Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -4 + 5 cos θ

The resulting expression for x when the algebraic expression is simplified is 2.4x - 4.4

The simplification of algebraic expressions follows an approach where we aim to solve for the unknown variables of the algebraic expression.

From the given algebraic expression, we have:

0.3(4x – 8) – 0.5(–2.4x + 4)

1.2x - 2.4 + 1.2x - 2

1.2x + 1.2x = 2.4 + 2

2.4x = 4.4

2.4x - 4.4

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Answer:

simply d

Step-by-step explanation:

Answer:

60 miles.

Step-by-step explanation:

We have been given that the scale map is 0.5 inch : 20 miles. On the map, the distance between two cities is 1.5 inches. We are asked to find the actual distance between the two cities.

We will use proportions to solve for the actual distance between both cities as:

[tex]\frac{\text{Actual distance}}{\text{Map distance}}=\frac{20\text{ miles}}{\text{0.5 inch}}[/tex]

[tex]\frac{\text{Actual distance}}{\text{1.5 inches}}=\frac{20\text{ miles}}{\text{0.5 inch}}[/tex]

[tex]\frac{\text{Actual distance}}{\text{1.5 inches}}*\text{1.5 inches}=\frac{20\text{ miles}}{\text{0.5 inch}}*\text{1.5 inches}[/tex]

[tex]\text{Actual distance}=20\text{ miles}*3[/tex]

[tex]\text{Actual distance}=60\text{ miles}[/tex]

Therefore, the actual distance between both cities is 60 miles.

I believe the answer is D.

Answer:

B) Median, because there is one outlier that affects the center

Answer:  The required ratio of the volumes of two spheres is 125 : 512.

Step-by-step explanation:  Given that the ratio between the radii of the two spheres is 5 : 8.

We are to find the ratio of the volumes of the two spheres.

Let, 'r' and 'R' represents the radii of the two spheres, so

r : R = 5 : 8.

The volume of a sphere  with radius 'r' units is given by the formula:

[tex]V=\dfrac{4}{3}\pi r^3.[/tex]

Let, V and V' be the volumes of the spheres with radius r and R units respectively.

Then, the ratio of the volumes of the two spheres will be

[tex]\dfrac{V}{V'}=\dfrac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}=\dfrac{r^3}{R^3}=\left(\dfrac{r}{R}\right)^3=\left(\dfrac{5}{8}\right)^3=\dfrac{125}{512}\\\\\\\Rightarrow V:V'=125:512.[/tex]

Thus, the required ratio of the volumes of two spheres is 125 : 512.

Answer: 125:512

Step-by-step explanation:

a p e x

The minimum value of the function occurs at [tex]\( x = -\frac{5}{2}[/tex], and the function reaches its minimum value of [tex]\( -\frac{1}{4} \)[/tex] at this point.

To find the minimum value of the quadratic function [tex]\( f(x) = x^2 + 5x + 6[/tex], we can use the vertex formula. The vertex of a quadratic function [tex]\( ax^2 + bx + c \) is given by the point \( \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right) \).[/tex]

[tex]For \( f(x) = x^2 + 5x + 6 \), \( a = 1 \), \( b = 5 \), and \( c = 6 \).[/tex]

The x-coordinate of the vertex is [tex]\( -\frac{b}{2a} = -\frac{5}{2(1)} = -\frac{5}{2} \).[/tex]

To find the minimum value, we substitute [tex]\( x = -\frac{5}{2} \)[/tex] into the function:

[tex]\[ f\left(-\frac{5}{2}\right) = \left(-\frac{5}{2}\right)^2 + 5\left(-\frac{5}{2}\right) + 6 \]\[ = \frac{25}{4} - \frac{25}{2} + 6 \]\[ = \frac{25}{4} - \frac{50}{4} + \frac{24}{4} \]\[ = \frac{-1}{4} \][/tex]

So, the minimum value of the function occurs at [tex]\( x = -\frac{5}{2}[/tex], and the function reaches its minimum value of [tex]\( -\frac{1}{4} \)[/tex] at this point.

The side of the triangle which is the hypotenuse side is [tex]2\sqrt{13}[/tex]

Using trigonometry, Trigonometry is the area of mathematics that deals with particular angle functions and how to use them in computations. In trigonometry, an angle can have six common functions. The terms sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc) are their names and abbreviations.

[tex]c^{2} =4^{2} +6^{2} \\\\c^{2}=16+36\\\\c^{2}=52\\\\c=\sqrt{52} \\\\c= 2\sqrt{13}[/tex]

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The test result is not significant at α = 0.05 or α = 0.01.

For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 2.2. Given the information provided, the result is not significant at either α = 0.05 or α = 0.01. This conclusion is drawn based on the p-value and the 95% confidence interval.

On compared the test statistic to critical values for α = 0.05 and α = 0.01. Since the test statistic falls within the critical region for α = 0.05 but not for α = 0.01, we concluded that the result is significant at α = 0.05 but not at α = 0.01. The correct options B.

To determine the significance of the test statistic at different levels of significance, we need to compare it to critical values associated with the chosen alpha levels.

Given that the test statistic is 2.2, we need to refer to the critical values of the test statistic for a two-tailed test at α = 0.05 and α = 0.01. These critical values are typically obtained from statistical tables or software.

Let's assume the critical value at α = 0.05 is [tex]\( z_{\alpha/2} = \pm 1.96 \)[/tex]and the critical value at α = 0.01 is [tex]\( z_{\alpha/2} = \pm 2.58 \)[/tex](for a standard normal distribution).

If the test statistic falls within the range defined by these critical values, we can conclude that the result is significant at the corresponding alpha level. Otherwise, the result is not significant.

Since the test statistic of 2.2 falls between the critical values of [tex]\( \pm 1.96 \)[/tex] for α = 0.05 but outside the critical values of [tex]\( \pm 2.58 \)[/tex] for α = 0.01, we can conclude that:

The result is significant at α = 0.05 but not at α = 0.01.

Final answer: The result is significant at α = 0.05 but not at α = 0.01.

We compared the test statistic to critical values for α = 0.05 and α = 0.01. Since the test statistic falls within the critical region for α = 0.05 but not for α = 0.01, we concluded that the result is significant at α = 0.05 but not at α = 0.01. This interpretation aligns with standard hypothesis testing procedures.

Complete question

For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 2.2. Which of the following statements can you make about this finding?

A)The result is significant at both α = 0.05 and α = 0.01.

B)The result is significant at α = 0.05 but not at α = 0.01.

C)The result is significant at α = 0.01 but not at α = 0.05.

D)The result is not significant at either α = 0.05 or α = 0.01.

E)The result is inconclusive because we don't know the value of p.

Answer: c.  

6  

4

Step-by-step explanation:

The exponential function is given by :-

[tex]y=Ab^x[/tex], where A is the initial amount , b is common ratio and x is time period.

We know that in exponential functions, the ratio of the consecutive value of y is same.

From the table ,  [tex]b=\dfrac{6}{4}=\dfrac{3}{2}[/tex]

At x = 0

[tex]9=A(\dfrac{2}{3})^0\\\\\Rightarrow\ A=9[/tex]

At x=1

[tex]y=9(\dfrac{2}{3})^1=6[/tex]

At x=2

[tex]y=9(\dfrac{2}{3})^2=4[/tex]

Hence, the missing values for the exponential function : c.  6  4.

need to kind K

Y=k x 1/x^2 = k/x^2

Find K when y=4 & x=5

Y=k/x^2 =

4=k/5^2=

4=k/25

K=4*25 =100

When x = 2

Y=100/2^2

Y=100/4

Y=25

Answer:

x^2/25 + y^2/81 =1

Step-by-step explanation:

solved it