + 11 cm = 17 cm, which means that the three sides cannot form a triangle.

For the third case. 4 in., 4 in., 6 in.: Possible. The sum of any two sides is greater than the third side, since 4 in. + 4 in. = 8 in., which is greater than 6 in. Therefore, these lengths can form a triangle.

For the fourth case. 16 yd, 10 yd, 12 yd: Possible. Again, we see that the sum of any two sides is greater than the third side, since 10 yd + 12 yd = 22 yd, which is greater than 16 yd. Therefore, these lengths can form a triangle.

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Answer:

B) She should take the itemized deductions because they would be larger than the standard deduction.

Step-by-step explanation:

Given Kristina will file a single so her standard deduction for 2022 is $12,950.

For itemized deduction, she can include her mortgage interest of $6,320.00.

For her medical expenses, it has to be more than 7.5% of her gross income of $32,500 => 7.5% of $32,500 = $2437.5.

so her deduction for medical expenses is $19,500 - $2437.50 = $17,062.5

so her total itemized deduction is $6,320.00 + $17,062.50 = $23,382.50

Her itemized deduction is larger than standard deduction for single filing. So itemized deduction is the best option for Kristina.

The length of the center of the circle is approximately 391.9 cm

Let's call the point where the two chords intersect point P. To find the length of the center of the circle to point P, we need to find the distance between point O (the center of the circle) and point P.

To do this, we first need to find the distance from point O to each chord. We can use the Pythagorean theorem to do this. Let's call the midpoint of the first chord point A, and the midpoint of the second chord point B. Then:

OA = √((360 cm)^2 - (280 cm)^2) = 160√2 cm

OB = √((360 cm)^2 - (320 cm)^2) = 40√17 cm

Next, we need to find the distance from each midpoint (A and B) to point P. We can use the formula for the length of a chord that passes through the center of a circle:

AP = BP = √(2r^2 - d^2)

where r is the radius of the circle and d is the length of the chord. Then:

AP = BP = √(2(360 cm)^2 - (560 cm)^2) = 320√2= 320√(2) cm

Now we can use the Pythagorean theorem again to find the distance from point O to point P:

OP = sqrt(OA^2 - AP^2) = √(160√2 cm)^2 - (320√(2) cm)^2) ≈ 391.9 cm

Therefore, the length of the center of the circle to the crossing point of the chords is approximately 391.9 cm.

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Answer: 280cm

Step-by-step explanation:

Use some graph paper and draw the question scaling it down by 0.01.

5.6cm 6.4cm and the radius 3.6cm.

Then multiply the answer by 100.

This is one way to get the answer, but I am sure there are more and one way to get to the 280cm.

Good luck, and share your ideas.

the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8} is 0.6 or 60%.

How we solved?

To determine the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8}, we first need to identify which numbers in the set are prime.

The prime numbers in the set are 5 and 7, so the non-prime numbers are 4, 6, and 8.

The total number of cards in the set is 5.

Therefore, the probability of selecting a non-prime card is:

P(not prime) = number of non-prime cards / total number of cards

P(not prime) = 3 / 5

P(not prime) = 0.6 or 60%

So the probability of selecting a card that is not prime from the set {4, 5, 6, 7, 8} is 0.6 or 60%.

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By using the substitution method, the value of x is equal to -1 and the value of y is equal to 1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

2x - 3y = -5      .......equation 1.

3x + y = -2          .......equation 2.

From equation 2, we have:

y = -3x - 2

By using the substitution method to substitute equation 3 into equation 1, we have the following:

2x - 3(-3x - 2) = -5

2x + 9x + 6 = -5

11x = -5 - 6

x = -11/11

x = -1

For the value of y, we have:

y = -3x - 2

y = -3(-1) - 2

y = 1.

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Answer:

To determine how much the tourist will receive while leaving Nepal, we need to know the total cost of the 5 Nepali caps including VAT, and then subtract any taxes or fees that the tourist may have paid when purchasing the caps.

Given that the tourist bought 5 Nepali caps at a cost of Rs 452 per piece including VAT, we can calculate the total cost of the caps as:

Total cost of 5 Nepali caps = 5 x Rs 452 = Rs 2260

Since the cost already includes VAT, we do not need to add any additional taxes or fees.

Therefore, if the tourist does not make any additional purchases or incur any other expenses while in Nepal, they will receive back Rs 2260 when leaving Nepal.

Answer:

54.2 cakes

Step-by-step explanation:

divide 380 by 7 and you'll get 54.2 as your answer

Robin Nest's average daily sales were $1,644 based on credit sales and net receivables.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Average daily sales are the estimated amount of sales made daily in a year.

It can be found by the formula:

= Net credit sales / Number of days in the period

Solving gives:

= 600,000 / 365 days

= $1,644

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The complete question is given below.

Robin's Nest had net credit sales for the current period of $600,000 and average net receivables were $50,000. What is Robin's Nest's average daily sales

The value of f(13.8) = 636.8

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

For example f(y) = 5y+7

Similar the function given ;

f(x)=46x+2

when x = 13.8

f(13.8) = 46(13.8) + 2

= 636.8

therefore the value of the function f(x)=46x+2 at x = 13.8 is 636.8

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The value of the function f(x) = 46x + 2 at x = 13.8 is 636.8.

Function is a rule that assigns a unique output value to each input value. A function is typically denoted by a letter such as f(x), where x is the input variable and f(x) is the output value.

To evaluate the function f(x) = 46x + 2 at x = 13.8, we simply substitute x = 13.8 into the expression for f(x):

f(13.8) = 46(13.8) + 2

Simplifying this expression, we get:

f(13.8) = 634.8 + 2

f(13.8) = 636.8

Therefore, the value of the function f(x) = 46x + 2 at x = 13.8 is 636.8.

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The possible ratios of dogs to cats that could be made is

12 : 48 , 6 : 24 , 3 : 12 , 1 : 4 and soon.

What is ratio in math?

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A percentage is an equation in which two ratios are made equal to one another.

                             As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)

Given ,

If there are 12 dogs and 48 cats at a pet daycare,

So, we have to fill out all of the possible ratios of dogs to cats that could be made.

ratio could be  = 12 : 48

12 : 48  = 1 : 4

6 : 24 = 1 : 4

3 : 12 = 1 : 4

1 : 4 = 1 : 4

Therefore, The possible ratios of dogs to cats that could be made is

12 : 48 , 6 : 24 , 3 : 12 , 1 : 4 and soon.

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The fraction of May's property that is left is 7/15.

A fraction is a value derived in such a way that it is a part of a given initial value. An example is one third of 12 is 4. In this case, 4 is a fraction of 12.

Considering the given question, we have;

let the total property of May be represented by 1, so that

fraction left after giving 1/5 to her son = 1 - 1/5

                             = (5 - 1)/ 5

                             = 4/ 5

The fraction left after giving 1/5 of her property to her son is 4/ 5.

So that;

the fraction left after she gave 1/3 to her daughter = 4/ 5 - 1/ 3

                                               = (12 - 5)/ 15

                                               = 7/ 15

Therefore, the fraction of her property left is 7/ 15.

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Applying the secant-tangent theorem, the value of x is calculated as: x = 5.

The secant-tangent theorem states that if there is a point outside of a circle and we draw a tangent line and a secant line from that point to the circle, then the length of the tangent line squared is equal to the length of the secant line multiplied by the length of the part of the secant line that is outside the circle.

Therefore, applying the secant-tangent theorem:

4 * (x + 4) = 6²

4x + 16 = 36

4x = 36 - 16

4x = 20

4x/4 = 20/4

x = 5

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A function f(x) is said to have a jump discontinuity at x = a if:

3. The left and the right limits are not equal.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

Since the lateral limits have to be equal, one of the conditions is that the limit must exist.

A jump discontinuity is when the limits do not exist, that is, if the lateral limits are different.

Hence option 3 is the correct option for this problem.

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The value of x is given as follows:

x = 3.

Applying the secant-tangent theorem, we have that the following equation holds true:

4x² = 6².

Hence we can solve the equation for x to obtain the value of x, as follows:

4x² = 36

x² = 36/4

x² = 9

x = sqrt(9)

x = 3.

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The area of the surface generated by revolving the curve y = 7x about the x-axis over the interval [0, 1] is approximately 15.43 square units.

What is integration ?

Integration is a fundamental concept in calculus that involves finding the integral of a function, which is the area under the curve of the function between two given limits. It is the reverse process of differentiation and is used to find the antiderivative of a function. In other words, integration involves finding a function whose derivative is a given function. Integration is a powerful tool that is used in many fields, including physics, engineering, economics, and statistics, to name a few.

Given by the question:

To find the area of the surface generated by revolving the curve y = 7x about the x-axis over the interval [0, 1], we can use the formula:

[tex]A =2\pi \int\limits^a_b {y} \, ds[/tex]

where a and b are the limits of integration, ds is the arc length element, and y is the height of the curve at each point.

In this case, we can rewrite the curve as x = y/7 and use the formula for arc length:

[tex]ds = \sqrt[]{(1 + (dx/dy)^2) dy}[/tex]

We have dx/dy = 1/7, so [tex]ds =\sqrt{(1 + (1/49)) dy}[/tex].

Substituting this into the surface area formula, we get:

[tex]A = 2\pi \int\limits^1_0 {y \sqrt{(1 + (1/49)) } } \, dy[/tex]

Integrating, we get:

[tex]A = 2\pi (49/72) [y\sqrt{(1 + (1/49)) } + (1/3) *(1 + (1/98)^{3/2} ][/tex] from 0 to 1

[tex]A = 2\pi (49/72) [(1/7) \sqrt{(50/49)} + (1/3)*(99/98)^{3/2} ][/tex]

[tex]A = 2\pi (49/72) [(5/7)\sqrt{2} + (1/3)* (99/98)^{3/2} ][/tex]

A ≈ 15.43

Therefore, the area of the surface generated by revolving the curve y = 7x about the x-axis over the interval [0, 1] is approximately 15.43 square units.

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a. The period of y = 2tan(4x) on the interval [0,pi] is pi/2.

Justification: The period of a tangent function is pi/b where b is the coefficient of x. Therefore, the period of 2tan(4x) is pi/4, and the function completes two periods on the interval [0,pi], giving a total period of pi/2.

b. The location of vertical asymptotes for y = 2tan(4x) on the interval [0,pi] is x = (2n + 1)pi/8 where n is an integer.

Justification: The vertical asymptotes of a tangent function occur where the cosine of the angle in the argument is equal to zero. In this case, the cosine is equal to zero at (2n + 1)pi/8, giving the location of the vertical asymptotes.

c. The domain of y = 2tan(4x) on the interval [0,pi] is [0, pi/4) U (pi/4, pi/2) U (pi/2, 3pi/4) U (3pi/4, pi].

Justification: The tangent function has vertical asymptotes at odd multiples of pi/2, so the function is undefined at these points, and thus excluded from the domain.

d. The range of y = 2tan(4x) on the interval [0,pi] is (-∞, ∞).

Justification: The range of the tangent function is the set of all real numbers.

e. The x-intercepts of y = 2tan(4x) on the interval [0,pi] are x = k(pi/8), where k is an integer.

Justification: The x-intercepts of a tangent function occur where the function is equal to zero, which happens at integer multiples of pi.

f. The y-intercept of y = 2tan(4x) on the interval [0,pi] is (0,0).

Justification: The y-intercept of a function occurs where x=0, so the y-intercept of this function is (0, 0), as 2tan(4*0) = 0.

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Answer:

Step-by-step explanation:

a. The average rate of change in the cost of the hamburger during the period from 2012 to 2022 can be calculated as the difference in the cost of the hamburger divided by the number of years between the two prices.

So, the average rate of change in the cost of the hamburger is:

(6.12 - 4.32) / (2022 - 2012) = 0.18

Therefore, the average rate of change in the cost of the hamburger during this period is $0.18 per year.

b. We can use the point-slope form of a linear equation to model the cost of the hamburger as it changes over time. Let y be the cost of the hamburger in dollars, and t be the number of years since 2012. We know that the cost of the hamburger in 2012 was $4.32, so we have a starting point of (0, 4.32).

Using the average rate of change calculated in part a, we can find the slope of the line:

slope = (6.12 - 4.32) / (2022 - 2012) = 0.18

Now we can write the equation of the line as:

y - 4.32 = 0.18t

y = 0.18t + 4.32

So, the linear equation that models the cost of the hamburger in terms of years since 2012 is y = 0.18t + 4.32.

c. To find when the cost of the hamburger will reach $7.02, we can substitute y = 7.02 into the equation we found in part b and solve for t:

7.02 = 0.18t + 4.32

2.7 = 0.18t

t = 15

So, the cost of the hamburger will reach $7.02 in the year 2012 + 15 = 2027.

Answer:

b = 82

Step-by-step explanation:

Given

a =46 degrees

c = 52 degrees

Since XY is a straight line, it has an angle of 180 degrees

So, Angle a + angle b + angle c = 180 degrees

46 + angle b + 52 = 180

angle b + 98 = 180

angle b = 180 - 98

angle b = 82 degrees

Therefore angle b is equal to 82 degrees

Answer:

180 in a straight line

Step-by-step explanation:

there is 180⁰ in straight line.

46 + 52 is 98

180 - 98 is 82