What is the solution to the equation?
3 (4x - 1) + x = 5x – 4(1 – 2x) +1

Answer:

them some fast growing apples

Step-by-step explanation:

realy

Answer:

is $27.50 per each teacket

The expression which is equivalent to -5(b - 6) as required to be determined in the task content is; -5b + 30.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Since the expression given is; -5(b- 6).

By using the distributive property of numbers

= (-5 × b) + (-5 × -6)

= -5b + 30

Thus, the linear expression which is equivalent to -5(b - 6) as required is; -5b + 30.

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The Question attached seems to be incomplete/ inappropriate. the complete Question is:

Which expression is equivalent to -5(b - 6).

Answer:

-8

Step-by-step explanation:

Slope = (y1-y2) / ( x1-x2)

            = ( f-4) / (-8 - -6)      =  6

                  (f-4) / -2    = 6

                    f-4 = -12

                     f = - 8

Answer:

f = -8

Explanation:

Find slope:

\(\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points\)

Here given:

Inserting into slope formula:

\(\sf \rightarrow \dfrac{4-f}{-6-(-8) } = 6\)

\(\sf \rightarrow \dfrac{4-f}{2 } = 6\)

\(\sf \rightarrow 4-f = 12\)

\(\sf \rightarrow -f = 12-4\)

\(\sf \rightarrow -f =8\)

\(\sf \rightarrow f =-8\)

Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:

��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!

For the rock songs, we have three from a set of eleven, hence:

�11,3=11!3!8!=165C11,3=3!8!11!=165

For the alternative songs, we have four from a set of five, hence:

�5,4=5!4!1!=5C5,4=4!1!5!=5

For the rap songs, we have three from a set of four, hence:

�4,3=4!3!1!=4C4,3=3!1!4!=4

Since the songs are independent, the total number of ways is given by:

�=165×5×4=3300T=165×5×4=3300

hope this helps you

Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:

��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!

For the rock songs, we have three from a set of eleven, hence:

�11,3=11!3!8!=165C11,3=3!8!11!=165

For the alternative songs, we have four from a set of five, hence:

�5,4=5!4!1!=5C5,4=4!1!5!=5

For the rap songs, we have three from a set of four, hence:

�4,3=4!3!1!=4C4,3=3!1!4!=4

Since the songs are independent, the total number of ways is given by:

�=165×5×4=3300T=165×5×4=3300

hope this helps you

Answer:

its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2

Answer:

When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.

Multiply b^2 * b^3 = b^5  (add the exponent 2 + 3 = 5)

Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)

Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)

b^2 * b*2 = b^4 (add exponents)

7b * b^2 = 7b^3 (add the exponents 1 + 2)

4 * b^2 = 4b^2

              b^2             +               7b             +        4

b^3           b^5              +           7b^4            +   4b^3

+                                                                                      

b^2           b^4             +           7b^3            + 4b^2

b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2

\(b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2\)

The surface area of Neelah's package is 214 square inches.

What is surface area, and how is it calculated?

The surface area is the measure of the total area that the surface of an object occupies. It is calculated by adding up the areas of each face or surface of the object.

Calculation of the surface area:

To find the surface area of Neelah's package, we first need to determine the dimensions of the package. We are given that the volume of the package is 748 cubic inches and that the equation 4 x 11 x h = 748 can be used to find the height of the package.

Solving for h, we have:

4 x 11 x h = 748

44h = 748

h = 17

Therefore, the dimensions of the package are 4 inches by 11 inches by 17 inches.

To find the surface area of the package, we need to add up the area of each face of the package. The package has six faces, so we calculate the area of each face as follows:

Front and back faces: 4 inches x 17 inches = 68 square inches each

Top and bottom faces: 11 inches x 17 inches = 187 square inches each

Left and right faces: 4 inches x 11 inches = 44 square inches each

Therefore, the total surface area of the package is:

2(68) + 2(187) + 2(44) = 136 + 374 + 88 = 598 square inches

However, this calculation includes the interior of the package, and we are only interested in the external surface area. The top and bottom faces are not part of the external surface area, so we need to subtract them from the total:

598 - 2(187) = 224 square inches

Therefore, the surface area of Neelah's package is 214 square inches.

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The bus that is the most consistent, given the data collected on travel times to school from two groups of students is C Bus 18, with a range of 10

To determine which bus is the most consistent, we should use the interquartile range (IQR) as the measure of variability. The IQR measures the spread of the middle 50% of the data, which makes it less sensitive to outliers compared to the range.

Bus 47:

Median (Q2): 16

Q1: 10

Q3: 22

IQR = Q3 - Q1 = 22 - 10 = 12

Bus 18:

Median (Q2): 12

Q1: 8

Q3: 18

IQR = Q3 - Q1 = 18 - 8 = 10

Bus 18 has a smaller IQR than Bus 47 (10 vs. 12), which means the travel times for Bus 18 are more consistent.

Note: Figures might be different due to options being for different variant but Bus 18 is the most consistent.

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The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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Answer:

F. 824.8 ft³

Step-by-step explanation:

To find the volume of a cube, you want to multiply the length by width by height.

l = 8.2

w = 9.4

h = 10.7

l • w • h

8.2  • 9.4 • 10.7

= 824.756

Round to the nearest tenth.

824.8 ft³

Hope this helps!

9514 1404 393

Answer:

  k = 100/9

Step-by-step explanation:

Cross-multiply to eliminate fractions.

  9k = 10·10

Divide by the coefficient of k.

  k = 100/9

The probability of getting a tail on each toss is:

Since there is only one way of getting all tails, it follows that the required probability is given by:

Hence, the required probability is approximately 0.0020

Answer:

Equations: 10+1 & 10-1

This would trick them good!

Answer:

a) SE = 25

b) MOE = 41

c) CI = 1951 ; 2049

Step-by-step explanation:

Normal distribution

Population mean  unknown

Population standard deviation    σ  = 350     Kwh

a) The standard error of the mean SE is

SE  =  σ/√

SE = 350 /√196

SE = 350/14

SE = 25

b) If confidence nterval is 95%    or 0,95  then

α = 0,05

And from z table we get     z(c) = 1,64

MOE = z(c) * SE

MOE = 1,64 * 350/√196

SE = 1,64 * (350)/14

SE = 41

MOE = And from z tabl we get     z(c) = 1,64

MOE = 1,64 * 350/√196

MOE = 1,64 * (350)/14

MOE = 1,64 * 25

MOE = 41

c) The confidence interval is:

Z = 2000

α = 1- 0,95

α = 0,05       ⇒   α/2   =  0,025

CI  =   Z - z(α/2) * σ/√n   ;    Z + z(α/2) * σ/√n

z(α/2)   from z-table is:     z(0,025)  = 1,96

CI = 2000 -  1,96* 350/√196   ;   2000 + 1,96* 350/√196

CI = 2000 - 1,96*25  ;  2000 +  1,96*25

CI = 2000 -  49 ;  2000 + 49

CI = 1951 ; 2049

Answer:

120

Step-by-step explanation:

(+2) x (-5) x (+4) x (-3)
= (-10) x (-12)
= (-)(-) (10 x 12)
= + 120

AC/BC = 11 / 5

To find the ratio AC / BC

Step 1: Identify the coordinates of A, B and C

A ( -5, 0), B( 1, 0), C(6, 0)

Step 2: Find the distance AC and BC

For the distance AC:

A ( -5, 0), C(6, 0)

For the distance BC:

B( 1, 0), C(6, 0)

AC/BC = 11 / 5

The simplified expression is \(\frac{-1}{9x} -9x - 10\).

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).

Here, the given expression

           \(\frac{1}{x}+\frac{-10x/9}{x^2}-9x-10\)

            \(\frac{1}{x}+\frac{-10}{9x}-9x-10\)

             \(\frac{9-10}{9x} -9x -10\)

                 \(\frac{-1}{9x} -9x - 10\)

Thus, the simplified expression is \(\frac{-1}{9x} -9x - 10\).

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Answer:

Step-by-step explanation:

You want integers q and r such that 26 = 50q +r, and 0 ≤ r < 50.

Solving for q, we have ...

  (26 -r)/50 = q

For r in the range 0–49, possible values of q are in the range ...

   (26 -0)/50 ≥ q > (26 -49)/50

   0.52 ≥ q > -0.46

The only integer in that range is ...

  q = 0

Then the value of r is ...

  26 = 50·0 +r

  r = 26

<95141404393>

Answer:

The tightened spot is 10 feet away from the foot of the pole.

Step-by-step explanation:

1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.

2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.

⭐What is the Pythagoras' Theorem?

3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.

Let B= the distance from the tightened spot to the foot of the pole.

\((C)^2 = (A)^2 + (B)^2\)

\(26^2 = 24^2 + B^2\)

\(676 = 576 + B^2\)

\(100 = B^2\)

\(\sqrt{100} = \sqrt{(B)^2}\)

\(10 = B\)

∴ The tightened spot is 10 feet away from the foot of the pole.

Diagram:

Answer:

1/4

Step-by-step explanation:

2/3 - 5/12

first denominators must be equal to do math with them, find the lowest common denominator and change numerator according to changed denominator

8/12 - 5/12 = 3/12

for simplest form divide by number that fits both numerator and denominator, which in this case is 3

3/12 divided by 3/1

= 1/4

Answer:

  (a)  3x +y = 2

Step-by-step explanation:

You want the equation y = -3x +2 written in standard form.

The standard form of a linear equation is ...

  ax +by = c

where a, b, c are mutually prime integers with a ≥ 0. If a=0, then b > 0.

To put the given equation into that form, we can add 3x to both sides:

  3x +y = 3x -3x +2

  3x +y = 2

Answer:

The percent of households with rates from $100 to $115. is      \(P(100 < x < 115) =\)94.1%

Step-by-step explanation:

From  the question we are told that  

   The  mean rate is \(\mu =\)$ 106.50  per month

    The standard deviation is  \(\sigma =\)$3.85

Let the lower rate be  \(a =\)$100

Let the higher rate  be  \(b =\)$ 115

Assumed from the question  that the data set is normally

The  estimate of the percent of households with rates from $100 to $115. is mathematically represented as

         \(P(a < x < b) = P[ \frac{a -\mu}{\sigma } } < \frac{x- \mu}{\sigma} < \frac{b - \mu }{\sigma } ]\)

here x is a random value rate  which lies between the higher rate and the lower rate so

     \(P(100 < x < 115) = P[ \frac{100 -106.50}{3.85} } < \frac{x- \mu}{\sigma} < \frac{115 - 106.50 }{3.85 } ]\)

      \(P(100 < x < 115) = P[ -1.688< \frac{x- \mu}{\sigma} < 2.208 ]\)

Where  

      \(z = \frac{x- \mu}{\sigma}\)

Where z is the standardized value of  x

So

     \(P(100 < x < 115) = P[ -1.688< z < 2.208 ]\)

     \(P(100 < x < 115) = P(z< 2.208 ) - P(z< -1.69 )\)

Now  from the z table we obtain that

      \(P(100 < x < 115) = 0.9864 - 0.0455\)

     \(P(100 < x < 115) = 0.941\)

    \(P(100 < x < 115) =\)94.1%

The number of terms  - 2.

Here we assume that \(a_{n}\) > 0 or all n, the terms are monotone decreasing and \(\lim_{n \to \infty} a_n\) =0. This guarantees the convergence of the series. Now, if we choose a finite value N, and approximate the series by Σ \((-1)^{n}\)\(a_{n}\) , the error in the approximation of the infinite series by this finite sum is bounded by \(a_{N + 1}\) .

We are given the infinite alternating series

                      n=4,              ∑ \(\frac{(-1)^{n+1} }{n^{4} }\)

and wish to approximate the sum with an error of less than 0.001.

Define \(a_{n}\) = \(\frac{1}{n^{4} }\) . Then we will solve the inequality \(a_{n}\) < 0.001 :

                     \(\frac{1}{n^{4} }\) < 0.001

                     \(n^{4}\) > 1000

                     n > \(\sqrt[4]{1000}\)

                        ≈ 5.62

Therefore, if we stop at n=5, the error will be less than 0.001. Since the series starts at n=4, we need only use 2 terms.

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Answer:

19:37

Step-by-step explanation:

1 h and 54 m of the movie + 13 minutes that he paused is 2h and 7 m and adding that to the time it was makes it 19:37 or 7:37 pm

The time when the movie finished is 19:37 if Sebastian started watching the movie at 17:30. The movie was 1 hour and 54 minutes long.

For legal, commercial, and social purposes, a time zone is a region that observes a uniform standard time. Instead of strictly following longitude, time zones tend to follow the borders between countries and their subdivisions.

It is given that:

Sebastian started watching a movie at 17:30. The movie was 1 hour and 54 minutes long, but part-way through he paused it for 13 minutes.

The total duration of the movie = 1 hour and 54 minutes

The total duration of the movie with 13 minutes pause

= 1 hour and 54 minutes + 13 minutes

= 2 hours 7 minutes

The movie starts at 17:30

Movies will end at 19:37

Thus, the time when the movie finished is 19:37 if Sebastian started watching the movie at 17:30. The movie was 1 hour and 54 minutes long.

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Answer:

2t + 16

Explanation:

The graph shows that there is a linear relationship between height and time. So, we need to find the equation of a line with the form:

h = mt + b

Where m is the slope of the line and b is the y-intercept.

So, b is equal to the value of the height after 0 seconds, therefore, b or the y-intercept is equal to 16

b = 16

On the other hand, the slope can be calculated as:

Where t1 and t2 are two values of time in the table and h1 and h2 are their respective values of height.

So, if we replace t1 by 1, h1 by 18, t2 by 2, and h2 by 20, we get:

Therefore, the expression for the height of the flag after t seconds is:

h = 2t + 16

Given the points:

(x1, y1) ==> (1, 1)

(x2, y2) ==> (3, 7)

To find an equation of the line that goes through the points, first find the slope using the slope formula below:

Substitue values into the formula and solve for the slope, m:

The slope of the line, m is = 3.

Now, use the point slope form:

(y - y1) = m(x - x1)

Substitute 1 for y1, 1 for x1, and 3 for m:

(y - 1) = 3(x - 1)

Let's rewrite the equation to slope intercept form: y = mx + b

Where m is the slope and b is the y-intercept

y - 1 = 3(x) + 3(-1)

y - 1 = 3x - 3

Add 1 to both sides:

y - 1 + 1 = 3x - 3 + 1

y + 0 = 3x - 2

y = 3x - 2

Therefore, the equation of the line in slope intercept form is:

y = 3x - 2

ANSWER:

y = 3x - 2

Answer:

Area: 9cm²

Perimeter: 12 cm

Explanation:

Area is length x width

It's a square so length and width are the same

3 times 3 is 9

And to find the perimeter you just add the side lengths

Squares have 4 sides and the given side length is 3 so 3x4 OR 3+3+3+3 is how you get the perimeter.

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There are two parts in this question. In first part we have to find area and in second part we have to find perimeter of a Square.

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To find Area of a Square :

we know:

\(\bigstar \boxed{ \tt{Area \: of \: a \: Square = }{ \tt{side}^{2} }}\)

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So :

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\(\dashrightarrow \sf{Area \: of \: a \: Square = }{ \sf{side}^{2} }\)

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\(\dashrightarrow \sf{Area \: of \: a \: Square = }{ \sf{3}^{2} }\)

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\(\dashrightarrow \sf{Area \: of \: a \: Square = }{ \sf3 \times 3}\)

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\(\dashrightarrow \sf{Area \: of \: a \: Square = }{ \sf9cm {}^{2} }\)

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\( \therefore \underline \textsf{ \textbf{Area \: of \: a \: square \: = \red{9 {cm} }}} \red{ \bf^{2}}\)

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To find perimeter of square :

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\(\bigstar \boxed{ \tt{Perimeter \: of \: a \: Square = }{ \tt4 \times {side}}}\)

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\(\dashrightarrow \sf{Perimeter \: of \: a \: Square = }{ \sf4 \times side} \\ \)

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Answer:

The answer is letter B

Step-by-step explanation:

Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is  y =  0 .

Horizontal Asymptote:  

y =  0

The distance from the midpoint of the hypotenuse of any vertex is:

\(\sqrt{(0-a)^2 +(2b - b)^2} \\\)   = \(\sqrt{(2a - a)^2 +(0 -b)^2}\)

= \(\sqrt{a-0)^2 + (b -0)^2}\)

Right Angle Triangle:

A right triangle is a triangle with one of its angles 90 degrees. An angle of 90 degrees is called a right angle, so a triangle with a right angle is called a right triangle. In this triangle, we can use the Pythagorean law to easily understand the relationship of the various sides. The side opposite the right angle is the largest side and is called the hypotenuse.

In a right triangle we have:

                  (Hypotenuse)2 = (Base)2 + (Altitude)2

Mid point Theorem:

The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half the length of the third side. This theorem is used in many places in real life. For example, if we don't have a measuring tool, you can use the midpoint theorem to cut a bar in half.

If we have a line segment whose endpoint coordinates are given by

(x₁, y₁) and (x₂, y₂), we can find the coordinates of the midpoint of the line segment using the following formula:

Let (xₙ , yₙ ) Coordinates of the midpoint of the segment. Then

(xₙ, yₙ) = ( (x₁+ x₂/2 , (y₁ + y₂)/2 )

This is known as the midpoint theorem.

According to the Question:

Suppose that we have two points (x₁ ,y₁)  and (x₂, y₂). The distance between them is given by:

D = \(\sqrt{(x_2-x_1)^2 + (y_2- y_1)^2 }\)

Hence the distance from the midpoint of the hypotenuse to any vertex is given by:

    \(\sqrt{(0-a)^2 +(2b - b)^2} \\\)

= \(\sqrt{(2a - a)^2 +(0 -b)^2}\)

= \(\sqrt{a-0)^2 + (b -0)^2}\)

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