Answer:
(A)Quotient Identity
Step-by-step explanation:
To Prove: [tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\tan \left(\alpha +\beta \right)[/tex]
Rewrite the numerator on the left side of the identity using the sum and difference formulas.
[tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\dfrac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta -\sin \alpha \sin \beta }[/tex]
Next, Divide the numerator and denominator by[tex]cos\alpha \text{cos}\beta[/tex]
[tex]=\dfrac{\frac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta }}{\frac{\cos \alpha \cos \beta -\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
Rewrite the fraction from the previous step such that it is a sum or difference of two expressions as shown below
[tex]=\dfrac{\frac{\sin \alpha{\cos \beta }}{\cos \alpha{\cos \beta }}+\frac{{\cos \alpha }\sin \beta }{{\cos \alpha }\cos \beta }}{\frac{{\cos \alpha }{\cos \beta }}{{\cos \alpha }{\cos \beta }}-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
Divide out any common factors in the expression from the previous step.
[tex]=\dfrac{\frac{\sin \alpha }{\cos \alpha }+\frac{\sin \beta }{\cos \beta }}{1-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]
The expression from the previous step then simplifies to [tex]\tan \left(\alpha +\beta \right)[/tex] using the Quotient Identity
[tex]=\dfrac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }=\tan \left(\alpha +\beta \right)[/tex]
An aquarium Is 8 feet long , 5feet wide , and 5.5 feet deep . What is the volume of the tank ?
Answer:
220 ft^3
Step-by-step explanation:
Assuming a rectangular tank,
V = l*w*h
= 8*5*5.5
=220 ft^3
For this question please tell me if I'm right or wrong. If I'm wrong please correct me.
Please use the following image below in order to answer the question correctly:
Tell whether KN is best described as a radius, chord, diameter, secant, or tangent of ⊙P.
What can be KN best described as?
Please show all the work on how you got your answer. ( I'm not asking for an explanation. All I want is the work shown so I can understand how you got your answer)
Answer:
KN can be best described as a Diameter, as it is a chord(Line that goes between two distinct points in a circle) and goes through the radius.
An example of a radius would be segment KP or PN.
An example of a chord would be segments KN or NM.
An example of a secant would be line LN
An example of a tangent would be line JL.
Answer:
C) diameter
Step-by-step explanation:
KN is a straight line passing through the centre and not outside the circle, so it's a diameter
PLZZZZZ HELP!!!!! WILL MARK BRAINLIEST. solve for t
–4(t − 12) + 12 = –4
t =
Answer:
t = 16
Step-by-step explanation:
–4(t − 12) + 12 = –4
-12 -12
-4(t - 12) = -16
/-4 /-4
t - 12 = 4
+12 +12
t = 16
or
–4(t − 12) + 12 = –4
distribute the -4
-4t + 48 + 12 = -4
simplify
-4t + 60 = -4
-60 -60
-4t = -64
/-4 /-4
t = 16
Answer:
64/3
Step-by-step explanation:
Simpliest expression for (12.7y-3.1x)+5.9y-(4.2y-x)
Answer:
-2.1x +14.4y
Step-by-step explanation:
Use the distributive property to eliminate parentheses. Then combine like terms.
(12.7y-3.1x)+5.9y-(4.2y-x)
= 12.7y -3.1x +5.9y -4.2y +x
= x(-3.1 +1) +y(12.7 +5.9 -4.2)
= -2.1x +14.4y
Two angles in a triangle have measures of 23 and 98 what is the third measure of the third angle
Answer:
59
Step-by-step explanation:
As far as I know every triangle has to equal 180°
So if you add 98+23 you would get 121
subtract that from 180 and get 59
Hope this helps!
Assuming the pattern in the table continues, what is the function value when x = 6?
Answer:
486
Step-by-step explanation:
it multiplies by 3 each time
Answer:
486
Step-by-step explanation:
I just did 6/2 and got three and that was the rate of change so I multiplied 3 to 2 to get 6 and then multiplied 3 again to get 18 and kept going until I got to 162 and multiplied that to 3 to get 486.
The lower supports are and the area of the two supports is square meters. The upper arch can be decomposed as one semicircle with radius meters minus a semicircle with radius 3 meters. The area of the archway is (π + 24) square meters
Answer:
The lower supports are Congruent Rectangles and the area of the two supports is 24 square meters.
The upper arch can be decomposed as one semicircle with radius 6 meters minus a semicircle with radius 3 meters.
The area of the archway is (13.5 π + 24) square meters.
Step-by-step explanation:
See attachment for the firgure,
In order to determine the area of archway = The area of upper support + area of lower support.
As given, the lower support are two congruent rectangles consists of dimension 3 m × 4 m
Therefore, the area of lower support can be written as,
The area of lower support = 3 × 4 + 3 × 4 = 12 + 12 = 24 square m.
Now, the upper support arch can be decomposed as the two concentric semi circles having radius 3 m and 6 m,
Hence, the area of the upper support = Area of semi circle having radius i.e 6 m - Area of semi circle having radius i.e 3 m
=> π6²/2 - π3²/2= 27π/2= 13.5π square m
Therefore, the area of the archway = (13.5 π + 24) square meters
Answer:
1. congruent rectangles
2. 24
3. 6
4. 13.5
Step-by-step explanation:
Got it right, have a nice day!
Eight less than twice a number is fourteen.
Answer:
x = 11
Step-by-step explanation:
2x - 8 = 14
2x = 22
x = 11
Tell me if I am wrong.
Can I get brainliest
Answer:
Let that number be 'x'
Now first part of the question tells us that 8 less than twice a number which is"x".
so twice a number would be 2x
then 8 less than would 2x-8
and the given result of the equation is 14
so the equation iis 2x-8=14
2x=14+8
2x=22
x=22/2
x=11 So the number is 11
Hope you find it helpful
I need to find the surface area
Answer:
389.846
Step-by-step explanation
Sorry if its wrong
Which describes the relationship between 15,700 and 157,000? A 15,700 is 1/10 of 157,000 B 157,000 is 1/10 of 15,700 C 15,700 is 1/100 of 157,000 D 157,000 is 1/100 of 15,700
Answer: 15,700 is 1/10 of 157,000 (A)
Step-by-step explanation:
The relationship between 15,700 and 157,000 is that 15,700 is 1/10 of 157,000
1/10 × 157,000 = 15,700
A 15,700 is 1/10 of 157,000
= 1/10 × 157,000
= 15700 (Correct)
15700 equals 15700
B 157,000 is 1/10 of 15,700
= 1/10 × 15700 = 1570 (Wrong)
1570 is not equal to 157000
C 15,700 is 1/100 of 157,000
= 1/100 × 157,000 = 1570 (Wrong)
1570 is not equal to 15700
D 157,000 is 1/100 of 15,700
1/100 × 15700 = 157 (Wrong)
157 is not equal to 157000
I need help finding the answers to these questions thank you soo much!!!!
Name: Joseph Sandoval, single, 1 exemption. Pay Rate: 5? per unit Unit produced: M-900, T-840, W-825, T-905, F-910
Answer:
1-4380 2-219 3-15.44 4-37.1 5-6.13 7-58.67 8-160.33
Step-by-step explanation:
A home decor store donated a percent of every sale to charity .The total sales were $7,400 so the store donated $148.What percent of $7,400 was donated to charity
The correct answer is 2%. The store donated 2% of $7,400 to charity.
To find out what percent of $7,400 was donated to charity, we need to divide the amount donated by the total sales and then multiply by 100 to convert it into a percentage.
Let's denote the percent donated as P. The amount donated is given as $148, and the total sales are $7,400. The relationship between the percent donated, the total sales, and the amount donated can be expressed as:
[tex]\[ P \times 7,400 = 148 \][/tex]
To find P, we divide both sides of the equation by 7,400:
[tex]\[ P = \frac{148}{7,400} \][/tex]
Now, we calculate the value of P:
[tex]\[ P = \frac{148}{7,400} = \frac{2}{100} \] \[ P = 0.02 \][/tex]
To express P as a percentage, we multiply by 100:
[tex]\[ P = 0.02 \times 100 \] \[ P = 2\% \][/tex]
A random sample of 50 recent college graduates results in a mean time to graduate of 4.58 years, with a standard deviation of 1.10 years. Compute and interpret a 90% confidence interval for the mean time to graduate with a bachelor’s degree. Does this evidence contradict the belief that it takes 4 years to complete a bachelor’s degree?
Answer:
The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).
Yes, this confidence interval contradict the belief that it takes 4 years to complete a bachelor’s degree.
Step-by-step explanation:
The (1 - α)% confidence interval for population mean μ, when the population standard deviation is not known is:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
The information provided is:
[tex]\bar x=4.58\\s=1.10\\\alpha =0.10[/tex]
Compute the critical value of t for 90% confidence interval and (n - 1) degrees of freedom as follows:
[tex]t_{\alpha/2, (n-1)}=t_{0.10/2, (50-1)}=t_{0.05, 49}=1.671[/tex]
*Use a t-table for the probability.
Compute the 90% confidence interval for population mean μ as follows:
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]
[tex]=4.58\pm 1.671\times \frac{1.10}{\sqrt{50}}\\=4.58\pm 0.26\\=(4.32, 4.84)[/tex]
Thus, the 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).
If a hypothesis test is conducted to determine whether it takes 4 years to complete a bachelor’s degree or not, the hypothesis will be:
Hₐ: The mean time it takes to complete a bachelor’s degree is 4 years, i.e. μ = 4.
Hₐ: The mean time it takes to complete a bachelor’s degree is different from 4 years, i.e. μ ≠ 4.
The decision rule based on a confidence interval will be:
Reject the null hypothesis if the null value is not included in the interval.
The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32 years, 4.84 years).
The null value, i.e. μ = 4 is not included in the interval.
The null hypothesis will be rejected at 10% level of significance.
Thus, it can be concluded that that time it takes to complete a bachelor’s degree is different from 4 years.
Final answer:
The 90% confidence interval for the mean time to graduate ranges from approximately 4.32 to 4.84 years, indicating it may take longer than 4 years to complete a bachelor's degree on average.
Explanation:
To calculate the 90% confidence interval for the mean time to graduate, we'll use the sample mean (Ü), standard deviation (s), and the sample size (n).
The formula for the confidence interval is:
Ü ± (t* × (s/√n))
Where
t* is the t-score that corresponds to the 90% confidence level and n-1 degrees of freedom.
Since our sample size (n) is 50, we have 49 degrees of freedom.
Using a t-distribution table or calculator, we can find the appropriate t* value.
Now, let's use the provided information: Ü = 4.58 years, s = 1.10 years, and n = 50.
Assuming that the t-score (t*) is approximately 1.676 for 49 degrees of freedom at the 90% confidence level, we can compute the margin of error (ME):
ME = 1.676 × (1.10/√50) ≈ 0.26 years
Thus, the 90% confidence interval is:
4.58 ± 0.26 years
This interval ranges from approximately 4.32 to 4.84 years. It suggests that we can be 90% confident that the true mean time for graduates to complete a bachelor's degree is within this range.
The confidence interval does not contain the value of 4 years. Thus, this may indicate that it takes longer than 4 years on average to complete a bachelor's degree, contradicting the belief that it takes exactly 4 years.
1. What is the volume in cubic inches of the prism?
3inx5inx8in
Answer:
120 in or 60in or 60^2
Step-by-step explanation:
brainly pls
Solve the equation v3 = 36.
Answer:
The answer is v=12.
Step-by-step explanation:
[tex]\frac{v3}{3} =\frac{36}{3\\}[/tex]
[tex]v= \frac{36}{3}[/tex]
[tex]v=12[/tex]
The solution of v³ = 36 for v will be 3.32.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.
Given the equation,
v³ = 36
Now,
By taking inverse exponents,
v = [tex]36^{1/3}[/tex]
v = 3.32
Hence "The solution of v³ = 36 for v will be 3.32".
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Toms parents let him choose whether to play his favorite board games for 7/8 hours or 8/8 hours explain which amount of time you think tom should choose and why ?
Answer:
8/8
Step-by-step explanation:
8/8 is equal to one, so it would mean he would get to play his favorite board games for a full hour.
7/8 is only about 50 or so minutes, which is less than an hour.
If Tom chooses 8/8 of an hour, he will get to play longer.
if y varies inversely with x, and y = 4.75 when x =38, find y when x = 50
Answer:
y=3.61
Step-by-step explanation:
y=k/x
4.75= k/38
(4.75)(38)=k
k=180.5
y=180.5/50
y=3.61
Final answer:
y varies inversely with x, which means y = k/x. With y = 4.75 when x = 38, the constant k equals 180.5.
Hence, when x = 50, y equals 3.61.
Explanation:
If y varies inversely with x, this means the relationship between y and x can be described by the equation y = k/x, where k is a constant. Given that y = 4.75 when x = 38, we can first find the constant k by multiplying y by x:
k = y * x = 4.75 * 38 = 180.5
Now that we have found the constant k, we can use it to find y when x = 50. Using the inverse variation formula again, we have y = k/x:
y = 180.5 / 50 = 3.61
Therefore, when x is 50, y is 3.61.
True or false you can represent the distance of an object underground using negative numbers
Answer:
True
Step-by-step explanation:
Since if you use negative number you can determine the length between -3 and 0.
In this question, all lengths are in cm. ABC. 3x-4, 2x+12, 7x-2. Given that AB:AC = 1:2 Show that AC:BC = 2:3
Answer: AC : BC = 22 : 33 = 2 : 3
Step-by-step explanation:
Since we have given that
AB = 3x-4
AC= 2x+12
BC = 7x-2
And AB: AC = 1 : 2
and To show : AC : BC = 2 : 3
So, it becomes ,
[tex]\dfrac{AB}{AC}=\dfrac{3x-4}{2x+12}=\dfrac{1}{2}\\\\2(3x-4)=2x+12\\\\6x-8=2x+12\\\\6x-2x=12+8\\\\4x=20\\\\x=\dfrac{20}{4}\\\\x=5[/tex]
So, AC: BC becomes:
[tex]\dfrac{AC}{BC}=\dfrac{3x-4}{7x-2}=\dfrac{2(5)+12}{7(5)-2}=\dfrac{22}{33}=\dfrac{2}{3}[/tex]
Hence, proved.
Step-by-step explanation:
First find x:
AB:AC=1:2
2(3x-4)=2x+12
6x-8=2x+12
4x-8=12
4x=20
x=5
Substitute:
AC=2x+12
=(2x5)+12
=10+12
=22
BC=7x-2
=(7x5)-2
=35-2
=33
22/33=2/3
Therefore AC:BC = 2:3
okay so The top of the slide is 12 feet from the ground and has an angle of depression of 53 degree . What is the length of the slide? Round your answer to the nearest whole number. please help!!!
To find the length of the slide, you can use trigonometry and the angle of depression. The length can be found using the tangent function, and rounding to the nearest whole number gives an answer of approximately 9 feet.
Explanation:To find the length of the slide, we can use trigonometry and the angle of depression. We can use the tangent function, which is opposite over adjacent, to find the length of the slide. In this case, the opposite side is the height of the slide (12 feet) and the adjacent side is the length of the slide. So we have:
tan(53 degrees) = opposite/adjacent
tan(53 degrees) = 12/adjacent
To solve for the length of the slide, we can rearrange the equation:
adjacent = 12/tan(53 degrees)
Using a calculator, we can find that the length of the slide is approximately 9 feet when rounded to the nearest whole number.
Pete is conducting a survey to determine his customers’ overall satisfaction about the quality of his company’s products. He sends out surveys to the 5 customers who have purchased the largest number of items over the past year. Are his results likely to be representative of the population he is trying to analyze? Explain.
The sample is from the right population, his customers. However, because he is surveying such a small number of people and only asking his best customers (who are probably the most satisfied, or they would not buy so much from him), the results are going to be biased, most likely positive, and not representative of his entire customer base.
No, Because, when to do some sort of analysis (such as this one), you need to take (for example) a Random sample from the population of the problem that is being analyzed.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Pete is conducting a survey to determine his customers’ overall satisfaction about the quality of his company’s products.
Let an example a Random sample from the population of the problem that is being analyzed.
In this example (problem), Pete wants to evaluate overall satisfaction of customers, so he should not send the surveys only to the customers who have purchased the largest number of items, but to the randomly selected customers, in order to obtain representative results of the overall satisfaction.
If he sends the surveys only to the customers who have bought the largest number of items, he will obtain very high satisfaction of customers, as results, of course, and this will not be representative results.
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In order to answer the question correctly, please use the following image below:
Points Y and Z are points of tangency. Find the value of c.
C= (blank)
What is the value of C?
Please show all the work on how you got your answer. ( I'm not asking for an explanation. All I want is the work shown so I can understand how you got your answer)
Answer:
C = 2
Step-by-step explanation:
9c + 14 = 2c^2 + 9c + 6
-9c -9c
14 = 2c² + 6
-6 -6
8 = 2c²
4 = c²
c = 2
The value of c on the circle is 4 or -4.
What is tangent on a circle?In geometry, the tangent of a circle is a line that intersects the circle at only one point, known as the point of tangency.
The tangent line is perpendicular to the radius of the circle at that point.
We have,
XY and XZ are tangent on the same circle.
So,
XY = XZ
This means,
2c² + 9c + 6 = 9c + 14
Combining like terms.
2c² + 9c - 9c + 6 - 14 = 0
2c² - 8 = 0
2c² = 8
c² = 8/2
c² = 4
c = √4
c = ±4
Thus,
The value of c is 4 or -4.
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The weight distribution of parcels sent in a certain manner is normal with mean of 12 lb and standard deviation of 3 lb. The parcel service wishes to establish a weight value c beyond which there will be a surcharge. What value of c is such that 99% of all parcels are under the surcharge weight?
Answer:
21.16
Step-by-step explanation:
Starting from the theory we have the following equation:
[tex]fi*P(x<c-1) = 0.99[/tex]
Using the data supplied in the exercise, we have subtracting the mean and dividing by the standard deviation:
[tex]P( z \leq \frac{c-1-12}{3.5}) =0.99/fi[/tex]
solving for "c", knowing that fi is a tabulating value:
[tex]\frac{c-13}{3.5}=0.99/fi\\\frac{c-13}{3.5}=2.33\\c-13=2.33*3.5\\c = 8.155 +13\\c = 21.155[/tex]
therefore the value of c is equal to 21.16
Mrs. Shelly paid $3 for 6 muffins and Mrs. Kloske paid $9 for 18 muffins. Is the amount Mrs. Kloske and Mrs. Shelly paid equivalent
Answer:
Yes
Step-by-step explanation:
Mrs. Shelby
$3 for 6 muffins
$3 for every 6 muffins 3 X 6 =18
$3...6
$6...12
$9....18
Mrs. Kloske
$9 for 18
They are equivalent in the sense that the price break down would be the same.
whats 4,583,000,000 in scientific notation?
Answer:
4.583 *10^9
Step-by-step explanation:
for scientific notation, the number has to be 1<x<10
so in this case, move the decimal point behind the 4. since there are 3 other non 0 digits behind the 4, write it as 4.583
now count how many spaces there are after the 4 and put that as the exponent for 10
Answer:
4.58 x 106
Step-by-step explanation:
i hope this help
What’s the inverse of 2(x-2)^2 = 8(7+y)
Answer:
y= (x-2)^2/4-7
Step-by-step explanation:
If 5^3b-1 = 5^b-3 what is the value of b?
Answer:
b = -1
Step-by-step explanation:
Your equation is ...
(5^3)b -1 = 5^b -3
This is a mix of exponential and linear terms, and cannot be solved algebraically.
___
We suspect you might mean ...
5^(3b -1) = 5^(b -3)
We can equate the exponents to find a value for b:
3b -1 = b -3
2b = -2 . . . . add 1-b to both sides
b = -1 . . . . . . divide by 2
Rewrite x^2 + 6x +15 in the form of a perfect square and a constant
Answer:
[tex](x+3)^{2}+6[/tex]
Step-by-step explanation:
The given expression is:
[tex]x^2+6x+15[/tex]
We have to re-write the given expression in form of perfect square. The above equation can be rewritten as:
[tex](x^2+6x)+15\\\\ =(x^2+2(x)(3))+15[/tex]
The general formula of a perfect square is:
[tex](a+b)^{2}=a^{2}+2(a)(b)+b^{2}[/tex]
Comparing previous two equations we can conclude that:
We have the square of first term(x), we have twice the product of first term(x) and second term(3). The square of second term(3) is missing. We can rewrite the previous equation as:
[tex](x^2+2(x)(3))+9+6\\\\ =(x^2+2(x)(3)+9)+6\\\\ =(x^2+2(x)(3)+3^{2})+6\\\\ =(x+3)^{2}+6[/tex]
This is the required form of the given expression.
Determine the length of arc JL. A) 25/ 9 π B) 5 /13 π C) 25 /18 π D) 14 /17 π
Answer:
Option C is the right choice where length of the arc is 25/18π.
Step-by-step explanation:
Given:
Length of the radius of the circle, [tex]r[/tex] = 2 unit
Angle between the arc, [tex]\theta[/tex] = 125°
We have to find the arc length.
Let the arc length JL be "a" unit.
Formula to be used:
Arc length = (Circumference times angle ) / 360°
Using the above formula and plugging the values.
⇒ Arc length, JL, 'a' = [tex]2\pi r\times (\frac{\theta}{360})[/tex]
⇒ [tex]a=2\pi r\times (\frac{\theta}{360})[/tex]
⇒ [tex]a=2\pi (2)\times (\frac{125}{360})[/tex]
⇒ [tex]a=4\pi \times (\frac{125}{360})[/tex]
⇒ [tex]a=\frac{4\pi \times 125}{360}[/tex]
⇒ [tex]a=\frac{500\pi }{360}[/tex]
⇒ [tex]a=\frac{50\pi }{36}[/tex]
⇒ [tex]a=\frac{25\pi }{18}[/tex] ... reducing to lowest term.
So,
The length of the arc JL is 25/18π and option C is the right choice.