Let's expand our thinking into the Third dimension. Can you think of a few ways to build a sphere? (No formula, just descriptions)

Based on the survey results, a typical parent would spend around $44 on their child's birthday gift, with a margin of error of approximately $2.9 at a 99% confidence level.

To estimate how much a typical parent would spend on their child's birthday gift, we use the sample mean and standard deviation as estimates of the population parameters. The sample mean of $44 serves as the point estimate for the population mean.

To determine the margin of error, we use the standard error, which is the standard deviation divided by the square root of the sample size. In this case, the standard error is approximately $2.5 (standard deviation of $10 divided by the square root of 20). Multiplying the standard error by the critical value corresponding to a 99% confidence level (z-value of 2.58 for a large sample size) gives us the margin of error.

Therefore, the typical amount spent on a child's birthday gift is estimated to be $44, with a margin of error of approximately $2.9. This means that we can be 99% confident that the true mean amount spent by parents falls within the range of $41.1 to $46.9.

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Answer:

The surface area of the star is approximately 1.004 times larger than the earth's surface area

Step-by-step explanation:

To find the number of times b which the area of the star is larger than that of the earth, we will divide the area of the area of the star by the area of the earth.

Area of surface of star = 1015 square miles

Area of surface of the earth = 1011 square miles

∴ (Area of star) ÷ (Area of the earth)

= 1015 ÷ 1011 = 1.00395 times

Therefore the surface area of the star is approximately 1.004 times larger than the earth's surface area

In an arithmetic sequence, the difference between every pair of consecutive terms in the sequence is the same.

The general formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

n is position of term

d is common difference

Thus, we see that the difference between consecutive terms is always the same as common difference.

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Answer:

If we let the number be represented by the variable "x", then "three less than a number" can be expressed as:

x - 3

Using the quotient property we would have

This follows the rule

From the simplified expression as shown above

Thus;

Therefore

We can not simplify the 3 and the r raised to power of 9 as their power is not even, hence the final answer is given below

The final answer is :

Answer:

We can write 36 as a product of prime factors: 36 = 2² × 3². The expression 2² × 3² is said to be the prime factorization of 36.

Answer:

2² x 3²

Step-by-step explanation:

The prime factors of 36:

2 x 2 x 3 x 3

= 2² x 3²

Answer:

If s = 1 over 3 unit and A = 18s² what is the value of A, in square units? ____ square unit(s).Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

(x-2)2 - ((x-3)2 • 22)     -3x2 + 20x - 32

——————————————————————  =  

          22                      4      

Divide by 5 both sides

3^x=60/5

3^x=12

Apply log both sides

log(3^x)=log(12)

xlog(3)=log(12)

x=log(12)/log(3)

using a calculator

The simplest form by adding two number is \(3\sqrt{5}+2\sqrt{2}\)  and it is irrational number.

The square root of any number is equal to a number, which when squared gives the original number. Let us say n is a positive integer, such that  \(\sqrt{n.n}=\sqrt{(n)}^2=n\)

Given that, the two numbers,

3 square root of 5= \(3\sqrt{5 }\)

2 square root of 2 = \(2\sqrt{2}\)

Sum of these two numbers = \(3\sqrt{5}+2\sqrt{2}\)

We cannot simplify this term further.

The simplest form by adding two numbers is \(3\sqrt{5}+2\sqrt{2}\)

As it is clear, it is a irrational number.

Because, \(\sqrt{2}\) and \(\sqrt{5}\) is a irrational number.

Hence, the simplest form by adding two number is \(3\sqrt{5}+2\sqrt{2}\)  and it is irrational number.

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Por propiedades de los cuadrados y triángulos rectángulos con ángulos internos 45 - 45 - 90, la medida x de la figura es igual a u.

Un cuadrado es un cuadrilátero con lados de igual medida y cuatro ángulos rectos, si se genera una diagonal que atraviesa una par de vértices opuestos, generándose dos triángulos rectángulos con ángulos internos 45 - 45 - 90.

De acuerdo con la figura, la diagonal mide √2 · u y cada lado mide x y por la geometría euclídea sabemos que la medida de un cateto en un triángulo rectángulo con ángulos internos 45 - 45 - 90 es igual a √2 / 2 veces la longitud de la hipotenusa. Por tanto, la medida x de la figura es igual a u.

La representación gráfica del cuadrado es borrosa, no obstante, se puede apreciar aunque con dificultad las cotas longitudinales con medida x.

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To eliminate x in the given system of equations, the equation y = x + 8 should be multiplied by 1/3. This multiplication allows us to match the coefficient of x in both equations, simplifying the elimination process.

Let's calculate the reciprocal of the coefficient of x in Equation 2 and determine the number by which Equation 1 should be multiplied to eliminate x:

Equation 1: y = x + 8

Equation 2: y = 3x - 11

The coefficient of x in Equation 2 is 3. The reciprocal of 3 is 1/3.

To eliminate x, we need to multiply Equation 1 by 1/3.

Multiplying Equation 1 by 1/3:

(1/3) * (y = x + 8)

This gives us:

1/3 * y = (1/3) * x + (1/3) * 8

Simplifying:

y/3 = (1/3)x + 8/3

Now, we have two equations:

y = 3x - 11   (Equation 2)

y/3 = (1/3)x + 8/3   (Equation 1, multiplied by 1/3)

By multiplying Equation 1 by 1/3, we have eliminated x from Equation 1.

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When looking at the results of a 90% confidence interval, we can predict the results of a two-sided significance test as follows: if the confidence interval does not include the null hypothesis value, then the two-sided significance test will reject the null hypothesis at the 10% significance level.

Conversely, if the confidence interval includes the null hypothesis value, then the two-sided significance test will fail to reject the null hypothesis at the 10% significance level. This is because the confidence interval provides a range of plausible values for the true population parameter, and if the null hypothesis value is not within this range, then it is unlikely to be true, leading to rejection of the null hypothesis.

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Answer:

y-(-8)= -6(x-2)

y+8= -6x+12

y = -6x+ 4

you're mistake was you did +8 in 3rd step but you need to -8 both side becoz y-(-8)= y+8

Step-by-step explanation:

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The student has incorrectly added 8 on both sides of the equation instead of subtracting it.

The general form of an equation is given as,

(y ₋ y₁)=m(x ₋ x₁)

where (x₁,y₁) is the point through which the line passes and m is the slope of the line.

Given that a line has a slope of -6 and passes through the point (2, –8). Therefore, substitute the slope and point in the above general form of the line and simplify.

(y ₋ y₁)=m(x ₋ x₁)

[y ₋ (-8)] = (-6)(x ₋ 2)

y + 8 = -6x + 12

Subtract 8 from both sides of the equation,

y + 8 - 8 = -6x + 12 - 8

y = -6x + 4

Now, if the steps are compared it can be seen that parenthesis are not opened properly and instead of subtracting 8, it is added to both sides of the equation.

Hence, the student has incorrectly added 8 on both sides of the equation.

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The temperature of the body was 37 °C at the time of the murder occurred approximately 38 minutes before the csi team's arrival.

Newton's Law of Cooling, states that the rate of change in the temperature of an object is proportional to the difference between the object's temperature and the ambient temperature.

The general form of Newton's Law of Cooling is given by:

dT/dt = -k(T - Tₐ)

where dT/dt represents the rate of change of temperature, T is the temperature of the object, Tₐ is the ambient temperature, and k is a constant.

In this case, we can use the following information

The initial temperature of the body (T₀) = 37 °C

The temperature of the room (Tₐ) = 17 °C

Temperature of the body after 10 minutes (T) = 20 °C

We need to find the time elapsed (t) in minutes before the CSI team's arrival when the murder occurred.

We can set up the following equation using the initial temperature and the temperature after 10 minutes:

20 = (T₀ - Tₐ) × \(e^{-10k}\)

To solve for k, we rearrange the equation:

k = -ln((T - Tₐ) / (T₀ - Tₐ)) / 10

Substituting the given values:

k = -ln((20 - 17) / (37 - 17)) / 10

k ≈ 0.0693

Now, we can use the value of k to find the time (t) when the body's temperature was 37 °C:

37 = (T₀ - Tₐ) ×\(e^{-kt}\)

t = -ln((37 - 17) / (T₀ - Tₐ)) / k

t = -ln((37 - 17) / (37 - 17)) / 0.0693

t ≈ 37.64 minutes

Rounding to the nearest whole minute, the murder occurred approximately 38 minutes before the CSI team's arrival.

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The narrator suggests that she now lives her life by striving to find optimism in even the worst circumstances when she adds, "I too have planted marigolds," at the conclusion of the story.

Because the narrator characterized the marigolds in the story as "Dazzling strips of bright petals bunch together in gigantic mounds warm and passionate in sun golden," the narrator's description of and response to seeing the marigolds is rather favorable.

The ability to comprehend and appreciate others as fully human beings serves as the story's central subject and marks the start of adulthood. Lizabeth felt ashamed when she realized she had wronged a genuine human being instead of a "witch" when she vented her anger at the marigolds and turned to look at Miss Lottie.

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The volume V of solid S is e - 1 cubic unit.

What is Volume?

Volume refers to the measure of three-dimensional space occupied by an object or a region. It quantifies the amount of space enclosed by the boundaries of an object or contained within a given region. In mathematical terms, volume is often calculated by integrating the cross-sectional areas of the object or region along a particular axis. Volume is typically expressed in cubic units, such as cubic meters (m^3) or cubic centimeters (cm^3). It is an essential concept in geometry, physics, engineering, and other scientific fields where the measurement of three-dimensional space is involved.

To find the volume of solid S, we need to integrate the areas of the cross sections perpendicular to the x-axis along the interval \([e, \infty).\)

The area of each square cross-section is equal to the square of the side length, which in this case is \(y = \sqrt{\ln(x)}.\)

Therefore, the volume V of solid S can be calculated as:

\(V = \int_{e}^{\infty} (\sqrt{\ln(x)})^2 dx\)

To evaluate this integral, we can simplify the expression:

\(V = \int_{e}^{\infty} \ln(x) dx\)

Using integration by parts, we let \(u = \ln(x)\)and dv = dx:

\(du = \frac{1}{x} dx\\v = x\)

Applying the integration by parts formula:

\(V = [uv] - \int v du= [x \ln(x)] - \int x \left(\frac{1}{x}\right) dx= x \ln(x) - \int dx= x \ln(x) - x + C\)

Evaluating the definite integral:

\(V = [x \ln(x) - x]_{e}^{\infty}= (\infty \cdot \ln(\infty) - \infty) - (e \cdot \ln(e) - e)= \infty - 0 - (1 - e)= e - 1\)

Therefore, the volume V of solid S is e - 1 cubic unit.

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Answer:

B,C,D

Step-by-step explanation:

Answer:

number 2

number 3

number 4

Step-by-step explanation:

The function P(x) representing Ayden's total pay on a day on which  he sell x dollar worth of computers is P(x) = 0.01x + 90

The base pay amount of Ayden per regardless of sales = $90

The commission of Ayden = 1% of the dollar amount of sales

Consider the total sales amount in a day as x

The function is the mathematical expression that shows the relationship between one variable and another variable. If one variable is dependent variable then the other variable will be independent variable.

Then the function will be

P(x) = 1% of x + 90

= 0.01x + 90

Therefore, the equation for the function P(x) = 0.01x + 90

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Answer:

    x = 54

Step-by-step explanation:

Let x be the "mystery number."

If we divide x by 6000 [(x/6000)] and then multiply by 41 [(x/6000)*41] and then add 0.31 [(x/6000)*41 + 0.31], the result is 0.679:

  (x/6000)*41 + 0.31 = 0.679

 ( 41x/6000) + 0.31 = 0.679

( 41x/6000) = 0.369

     x = (0.369*(6000))/41

    x = 54

1) approximately 68% of the kids spend between 1,250 hours and 1,750 hours watching TV per year.

2) approximately 95% of the kids spend between 1,000 hours and 2,000 hours watching TV per year.

3) approximately 99.7% of the kids spend between 750 hours and 2,250 hours watching TV per year.

What is Empirical Rule?

The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical rule that helps us understand the distribution of data.

The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

1) The empirical rule, also known as the 68-95-99.7 rule or the three-sigma rule, is a statistical guideline that applies to data that follows a normal distribution. It states the following:

Approximately 68% of the data falls within one standard deviation of the mean.

In this case, it means that about 68% of the kids spend their TV watching time within one standard deviation of the mean, which is 1,500 ± 250 hours.

Therefore, approximately 68% of the kids spend between 1,250 hours and 1,750 hours watching TV per year.

2) Approximately 95% of the data falls within two standard deviations of the mean.

This implies that about 95% of the kids spend their TV watching time within two standard deviations of the mean, which is 1,500 ± 2 * 250 hours. So, approximately 95% of the kids spend between 1,000 hours and 2,000 hours watching TV per year.

Approximately 99.7% of the data falls within three standard deviations of the mean.

3) According to the rule, about 99.7% of the kids spend their TV watching time within three standard deviations of the mean, which is 1,500 ± 3 * 250 hours. Therefore, approximately 99.7% of the kids spend between 750 hours and 2,250 hours watching TV per year.

In summary, the empirical rule suggests that for a normal distribution of the time spent by kids watching TV per year (modeled with a mean of 1,500 hours and a standard deviation of 250 hours), the majority of kids (around 68%) spend between 1,250 and 1,750 hours watching TV, while an even larger proportion (around 95%) spend between 1,000 and 2,000 hours.

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Three straight sides and three angles make up the shape of a triangle. The angles of a triangle can either be acute, right, or obtuse. An angle with three acute angles is a triangle where all three angles measure less than 90 degrees.

A triangle is a three-sided shape with three angles. The sum of the internal angles of a triangle is always 180 degrees. An angle is the amount of turn or change in direction between two lines. There are three types of angles, acute, right and obtuse. An acute angle is an angle which measures less than 90 degrees. A right angle is an angle which measures exactly 90 degrees, and an obtuse angle is an angle which measures more than 90 degrees. Therefore, an angle with three acute angles is a triangle where all three angles measure less than 90 degrees. A triangle with three acute angles is also known as an acute triangle. All three angles must add up to 180 degrees, so the measure of each angle must be less than 60 degrees.

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Answer:

y - 3 = -3 ( x - 7 )

Step-by-step explanation:

→ It is true for all values as you substitute in the x value and get the y as the output