Determine the length of the unknown side given: abc ~efg

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 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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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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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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Answer:

b)

Step-by-step explanation:

As here it's stated that average of first 9 numbers is 23

so,

sum of 9 numbers = 9×23 = 207

Average of first 5 numbers is 20

so,

Sum of first 5 numbers = 5×20 = 100

Sum of remaining numbers = 207-100 = 107

Average of last five numbers = 25

So,

Sum of last five numbers = 5×25 = 125

Fifth Number = Sum of last five numbers- Sum of remaining numbers

                      = 125 - 107 = 18

The required measurement of the remaining two sides of the given triangle are 8 and 6 meters.

Heron's formula is a formula for calculating the area of a triangle in terms of the lengths of its sides that is credited to Heron of Alexandria.

Given that, a triangle having area of √135 square meter and perimeter 18 meter has a side 4 meter.

Let other two sides be x and y,

Therefore,

x + y + 4 = 18

x + y = 14.....(i)

Now, according to Heron's formula,

Area of a triangle = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c) / 2.

Therefore,

√9(9 - 4)(9 - x)(9 - y) = √135

Squaring both sides

45(9-x)(9-y) = 135

(9-x)(9-y) = 3

81 -9y - 9x + xy = 3

9(x+y)-xy = 78

Put x+y = 14 from eq(i)

9×14-xy = 78

xy = 48

Now finding the factors of 48

48 = (6, 8), (12, 4), (24, 2), (16, 3), (48, 1)

If we consider (6, 8) this is satisfying eq(i)

6+8 = 14

Therefore, we can say the other two sides of the triangle are 8 and 6.

Hence, the required measurement of remaining two sides of the given triangle are 8 and 6 meters.

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The change in momentum is 22120Ns

The change in momentum (Δp ) is defined as the change in the product of an object's mass and velocity. A force is required to change the momentum of an object. This applied force can increase or decrease the momentum or even change the object's direction.

Therefore the change in momentum = Final momentum - initial momentum

i.e mv -mu

where m is the mass

v is the final velocity

u is the initial velocity

The change of momentum is also called impulse. impulse is the product of the force and the time in applying it.

Change in momentum = force × time

= 2800× 7.90

= 22120 Ns

Therefore the change in momentum of the car is 22120Ns

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Answer:

Step-by-step explanation:

if you meant just 2 years the answer is 74,845,440 if you meant 2,000 its 74,845,440,000

The number of heartbeats for a person with an average heartbeat of 71.2 BPM for 2,000 years is 86,567,520,000 heartbeats.

The formula to calculate the number of heartbeats in a given period of time is:

Number of heartbeats = Beats per minute (BPM) x Minutes in the period

In this case, the given information is the BPM (71.2) and the period of time is 2,000 years, which is equal to 1,209,600,000 minutes.

Therefore, the number of heartbeats for a person with an average heartbeat of 71.2 BPM for 2,000 years is:

Number of heartbeats = 71.2 BPM x 1,209,600,000 minutes

Number of heartbeats = 86,567,520,000 heartbeats.

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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 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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The equation to model the value of Maureen's car x years after purchase can be written in the form of y = a(b)^x , where y is the value of the car, x is the number of years after purchase, and a and b are constants.

Using the information given, we can find the values of a and b.

We know that the value of the car one year after purchase is $24,403.

So, we can substitute this value into the equation:

24403 = a(b)^1

We also know that the car's original value is $26,525

So we can substitute this value into the equation:

26525 = a

Now we can use these two equations to find the value of b

24403 = 26525 (b)^1

b = 24403 / 26525

b = 0.9153

So the final equation is:

y = 26525 (0.9153)^x

where y is the value of the car, x is the number of years after purchase, and a = 26525 and b = 0.9153

Answer:

The rate of change of a linear function is its slope, which is the coefficient of the x-term in the equation.

Item I: y = 0.25x + 2

The slope of this line is 0.25.

Item II: y = 2

This is a horizontal line with zero slope, so it has a rate of change of 0.

The slope of Item I is greater than the slope of Item II, therefore option C is correct: "The rate of change of item I is greater than the rate of change of item II".

Step-by-step explanation:

The value of x for the expression (x – 7)² = 36 is 13. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is  (x – 7)² = 36. The value of x will be calculated as:-

(x – 7)² = 36

(x – 7) = √36

(x - 7) = 6

x = 13

Hence, the value of x for the expression (x – 7)² = 36 is 13. The correct option is A.

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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

Answer: 14.46

Step-by-step explanation:

sin 56 = 12/x

0.83 = 12/x

0.83x = 12

x = 12/0.83

x = 14.46

Answer: 14.475

Step-by-step explanation:

Since we are given the angle 56°, this means that the other angle is 34°. We are given the side 12 this means that x, or the hypotenuse, is 14.475.

The hypotenuse is c, b is 12, and a is the side with the 90° angle.

What we do is c = a/sin(a) = b / sin(56°)

Lexi's reasoning is correct because the theoretical probability of picking a yellow golf ball is 1 out of 2, or 1/2. This is because there are two yellow golf balls in the bag and one ball is being selected.

Theoretical probability is the ratio of the number of outcomes for a certain event to the total number of possible outcomes.

In this case, Lexi found the ratio of one yellow golf ball to the total number of balls in her bag (two balls: one yellow and one green).

This equals a theoretical probability of 1/2 or 0.5, meaning there is a 50% chance of picking a yellow golf ball.

This is the correct way to calculate theoretical probability.

Lexi's reasoning is correct in this situation. The theoretical probability of picking a yellow golf ball is 1 out of 2, or 1/2. This is because there are two yellow golf balls in the bag and one ball is being selected.

This ratio of 1/2 is the same as the theoretical probability of picking a yellow golf ball. Theoretical probability is based on the ratio of the outcomes being considered to the total number of possible outcomes.

In this case, the two yellow golf balls represent the possible outcomes, and the total number of golf balls in the bag is two. Therefore, the theoretical probability of picking a yellow golf ball is 1/2.

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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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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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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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The type of random variable is continuous

The term called variable in math is known as a quantity that may change within the context of a mathematical problem or experiment.

Here we know that the f1,v random variable can be thought of as the square.

Here the term random variable is known as a set of possible values from a random experiment and the domain of a random variable is called sample space

As we all know that random variables are classified into discrete and continuous variables.

Here the main difference between the two categories is the type of possible values that each variable can take.

The value of the function is continuous one.

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The price of the jeans will be $27 if you apply the function  composition h(x). The price of the jeans will be $30 if you apply the composition j(x). Because it is less expensive.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found.

If you first use the coupon and then utilize the shop discount, the price of the jeans is represented by the function h(x). The combination of the functions f(x) and g may be used to calculate the function h(x) (x). If you first apply the shop discount and then utilize the coupon, the cost of the jeans is represented by the function j(x). The combination of the functions g(x) and f may be used to calculate the function j(x) (x).

The price of the jeans will be $27 if you apply the composition h(x). The price of the jeans will be $30 if you apply the composition j(x). Because it is less expensive, the composition h(x) will provide you a bigger discount.

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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 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

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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[tex](x + 2)x( {x }^{2} + x + 3)[/tex]

Answer:

[tex] \frac{1}x{} [/tex]

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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The image of the point after the reflection across the y-axis is:

(-13, 8)

Remember that for a general point (x, y), a reflection across the y-axis just changes the sign of the x-component, so the new point will be:

(-x, y)

Here we want to apply this reflection to (13, 8), using the rule above, we can see that the new coordinates after the reflection are:

(-13, 8)

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By splitting the range into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of f(x) from x=-2 to x=4 is calculated.

Area = (55 - (-2)^2) + (55 - (1)^2) + (55 - (4)^2) = 55 + 9 + 1 = 65

By splitting the interval into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of

f(x)=55x2 from x=2 to x=4

is calculated. We begin by calculating the area of the rectangle whose right endpoint is at

x = -2. F(-2)

provides the height of this rectangle, which is equal to

55 - (-2)2 = 55 + 4 = 59.

The rectangle's width is

(4 - (-2))/3 = 6/3 = 2.

The area of this rectangle is therefore 59 x 2 = 118. The area of the rectangle with x = 1 as its right terminus can also be determined in a similar manner. This rectangle has a height of f(1), which equals

55 - (1)2 = 55 - 1 = 54.

The rectangle's width is

(4 - (-2))/3 = 6/3 = 2

The area of this rectangle is therefore 54 x 2 = 108. f(4), which equals 55 - (4)2 = 55 - 16 = 39, gives the area of the rectangle with x = 4 as the right endpoint. The rectangle's width is

(4 - (-2))/3 = 6/3 = 2.

The area of this rectangle is therefore 39 x 2 = 78. The sum of the areas of the three rectangles, which equals 118 + 108 + 78 = 304, represents the total area under the graph.

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