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Solve negative three minus one and two fifths.

three fifths
one and two fifths
negative four and two fifths
four and two fifths

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 30}}{\left( \cfrac{70}{100} \right)30}\implies 21[/tex]

Answer: 21

Step-by-step explanation:

70% of 30 students is 21

Hope this helped :)

The value of k for the expression, 3 (2− k) = −3k + 2, does not exist.

According to the question,

We have the following expression:

3 (2− k) = −3k + 2

Now, we will multiply 3 into the bracket:

6-3k = -3k+2

Now, moving -3k from the left hand side to the right hand side will result in the change of the sign from minus to plus:

6-3k+3k = 2

Now, 3k will get subtracted from 3k. So, we do not have any variable left for this equation.

Hence, the value of k  for the expression, 3 (2− k) = −3k + 2, does not exist.

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Answer: yes, because -2 is the opposite of the leading coefficient

Step-by-step explanation:

Identifying the domain and range is important when defining a function because domain gives all the input values and range gives all the output values a function can take. It is very essential to know domain and range of a function.

Domain are represented by independent variable and are graphed on x coordinate of the axis.

Range are dependent values and are graphed on y axis of the graph.

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Answer:

x = -2 ; x = 6/5

Step-by-step explanation:

5x + 2 >=0

5x >= -2

5/5 x >= -2/5

x >= -2/5

if x >= -2/5

5x +2 = 8

5x = 8 -2

5x = 6

5/5 x = 6/5

x = 6/5

if x < -2/5

-5x -2 = 8

-5x = 8+2

-5x = 10

-5/-5 x = 10/-5

x = -2

Given that the coefficient of x³ is twice the coefficient of x² in the binomial expansion of f(x)

(a) It is proved that n = 6k + 2

(b)k = 2 and n=14

(c) After expansion, the equation is
   1 + 14x + 91/4x^2 + 1001/2x^3 + 1001/16x^4 + 1001/16x^5

What is the binomial theorem?

The algebraic expansion of a binomial's powers is described by the binomial theorem (also known as binomial expansion) in elementary algebra.
The theorem states that the polynomial (x + y)n can be expanded into a sum including terms of the form axbyc, where the exponents b and c are nonnegative integers and b + c = n, and the coefficient an of each term is a particular positive integer dependent on n and b.

Solution Explained:

f(x)= (1+x/k)^n

Given that the coefficient of x^3 is twice the coefficient of x^2 in the binomial expansion of f(x)

a)

Coeff of x^3 = 1/6[n(n-1)(n-2)/k3]

Coeff of x^2 = 1/2[n(n-1)/k2]

1/6[n(n-1)(n-2)/k3] = 2* 1/2[n(n-1)/k2]

Canceling on both sides gives:

(n-2)/(6k) = 1

n = 6k+2        Hence proved

Given also that the coefficients of x^4 and x^5 are equal and non-zero,

b)

Coeff x^4 = 1/24 [n(n-1)(n-2)(n-3)/k4

Coeff x^5 = 1/120 [n(n-1)(n-2)(n-3)(n-4)/k5

1/120 [n(n-1)(n-2)(n-3)(n-4)/k5 = 1/24 [n(n-1)(n-2)(n-3)/k4

Canceling gives:

(n-4)/(120k) = 1/24

n = 5k+4

From previous:

n = 6k+2 = 5k+4

k = 2

n=14

Using these values of k and n,

c)

Give each coefficient as an exact fraction in its lowest terms
1 + 14x + 91/4x^2 + 1001/2x^3 + 1001/16x^4 + 1001/16x^5

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Answer: [tex]y=-\frac{1}{2}x+6[/tex]

Step-by-step explanation:

The slope of the line segment is [tex]\frac{-1-7}{4-8}=2[/tex].

The midpoint of the line segment is [tex]\left(\frac{4+8}{2}, \frac{-1+7}{2} \right)=(6, 3)[/tex].

Thus, the equation is:

[tex]y-3=-\frac{1}{2}(x-6)\\\\y-3=-\frac{1}{2}x+3\\\\y=-\frac{1}{2}x+6[/tex]

Answer:

The answer is 169

Step-by-step explanation:

Answer:

thats correct

Step-by-step explanation:

In 2267 year, this population would be 400000.

From the question, we have

population is growing as  Pn = 200*(1.03)n

substituting the value, we get

400000 = 200*(1.03)n

2000 = 1.03n

ln(2000) = n*ln(1.03)

n = ln(20000) / ln(1.03)

n = 257.15

2010 + 257.15 = 2267 year , this population would be 400000.

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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The standard error for the sample was 0.13 when "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89."

The standard deviation of a statistic's sampling distribution, or an estimate of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean. By dividing the standard deviation by the square root of the sample size, the standard error is determined. By taking into account the sample-to-sample variability of the sample means, it provides the precision of a sample mean.

Here,

The standard error=standard deviation/√number of samples

=0.65/√25

=0.65/5

=0.13

When "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89," the standard error for the sample was 0.13.

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Answer:

30%

Step-by-step explanation:

To calculate the percent of change, you find the amount of change and divide that my the original amount

[tex]\frac{3-2.1}{3}[/tex] = [tex]\frac{.9}{3}[/tex] = .3  As a percent, this would be 30%

Answer:

One number is 19 and the other is 6

Step-by-step explanation:

25 = x + (x- 13)

25 = x + x - 13

38 = 2x

19 = x

x = 19

25 - 19 = 6

Answer: M = 1876 - 30n  will give the amount of Money (M) remaining after n months of withdrawing exactly $30 per month, PROVIDED NOTHING ELSE IS EVER ADDED TO OR WITHDRAWN FROM THE ACCOUNT.  (Not very realistic.)

Use n=6 to provide the balance after 6 months.

Step-by-step explanation:

Answer:

a) 2.0 x 10^5

b) 8.0 x 10^4

c) 9 x 10^9

d) 1 x 10^10

The equation of the parabola is f(x) = 7(x-3)^2+5.

Given:

The equation of the parabola that has the same shape has f(x) = 7x^2 but with vertex(3,5) in the form of f(x) = a(x-h)^2 + k.

If the parabola has same shape then its a values are same.

so f(x) = 7x^2

here a = 7

so the equation with vertex (3,5) also has a value is 7.

(h,k) = (3,5)

f(x) = a(x-h)^2+k

= 7(x-3)^2 + 5.

Therefore the equation of the parabola is f(x) = 7(x-3)^2+5.

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Answer:

70,000

Step-by-step explanation:

Round up if the next digit is higher than or equal to 5.

edit: accidentally answered twice

Answer:

70,000

Step-by-step explanation:

Round up if the next digit is higher than or equal to 5.

Answer:

(a-5)(a+4)

Step-by-step explanation:

[tex]a^{2}[/tex]-a-20

[tex]a^{2}[/tex]+4a-5a-20

a(a+4) -5(a+4)

(a-5)(a+4)

The time at which Liz will catch up with Mandy is 1 pm.

Here we have to find the time when Mandy and Liz meet.

Let t be the time taken by Liz to meet Mandy

Given:

Speed of Mandy = 30mile/hr

Speed of Liz = 36 miles/hr

Formula:

Speed = Distance/ time

Distance by Mandy = 30t

Distance by Liz = 36( t - 20/60)

As the distance covered by both is the same. So we have

30t = 36( t - 1/3)

6t = 12

t = 2

2 hours past 11 am is 1 pm.

Therefore Liz catch Mandy at 1 pm.

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Answer:

x = 12

Step-by-step explanation:

Angles in a triangle add up to 180 degrees.

This means that 6x - 19 + 3x + 7 + 84 = 180

6x - 19 + 3x + 7 + 84 = 180

==> combine like terms

9x + 72 = 180

==> subtract 72 from both sides

9x = 108

==> divide both sides by 9

x = 12

If our circadian clocks are not reset each morning by exposure to light, they a. tend to run a cycle that is a little longer than 24 hours.

Chronobiology, the study of the body's circadian rhythms, contends that our daily routine, including when we eat, exercise, go to bed, and are exposed to light, may have a significant impact on how our bodies function on a day-to-day basis.

According to the National Institute of General Medical Sciences, circadian rhythms are the normal physical, mental, and behavioral changes that take place in the body on a 24-hour cycle, typically in reaction to light and darkness. One illustration is resting at night and remaining awake during the day.

You might not be able to avoid daytime sleep and evening work if you work an overnight shift or other irregular hours. According to Wright, those people should pay extra close attention to making other healthy decisions a priority, such as getting enough exercise and quitting smoking.

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Answer:

Step-by-step explanation:

b) The value of 12⁰ will be?

→ 12⁰ = ?

→ 12⁰ = 1

Hence, the solution is 1.

c) The value of (3)^(-2) will be?

→ (3)^(-2) = ?

→ (3)^(-2) = 0.1

Hence, the solution is 0.1.

Answer:

44.24

Step-by-step explanation:

The 2 in the thousandths place is lower than 5 therefore it does not round the 4 to a 5

Answer:

44.24

Step-by-step explanation:

hopes this helps please mark brainliest

Michael drinks 33.5 fl oz more fluid ounces than Lydia.

Given in question,

30 ml = 1 fl oz

  1 ml = 1/30 fl oz

1 bottle = 335 milliliters

No. of bottles of water Michael drank = 6

                                                              = 6 * 335 milliliters

                                                              = 2010 milliliters

                                                              = 2010/30 fl oz

                                                              = 67 fl oz

No. of bottles of water Lydia drank = 3

                                                           = 3 * 335 milliliters

                                                           = 1005 milliliters

                                                           = 1005/30 fl oz

                                                           = 33.5 fl oz

Therefore, 67 - 33.5 = 33.5

Hence, Michael drinks 33.5 fl oz more fluid ounces than Lydia.

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The elevation of the road is 4800 feet.

From the question, we have

y = mx + b

where m is the rate of change, b is the initial value of y and y, x are variables.

Let y represent the elevation of the road after x miles.

After 2 miles, the elevation is 5500 feet above sea level.

5500 = 2m + b   (1)

After 4 miles, the elevation is 6200 feet above sea level.

6200 = 4m + b   (2)

Solving equation 1 and 2, we get

m = 350, b = 4800

The elevation of the road 4800 feet.

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers. The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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Answer:

45/20

Step-by-step explanation:

Answer:

9/4 divided by 6/5 is 15/8

Step-by-step explanation:

9/4 ÷ 6/5 turns into 9/4 × 5/6 which is the reciprocal

9/4 × 5/6 = 45/24

Divide the numerator and denominator by 3 to get 15/8

15/8 is in its simplest form

the quotient as a power. a^21/a is a^20.

What is Power?

In mathematics, power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.

What is quotient?

The number we obtain when we divide one number by another is the quotient.

What is exponential function?

An exponential function is a mathematical function of the following form: f ( x ) = a x. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.

Given that,

a^21/a

quotient as power = a^21/a

                             =  a^(21-1)

                             = a^20

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