Jan spends part of her year as a member of a gym. She then finds a better deal at another gym, so she
cancels her membership with the first gym and spends the rest of the year with the second gym. The
membership to the first gym costs $80 per month, while the membership for the second gym costs $45 per
month. If she ends up spending a total of $645 over the course of the year, how much time did she spend at
each gym?

In a consistent system with more variables than equations, the augmented column of the reduced row echelon form (rref) contains the solution set of the system of linear equations.

The Reduced Row Echelon Form denoted as "rref"  is a matrix representation of the system in which the leading non-zero entry in each row is 1 and is called the pivot. The pivots in the rref correspond to the basic variables in the solution set, and the non-pivot variables are free variables.

In the augmented column of "rref" , the entries corresponding to the pivot columns give the values of the basic variables in the solution set, while the entries corresponding to the non-pivot columns give the coefficients of the free variables,  free variables can take any value and do not affect the solution set,

Therefore, information contained in augmented column of the rref gives the values of the basic variables and the coefficients of the free variables in the solution set of the system.

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Answer:

x = arccos(sqrt((1 + sin(x))/2)) + 2npi or x = pi - arccos(sqrt((1 + sin(x))/2)) + 2npi

Step-by-step explanation:

cos^2(x) - sin^2(x) = sin(x) can be rewritten as cos^2(x) = sin^2(x) + sin(x)

Using the identity sin^2(x) + cos^2(x) = 1, we can simplify the equation as

cos^2(x) = 1 - cos^2(x) + sin(x)

Solving for cos^2(x), we get

cos^2(x) = (1 + sin(x))/2

Therefore, cos(x) = sqrt((1 + sin(x))/2) or cos(x) = -sqrt((1 + sin(x))/2)

To find the possible values of x, we need to find the values of sin(x) that satisfy this equation.

For the domain [0, 2pi), the range of sin(x) is [-1, 1], so we have:

cos(x) = sqrt((1 + sin(x))/2) for -1 <= sin(x) < 1

cos(x) = -sqrt((1 + sin(x))/2) for -1 <= sin(x) < 1

So, the solution is

x = arccos(sqrt((1 + sin(x))/2)) + 2npi or x = pi - arccos(sqrt((1 + sin(x))/2)) + 2npi

where n is an integer.

Absolute value represents how far you are from zero on the number line.

Examples:

The output of an absolute value function is never negative. Negative distance does not make sense. Therefore, we have no way to reach an output of -7. This is why we have no solutions here.

The compound experiment is the probability of heads on a coin and 4 on a number cube which is P = ( 1/12 )

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability be represented as P

Now , the equation will be

a)

The probability of heads on a coin and 4 on a number cube

Now , the probability of tossing a heads on a coin = 1/2

The probability of rolling a 4 on number cube = 1/6

So , the compound probability P = ( 1/2 ) ( 1/6 )

On simplifying the equation , we get

P = 1/12

b)

The probability of 3 on a six spaced spinner

The value of P = 1/6

c)

The probability of rolling a 6 on a number cube

The value of P = 1/6

d)

The probability of drawing a King from a regular deck of cards

The value of P = 4/52

On simplifying the equation , we get

The value of P = 1/13

Hence , the compound probability is P = 1/12

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Answer:

  C. 45 × 45

Step-by-step explanation:

You want to know the expanded form of 45 squared.

A square is signified by an exponent of 2:

  45 squared = 45²

The exponent tells you the number of times the base appears as a factor in the product:

  45² = 45 × 45 . . . . . . . 45 is a factor 2 times in the product

__

Additional comment

The value "45 squared" is the area of a square of side length 45.

The value "45 cubed" is the volume of a cube of side length 45.

The requried match to the expression is given as,
x²+ 2x + 2             (x + 1 + i ) (x + 1 − i)
x² - 4x + 8             (x − 2 + 2i)(x − 2 − 2i)
x² + 4                     (x + 2i)(x − 2i)

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
1. expression,
= x²+ 2x + 2

Simplifying the above expression,
= x²+ 2x + 2

We know that,

x = -b ± √{b² - 4ac} / 2a
x = -2 ± √(4 - 8)/2
x = -1 ± i    (i = √-1)

So,
The factored form of the given expression is given as,
= (x + 1 + i ) (x + 1 − i)

Similarly,
x² - 4x + 8 = (x − 2 + 2i)(x − 2 − 2i)
x² + 4 = (x + 2i)(x − 2i)

Thus, following the pattern of each expression to its equivalent standard form can be determined.

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Step-by-step explanation:

the picture is so fuzzy, I can hardly read the details.

I suspect the orange line is

f(x) = 6^x

the black line is

g(x) = 6^x + k⁵

to find k we simply create

(g - f)(x) = 6^x + k⁵ - 6^x = k⁵

as we can see, the difference (up/down distance) between both functions is a constant k⁵.

the best and most reliably we can see and calculate that difference at x = 0 :

2

k⁵ = 2

[tex]k = \sqrt[5]{2} [/tex]

which is 1.148698355...

but I see, I might have misunderstood the 5 of the coordinate axis as exponent of k.

so, the function might be

g(x) = 6^x + k

and then

the difference is simply k, and

k = 2

The number of monic polynomials of degree n in Fp[x] that do not take on the value 0 for x ∈ Fp is pⁿ - 1.

The number of monic polynomials of degree n in Fp[x] is pⁿ. In this case, "monic" means that the coefficient of xⁿ is 1.

In Fp[x], there are p possible values for the coefficient of each power of x, from x⁰ to xⁿ. Hence, there are pⁿ possible polynomials of degree n.

The number of polynomials that do not take on the value 0 for x ∈ Fp is pⁿ - 1 because if a polynomial is zero for all values of x in Fp, then it must be the zero polynomial. The zero polynomial is not counted because it is not monic, as it has a coefficient of 0 for the xⁿ term.

So, the number of monic polynomials of degree n in Fp[x] that do not take on the value 0 for x ∈ Fp is pⁿ - 1.

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Answer:

x = 12.5 degree

y = 220 degree

Step-by-step explanation:

The 1/2y is equal to the 110-degree angles, so to find the y, we take

110 times 2 = 220. So, the answer for y is 220.

The (4x + 20) and 1/2y must add up to 180 degrees. We know one is 110 degrees, so the (4x + 20) must be equal to 70 degrees.

4x + 20 = 70

4x = 50

x = 12.5 degree

So, x = 12.5 degrees and y = 220 degrees.

Answer:

10

Step-by-step explanation:

(x-3)² = 7²

so x-3 = 7

x =10

given two positive numbers a and b such that b < a. it turns out that a/b is the same as the ratio (a+ b)/a=b/(a-b)

Integers are a set of counting numbers (positive and negative), along with zero, that can be written without a fractional component. As mentioned above, an integer can be either positive, negative or zero.

All natural numbers are also integers that start from 1 and end at infinity.

All whole numbers are also integers, starting from 0 and ending at infinity.

We have two positive numbers a and b and b less a . the ratio of a and b is the same of (a+b)/a .

a:b=(a+b):a

[tex]a^2=b(a+b)\\[/tex]

(a+b)(a-b)=ab

(a+b):a=b:(a-b)

The ratio of a/b = b:(a+b).

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The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable takes a value less than or equal to z.

In order to model continuous phenomena or quantities that depend on chance, such as time, length, and mass, continuous random variables are utilized.

The likelihood that the random variable takes a value inside that interval is defined as the area under the density function over an interval. Therefore, the probability that the random variable will have a value less than or equal to z is given by the area under the normal curve from negative infinity to z.

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On solving the provided question, we can say that the linear equation formed will be y = -2x+18

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

In xx hours, Justin can iron 40x40x shirts since he can iron 40 shirts every hour. Daniel can iron 20 shirts each hour, or 20y20y shirts, in y hours. There were 360 shirts ironed in all (40x+20y):

[tex]40x+20y=360\\40x+20y=360\\x+y=14\\40x+20y= 360\\x+y=14\\40x+20y = 360 x+y = 14 20y = -40x+360 \\y = -2x+18[/tex]

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Answer:

46

Step-by-step explanation:

18+21+12+12+23=86

22×6=132

132-86=46

46

The equation of the line is y =3x + 40

The general formula for the equation of a line is expressed s;

y = mx+ c

Given that the parameters are;

From the information given, we have that the points are;

Slope, m = 3

Intercept, c = unknown

Now, substitute the values, we get;

10 = 3(-10) + c

Now, expand the bracket

10 = -30 + c

Collect like terms

c= 40

Hence, the equation is y = 3x + 40

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Answer:

17/7

Step-by-step explanation:

2 3/7 = 17/7

2 times 7 = 14 + 3 = 17/7

So, the answer is 17/7

The column cells are similarly filled by dividing the column cells by the corresponding column totals.

A table that displays the distribution of a characteristic's occurrence frequency in accordance with a specific set of class intervals.

Two sorts of data, or data in two categories, one pertaining to the columns and the other to the rows, make up a two-way relative frequency table.

                                Response                              

Shift                             Yes                 No                      Total

Day                            67%                  33%                     100%          

Night                         23%                  77%                      100%            

Total                          45%                   55%                    200%        

This table contains information about two categories, day/night and yes/no.

The day/night data percentages are computed along the rows.

The percentages of the yes/no values are calculated along the columns.

Shift                                     Response                              

                         Yes                        No                        Total

Day                  67/100 × 100           33/100 ×100           100

                            = 67%                  =33%                     100%

Night                23/100×100           77/100×100               100

                         = 23%                     =77%                        100%

Total              90/200×100               110/200×100           200

                        = 45%                       =   55%                   200%

To make these computations, divide the row cells by the corresponding row totals.

The column cells are similarly filled by dividing the column cells by the corresponding column totals.

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The test statistic for a Z-test is the Z-statistic, which has the standard normal distribution under the null hypothesis

A test statistic shows how closely your data’s distribution fits the distribution anticipated by the statistical test’s null hypothesis. The frequency with which each observation happens is defined by the distribution of data, which may be represented by its central tendency and variance around that central tendency.

Z= (x – y)/(x2/n1 + y2/n2) is the formula for calculating the test statistic when comparing two population means. To compute the statistic, we must first compute the sample means (x and y) and standard deviations (x and y) for each sample independently. In statistics, there are many different types of tests, such as the t-test, Z-test, chi-square test, anova test, binomial test, one sample median test, and so on. If parametric tests are applied,

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We have to show that the set of numbers of the form a + b√2, where a and b are rational numbers, forms a field with respect to addition and multiplication.

To start, we need to show that the set of numbers is closed under addition and multiplication. This means that if we add or multiply two numbers in the set, the result must also be in the set.

For addition, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we add them, we get (a1 + a2) + (b1 + b2)√2. Since a1, a2, b1, and b2 are all rational numbers, their sum is also a rational number. So, the result of adding two numbers in the set is always another number in the set, which means that the set is closed under addition.

For multiplication, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we multiply them, we get (a1a2 + 2b1b2) + (a1b2 + a2b1)√2. Again, since all the numbers involved are rational, the result is also a rational number. This means that the set is closed under multiplication as well.

Next, we need to show that the set satisfies the commutative, associative, and distributive laws for both addition and multiplication. This means that the order in which we add or multiply numbers in the set does not matter, and that addition and multiplication can be combined in a predictable way.

The commutative, associative, and distributive laws for addition and multiplication are well-known for rational numbers, and it can be easily verified that they hold for this set as well.

Finally, we need to show that the set has additive and multiplicative inverses. This means that for each number in the set, there exists another number in the set such that when added (or multiplied) to the original number, the result is 0 (or 1).

It can be shown that for any number of the form a + b√2, its additive inverse is -a - b√2, and its multiplicative inverse is (a / (a^2 + 2b^2)) - (b / (a^2 + 2b^2))√2, assuming that a^2 + 2b^2 is not equal to 0. Both of these are also rational numbers, since they are obtained by dividing rational numbers.

So, we have shown that the set of numbers of the form a + b√2, where a and b are rational numbers, is closed under addition and multiplication, satisfies the commutative, associative, and distributive laws, and has additive and multiplicative inverses. This means that the set of numbers forms a field with respect to addition and multiplication.

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Mr. Estes paid $136,000 for the SUV after the discount was applied.

Markdown percentage is defined as the decrease in the price which is calculated as a percent of the selling price.

We have the formula,

Selling price = (1 - markdown rate) Original price

Here,

Markdown percentage = 15%

Markdown rate = 15/100 = 0.15

Original price of the car = $160,000

Selling price = (1 - 0.15) × 160,000

                     = 0.85 × 160,000

                     = 136,000

Hence the selling price of the car is $136,000.

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For the expressions (32 - 13) (54 -45) and (23.1 - 17)/(3.2 - 13), the inequality will be (32 - 13) (54 - 45) > (23.1 - 17)/(3.2 - 13).

For the expressions -(14/5) - 19.7 and (19.7)⁴, the inequality will be -(14/5) - 19.7 < (19.7)⁴.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The first two expressions are -

(32 - 13) (54 -45) and (23.1 - 17)/(3.2 - 13)

Solve the expression (32 - 13) (54 -45) first.

(32 - 13) (54 - 45)

Use the arithmetic operation of subtraction -

(19)(9)

Use the arithmetic operation of multiplication -

171

Now solve the expression (23.1 - 17)/(3.2 - 13).

(23.1 - 17)/(3.2 - 13)

Use the arithmetic operation of subtraction -

6.1/-9.8

Use the arithmetic operation of division -

-0.622

Now, it can be seen that -0.622 is less than 171.

Therefore, the inequality symbol > will be used.

The second two expressions are -

-(14/5) - 19.7 and (-19.7)⁴

Solve the expression -(14/5) - 19.7 first.

-(14/5) - 19.7

Use the arithmetic operation of division -

-2.8 - 19.7

- 22.5

Now solve the expression (-19.7)⁴.

(-19.7)⁴

Expand using the powers rule -

150613.848

Now, it can be seen that - 22.5 is less than 150613.848.

Therefore, the inequality symbol < will be used.

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The value of b is 0.927. Therefore, the correct answer is option A.

To find b, we need to substitute the given values into a formula for computing the area under a curve. The formula for the area under the curve y=sinx from x=b to x=π is:

Area = ∫πb sinxdx

We do this by splitting the integral into the following two parts:

Area = ∫πbg+∫bg sinxdx

We can evaluate the first integral easily, since bg is a constant:

∫πbg=bg∫π=bgπ

For the second integral, we use integration by substitution:

Let u=x −b, so du=dx. Then the integral can be rewritten as:

∫bg sinx dx=∫bg sin(u+b)du

Where u varies from 0 to π−b. Now that the integral is in a form we can easily integrate:

∫bg sin(u+b)du=∫π−b0 sin(u+b)du

And using the Pythagorean identity:

sin(u+b)=sinubcosb+cosubsinb

We can rewrite the integrand as:

sin(u+b)=sinucosb−cosusinb

And then using integration by parts:

∫π−b0 sin(u+b)du=−cosubcosb|π−b0+∫π−b0 cosusinbdu

And the second integral can be simplified the same way we did the first one.

∫π−b0 cosusinbdu=−sinubsinb|π−b0+∫π−b0 sinubcosbdu

Which can be easily calculated as:

∫π−b0 cosusinbdu=π−b2sinbcosb

Now that both integrals are solved, we can substitute them back into the formula for the area and then solve for b:

Area=bgπ+π−b2sinbcosb

Substituting the value for the Area, we get:

0.4=bgπ+π−b2sinbcosb

Which can be simplified to:

b(π−b)=(π−0.4)/sinbcosb

Solving for b, we get:

b=0.927

Therefore, the correct answer is option A.

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"Your question is incomplete, probably the complete question/missing part is:"

If 0≤b≤π and the area under the curve y=sinx from x=b to x=π is 0.4, what is the value of b?

A) 0.927

B) 1.159

C) 1.982

D) 2.214

Check the picture below.

[tex]\textit{Law of Cosines}\\\\ \cfrac{a^2+b^2-c^2}{2ab}=\cos(C)\implies \cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C \\\\[-0.35em] ~\dotfill\\\\ \cos^{-1}\left(\cfrac{21^2+32^2-26^2}{2(21)(32)}\right)=\measuredangle J \implies \cos^{-1}\left(\cfrac{ 789 }{ 1344}\right)=\measuredangle J\implies \boxed{54.1^o\approx \measuredangle J}[/tex]

Make sure your calculator is in Degree mode.

The function f(x)=√x with f:R→R is injective and surjective but not bijective.

Injective (or one-to-one): f(x) is injective, which means that if f(x1) = f(x2), then x1 = x2. In other words, if the square root of x1 is equal to the square root of x2, then x1 and x2 are equal.

Surjective (or onto): f(x) is surjective, which means that for every y in the codomain (R), there exists an x in the domain (R) such that f(x) = y. In other words, the square root of any real number can always be expressed as a real number.

Bijective: f(x) is not bijective. The square root function is not bijective because it is not defined for negative values of x.

Function: A function f is a function if for every x in the domain of f, there is exactly one y in the codomain of f such that f(x) = y. In other words, each x in the domain is mapped to exactly one y in the codomain.

In the case of f(x) = √x, it is a function. For every x in the domain of f, which is [0,∞), there is exactly one y in the codomain of f, which is [0,∞), such that f(x) = y.

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Answer:

x= -4

Step-by-step explanation:

-7(x-2)+4=46

-7x+14+4=46

-7x=46-18

-7x=28

x=28/-7

x= -4

Answer:

-4

Step-by-step explanation:

Hope it helps! =D

On solving the provided question we can say that the sides are = 10, 9 , 8 perimeter of the triangle will be = 10 + 9 + 9/ 3 = 27 / 3 = 9 units

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

the sides are = 10, 9 , 8

perimeter of the triangle will be = 10 + 9 + 9/ 3 = 27 / 3 = 9 units

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Answer:0.32$

Step-by-step explanation:2.56/8=0.32$

The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.

The rate of change between two variables is shown by the slope of the line in a scatter plot. The slope would show how much the number of performances varies with a change of one unit in the number of practises in the connection between the two numbers.

If the slope is upward, then as the number of practises rises, so do the number of performances. If the slope is negative, then fewer performances will occur as the number of practises rises.

The slope's magnitude tells us how steep the line is, which tells us how strongly the two variables are related.

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The answer to the question 5/9 divided (- 1/3) as a simplest form is 5/3

What is quotient of a number?

The number we obtain when we divide one number by another is the quotient. For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor.

The question -5/9 divided (- 1/3) can be re-written as

-5/9 ÷ -1/3

-5/9 x -3/1

=15/9

=5/3

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