What is the solution of this equation if the extraneous solution is eliminated? Use the options in the drop-down menus to form the correct answer
in decimal form. Help meeee pls :)

The total path length covered in 5 second will be 69.45 meter.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a train going at 70 km/h must reduce its speed to 30 km/h when passing over a bridge. It performs the operation in five seconds.

Using the first equation of motion -

v = u + at

(30 x 5/18) = (70 x 5/18) + 5a

(30 x 5/18) - (70 x 5/18)  = 5a

- (5/18) x 40 = 5a

- (200/18) = 5a

a = - (40/18)

a = - 2.22 m/s²

S = 19.44 x 5 + 0.5 x (- 2.22) x 25

S = 97.2 - 27.75

S = 69.45 meter

Therefore, the total path length covered in 5 second will be 69.45 meter.

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[Question translation in english -

A train going at 70 km/h must reduce its speed to 30 km/h when passing over a bridge if it performs the operation in five seconds what total path has been traveled in that time.]

There is a Weak positive association between the amount of goals scored and the number of wins a hockey team has. Most of the data points fall between 4 goals scored and 5  number of wins. Causation cannot be established because their relationship was not in a controlled setting.

When if a relationship between two variables is said to be  negative, it is one that does not just necessarily mean that the association is weak. Although though both variables tend to increase in reaction to one another, a weak positive correlation depicts that the relationship is not very strong.

Therefore, even though  the data tells us that there is a weak positive relationship that exist between the two variables, it is vital to know that that correlation does not equal causation.

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The standard deviation of the restaurant profits in 2021 is given by $71181.

Restaurant profit for outcome 'move to A' = $ 260000

Restaurant profit for outcome 'move to B' = $ 120000

Restaurant profit for outcome 'stay in C' = $ 100000

The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.

Standard deviation of the restaurant profits in 2021 is given by

= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)

= $ √(((100000)² + (40000)² + (60000)²)/3)

= $ √(15200000000/3)

= $ √5066666667

= $ 71181 (rounded to the nearest dollar)

Hence standard deviation of the restaurant profits in 2021 is given by $71181.

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The question is incomplete. The complete question will be -

Answer:

I think Courtney's will. My reason is because, she travels the fastest ever minuet. She will get there first, because she travels 5.5 every minute, while the others travel 4, and 3.5 per minute.

Answer:

Sample Response: Courtney will win the race. Her unit rate is the greatest,which means she walks farther in one minute than the other two turtles.

Step-by-step

It said that this is correct.

                                                    hope it helps

Answer: Your answer would be 99 sq.ft

Step-by-step explanation: We first find the triangle which has an area of 21 sq.ft, then we find the rectangle which is 120 sq.ft. Finally we subtract both numbers, and receive our answer.

Hope it helps.

Answer:

I believe the area of the shaded figure is 1,179 ft^2

Step-by-step explanation:

the area of the triangle: 21 ft^2 (6*7=42, 42/2=21)

the area of the rectangle: 1,200 ft^2 (12*10= 1,200)

1,200 - 21 = 1,179

The value correct is 8

Equal signs - the result will be positive

Different signs - the result will be negative

88 + (-80)

88 - 80

8

Therefore, the value is 8

Answer:

2.36705065488

The average value of the given function on the given interval is = 7/2 and 6.25 respectively

What is Average?

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

(a) f(x) = x2 – 8x + 10

f = 1/b-a \(\int\limits^b_a {f(n)} \, dx\)

f = 1/5-2 \(\int\limits^5_2 {x^{2} -8x+10} \, dx\)

Here, a=2

b=5

f(x) =x2 – 8x + 10

f = 1/3 (x³/3 - 8x²/2+10x)5/2

f = -25/9 -20/9

f = -45/9

= -5

Mean Value Theorem

If f(x) = continous on (a, b)

If f(x) = differentiable on (a, b)

Then f(c) = f(b) -f(a)/b-a

were c∈ (a,b)

Here, f(c) = f(-5)-f(2)/5-2

f(c) = -5+2/3

f(c) = -1 ......................(1)

Here, f(x) = x²-8x+10

f(c) = c²-8c+10

f(x) = 2c-8...................(2)

equating 1&2

2c -8 = -1

2c = -1 +8

c = 7/2

c∈ (2,5)

(b) f(x) = Vx on [1, 16]

f = \(\sqrt{x}\) on (1 ,16)

f= 1/b-a \(\int\limits^b_a {f(n)} \, dx\)

f = 1/16-1 \(\int\limits^6_1 {\sqrt{x} } \, dx\)

f = ( 2x (3/2)/45)₁¹⁶

f = 128/45-2/45

f = 126/45

= 14/5

Mean Value Theorem

f(x) = \(\sqrt{x}\)

f(c) =\(\sqrt{c}\)

f(c) = 1/2\(\sqrt{c}\)....................(1)

we know that

f(c) = f(b)-f(a)/b-a

f(c) = f(16)-f(1)/16-1

f(c) = \(\sqrt{16}\) -\(\sqrt{1}\)/15

f(c) = 4-1/15

= 3/15.....................(2)

Equating (1) and (2)

1/2\(\sqrt{c}\) = 3/15

2\(\sqrt{c}\) = 15/3

2\(\sqrt{c}\) = 5

\(\sqrt{c}\) = 5/2

c = (5/2)²

=25/4

c≅ 6.25

6.25 = (1 ,16)

The average value of the given function on the given interval is = 7/2 and 6.25 respectively

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The area of the triangle MNO to the nearest tenth of an inch is 14.2 inches².

Given a triangle MNO.

It is given two sides and the included angle of the triangle.

The area of a SAS triangle can be found using the formula,

Area = \(\frac{1}{2}\) × ab × sin (C)

where a and b are the given sides and C is the included angle.

Here the given sides are,

n = 7.3 inches and o = 4.4 inches

Included angle is,

∠M = 118°

Using the formula,

Area = \(\frac{1}{2}\) × no × sin (M)

        =  \(\frac{1}{2}\) × (7.3)(4.4) × sin (118°)

        =  \(\frac{1}{2}\) × (7.3)(4.4) × 0.883

        = 14.18 ≈ 14.2 inches²

Hence the required area is 14.2 inches².

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Answer:

25% is greater then -25.

Step-by-step explanation:

-25 is in the negiatives, and is to the left of 0. Anything to the left of 0 will be less then anything on the right of 0. :D

-25% will always be less than 25% because a negative number, being less than 0, will always be less than a positive number, being greater than 0.

Thus, -25% is less than 25% or 25% is greater than -25%

Answer:

  12x²y² +2xy -2

Step-by-step explanation:

The distributive property is used to multiply polynomials.

  (3xy -1)(4xy +2) . . . . . . . . . . . . . given

  = (3xy)(4xy +2) -1(4xy +2) . . . . multiply the 2nd by the terms of the 1st

  = (12x²y² +6xy) +(-4xy -2) . . . . here are those products

  = 12x²y² +2xy -2 . . . . . . . . . collect terms (6xy-4xy = 2xy)

Answer:

7. 4^2 = 6

8. 7^2 = 49

9. 6^4 =1296

10. 1^2 = 1

11. 5^3 =125

12. 1^3 =1

Step-by-step explanation:

Answer:

C) Infinitely many

Step-by-step explanation:

7x+3-x=3(1+2x)

6x+3=3+6x

Subtract 3 from both sides

6x = 6x

Infinitely many solutions

The following can be determined about the slopes and y-intercepts of the system of equations: A. The slopes are different, and the y-intercepts are different.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we have the following system of equations in standard form:

4x + 2y = −2

x − 3y = 24

By rewriting system of equations in slope-intercept form, we have:

y = -2x - 1  ⇒ m = -2, b = -1

y = x/3 - 8  ⇒ m = 1/3, b = -8

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Graph A represents the solution set of the equations y = x² + 4x + 3 and y = 2x + 6.

The vertex of the parabola is (-2,-1), which corresponds to Graph A. We can find it we the formula  h = -b/(2a)

a is the coefficient of x² (which is 1 in this case) and b is the coefficient of x (which is 4 in this case).

h = -4/(2×1) = -2.

To find the y-coordinate of the vertex, we substitute x = -2

y = (-2)² + 4(-2) + 3 = -1.

∴ vertex ⇒ (-2,-1), which corresponds to Graph A.

The equation y = 2x + 6 is a linear equation and represents a straight line with a slope of 2 and y-intercept of 6.

The line passes through the points (-3, 0) and (1, 8), which also corresponds to Graph A.

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The expression that shows the volume of the prism is x³ - x² - 6.

The prism above is a rectangular prism. The volume of the prism can be found as follows:

The volume of the prism can be found as follows:

volume of the rectangular prism = lwh

where

Therefore,

volume of the rectangular prism = (x - 3)(x)(x + 2)

volume of the rectangular prism = (x² - 3x)(x + 2)

volume of the rectangular prism = x³ + 2x² - 3x² - 6

volume of the rectangular prism = x³ - x² - 6

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The correct answer is Option 1.

The remainder you got when 3x³ - 5x² - 23x + 24 is divided by x - 3 is -9.

Polynomials are expressions in algebra which consist of both variables and coefficients. Sometimes, variables are also known as indeterminates. Polynomials are classified as monomials, binomials, and trinomials based on the degree of the variables in the expression.

Variables in the monomials, binomials and trinomials have the highest degree equals 1, 2 and 3 respectively.

By doing the long division method, we will bet the quotient as 3x² + 4x - 11 and the remainder equals -9.

Let's check this using division algorithm.

Dividend = 3x³ - 5x² - 23x + 24

Divisor = x - 3

Quotient = 3x² + 4x - 11

Remainder = -9

By division algorithm,

Dividend = (Divisor × Quotient) + Remainder

3x³ - 5x² - 23x + 24  = [(x - 3) (3x² + 4x - 11)] + -9

                                 = [3x³ + 4x² - 11x - 9x² - 12x + 33] + -9

                                 = 3x³ + 4x² - 9x² - 11x - 12x + 33 - 9

                                 = 3x³ - 5x² - 23x + 24

Hence -9 is the remainder of this division process.

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Answer:

The confidence interval is \((\overline{x} - 1.99\frac{\sigma}{\sqrt{35}}, \overline{x} + 1.99\frac{\sigma}{\sqrt{35}})\), in which \(\overline{x}\) is the sample mean and \(\sigma\) is the standard deviation for the population.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.99}{2} = 0.005\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.005 = 0.995\), so Z = 2.575.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

In this question:

\(M = 1.99\frac{\sigma}{\sqrt{35}}\)

The lower end of the interval is the sample mean subtracted by M, while upper end of the interval is the sample mean added to M. Thus, the confidence interval is \((\overline{x} - 1.99\frac{\sigma}{\sqrt{35}}, \overline{x} + 1.99\frac{\sigma}{\sqrt{35}})\), in which \(\overline{x}\) is the sample mean and \(\sigma\) is the standard deviation for the population.

Step-by-step explanation:

Numerical climate models use quantitative methods to simulate the interactions of the important drivers of climate, including atmosphere, oceans, land surface and ice. They are used for a variety of purposes from study of the dynamics of the climate system to projections of future climate.

Answer:

16 units

Step-by-step explanation:

We need to find the distance between (-4, 8) and (12, 8) on the coordinate plane.

We know that the distance between two points on the coordinate plane is given by :

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

Put x₁ = -4, x₂ = 12, y₁ = 8 and y₂ = 8

So,

\(D=\sqrt{(12-(-4))^2+(8-8)^2}\\\\=16\ units\)

So, the distance between the two points is equal to 16 units.

Answer:

56

Step-by-step explanation:

khan answer

The combination helps us to know the number of ways an object can be arranged without a particular manner. The number of ways in which Amari can choose different sets of 3 colors is 56.

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

\(^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}\)

where,

n is the number of choices available,

r is the choices to be made.

Given that Amari has 8 paint colors available, he wants to mix 3 of them to create a new color. Therefore, the number of ways in which Amari can choose different sets of 3 colors is,

Number of ways = ⁸C₃ = 8!/[3!(8-3)!] = 56

Hence, the number of ways in which Amari can choose different sets of 3 colors is 56.

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The number of soda bottles the machine can make per minute is 25

From the question, we have the following parameters that can be used in our computation:

The linear relation

Where we have the points

(2, 50) (6, 150)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

m = unit rate i.e the required slope

So, we have

2m + c = 50

6m + c = 150

Next, we have

4m = 100

Evaluate

m = 25

So, we have

2 * 25 + c = 50

Evaluate

c  0

So, we have

y = 25x

Hence, the equation of the line in fully simplified slope-intercept form is y = 25x

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For each relation, we would determine whether or not it is a function as follows;

Relation 1 is: B. not a function

Relation 2 is: B. not a function.

Relation 3 is: B. not a function

Relation 4 is: A. a function.

In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

This ultimately implies that, an independent value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the value on the y-coordinate of a cartesian coordinate.

Based on relations 1, 2, and 3, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).

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Answer:

False. The product of two negative integers is a positive integer.

Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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Edit, my calc is broken, sorry for the inconvenience, please disregard.

The number decreased by 14%  is found as the 133.7.

A percentage is defined as a relative value that represents the hundredth part of any quantity. Each percent (symbolized 1%) is one hundredth portion; thus, 100 percent symbolizes the entire amount and 200 percent defines twice the given amount.

Let the original number be 'x'.

number decreased by 14%

That means of x = 460.

Then,

86% of x = 1115

86x/100 = 115

x = 11500/86

x = 133.7

The original number be 133.7.

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