Answer: The equivalent expression in degrees is 60°.
Step-by-step explanation: We are given to find the equivalent of the following expression in degrees.
[tex]E=\dfrac{\pi}{3}~\textup{radians}.[/tex]
We will be using the UNITARY method the solve the given problem.
We know that
[tex]\pi~\textup{radians}=180^\circ\\\\\\\Rightarrow 1~\textup{radian}=\left(\dfrac{180}{\pi}\right)^\circ\\\\\\\Rightarrow \dfrac{\pi}{3}~\textup{radians}=\left(\dfrac{\pi}{3}\times\dfrac{180}{\pi}\right)^\circ=60^\circ.[/tex]
Thus, the equivalent expression in degrees is 60°.
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I need some assistance in figuring this out
Find the value of 'y' in the equation 3/y-3 =8
A.) y= -2 3/8
B.) y= -1 5/8
C.) y= 1 5/8
D.) y= 2 3/8
A local university accepted 2300 students out of 4500 applicants for admission. What was the acceptance rate expressed as a percent
If y varies inversely as the square of x and y=4 when x=5, find y when x is 2
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
Find the missing values for the exponential function represented by the table below.
xy
-2 4
-1 6
0 9
1
2
a.
-13.5
-20.25
c.
6
4
b.
-13.5
20.25
d.
13.5
20.25
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.
Given a polynomial f(x), if (x + 7) is a factor, what else must be true? Help plzzz im running out of time
f(0) = 7
f(0) = −7
f(−7) = 0
f(7) = 0
If the ratio between the radii of the two spheres is 5:8, what is the ratio of their volumes?
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
Help!!!!ASAP PLEASE
Solve for the unknown side.
last option is none of these
The side of the triangle which is the hypotenuse side is [tex]2\sqrt{13}[/tex]
What is the hypotenuse side?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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Ryan flew from Wiley Post to Ponca City and back. Ryan maintained an average rate of 450 mph going to Ponca City and an average rate of 400 mph returning to Wiley Post. If the actual flying time for the round trip was one hour, about how far is it from Wiley Post to Ponca City? Round to nearest mile.
A.
0.47 miles
B.
212 miles
C.
239 miles
D.
3,600 miles
What are radians, how do I solve for the measurement of radians in the angle of BAC
how do you solve this system of linear equation by substitution
x-3y=-12
y=2x+9
Provide the reasons for the proof:
Given: Trapezoid RIAG with RI = RG = GA
m angle I = m angle NAG
Prove: angle T ≈ angle N
An 800 gallon swimming pool is being drained. After five hours, 500 gallons have been drained. If the rate of drainage continues, how long will it take to drain the pool?
A) 0.125 hours
B) 5 hours
C) 8 hours
D) 9 hours
For what values of x does f(x) = x^2 +5x +6 reach its minimum value?
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.
Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.
If x = 4, then x2 = 16
Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 10.
Answer:
x^2/25 + y^2/81 =1
Step-by-step explanation:
solved it
Hey rectangular pan has a link that is for third the with the total area of the pan is 432 in.² what is the width of the cake pan
If x is inversely proportional to y, and x = 60 when y = 0.5, find x when y = 12. A. 0.4 B. 25 C. 360 D. 2.5
Suppose that $88 comma 00088,000 is invested at 3 and one half3 1 2% interest, compounded quarterly. a) find the function for the amount to which the investment grows after t years
Which equation would best help solve the following problem? Rennie kicks a field goal with an initial vertical velocity of 31 m/s. How long will it take the football to hit the ground?
–4.9t2 + 31t = 0
–4.9t2 – 31t = 0
16t2 + 31t = 0
–16t2+ 31t = 0
A mouse spots an owl flying 10.1 feet over a nearby bush. The mouse is 30 feet away from the bush, and it sees the owl at a certain angle of elevation.
Which trigonometric equation can be used to solve for x, the angle of elevation from the mouse to the owl?
When 0.3(4x – 8) – 0.5(–2.4x + 4) is simplified, what is the resulting expression?
The resulting expression for x when the algebraic expression is simplified is 2.4x - 4.4
What is the simplification of an algebraic expression?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)
Open brackets1.2x - 2.4 + 1.2x - 2
Collect like terms1.2x + 1.2x = 2.4 + 2
2.4x = 4.4
2.4x - 4.4
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Answer:
simply d
Step-by-step explanation:
A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 35 that have no defects. what is the probability that at least one of the calculators is defective?
The scale of a map is 0.5 inch : 20 miles. on the map, the distance between two cities is 1.5 inches. what is that actual distance between the two cities?
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.
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?
The result is significant at both α = 0.05 and α = 0.01.
The result is significant at α = 0.05 but not at α = 0.01.
The result is significant at α = 0.01 but not at α = 0.05.
The result is not significant at either α = 0.05 or α = 0.01.
The result is inconclusive because we don't know the value of p.
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.
A man paid the bank $4,080 at the end of three years. This was the amount borrowed plus 12% interest for three years. How much money had he borrowed?
Circle A is inscribed in a quadrilateral. What is the perimeter of the quadrilateral?
Determine how many, what type, and find the roots for f(x) = x^3 - 5x^2 – 25x + 125