last year Austin texas received 23.5 inches of rainfall. this year Austin received 21.2 inches of rainfall find the percent of decrease in the number of inches of rainfall
a)2.3%
b)9.8%
c)10.8$
d)13.6%

The equation of the ellipse with focus at (-2,0) and vertices at (±7, 0) is given as follows:

x²/49 + y²/45 = 1.

The equation of an ellipse of center (h,k) is given by the equation presented as follows:

(x - h)²/a² + (y - k)²/b² = 1.

The center of the ellipse is given by the mean of the coordinates of the vertices, as follows:

Hence:

x²/a² + y²/b² = 1.

The vertices are at x + a and x - a, hence the parameter a is given as follows:

a = 7.

Considering the focus at (-2,0), the parameter c is given as follows:

c = -2.

We need the parameter c to obtain parameter b as follows:

c² = a² - b²

b² = a² - c²

b² = 49 - 4

b² = 45.

Hence the equation is given as follows:

x²/49 + y²/45 = 1.

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check images :) and yeah i agree i hate when people just put random letters to get points

Answer:

Formula for area of a circle is \(\pi\)\(r^{2}\)

10 squared is 100cm. 100cm*3.14 equals 314cm.

The area of the circle is \(314cm^{2}\)

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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Yes, if k is a subgroup of h and h is a subgroup of g, then k must be a subgroup of g. The reason for this is rooted in the definition of subgroups and the transitive property of containment.

To prove that k is a subgroup of g, we need to establish two key properties: closure under the group operation and the existence of inverses. Since k is a subgroup of h, it inherits the closure property from h. This means that for any elements a, b in k, their product ab must also be in k. Similarly, since h is a subgroup of g, it satisfies the closure property with respect to the group operation in g. Thus, any element in h, including those in k, multiplied with another element in h, will remain in h. Therefore, k satisfies closure under the group operation in g. Regarding the existence of inverses, if an element a is in k, then its inverse, denoted by a^(-1), must also be in k. Since h is a subgroup of g, every element in h has an inverse in h. Therefore, if an element a is in k, it is also in h, and its inverse is in h as well. Hence, k satisfies the requirement of having inverses within g. By demonstrating that k satisfies both closure under the group operation and the existence of inverses, we have established that k is a subgroup of g. Thus, if k is a subgroup of h and h is a subgroup of g, k must also be a subgroup of g, fulfilling the transitive property of containment.

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Answer:

c

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (6, 7) and (x₂, y₂ ) = (- 2, - 1) ← 2 ordered pairs from the table

m = \(\frac{-1-7}{-2-6}\) = \(\frac{-8}{-8}\) = 1

Answer:

I tried as I can to solve it

Null Hypothesis is equal to  \($H_a: \mu > 275$\) and  \(\quad \beta=0.926 \quad\)

Null Hypothesis

\($H_0: \mu=275$\)

Alternate Hypothesis

\($H_a: \mu > 275$\)

\($\sqrt{7}=55$\)

n=30

\($\bar{x}=292$\)

\($z=\frac{\bar{x}-\mu}{\sigma /\sqrt{x} { }}$\)

\($=\frac{292-275}{55 / \sqrt{30}}$\)

\($=1.69$\)

at \(\alpha=0.05, z$ is $1.96$\)

\($$\begin{aligned}z &=\frac{\bar{x}-\mu}{\sigma / \sqrt{n}} \\1.96 &=\frac{\bar{x}-275}{55 / \sqrt{30}}\end{aligned}$$\)

\($\begin{aligned} \bar{x}-294 \cdot 6 \\ z=& \frac{294 \cdot b=280}{55 / \sqrt{30}} \\ \frac{(14.6)(\sqrt{30})}{55} \end{aligned}$\)

\($z=1.45$\)

\(p(x < z)=0.926$.\)

\($\therefore \quad \beta=0.926 \quad($\) Type II)

The null hypothesis in inferential statistics states that two possibilities are the same. The null hypothesis states that the observed difference is solely attributable to chance. The likelihood that the null hypothesis is true can be calculated using statistical testing.

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Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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The answer is 6 divided by f

sannie =w=

Answer:

it is kind of sequence that recursive sequence because that is a ex. of recursive sequence

Answer:

Step-by-step explanation:

according to the question ur algebraic expression is

8-w

The algebric function will be 8-w

Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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We can form a total of 42 stacks of 8 cans each from the 7 boxes of cat food received by the pet store.

Now, We can use a bar model to represent the total number of cans and the number of stacks that can be formed.

First, let's find the total number of cans:

7 boxes x 48 cans/box = 336 cans

Now, let's use a bar model to represent this total:

| 336 cans of food  |

Next, we want to find how many stacks of 8 cans we can form. We can use a separate bar model to represent the size of each stack:

| 42 stacks of 8 cans each |

Hence, The number of stacks that can be formed, we need to divide the total number of cans by the number of cans in each stack:

336 cans ÷ 8 cans/stack = 42 stacks

So the final bar model looks like this:

| 336 cans of food  | = | 42 stacks of 8 cans each |

Therefore, we can form a total of 42 stacks of 8 cans each from the 7 boxes of cat food received by the pet store.

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The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7,negative 0.5,0.9 and 1.9 are plotted."

Here the values are

-0.5,-2.8,1.9,0.9 and -1.7

The number line a graphical representation that a line on which numbers are marked at intervals, used to represents the simple numerical operations.
Here there are three negative numbers -0.5,-2.8 and -1.7

The positive numbers are 1.9 and 0.9

The statement "A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5,0.9 and 1.9 are plotted" is suited of all the given conditions

Hence, The statement that shows the values of -0.5,-2.8,1.9,0.9 and -1.7 plotted on a number line is " A number line starting at negative 3.3 with tick marks every one tenth unit up to 2.1. The values for negative 2.8, negative 1.7, negative 0.5, 0.9, and 1.9 are plotted."

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Simplify the expression.

2m

We are given that ABCDE is congruent to TVSRK and want to find what corresponds to VSR.

Look at the ordering of the letters. VSR is the second, third, and fourth letters of TVSRK, respectively.

Thus, we just have to select the second, third, and fourth letters of ABCDE and we get BCD.

Thus, VSR corresponds to BCD. Let me know if you need any clarifications, thanks!

Answer:

3.2

Step-by-step explanation:

The rectangle with the maximum area, formed by its base on the x-axis and two vertices on the parabola y = 49 - x^2, has dimensions of length 14 units and height 0 units.

To find the dimensions of the rectangle that maximize its area, we need to consider the relationship between the rectangle's dimensions and the parabola.

Let's assume the length of the rectangle is 2x, and the height is y. Since the base of the rectangle lies on the x-axis, the y-coordinate of the two vertices on the parabola will be zero.

Substituting the y-coordinate into the equation of the parabola, we have:

0 = 49 - x^2

Rearranging the equation:

x^2 = 49

Taking the square root of both sides:

x = ±√49

Since we are interested in the positive value of x, we have:

x = 7

Now, substituting this value back into the equation of the parabola, we can find the height:

y = 49 - (7^2)

y = 0

Therefore, the dimensions of the rectangle that maximize its area are:

Length = 2x = 2 * 7 = 14 units

Height = y = 0 units

The rectangle is a degenerate rectangle, which means it has a height of zero. In this case, the maximum area is achieved when the rectangle becomes a line segment on the x-axis with a length of 14 units.

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The given question is incomplete, the complete question is,

What are the dimensions of the rectangle that can be constructed with its base on the x-axis and two vertices on the parabola y = 49 - x^2, in order to maximize its area?

The new triangle has sides of 3m, 4m, and 5m as the attached picture below.

The new triangle has sides of 1/3 of the original. Then:

1/3 x 15 m = 5m

1/3 x 9 m = 3 m

1/3 x 12 m = 4 m

The new triangle is as the attached picture below

The perimeter of the original triangle is:

P original = 15 + 9 + 12

P original = 36 m

The perimeter of the new triangle is:

P new = 5 + 3 + 4

P new =  12 m

The area of the original triangle is:

Area original = 1/2 x 12 x 9

Area original = 54 m

The area of the new triangle is:

Area new = 1/2 x 4 x 3

Area new = 6

The relationship between both triangles' perimeter is:

P original : P new = 36 : 12

                             = 3 : 1 --> ratio of both triangles

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Answer:

9*10^4

Step-by-step explanation:

Answer:

90,000 is written and 9x 10^4 in scientific notation

Answer: Two triangles have the same side lengths (Ex: both triangles have sides 3, 4, and 5 cm)

Step-by-step explanation:

1) This would guarantee similarity, but not necessarily that they are identical.

2) The angle has to be included between the two sides, which is not specifed.

3) This would work (SSS congruence)

4) It is not specified if the side is opposite the corresponding angles.

Answer:

n(A)

Step-by-step explanation:

Refer to the attachment that I drew. First, draw a diagram of two sets A and B together. The diagram of A - B represents all elements in A only - the intersection part does not count in.

The diagram of A ∩ B represents the intersection part of A and B, meaning both A and B have same elements and that belong to the intersection part.

Now, add two shades together and it’ll result in set A being full-shade while set B only has the intersection part shaded but not full part. Let’s consider each choices:

Therefore, the first choice n(A) is correct.

Answer:

Steps:

w = 180 - (85+42) = 180 - 127 = 53°

y = 180 - (88+w)

y = 180 - (88+53)

y = 180 - 141

y = 39°

Answer:

y = 39

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of both triangles , then

x = 42 + 85 = 127

and

y + 88 = 127 ( subtract 88 from both sides )

y = 39

Answer:

Is this what you need? Also slope = 10/1 and y intercpet = -1

Step-by-step explanation:

Answer: its time for mathacmathists

Step-by-step explanation: i dont see it