Solve (v +8) ^4/5= 2

We use Integers in everyday life when we solve real-world problems.

Let’s understand a real-life problem using integers.

Christian borrowed $1000 to buy a computer. After some time, she has paid back $250. How much does Christian still owe?

First, we will write a simple equation to represent the problem.

Let the amount that Christian still owes = 'x'

1000 = 250 + x

Now, we will rearrange the equation to isolate .

Then, solve for x.

The answer is 750.

Christian still owes = $750.

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It will take 12 weeks for Praisys corn to be ready for picking.

We have been given that,

 Maya plants corns In = 4 rows

 Praisy plants corns in  = 6 rows

Maya corns ready to be picked in = 8 weeks

We have to find the number of weeks will it take Praisys corn to be ready for picking.

To find we will use the unitary method that is,

            4 rows = 8weeks

            6 rows = 8/4*6 weeks

                         = 12 weeks

Thus 12 weeks will it take Praisys corn to be ready for picking.

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The domain and the range of the graph in interval notation are (-∝, ∝) and [-3, ∝) respectively

The domain of the function is the set of input values of the graph while the range of a function is the set of output values of the graph.

The graph represents the given parameter

Based on the definition above, the range of a function is the set of y values of the graph while the domain is the set of x values of the graph

On the graph, we can see that:

The x values extend indefinitely on the graph;

This means that the domain is (-∝, ∝)

While y values start from -3 and increases up

This means that the range is [-3, ∝)

Hence, the domain and the range of the function in interval notation are (-∝, ∝) and [-3, ∝) respectively

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The value of f(x) when x equals -5 is 15. Option D

A function can be defined as an expression, law or rule that explains the relationship between two variables;

Given the function;

f(x) = 5x + 40

To determine the value of the function when x = - 5, we have to substitute the value of x as -5 in the function.

With this, we have;

f(-5) = 5(-5) + 40

Now, expand the bracket

f(-5) = -25 + 40

Add the values, we have;

f(-5) = 15

We can see that the value of the function with the input of the variable x as -5 is 15

Thus, the value of f(x) when x equals -5 is 15. Option D

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The set (A∩C)' is {1, 3, 5, 6, 7}.

Simply said, a set in mathematics is a grouping of different items. Any group of objects, such as a collection of numbers, days of the week, different kinds of cars, etc., can be included in a set. An element of the set is any component of the set. When writing a set, curly brackets are utilized. An extremely basic set might look somewhat like this. Set A = {1,2,3,4,5}. The components of a set can be represented using a variety of notations. Typically, sets are represented by a set builder form or a roster form.

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Answer: D

Step-by-step explanation: It said the grandparents were less than 89 years old, if it said that the grandparents that were 89 and younger had remembered that's when you would use a solid circle because the 89 would be included. But since 89 isn't included then it's an open circle.

The variance and standard deviation for the given frequency of pupils per teacher in some states of US is

Variance= 4.62 = 4.6

Standard Deviation = 2.14 = 2.1

The frequency distribution shows the average number of pupils per teacher in some states of the United States.

Variance(σ²) is a measure of dispersion. A measure of dispersion is a quantity that is used to check the variability of data about an average value. Data can be of two types - grouped and ungrouped. When data is expressed in the form of class intervals it is known as grouped data. On the other hand, if data consists of individual data points, it is called ungrouped data. The sample and population variance can be determined for both kinds of data.

The standard deviation(σ) of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.

That means Standard Deviation = √variance.

For the given data the sum of frequencies(ni) = 1+16+11+7+1+2= 38.

Midpoint(mi) is 12,15,18,21,24,27.

ni * mi = 12,240,198,147,24,54.

Sum of ni * mi = 675.

Mean (u) =  17.76

mi - u    is -5.76,-2.76,0.24,3.24,6.24,9.24.

(mi - u)^2 is 33.17,7.61,0.057,10.49,38.93,85.37.

Sum of (mi - u)^2 = 175.62.

Variance = Sum of (mi - u)^2 / sum of frequencies

=> 175.62/38

=> 4.62 = 4.6.

Standard deviation = √variance.

=> √4.62

=> 2.14 = 2.1.

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Answer:

Step-by-step explanation:  You could try to times 15 by each side or add them or turn it into an expression like E*15=0

The appropriate way to calculate the monthly rent over time is 1190 × 1.017^n.

From the information, it was stated that the monthly rent for the first house is $1,190, and the Bainters can expect it to increase 1.7% every year and that the Bainters want to calculate their monthly rent over time.

Therefore, the appropriate expression will be:

= 1190 × (1 + 1.7%)^n

where n = number of years

= 1190 × 1.017^n

Therefore, the appropriate way to calculate the monthly rent over time is 1190 × 1.017^n.

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Answer:

[tex]\frac{\pi r^2}{2}[/tex]

Step-by-step explanation:

The area of a semicircle is half the area of a circle

The area of a circle is [tex]\pi r^2[/tex], where r is the radius of the circle, and [tex]\pi[/tex] is a mathematical constant, approximately 3.14. The area of the semicircle is half the area of the circle, or [tex]\frac{\pi r^2}{2}[/tex].

Answer:

Step-by-step explanation:

It's just a countdown sequence

2 1 0 -1 -2 ....

Because the remainder is 0, then the binomial x + 3 is a factor of the polynomial (-3)^2 + 5(-3) + 6

A division problem is an expression or an equation that involves the quotients of numbers or polynomials

To create the division problem, we make use of the following expression

(x^2 + 5x + 6)/(x + 3)

Using the remainder theorem, we have

Dividend = x^2 + 5x + 6

Divisor = x + 3

Set the divisor to 0,

So, we have

x + 3 = 0

This gives

x = -3

Substitute x = -3 in the dividend to get the remainder

So, we have

Remainder = (-3)^2 + 5(-3) + 6

Evaluate

Remainder = 0

Because the remainder is 0, then the binomial x + 3 is a factor of the polynomial (-3)^2 + 5(-3) + 6

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Answer: right

Step-by-step explanation:

Answer:

s = √77

it is not rational since 77 not a perfect square

Step-by-step explanation:

area = s^2 = s * s = 77

==> s = √77

The range could be written in inequality form will be:

-2500 ≤ x ≤ -100.

Living in the deep sea are slitsnails. It is assumed that they inhabit depths ranging from 100 to 2500 feet.

Let x represents the distance between the water and the surface.

The depth will decrease as we sink further into the water.

Therefore, the depth could range from 100 to 2500 feet.

The maximum depth is 2500 feet, and the lowest depth should be 100 feet.

So, the range could be expressed as follows in inequality form:

-2500 ≤ x ≤ -100.

Hence the required compound inequality is framed.

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The transforming the winner's age to a z-score is 1.03 and z-score is below the mean age of the winners.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Mean = (Sum of all the observations/Total number of observations).

Given:

Population mean,

μ=27.7 years

Population standard deviation,

σ=3.2 years

Winner's age =31 years

According to given question we have

If "x" represents the age of the winner then the z-score for "x":

z=x−μ/σ

a) Transforming the winner's age to a z-score

 z=31−27.7/3.2

   =1.03

(b) Interpretation of the z-score:

The winner's age of 31 years is 1.03 standard deviation below the mean age of the winners.

Therefore, the transforming the winner's age to a z-score is 1.03 and z-score is below the mean age of the winners.

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To find the

a) Transforming the winner's age to a z-score

(b) Interpretation of the z-score

is missing

The perimeter of the walkway in terms of y will be y = 50 + 8x. The slope will be 8.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

Given that the length and width of a rectangular garden are 15 meters and 10 meters, respectively. A walkway of width x surrounds the garden.

The perimeter will be calculated as:-

Perimeter = 2 ( W + L )

Perimeter = 2 [ ( 15 + 2x ) + ( 10 + 2x ) ]

Perimeter = 2 ( 10 + 2x + 15 + 2x )

Perimeter  = 2 ( 25 + 4x )

y = 50 + 8x

Compare the equation with the general form of the equation:-

y = 50 + 8x

y = mx + c

Slope = 8

Therefore, the perimeter of the walkway in terms of y will be y = 50 + 8x. The slope will be 8.

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Answer:

(9p^4+10)(9p^4−10)

Using the z-distribution, the limits of the 95% confidence interval are given as follows:

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the parameters are given as follows:

[tex]n = 200, \pi = \frac{152}{200} = 0.76[/tex]

Then the bounds are given as follows:

Which are the lower and upper limits, respectively.

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Answer:

A. You can write the number as a Ratio of two entegers

D. You know what the next number is

Step-by-step explanation:

we have 2 points on the line :

(15, 64) and (26, 112)

the standard form I assume is the slope-intercept form :

y = ax + b

"a" being the slope, "b" being the y-intercept (the y value when x = 0).

the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

the direction does not matter, but when picking one for one coordinate difference calculation, we have to use the same direction for the other.

I prefer to go from left to right.

so, in our case here

x changes by +11 (from 15 to 26).

y changes by +48 (from 64 to 112).

the slope "a" is +48/+11 = 48/11

so, our equation looks already like this :

y = 48/11 x + b

now, we use any of our points to get b.

let's pick (15, 64) :

64 = 48/11 × 15 + b = 720/11 + b

704/11 = 720/11 + b

-16/11 = b

and our full equation is

y = 48/11 x - 16/11

or

y = 1/11 × (48x - 16/11)

or

y = 16/11 × (3x - 1)

The probability that Nacho will get all 4 questions wrong will be 0.3164.

From the information, Nacho takes a multiple choice test, the test has 4 questions and each question has 4 choices.

The probability of getting the correct option is 1 out of 4 which is 0.25 and the incorrect option is 0.75.

Therefore, the probability that Nacho will get all 4 questions wrong will be:

= (0.75)⁴

= 0.3164

Therefore, the probability that Nacho will get all 4 questions wrong will be 0.3164.

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The variable have positive integer exponent. so f(x) = -5x² + 3x +3 is a polynomial function.

A polynomial function is one that uses only non-negative integer powers or positive integer exponents of something like a variable in an equation such as the quadratic equation, cubic equation, and so on. For illustration, 2x+5 is a polynomial with an exponent of one.

A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, as well as division (No division operation by a variable).

f(x) = -5x² + 3x +3

Make the leading coefficient positive:

= 5x² - 3x -3

identify the coefficient:

a = 5, b = -3, c = -3

substituting into the:

[tex]$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$[/tex]

[tex]$x=\frac{-(-3)+\sqrt{(-3)^2-4 \times 5 \times(-3)}}{2 \times 5}$[/tex] or [tex]$x=\frac{-(-3)-\sqrt{(-3)^2-4 \times 5 \times(-3)}}{2 \times 5}$[/tex]

[tex]$x=\frac{3+\sqrt{3^2+4 \times 5 \times 3}}{2 \times 5}$[/tex] or

[tex]$x=\frac{3+\sqrt{9+4 \times 5 \times 3}}{2 \times 5}$[/tex]

[tex]$x=\frac{3+\sqrt{69}}{10}$[/tex]

x = ± [tex]\frac{3+\sqrt{69}}{10}$[/tex]

As we can see that the general form of a power function is f(x) = axⁿ , where a is a non zero co-efficient and 'n' is a real number.

so the given function is not a power function.

So,

the variable have positive integer exponent. so f(x) = -5x² + 3x +3 is a polynomial function.

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Answer:

For 12a - 37 > 0 answer is   a > 37/12

For 6a ≤ 42 answer is a ≤ 7

Step-by-step explanation:

The net income of Adventure Travel using its  Adjusted Trial Balance for Year Ended December 31, 20XX, is $14,640

What is net income?

The net income is the excess of fees earned by Adventure Travel  in the year ended  over its total expenses, in essence, we need to determine its total expenses first and foremost, which comprises of salaries expense, rent expense, depreciation expense, advertising expense and office supplies expense

total expense=32,800+16,800++3960+4000+2800

total expenses=60,360

fees earned=75,000

net income =fees earned-total expenses

net income=75,000-60,360

net income=$14,640

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Answer:

If it takes one minute to use 5.7 calories, it’ll take 190/5.7 minutes to use 190 calories. This simplifies to 100/3 minutes. So this person must walk for 33 minutes and 20 seconds to use 190 calories (assuming the rate of calorie usage remains constant throughout).

The probability that X is more than 3 i.e. P(x > 3) is 0.945

The given parameters are

The probability that X is more than 3 can be calculated using the following equation

P(x <= 3) + P(x > 3) = 1

So, we have

P(x > 3) = 1 - P(x <= 3)

This gives

P(x > 3) = 1 - P(0) - P(1) - P(2) - P(3)

The individual probabilities are calculated using

P(x) = C(n,x) * p*x * (1 -p)^(n-x)

So, we have

P(0) = C(10,0) * 0.6^0 * (1 -0.6)^(10 - 0) = 0.0001

P(1) = C(10,1) * 0.6^1 * (1 -0.6)^(10 - 1) = 0.00157

P(2) = C(10,2) * 0.6^2 * (1 -0.6)^(10 - 2) = 0.01062

P(3) = C(10,3) * 0.6^3 * (1 -0.6)^(10 - 3) = 0.04247

So, we have

P(x > 3) = 1 - 0.0001 - 0.00157 - 0.01062 - 0.04247

Evaluate

P(x > 3) = 0.945

Hence, the probability that X is more than 3 is 0.945

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