Translate the expression “the product of triple a number and 19”

Answer: I would say non linear. I have done problems like these before and anytime there is an exponent in the equation it always ends up being non linear. Also remember for it to be linear it most form a straight line that passes through the origin.

Step-by-step explanation:

The required value of a₄ is 10,202 to the given recursive formula.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The given recursive formula in the question as:

aₙ = (aₙ ₋₁ )² + 1 ....(i)

And, a₁ = 3

Substitute the value of a₁ = 3 in equation (i), and solve for n = 2

a₂ = (a₁)² + 1

a₂ = (3)² + 1

a₂ = 9 + 1 = 10

Substitute the value of a₂ = 10 in equation (i), and solve for n = 3

a₃ = (10)² + 1

a₃ = 100 + 1 = 101

Substitute the value of a₃ = 101 in equation (i), and solve for n = 4

a₄ = (101)² + 1

a₄ = 10,201 + 1

a₄ = 10,202

Therefore, the required value of a₄ is 10,202.

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The value of x in the remote angles of the triangle  is 22.

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.  

In other words the sum of the remote interior angle is equals to the external angle.

Therefore,

110 = 3x + 2x

110 = 5x

divide both sides by 5

110 / 5 = 5x / 5

x = 22

Therefore, using exterior angle theorem, the value of x is 22.

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Answer:

(0, 6)

Step-by-step explanation:

Given function:

[tex]y=\log_4(2x+64)+3[/tex]

The y-intercept of a function is the point at which the curve crosses the y-axis, so when x = 0.

Therefore, to find the y-intercept, substitute x = 0 into the function:

[tex]\implies y=\log_4(2(0)+64)+3[/tex]

[tex]\implies y=\log_4(64)+3[/tex]

Rewrite 64 as 4³:

[tex]\implies y=\log_4(4)^3+3[/tex]

[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies y=3\log_4(4)+3[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies y=3(1)+3[/tex]

[tex]\implies y=3+3[/tex]

[tex]\implies y=6[/tex]

Therefore, the y-intercept of the given function is (0, 6).

The mean sleep time is 16.54 hours per day for newborn babies

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The mean sleep time is 16.54 hours per day for newborn babies.

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Answer:

x=-3

Step-by-step explanation:

we can fill the y into the first equation since we already know what it is equal to

5x+4(1-x)=1

5x+4-4x=1

x+4=1

  -4. -4

x=-3

Hopes this helps please mark brainliest

Answer:

5x + 4y = 1

Answer: x = 1/5 - 4y/5

y = 1 - x

Answer: x = −y + 1

Step-by-step explanation:

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They should produce 1091 units each day to yield a minimum cost.

What is the vertex formula?

When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).

We know that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.

We have,

C = 70,000 - 120x + 0.055x²

C = 0.055x² - 120x + 70,000

Hence, for this equation, the graph will be parabola opening upward.

For that, the vertex will be the minimum cost

x = (-b) / 2a

Here, a = 0.055 , b = -120

Now, find and put the values of x.

minimum cost (x) = ( -(-120) ) ÷ ( 2 × 0.055 )

                           = 120 ÷ 0.11

                           = 120 ÷ 0.11

                           = 1090.90  ≈ 1091 units

The minimum cost will be yield for 1091 units.

Therefore, They should produce 1091 units each day to yield a minimum cost.

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According to the triangle inequality, the length of a triangle's third side must be greater than the sum of any two other triangle lengths, so the length of the steel piece will likely be 4 or 5 inches.

Triangle inequality is a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side; it is represented by the symbols a + b≥ c. The basic tenet of the theorem is that a straight line connects any two points.

Here,

If they are an integer number of inches long and less than six, the following lengths are possible: 4 ,5

According to the triangle inequality, any two other triangle lengths must be greater than the third side of a triangle's length:4+4 = 8 > 6

4+6 = 10 > 4

5+5 = 10 > 6

6+5 = 11 > 5

According to "The Triangle Inequality," which states that the length of a triangle's third side must be greater than the sum of any two other triangle lengths, the piece of steel's potential length will be 4 or 5 inches.

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The derivative of the given polynomial equation is 16x³ - 6x + 6.

We are given an equation. The equation represents a polynomial in one variable. The degree of the polynomial is four; hence, it is called biquadratic. We need to find the derivative of the given polynomial. The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.

The equation is given below.

y = 4x^4 - 3x² + 6x + 14

dy/dx = (d/dx)(4x^4 - 3x² + 6x + 14)

dy/dx = (d/dx)(4x^4) - (d/dx)(3x²) + (d/dx)(6x) + (d/dx)(14)

dy/dx = [4*4x^(4 - 1)] - [3*2x^(2 - 1)] + [6*1x^(1 - 0)] + [14*0x^(0 - 1)]

dy/dx = 16x³ - 6x + 6

Hence, the derivative of the given polynomial equation is 16x³ - 6x + 6.

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A. The translations used in the transformation of f(x) to g(x) can be given as follows:

B. The solutions for k are given as follows:

C. The rules are given as follows:

There are four cases for the translation of an image, and they can be represented as follows:

From the graph of the linear functions shown at the end of the answer, two translations are possible, listed as follows:

The values of k are equivalent to the values of a in the bullet points listing the translations above, and the equations were also built from those bullet points.

The lines are shown by the image at the end of the answer.

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Answer:

A

Step-by-step explanation:

function because for every x there is only one y

the domain are the value of x

the range are the value of y

The probability of workers who earn between rs. 35,000 and rs. 52,000 is 99.62 %.

A data set with a normal distribution has the majority of its values clustered in the middle of the distribution and the remaining values tapering off symmetrical toward either end.

For the given question;

z = (x - μ)/σ

In which,

x = sample mean

μ = mean  (48,000)

σ = standard deviation (1500)

x = 35,000 and x = 52,000

For x = 35,000.

z = (35,000 - 48,000)/1500

z = -8.66

Check the p value from table

p(z = -8.66) = 0

For x = 52,000

z = (52,000 - 48,000)/1500

z = 2.66

p(z = 2.66) = 0.99617

P(35,000 < x < 52,000) = 0.99617 - 0

P(35,000 < x < 52,000) = 0.99617

Thus, the probability of workers who earn between rs. 35,000 and rs. 52,000 is 99.62 %.

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Using a 98% confidence interval, the total number of customers that should be sampled is 87.

The sample size refers to the number of observations in the data set, and as the sample size increases, the calculated value of population parameters becomes more reliable and true. In other words, as sample size increases, the value of the margin of error decreases.

Given,

Standard deviation σ=300

Confidence level: 0.98

Maximum allowable error: ε=75

The critical value is calculated using the standard normal table at the level of significance (0.02)

The critical value in this case is 2.326.

Sample size is calculated by,

n=((Z[tex]z_{\alpha /2}[/tex])²×σ²))/ε²

n=((2.326)²×(300)²)/(75)²

n=86.564≈87

Therefore, the required sample size is 87.

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The polynomial is, -24x⁴y⁵+16x²y³. One of the factor is (-8x²y³),So other factor is 3x²y²-2 by the factorization method.

Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The terms degree, standard form, monomial, binomial, and trinomial are all covered in this video. An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). 

Here,

The polynomial is,

=-24x⁴y⁵+16x²y³

One of the factor is (-8x²y³)

=-8x²y³*(3x²y²-2)

So other factor is 3x²y²-2.

One of the factor is (-8x²y³),So other factor is 3x²y²-2 by the factorization method for the The polynomial -24x⁴y⁵+16x²y³.

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The theatre sold 178 adult tickets and 261 children tickets for the play.

It is given that the total number of seats is 439 seats.

There are two types of tickets available- children and adults.

The price for adult tickets is $48 and that for children is $28.

Let the number of adult tickets sold be x

Let the number of children's tickets sold be y.

The show was a sold-out

Hence,

x + y = 439                                 [1]

48x + 28y = 15852                    [2]

From equation [1] we get

x = 439 - y

putting this result in equation [2] gives us

48(439 - y) + 28y = 15852

or, 21072 - 48y + 28y = 15852

or, -20y = - 5220

or, y = -5220/ -20

or, y = 261

Therefore,

x + 261 = 439

or, x = 439 - 261

or, x = 178

Hence, 178 adult tickets were sold and 261 children's tickets were sold.

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The fraction of all the circles in the shapes  is 23/90

Given that the:

Ratio of the number of white shapes to the number of black shapes is 7:3

Ratio of the number of white circles to the number of white squares is 2:7

Ratio of the number of black circles to the number of black squares is 1:2

Total share for both white and black shape = 7+3 = 10

share for white shape = 7/10 and share for black shape = 3/10

Total share for white circles and white squares = 2+7 = 9

share for white circles = 2/9 and share for white squares = 7/9

Total share for black circles and black squares = 1+2 =3

share for black circles = 1/3 and share for black squares = 2/3

White circles will take 2/9 of white colors i.e. 2/9 x 7/10 =   14/90 = 7/45

Black circles will take 1/3 of  black colors i.e. 1/3 x 3/10 = 3/30 = 1/10

Fraction of circles = 7/45 + 1/10

                              =  14+9/ 90

                             = 23/90

Therefore, the fraction of all the shapes that are circles is 23/90

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Answer:

A

Step-by-step explanation:

It is perpendicular because it forms a right angle with the second line

y= -4/3=-1.333

y= 5/2=2.500

Answer:

Step-by-step explanation:

If one spins a six-space spinner and then flips a coin, then the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]

As per the question statement, a person spins a six-space spinner and then flips a coin,

And we are required to determine the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes.

Now, on spinning a six-space spinner, any one of the 6 faces will come as outcomes, and if these outcomes are denoted by (1, 2, 3, 4, 5, 6).

And after spinning the six-space spinner, if one flips a coin, either of "heads" face or "tails" face will come as outcome, which can be denoted by {H, T}.

Therefore, If one spins a six-space spinner and then flips a coin successively as mentioned above, every possible outcome of the spinner will be accompanied by one of two the possible outcomes the coin. Hence, the sample space (S) of possible outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]

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Step-by-step explanation:

3.

we need to find the map size based on actual miles.

so, we find how many map ft are 1 actual mile :

5 ft / 20.5 corresponds to 1 actual mile.

5 / 20.5 = 10/41 ft

now, we have 15.5 actual miles, that is 15.5 times the 1 standard actual mile.

and so, this is

10/41 × 15.5 = 155/41 = 3.7804878048780... map ft

4.

30.5 model cm = 70.6 actual m

1 model cm = 70.6/30.5 = 2.314754098... actual m.

8 model cm = 8×2.314754098... =

= 18.51803279... actual m

5.

7 map m = 14 actual miles

1 map m = 14/7 = 2 actual miles.

14 map m = 14×2 = 28 actual miles.

6.

8 map km = 6 actual miles

we need to calculate the map km, so we need the standard actual mile

1 actual mile = 8/6 = 4/3 = 1.3333333... map km.

50.2 actual miles = 50.2×1.333333... =

= 66.93333333... map km.

7.

80.2 model cm = 40.2 actual m

1 model cm = 40.2/80.2 = 0.501246883... actual m

10 model cm = 10×0.501246883... =

= 5.01246883... actual m

8.

6 map m = 15 actual miles

1 map m = 15/6 = 5/2 = 2.5 actual miles

8.8 map m = 8.8×2.5 = 22 actual miles

9.

5 map ft = 16.5 actual miles

1 actual mile = 5/16.5 = 0.303030303... map ft

45.6 actual miles = 45.6×0.303030303... =

= 13.81818181... map ft

10.

65.8 model cm = 95.6 actual m

1 model cm = 95.6/65.8 = 1.452887538... actual m

12 model cm = 12×1.452887538... =

= 17.43465046... actual m

Hence, 17-unit percent change is (45/19)×17% = 40.26%

12-unit percent change is (43/16)×12% = 32.25%

18-unit percent change is (-25/20)×18% = -22.5%

8-unit percent change is (-50/5)×8% = -80%

Given, that

The 19-unit percent change is 45 %

Now, 1-unit percent change is 45/19

17-unit percent change is (45/19)×17%

= 40.26%

The 16-unit percent change is 43 %

Now, 1-unit percent change is 43/16

12-unit percent change is (43/16)×12%

= 32.25%

The 20-unit percent change is -25%

Now, 1-unit percent change is -25/20

18-unit percent change is (-25/20)×18%

= -22.5%

The 5-unit percent change is -50 %

Now, 1-unit percent change is -50/5

8-unit percent change is (-50/5)×8%

= -80%

Hence, 17-unit percent change is (45/19)×17% = 40.26%

12-unit percent change is (43/16)×12% = 32.25%

18-unit percent change is (-25/20)×18% = -22.5%

8-unit percent change is (-50/5)×8% = -80%

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With the help of probability we can conclude our answer.

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The correct way by using the power of a power property we can write as;

⇒ x¹⁵ = (x³)⁵

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x¹⁵

Now,

Since, The expression is,

⇒ x¹⁵

We can write the expression as by using the power of a power property as;

⇒ x¹⁵ = (x³)⁵

Thus, The correct way by using the power of a power property we can write as;

⇒ x¹⁵ = (x³)⁵

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The distance driven in city is 386.4 miles and same in highway is 213.6 miles.

Let the distance driven in city be x and driven in highway be y.

Now given that the mileage in city is 46 miles per gallon and in highway same is 51 miles per gallon.

The car is driven 621 miles in 13 gallon.

So suitable system of linear equations in two variables to solve this is,

x+y = 621 ……(1)

x/46+y/51 = 13 …….(2)

From (2) we get,

51x+46y = 30498

5x+46(x+y) = 30498

5x+46*621 = 30498

5x = 30498-28566

5x = 1932

x = 386.4

So from (1) we get,

y = 621-x = 621-386.4 = 213.6

Hence the car drove 386.4 miles in city and 213.6 miles in highway.

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Answer:

4.5 ounces of rice per container

Step-by-step explanation:

27 / 6 = 4.5

Hope this helps :)

Answer:

x≈-0.0200335+2kπ/5

x≈-0.648352+2kπ/5

Step-by-step explanation:

sin(-5x)=0.1

-sin(5x)=0.1

sin(5x)=-0.1

sin(5x)=1/10

5x=arcsin(- 1/10)

5x=π-arcsin(- 1/10)

5x=π-arcsin(- 1/10)

5x=π-arcsin(- 1/10)+2kπ

5x=π-arcsin(- 1/10)+2kπ

x=arcsin (1/10)/5 + 2kπ/5

x=arcsin (1/10)/5 + 2kπ/5

x≈-0.0200335+2kπ/5

x≈-0.648352+2kπ/5

Josiah read  at the rate of 17.5 pages per  hour.

Speed of reading is the number of pages read per hour.

Given here, Josiah read 28 pages in  1 ³/₅ hours which is in mixed fraction

now   1 ³/₅ = ⁸/₅ = 1.6 hours

therefore the speed of reading is = 28 / 1.6 = 17.5 pages hour.

Hence, Josiah's the speed of reading is  17.5 pages hour.

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After evaluating those terms,

we get the answer as

1.  -7/6 - (-1/9) =[tex]\frac{-19}{18}[/tex]

2.  -1/3 + 5/7   = = [tex]\frac{8}{21}[/tex]

A fraction is a number that has a numerator as well as a denominator.

1 / 2  is an example of a fraction. The top part of the fraction is the numerator and the bottom part of the fraction is the denominator.

Fractions represent one value. Dividing the numerator by the denominator shows what decimal value fractions have. For example,  1/2  is equal to 1  ÷  2 which equals 0.5.

in this we have to evaluate

1.    -7/6 - (-1/9)

= [tex]\frac{-7}{6}[/tex]  - ([tex]\frac{-1}{9}[/tex])

= [tex]\frac{-21+2}{18}[/tex]

=[tex]\frac{-19}{18}[/tex]

Hence , after solving we get the desired result as -19/18 .

2. -1/3 + 5/7

= [tex]\frac{-1}{3}[/tex] + [tex]\frac{5}{7}[/tex]

= [tex]\frac{-7 + 15}{21}[/tex]

= [tex]\frac{8}{21}[/tex]

Hence, after solving we get the desired result as 8/21 .

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