Fill in the blanks.The domain of f is the _____of f −1, and the _____ of f −1 is the range of f.

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

The smallest sample size that will result in a margin of error of no more than 5% for a 95% confidence interval is given as follows:

385.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The margin of error is modeled as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

We have no estimate, hence we consider that:

\(\pi = 0.5\)

The minimum sample size is obtained as n when M = 0.05, hence:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.05\sqrt{n} = 1.96 \times 0.5\)

\(\sqrt{n} = 1.96 \times 10\) (0.5/0.05 = 10).

\((\sqrt{n})^2 = (1.96 \times 10)^2\)

n = 384.16

Hence rounded to 385, as a sample size of 384 would have a margin of error slightly above 0.05.

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A graph of the solution to this inequality 3x ≤ 18 is: graph D.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would divide both sides of the inequality by 3 as follows;

3x ≤ 18

x ≤ 18/3

x ≤ 6.

In this exercise, we would use an online graphing calculator to plot the given inequality 3x ≤ 18 as shown on the number line attached below.

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The scatter plot suggests that there is a relationship between the number of chinups and push-ups, but it is not a perfect relationship

What is Scatter plot ?

A scatter plot is a type of graph that is used to display the relationship between two variables. It is a visual representation of a set of data points, where each point represents the values of two variables for a single observation.

Based on the scatter plot, it appears that there is a positive correlation between the number of chin-ups and push-ups several students did. This means that as the number of chin-ups increase, the number of push-ups also tend to increase.

We can see this trend in the general upward slope of the points in the scatter plot. However, there is also a fair amount of variability in the data, as some students did more push-ups than others even when they did a similar number of chin-ups.

Therefore,  the scatter plot suggests that there is a relationship between the number of chin-ups and push-ups, but it is not a perfect relationship

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Answer:

Let's start by rearranging this polynomial.

x^3 - 2x^2 + x - 2

x^3 + x - 2x^2 - 2

Now, factor out the common terms in the first two terms, and the second t wo terms. So we have: x(x^2 + 1) - 2(x^2 +1)

Apply the distributive property, and you have: (x-2)(x^2+1), which can't be factored further.

There's definitely something wrong with the answer choices here, or the problem itself.

Hopefully this helps!

The complete factorization of the polynomial is,

⇒ (x + i) (x - i) (x - 2)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The polynomial is,

⇒ x³ - 2x² + x - 2

Now, We can factor the polynomials as;

The polynomial is,

⇒ x³ - 2x² + x - 2

⇒ x² (x - 2) + 1 (x - 2)

⇒ (x² + 1) (x - 2)

⇒ (x + i) (x - i) (x - 2)

Therefore, The complete factorization of the polynomial is,

⇒ (x + i) (x - i) (x - 2)

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Answer:

A. 150

Step-by-step explanation:

Calculate the probability of landing on an odd number: 1/2.

Multiply the probability by the number of trials: (1/2) * 300.

Simplify the expression: 150.

Therefore, a reasonable prediction is that the event of landing on an odd number will occur 150 times out of the 300 rolls of the fair 6-sided die.

Answer:

Step-by-step explanation:

2(4x+1)<3(2x-3)

simplify to

8x+2<6x-9

we can add 9 to both sides and subtract 8x from both sides

11<-2x

divide by -2

-5.5>x

Answer: 65 = 1 x 65 or 5 x 13. Factors of 65: 1, 5, 13, 65. Prime factorization: 65 = 5 x 13.

Step-by-step explanation:

Answer:

$40

Step-by-step explanation:

If the perimeter of the larger farm is 80 yards in a 8:5 ratio, the perimeter of the smaller farm will be 50 yards.

Multiply this value by the cost of 0.50 per yard to get $40.

The matrix equation ax = ba is x = a²(-1) × (ba).

Given the matrix equation ax = ba, to solve for x.

To solve for x, multiply both sides of the equation by the inverse of a, assuming it exists that for matrix equations, the order of multiplication matters.

The correct solution should be:

ax = ba

To isolate x, multiply both sides of the equation by the inverse of a on the left:

a²(-1) × (ax) = a²(-1) × (ba)

Multiplying a²(-1) on the left side cancels out with a,

x = a²(-1) × (ba)

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If a and b are integers and c is an irrational number it will produce an irrational number .

Here a is an integer and b is an integer and c is an irrational number

So taking number accordingly

Let us take an example and take a = 5 , b = - 6 , c = √3

New number produces = a × b × c

Putting all the value in the equation we get,

New number produces = 5 × ( - 6 ) × √3

New number produces = 30√3

The new number produced 30√3 is an irrational number.

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Answer:

Step-by-step explanation:

8.10 / 4.5 pounds = 1.80 per pound of strawberries

Answer:

im pretty sure its D hope this helps

Answer:

C

Step-by-step explanation:

A. is wrong because having a different height for each seedling and not trying to keep it equal is simply worse than making sure the heights are identical.

B. Completely wrong because it would likely result in 1 plot having more melon seedlings than the other.

C. Correct because it makes sure the seedlings are the same height at the beginning of the experiment, allowing less randomness in the experiment.

D. Putting the taller of a each pair for 1 plot makes it the experiment rigged in favor of the plot with taller seedlings

E. Same issue as D.

Answer:

9x+64

Step-by-step explanation:

9x+8(6x+2)

9x+64

The solution of the equation is y = 3.

An equation between two variables that gives a straight line when plotted on a graph.

The solution to the equation is;

\(\rm y + 3 = -y + 9\\\\y+y=9-3\\\\2y=6\\\\y=\dfrac{6}{2}\\\\y=3\)

Hence, the solution of the equation is y = 3.

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Answer:

so the answer is the third one

Answer:

I think it's 19.21, but in your case it would be 19.2. Sorry if I'm wrong

The probability that each box contains 2 tiles is 1/9.

To find the probability that each box contains 2 tiles when tiles numbered 1-6 are randomly placed into three different boxes, we use a counting approach.

Since there are 6 tiles, the total number of possible outcomes is 3⁶ = 729.

The number of ways to choose 2 tiles from 6 is denoted as C(6,2), which can be calculated as:

C(6,2) = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = (6 * 5) / (2 * 1)

C(6,2) = 15

Similarly, the number of ways to choose 2 tiles from 4 is C(4,2), which can be calculated as:

C(4,2) = 4! / (2! * (4-2)!) = 4! / (2! * 2!) = (4 * 3) / (2 * 1) = 6

The number of favorable outcomes is C(6,2) * C(4,2) = 15 * 6

C(6,2) * C(4,2) = 90.

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 90 / 729

Probability = 1/9

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The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Answer:

6/90

Step-by-step explanation:

The graph is given below.

The area of the square TUVW is 9 square units.

We have,

The square TUVW with vertices

T = (-2, -4)
U = (-5, -4)

V = (-5, -1)

W = (-2, -1)

Now,

To find the area of the square TUVW, we need to find the length of its sides first.

Using the distance formula, we can find the length of TU:

TU = √((Ux - Tx)² + (Uy - Ty)²)

= √((-5 - (-2))² + (-4 - (-4))²)

= √(9)

= 3

Since TUVW is a square, all of its sides have the same length,

So UV = VW = WT = 3 as well.

The area of the square is the length of one side squared.

Area = side²

= 3²

= 9

Therefore,

The area of the square TUVW is 9 square units.

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The measure of two angles are 39 degree and 69 degree. By the Triangle Sum Theorem, the sum of all angles in a triangle is 180 degree, so the final angle is 72 degree. Therefore, the largest angle in the triangle is 72 degree.

According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.

Given:

\(The\;sum\;of\;two\;angles\;in\;a\;triangle\;is\;\frac{6}{5}\;of\;a\;right\;angle\;is,\;\frac{6}{5} \times 90^{\circ} = 108^{\circ}\)

\(let\;x\;is\;the\;measure\;of\;the\;first\;angle\)

\(one\;of\;these\;two\;angles\;is\;30\;larger\;than\;the\;other,\;is\;x+30=108\)

We know that sum of two angles is 108

\(x+x+30=108^{\circ}\)

\(2x+30=108\)

\(2x=108-30\)

\(2x=78\)

\(x=39^{\circ}\)

Second angle y is,

\(y=x+30\)

\(y=39+30\)

\(y=69^{\circ}\)

By the Triangle Sum Theorem, the sum of all angles in a triangle is 180 degree,

Third angle z is,

\(x+y+z=180\)

\(39+69+z=180\)

\(108+z=180\)

\(z=180-108\)

\(z=72^{\circ}\)

\(By\;comparing\;the\;angles\;39^{\circ},\;69^{\circ}\;and\;72^{\circ}, 72^{\circ}\; is\;greater\)

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Answer:

Step-by-step explanation:

-3 + 5 = 2

An ordered set of numbers or objects in which the order helps you predict what will come next is called the pattern.

It is required to explain about ordered set.

What is an ordered set?

An ordered set is a relational structure (S,⪯) such that the relation ⪯ is an ordering. Such a structure may be: A partially ordered set (poset) A totally ordered set (toset).

solution:

An ordered set and if the ordering is so tricky that every non-empty set has a minimal value, then it is a well ordered set.

An ordered set!

ordered set” is ambiguous, since it can mean either a partially ordered set, in which an ordering exists but not all elements are ordered relative to one another, or a totally ordered set, in which every element is either  ≥  or  ≤  every other element.

Therefore, an ordered set of numbers or objects in which the order helps you predict what will come next is called the pattern.

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The measure of ∠R =49, ∠T = 61 , ∠M = 70 , ∠N = 61, x = 7 and y = 13.

What are Congruent triangles?

When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent.

Given, ΔLMN ≅ ΔRST,

So, ∠L = ∠R  = 49

     ∠M = ∠S = 70

     ∠N = ∠T = 4y + 9

Now, In triangle RST,

∠R + ∠S + ∠T = 180 ( sum of all angles of a triangle is 180 )

49 + 70 + ∠T = 180

   ∴ ∠T = 61 = ∠N

and, 4y + 9 = 61

       y = 13.

Now, In triangle LMN ,

∠L + ∠M + ∠N = 180

49 + 10x + 61 = 180

    10x = 70

       x = 7

∴ ∠M = 70.

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Answer:

Domain: {-2,-9,8}

Range: {4,-2}

Step-by-step explanation:

For the domain, any values dealing with x is the domain. For range, any values dealing with y is the range. So we can see that all the x values is -2, -9, 8. For the y values, we can see that we have 4, and -2. Therefore your domain is {-2,-9,8} and you range is {4,-2}

Answer:

Domain = {-2, -9, 8}

Range = {4, -2,}

Step-by-step explanation:

The domain is the x-values

The range is the y-values

set notation doesn't have a particular order so I'll list them in the order they appear. {}

Domain = {-2, -9, 8}

Range = {4, -2,}

I hope this helps!

Answer:

$70

Step-by-step explanation:

You want 175% of $40.

175% as a decimal = 1.75

1.75 times 40 = 70

Therefore Liam put $70 in savings in April

Answer:

70

Step-by-step explanation:

Multiply 40$ by 175% :)

Answer:

$32

Step-by-step explanation:

Answer:

$32

Step-by-step explanation:

The volume of the region E is zero.

Using cylindrical coordinates, we can express the given surfaces as:

Paraboloid: ρ² - z = 24

Cone: z = 2ρ²

To find the volume of the region E enclosed between these surfaces, we need to determine the limits of integration in the cylindrical coordinate system.

The paraboloid and cone intersect when their corresponding equations are satisfied simultaneously. Substituting the equation of the cone into the paraboloid equation, we get:

ρ² - (2ρ²) = 24

-ρ² = 24

ρ² = -24

Since ρ² cannot be negative, this implies that there is no intersection between the paraboloid and the cone. Therefore, the region E does not exist, and the volume is zero.

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