Which number line shows the solution to the inequality n + 3 > 4?

If your business starts with 3% awareness and grows awareness by 5% per week (compounded), how long will it take to reach 75% awareness is b) 66 weeks

Compound growth denotes the procedure of generating profits not only on the investment's principal amount, but also on the accumulated interest.

It is essentially reallocating its earnings where the investor's interest is integrated with the beginning sum, while additional interest is contingent on this amplified amount.

The purposeful act of compounding can yield noteworthy accomplishments over time, since interest earned from pre-existing income inflates drastically in value due to accruing interest outlays, and hence boosts the final outcome substantially and rapidly- resulting in exponential growth of the given input.

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The standard error of the mean for a sample of size 8 and population mean 436 is equals to the 36.42.

The standard error of the mean, or usually say standard error, shows how different the population mean from a sample mean. We have a population with population mean, [tex]\mu[/tex] = 436

Standard deviations for population, [tex] \sigma[/tex] = 103

Sample size, n = 8

We have to determine the value of standard error of the mean. SEM is calculated simply as dividing the standard deviation by the square root of the sample size, n. Mathematically,

[tex]SE = \frac{ \sigma}{\sqrt n}[/tex]

Substitues all known values in above formula, [tex]= \frac{ 103}{\sqrt 8}[/tex]

= 36.42

Hence, required standard error value is 36.42.

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The volume of Ganymede is approximately 3.48 times the volume of the Moon, based on the given diameters of the two moons and the formula for the volume of a sphere.

The volume of a sphere is the amount of space occupied by the sphere in three-dimensional space. It can be calculated using the formula V = (4/3)πr³, where V is the volume of the sphere, r is the radius of the sphere, and π (pi) is a mathematical constant approximately equal to 3.14159. This formula states that the volume of a sphere is four-thirds of the product of pi and the cube of the sphere's radius.

In the given question,

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. Since we are given the diameters of the two moons, we can calculate their radii by dividing the diameters by 2. Therefore, the radius of Ganymede is 3,388/2 = 1,694 km, and the radius of the Moon is 1,245/2 = 622.5 km.

Now, we can calculate the volumes of the two moons:

V_Ganymede = (4/3)π(1694)³ ≈ 7.66 x 10^10 km³

V_Moon = (4/3)π(622.5)³ ≈ 2.2 x 10^10 km³

To find how many times larger Ganymede's volume is compared to the Moon's volume, we can divide the volume of Ganymede by the volume of the Moon:

V_Ganymede / V_Moon ≈ (7.66 x 10¹⁰) / (2.2 x 10¹⁰) ≈ 3.48

Therefore, the volume of Ganymede is approximately 3.48 times the volume of the Moon.

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The series can be represented in summation notation as follows: ∑(n = 7 to 207) (4n - 1)

In this notation, the Greek letter sigma (∑) represents the summation symbol, and n represents the index of summation. The series starts from n = 7 and goes up to n = 207, with each term being (4n - 1). The notation "n = 7 to 207" indicates the range of values that n takes on in the summation. The expression (4n - 1) represents the general term in the series, which changes as n varies from 7 to 207.

Summation notation, denoted by the Greek letter sigma (∑), is a shorthand way to represent the sum of a sequence of numbers. In this case, the series you provided is:

7 + 11 + 15 + … + 203 + 207

The general term of the series, which changes as "n" varies, is (4n - 1). This means that for each value of "n", we substitute it into the expression (4n - 1) to get the corresponding term in the series. For example, when "n" is 7, the corresponding term is (4 * 7 - 1) = 27. When "n" is 11, the corresponding term is (4 * 11 - 1) = 43, and so on, up to "n" = 207.

The summation notation "∑(n = 7 to 207) (4n - 1)" represents the sum of all the terms in the series, where "n" takes on values from 7 to 207, and the term for each "n" is (4n - 1). This notation allows us to compactly represent the entire series in a concise mathematical form.

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The statement "with respect to the 3-sigma rule used in reliability analysis, studies have shown that even experts tend to under-predict the range in parameter values (max-min). however, this is conservative because it leads to a smaller estimate of reliability" is true because studies have shown that experts tend to under-predict the range in parameter values when using the 3-sigma rule, leading to a conservative estimate of reliability.

The 3-sigma rule is a widely used method in reliability analysis that assumes the range of parameter values is within three standard deviations of the mean value. However, studies have shown that experts tend to under-predict the range of parameter values.

This under-prediction can result in a conservative estimate of reliability because it leads to a smaller range of possible outcomes. In other words, the estimated reliability is likely to be lower than the actual reliability. Therefore, it is important to take into account the potential for under-prediction when using the 3-sigma rule and to use other methods to estimate reliability as well.

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The exponential function f(x) = 2^x is given by the blue graph on the given graph.

The horizontal asymptote of a function is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

The function in this problem is defined as follows:

y = 2^x.

Two relevant numeric values are given as follows:

Hence the function is represented by the blue graph.

The horizontal asymptote is of y = 0, as when x goes to negative infinity, y goes to zero.

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Answer:

roughly 8.58

Step-by-step explanation:

long division I hope this helps bye !!! have a great day!!! :D

Answer: for future k-12 kids :)

Step-by-step explanation:

Answer:

  (a)  x² +y² -2x -6y -26 = 0

Step-by-step explanation:

You want the equation for the circle with center (1, 3) and radius 6 written in general form.

The standard form equation for a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

The radius and center are found from the graph, attached. For the circle centered at (h, k) = (1, 3) and radius r = 6, this is ...

  (x -1)² +(y -3)² = 6²

Expanding this equation gives ...

  x² -2x +1 +y² -6y +9 = 36

Written in general form, the equation becomes ...

  x² +y² -2x -6y -26 = 0 . . . . matches choice A

__

Additional comment

There is an image of this question showing the correct answer choice is the third one. However, that answer choice shows up first on this instance of the question. You will need to read and compare answer content to make sure you have the correct choice. You cannot go by the order of the the answers.

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after calculating both the expressions we can conclude that both expressions represent the same value of 12.

Mathematical operations including multiplication, division, addition, and subtraction are possible. The construction of an expression looks like this: Expression, number, and mathematical operator Numbers, variables, and functions are the elements of a mathematical expression (such as addition, subtraction, multiplication, and division, etc.). Expressions and phrases can be contrasted. Expressions are any equations that comprise numbers, variables, and an arithmetic operation. They are occasionally referred to as algebraic expressions. For instance, the value of m in the computation of 4m + 5 is the same as the word m in the provided equation, which has been separated from the figures 4m and 5 by the mathematical symbol +.

given,

Since subtracting a negative integer is equivalent to adding its positive counterpart, the expressions "10 - (-2)" as well as "-10 + 2" have the same meaning.

To be more precise, "10 - (-2)" denotes starting with a value of 10 and then deducting a negative value of -2. The positive value of an amount that is negative may be subtracted without affecting it, and vice versa. Therefore, "10 - (-2)" equals "10 + 2," making 12 the result.

The expression "-10 + 2" on the opposite hand suggests that we start with an amount of -10 and subsequently add a value of 2.

A positive number is equal to its negative counterpart when added to a negative number. Because of this, "-10 + 2" equals "-10 - (-2)", which also equals 12.

Therefore, both expressions represent the same value of 12.

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Answer:

Step-by-step explanation:

Split it into 3 shapes.

2 triangles and 1 square.

The squares answer is 53.25 And for the triangles you would get 26 and there are 2 triangles so 52.

52+53.25=105.25.

Here is the complete equation using the provided values

6x+8=2x+24

6x-2x+8=2x-2x+24

4x+8=24

4x+8-8=24-8

4x=16

x=4

Factorization is the process of finding the factors of a given number or expression. A factor is a number or expression that divides the original number or expression without leaving a remainder. In other words, factorization is the process of expressing a number or expression as a product of its factors.

For example, the number 12 can be factored into 2 and 6, or into 3 and 4, because 2 and 3 are factors of 12 and their product gives 12. Similarly, the expression x^2 - 4 can be factored into (x+2)(x-2), because if we multiply (x+2) and (x-2), we get x^2 - 4.

Factoring is an important tool in algebra, as it allows us to simplify expressions, solve equations, and work with polynomials in a more efficient way.

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ans. (c) 1/2

given line,

y = 1/2 x -2

we know that the slope form of the line is given by

y =mx+c

comparing both equations we get

m= 1/2

hence, the slope is 1/2

The surface area of the cube is  3 6/16 cm²

To determine the value of the surface area of the cube, we need too know the formula

The formula for calculating the surface area of a cube is represented as;

Surface area = 6a²

Such that the variable 'a' is the length of the side of the cube

From the information given, we have that;

a = 3/4

Substitute the value, we get;

Surface area = 6 (3/4)²

find the squares

Surface area = 6(9/16)

Multiply the values

Surface area = 3 6/16 cm²

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Answer:

Equation for Angle 3- 90-38=52

Angle 3= 52

Angle 5= 38

Angle 6= 52

Step-by-step explanation:

Angle is 90 degrees.

Angle 2 is 38 degrees.

If you are just looking at the bottom half(Angle 6, Angle 1, and Angle 2) They are all supposed to add up to equal 180 degrees because it is a supplementary angle.

So you add 90 and 38 and it gives you 52(Angle 6).
90+38+52=180

Then a complementary angle is two angles that equal 90 degrees.

So if you take Angle 2(38 degrees) and subtract it from 90, you get 52. Which is Angle 3.

You do the same with Angle 6 and Angle 5.

Angle 6(52 degrees) subtract from 90 and you get 38.

Then you add 38 and 52 and you get 90.

Then 180-90=90, so Angle 4 is 90 degrees.

The given triangles ABD and CBD are congruent because their corresponding sides and angles are equal.

Congruent triangles are two triangles that have exactly the same size and shape. In other words, all corresponding sides and angles of the two triangles are equal.

There are several ways to show that two triangles are congruent, including:

Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Angle-Side-Angle (ASA) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

In the given triangles ABD and CBD, each of their angles is 60⁰, since the triangles are equilateral, so the triangles are congruent.

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The required domain of the given function f(x) = √x+4 is (D) {x|x ≥ -4} respectively.

The domain of a function is the set of values that we are allowed to enter into our function.

This collection includes the x values for functions like f(x).

The set of values that a function can accept as input is known as its range.

The function outputs this list of values once we enter an x value.

Think about the equation y = f(x), where x and y are the independent and dependent variables.

If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

Considering the function's expression:

f(x) = √x+4

We are aware that the set of input values for which the function is real and defined constitutes the function's domain.

We are aware that for the function to continue to be defined, the value included within the radical expression must be larger than or equal to 0.

x+4 ≥ 0

Take 4 off of both sides.

x+4-4 ≥ 0-4

x ≥ 4

Then, the domain is:
{x|x ≥ -4}

Therefore, the required domain of the given function f(x) = √x+4 is (D) {x|x ≥ -4} respectively.

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Correct question:

The graph of the function f(x)=V x+4 is shown below. The domain of the function?

The Laplace transform of the given function f(t) = {0, 0 < t < 1, t², t ≥ 1} is 2s⁻³.

Given the function f(t) = {0, 0 < t < 1, t², t ≥ 1}, we need to find its Laplace transform. The Laplace transform of a function f(t) is denoted by F(s) and is defined as follows:

F(s) = L{f(t)} = ∫[0,∞) f(t)e⁻ᵃˣdt,

where s is a complex variable.

To find the Laplace transform of the given function, we need to split the function into two parts: one for 0 < t < 1 and another for t ≥ 1. For 0 < t < 1, f(t) = 0, so the integral becomes:

L{0} = ∫ 0e⁻ᵃˣdt = 0.

For t ≥ 1, f(t) = t², so the integral becomes:

L{t²} = ∫ t²e⁻ᵃˣdt.

To evaluate this integral, we can use integration by parts. Let u = t² and dv = e⁻ᵃˣdt, then du/dt = 2t and v = (-1/s) e⁻ᵃˣ. Using the integration by parts formula, we get:

L{t²} = ∫ t²e⁻ᵃˣdt = (-t²/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s)∫[0,∞) te⁻ᵃˣdt.

The first term in the above equation evaluates to zero because e⁻ᵃˣapproaches zero as t approaches infinity. Using integration by parts again for the second term, we get:

L{t²} = (-t²/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s)(-t/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s²)∫[0,∞) e⁻ᵃˣdt.

The first two terms in the above equation evaluate to zero for the same reason as before. The integral in the last term evaluates to (1/s²), so we get:

L{t²} = 2/s³.

Therefore, the Laplace transform of the given function f(t) is:

L{f(t)} = L{0} + L{t²} = 0 + 2/s³ = 2s⁻³.

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Answer: 44 ft²

Step-by-step explanation:

     We will find the area of the large rectangle and subtract the area of the square. The area of a rectangle (and square) can be used with this formula:

       A = LW

Large Rectangle:

       A = LW

       A = (12 ft)(4 ft)

       A = 48 ft²

Square:

       A = LW

       A = (2 ft)(2 ft)

       A = 4 ft²

Subtract:

48 ft² - 4 ft² = 44 ft²

Answer:

Vertical translation

Step-by-step explanation:

Let's compare each point to its corresponding point in the image.

First, look at point A. Look at point A'.

With respect to the shapes ABCD and A'B'C'D', they are in the same position (in between B/B' and D/D'; across from C/C').

If you look at the image again, you'll find that the shape A'B'C'D' is not a rotated version of ABCD.

Thus, we can rule out the option "90° clockwise rotation."

A reflection across the x-axis indicates that A'B'C'D' and ABCD would be symmetrical across the x-axis (a horizontal line).

Because ABCD and A'B'C'D' are not symmetrical across a horizontal line, we can also rule out "Reflection across the x-axis."

Now, look at the position of A'B'C'D' with respect to ABCD. It's directly next to ABCD. In other words, it was shifted sideways.

Translations are basically just shifts.

Recall that horizontal means up and down, while vertical means side to side.

Since this is a sideways shift, we can conclude that the translation was:

a vertical translation.

Answer:

7.5 cm.

Step-by-step explanation:

The height of a rectangle can be calculated using the rectangle's base and area using the following formula:

height = area / base

This formula can be derived from the formula for the area of a rectangle:

area = base x height

By rearranging this formula, we get:

height = area / base

Therefore, if we know the area and base of a rectangle, we can use this formula to calculate its height.

1) rewrite

Height = are / base

2) plug in

h = 30 cm / 4 cm

3) solve (divide)

height = 7.5 cm

Therefore, the height of the rectangle is 7.5 cm.

Answer:

Yes it is an exponential function

Step-by-step explanation:

The given equation can be written in the form y = abˣ , and:

a and b are constants (a = 2, b = 15)

a ≠ 0

b > 0

b ≠ 1

The missing points of the table at x = 5, y = 1 and y = 0 has been completed in the table attached.

In general, to complete a table based on a graph, you need to follow these steps:

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The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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Answer:

13

Step-by-step explanation:

The given angles are on a straight line and they are supplementary angles which means their sum is 180°

According to the above mentioned information, we can write the following equation to find the value of t:

9t + 3 + 4t - 5 = 180

13t - 2 = 180

13t = 182

t = 14

Answer: angle(s) A on the left.

Step-by-step explanation:

Complementary angles are angles whose sum equals 90, which is a righ angle (forms a corner)

The absolute maximum value of f(x) on the closed interval [-2, 4] occurs at x = -2 and x = 0, and the maximum value is 16. So the answer is option (e) -2.

To find the absolute maximum value of the function f(x) = x³ - 3x² + 12 on the closed interval [-2, 4], we need to evaluate the function at the critical points and at the endpoints of the interval, and then choose the largest value.

To find the critical points, we take the derivative of the function and set it equal to zero

f'(x) = 3x² - 6x = 3x(x - 2)

Setting f'(x) = 0 gives x = 0 and x = 2 as critical points.

Next, we evaluate the function at the critical points and at the endpoints of the interval

f(-2) = (-2)³ - 3(-2)² + 12 = 16

f(0) = (0)³ - 3(0)² + 12 = 12

f(2) = (2)³ - 3(2)² + 12 = 4

f(4) = (4)³ - 3(4)² + 12 = 4

Therefore, the correct option is (e) -2

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The absolute maximum value occurs at x = 4, with a value of 28. So, the answer is a) 4.

We occasionally encounter operations with hills and valleys. Hill and valley points in polynomial functions typically have many locations. We are aware that these places, which can be categorized as maxima or minima, are the function's critical points. The valley points are referred to as minimal and the hill points are as maxima. We must determine the locations of the function's global maxima and global minima, which are known as the minimum and maximum values, respectively, due to the fact that there are several maxima and minima.

To find the absolute maximum value of the function [tex]f(x) = x^3 - 3x^2 + 12[/tex] on the closed interval [-2, 4], we need to examine the critical points and the endpoints of the interval.

First, find the critical points by taking the derivative of f(x) and setting it equal to 0:
[tex]f'(x) = 3x^2 - 6x\\0 = 3x^2 - 6x\\0 = 3x(x - 2)[/tex]

The critical points are x = 0 and x = 2.

Next, evaluate the function at the critical points and the interval endpoints:

[tex]f(-2) = (-2)^3 - 3(-2)^2 + 12 = -8 - 12 + 12 = -8\\f(0) = 0^3 - 3(0)^2 + 12 = 12\\f(2) = 2^3 - 3(2)^2 + 12 = 8 - 12 + 12 = 8\\f(4) = 4^3 - 3(4)^2 + 12 = 64 - 48 + 12 = 28[/tex]

The absolute maximum value occurs at x = 4, with a value of 28. So, the answer is a) 4.

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Answer: The correct answer is 8.12%-11.88%.

We can use the formula for a confidence interval for a proportion:

p ± z*SE

where p is the sample proportion, z* is the z-score corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval), and SE is the standard error of the proportion.

SE = sqrt(p*(1-p)/n) = sqrt(0.1*0.9/1015) = 0.0094

Plugging in the values, we get:

0.1 ± 1.96*0.0094

= 0.1 ± 0.0184

So the 95% confidence interval is (0.0816, 0.1184), which is equivalent to 8.12%-11.88%.

Step-by-step explanation:

Answer:

8 weeks

Step-by-step explanation:

Ok, so the equation given is y=8x+40

If the school needs 104 cabinets in total, we have to find x, the number of weeks to complete this order.

We can input 104 as y as that's the total:

104=8x+40

We have to isolate x, so first, subtract 40 from both sides

64=8x

Next, divide both sides by 8

8=x

So, it will take 8 weeks to fulfill this order.

The GDP of the hypothetical country in this case is R363 billion.

To calculate GDP, we use the following formula:

GDP = C + G + I + NX

where:

C = consumer spending

G = government spending

I = business investment

NX = net exports (exports - imports)

Now, let's plug in the given values into the formula and calculate the GDP:

GDP = R220 billion (C) + R50 billion (G) + R100 billion (I) + (R25 billion - R32 billion) (NX)

GDP = R220 billion + R50 billion + R100 billion - R7 billion

GDP = R363 billion

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Percentiles provide information about the placement of data points in a quantitative dataset, histograms display the distribution of data, categorical data is grouped into categories, and ordinal data has an inherent order but no meaningful numerical differences.

Based on the terms you provided, we are looking for information about percentiles, histograms, categorical data, and ordinal data.
A percentile is a measure of placement in a sorted quantitative dataset.

It indicates the relative standing of a data point within the dataset.

For example, a score in the 80th percentile means that it is higher than 80% of the scores in the dataset.
A histogram is a graphical representation of the distribution of a dataset, typically used for continuous data.

The vertical axis of a histogram displays frequency or density, while the horizontal axis represents the data values divided into bins or intervals.
Categorical data is a type of data that can be divided into groups or categories, such as gender, ethnicity, or favorite color.

A numerical summary for categorical data usually involves counts or percentages for each category.
Ordinal data is a type of data where the order matters, but the difference between values is not meaningful, such as rankings or ratings.

A numerical summary for ordinal data can include measures of central tendency, such as the median or mode.

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