A plant is 4 inches tall. it grows 5 inches per year. which equation model is the height y of the plant after x years  

The point is [-13,-7] when the actual numbers are all at least two units away from 4.

Given that,

To specify the interval (or pair of intervals) on the real number line, use absolute value notation. (Utilize the x variable.) actual numbers are all at least two units away from 4.

We know that,

We get,

|-4-x| = 3

-3 = -4-x = 3

7 = -x = 13

-13 = x = -7

Therefore, The point is [-13,-7] when the actual numbers are all at least two units away from 4.

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its a and c maybe. cuz im smart

Answer:

16 turtles

20 frogs

32 fish

Step-by-step explanation:

let 't' = # turtles

let '4 + t' = # frogs

let '2t' = # fish

t + 4 + t + 2t = 68

4t + 4 = 68

4t = 64

t = 16 turtles

4 + 16 = 20 frogs

2(16) = 32 fish

Answer:

63 degrees as well because its a line intersected by two parallel lines

Answer:

Since m∠3 = 63° and m∠1 is corresponding angles (being on the same 180° line and they correspond each other), then m∠1 is also equal to 63°

Step-by-step explanation:

m∠3 = m∠1              

Corresponding angles (one that holds the same relative position as another angle somewhere else in the figure)

For the function f(x) = ⌊x²/3⌋, the values of f(s) for different sets s are as follows: a) f(s) = {1, 0, 0, 0, 1, 3}, b) f(s) = {0, 0, 1, 3, 5, 8}, c) f(s) = {0, 8, 16, 40}, d) f(s) = {1, 12, 33, 77}

The function f(x) = ⌊x²/3⌋ represents the floor of x²/3. To find f(s) for different sets s, let's evaluate it for each case:

a) For s = {-2, -1, 0, 1, 2, 3}:

  - For -2, (-2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For -1, (-1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 0, (0)²/3 = 0/3 = 0.

  - For 1, (1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 2, (2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For 3, (3)²/3 = 9/3 = 3.

  Therefore, f(s) = {1, 0, 0, 0, 1, 3}.

b) For s = {0, 1, 2, 3, 4, 5}:

  - For 0, (0)²/3 = 0/3 = 0.

  - For 1, (1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 2, (2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For 3, (3)²/3 = 9/3 = 3.

  - For 4, (4)²/3 = 16/3, and ⌊16/3⌋ = 5.

  - For 5, (5)²/3 = 25/3, and ⌊25/3⌋ = 8.

  Therefore, f(s) = {0, 0, 1, 3, 5, 8}.

c) For s = {1, 5, 7, 11}:

  - For 1, (1)²/3 = 1/3, and ⌊1/3⌋ = 0.

  - For 5, (5)²/3 = 25/3, and ⌊25/3⌋ = 8.

  - For 7, (7)²/3 = 49/3, and ⌊49/3⌋ = 16.

  - For 11, (11)²/3 = 121/3, and ⌊121/3⌋ = 40.

  Therefore, f(s) = {0, 8, 16, 40}.

d) For s = {2, 6, 10, 14}:

  - For 2, (2)²/3 = 4/3, and ⌊4/3⌋ = 1.

  - For 6, (6)²/3 = 36/3 = 12.

  - For 10, (10)²/3 = 100/3, and ⌊100/3⌋ = 33.

  - For 14, (14)²/3 = 196

The values of f(s) for the given sets show how the function ⌊x²/3⌋, which represents the floor of x²/3, behaves for different inputs.

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Answer:

A, B, F

- The radius of the circle is 3 units

- The center of the circle lies on the x-axis

- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9

Step-by-step explanation:

The first option is correct because the standard equation of the circle is:

\((x - 1)^{2} + {y}^{2} = 9\)

making the radius equal to 3.

The center is at (-1,0), therefore it lies on the x-axis.

And lastly, the last option is correct because both options have the radius of 3.

Answer:

x = 3

Step-by-step explanation:

Is x an exponent?

\( y = 3^x \)

\( 27 = 3^x \)

\( 3^3 = 3^x \)

\( x = 3 \)

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.

In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.

For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

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Answer:

graph A  

Hope that helps!                                                                                                  

Answer: Graph a

Step-by-step explanation: The points in graph A match the table provided. The points (-2,2), (-1,3), and (0,4) are all on the line in graph A. If the line continued it would pass through (1,5).

A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(\sigma)= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) \(=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\)

So n \(=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

Te given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(\(\sigma\))= 2×1.55

Standard deviation of resistance(\(\sigma\))= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5\()^2\)

n=(15.996\()^2\)

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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Answer:

1) greater than

2) less than

3) greater than

4)less than

5) greater than

6) greater than

Step-by-step explanation:

Using the concept of equations, 1552 people attended the festival last year.

Two algebraic expressions are combined to create an algebraic equation using the equals (=) sign. Algebraic equations are also known as polynomial equations since they contain polynomials on both sides of the equal sign. An algebraic equation consists of variables, coefficients, constants, and algebraic operations including addition, subtraction, multiplication, division, and exponentiation.

An integer or set of integers that satisfy the condition in the equation are the roots or solutions of an algebraic equation.

Let the number of people who attended the festival last year =x

Then, we can write an equation as

1785=1.15 × x

x = 1785/1.15

=1552 people

So, last year's attendance = 1552

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Answer:

x=5, y=-10

Step-by-step explanation:

y = x²-10x+15 --- eqn 1

y = -10 --- eqn 2

Sub eqn 2 into eqn 1:

     x²-10x+15 = -10

x²-10x+15+10 = 0

    x²-10x+25 = 0

            (x-5)² = 0

                x-5 = 0

                    x = 5

A graph of the solution of the inequality is: graph F.

In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would solve the given inequality by making x the subject of formula as follows;

x - 5 < 14

By adding 5 to both sides of the inequality, we have the following:

x - 5 + 5 < 14 + 5

x < 19

Note: The line on a number line should be open when the inequality symbol is greater than (>) or less than (<).

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Answer:

infinetily many solutions because the lines are overlapping

Step-by-step explanation:

In the given equation x = 9 is the value that satisfies the equation.

The square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 9 is 3, because \(3*3 = 9\). The symbol for square root is "√" and it can also be represented as "sqrt".

In the given equation \(x = 9\) is the value that satisfies the equation.

To find the value of x in the equation \(3 \sqrt{x} = 9\), we first need to square both sides of the equation to eliminate the square root.

\(3 \sqrt{x} = 9\)

Squaring both sides:

\((3 \sqrt{x} )^2 = 9^2\)

\(x = 9^2 / 3^2 = 9^2 / 9 = 9\)

Therefore, x = 9 is the value that satisfies the equation.

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Answer:

n1 = 13

n2 = 22

n3 = 19

Step-by-step explanation:

see attached for the work.

The numbers are 13, 19 and 22.

Let x represent the first number

Second number is 9 + x

Third number is 9 + x - 3 = 6 +  x

x + 9 + x + 6 + x = 54

3x + 15 = 54

3x = 54 - 15

3x = 39

x = 13

Second number = 13 + 9 = 22

Third number = 21  3 = 19

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The total cost of a $48.00 dinner bill, including 7% tax and 18% tip, is $60.

$40 change, you will get back from $100.00.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

The dinner costs $48.00.

The total cost of a $48.00 dinner bill, including 7% tax and 18% tip,

= 48 + (48 x 0.07) + (48 x 0.18)

= $60.

You will get the change,

= 100 - 60

= $40

Therefore, total cost is $60.

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Answer:

1)

(1, 4)

2)

(1, 3)

3)

x direction: +7

y direction: +7

4)

x direction: +4

y direction: -5

Step-by-step explanation:

Hope it helps!!

Answer:ur pretty

Step-by-step explanation:

The value of the sample proportionThe sample proportion is the percentage of individuals in a sample who have the attribute of interest. As a result, the sample proportion is computed by dividing the number of students who answered "yes" by the total number of students surveyed.

Here's the computation:Sample proportion= 220/400= 0.55Therefore, the sample proportion is 0.55.b. The standard error of the sample proportionThe standard error of the sample proportion can be determined using the following formula:Standard error of Standard error of the sample proportion= √[(0.55 * 0.45)/400]= √(0.00061875)= 0.0249Therefore, the standard error of the sample proportion is 0.0249.c. Constructing an approximate 95% confidence interval for the true proportion

A confidence interval is a range of values around a sample statistic, such as the sample proportion, that is expected to contain the true value of the population parameter with a certain degree of confidence. A 95 percent confidence interval implies that we are 95 percent certain that the true population parameter is within the specified interval.Let's first compute the margin of error:Margin of error= z* √[(p*q)/n]wherez= critical value of the standard normal distribution for a 95% confidence level= 1.96Margin of error= 1.96* √[(0.55*0.45)/400]= 0.0487Therefore, the margin of error is 0.0487. Now that we have the margin of error, we can construct the confidence interval using the following formula:Confidence interval= sample proportion ± margin of error= 0.55 ± 0.0487= (0.5013, 0.5987)Therefore, an approximate 95 percent confidence interval for the true proportion is (0.5013, 0.5987).

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The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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Answer: \(4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}\) .

Step-by-step explanation:

The given expression: \(\sqrt{\dfrac{16n}{m^3}}\)

'

since \(16=4^2\)

\(m^3=m^{2+1}= m^2\times m\)   [\(a^{n+m}=a^n\times a^m\)]

Now, the given expression becomes,

\(\sqrt{\dfrac{4^2n}{m^2\timesn}}=\dfrac{4\sqrt{n}}{m\sqrt{m}}\)

Since there is root in denominator , so we need to rationalize

\(\dfrac{4\sqrt{n}}{m\sqrt{m}}\times\dfrac{\sqrt{m}}{\sqrt{m}}=\dfrac{4\sqrt{mn}}{m\times\sqrt{m}\times\sqrt{m} }\\\\=\dfrac{4\sqrt{mn}}{m\times m}\\\\=\dfrac{4\sqrt{mn}}{m^2}\)

Hence, the correct option is \(4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}\) .

The function for the given compound interest will be A = 3000(1+6/4)  and A = 5000(1+7.2)  .

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate is raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

$3000 deposit that earns 6% annual interest compounded quarterly.

A = P (1 + r/4)4

A = 3000(1+6/4)

$5000 deposit that earns 7.2% annual interest compounded monthly.

A = P (1 + r)

A = 5000(1+7.2)  

Hence the function for the given compound interest will be A = 3000(1+6/4)  and A = 5000(1+7.2)  .

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The increase in the money supply is $5,000.

Definition of ratio -

Money multiplier m=1/1-r

where r is required reserve ratio

When fed purchases $700 of bonds, it gets 700 money supply.

Change in money supply = multipler * 700

=1/(1-0.14)*700

= $5,000

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Answer:

The jar contains 132 grams of zinc

Step-by-step explanation:

zinc to copper = 3 : 19

New equivalent weights

zinc to copper = x : 836

Now, let us solve for x as follows

\(\frac{zinc}{copper} = \frac{3}{19} = \frac{x}{836} \\\\cross-multiplying\\3 \times\ 836 = 19 \times\ x\\2508 = 19x\\x = \frac{2508}{19}\\x = 132\)

the jar contains 132 grams of zinc

To check if the answer is accurate, the answer gotten when the weight of zinc is divided by copper will be the same for both the old and new ratios:

old ratio: 3 ÷ 19 =  0.158

new ratio: 132 ÷ 836 = 0.158

Answer:

1

Step-by-step explanation:

Use the clues given.

We know that 5% is equal to 5/100 or .05. Using one of those numbers, we can find what the answer is.

Multiply by 20.

In this case, I will be using .05, just because it is the easiest. So, if we multiply .05 by 20, we will get 1.

Hope this helped,

Philip

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