Here, we must use one sample z test for the first question.
Since the population standard deviation is known in this instance. According to the new protein powder firm, it takes an average of 7 days to add 10% more muscle, with a population standard variation of 5.5 days.
Here, keep in mind that the t test should be used if the population standard deviations are unknown and the z test should be used if the population standard deviations are known.
The second question requires that we test the hypothesis to determine whether the MoCA test differs between the days before and after several exposures to a new tool.
Here, a z-test with two samples was utilized. Once the hypothesis has been stated, the z Statistic
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The supply function and the demand function for a product are linear and are determined by the tables that follow.
Supply Function
Price ($) Quantity
75 125
150 150
300 200
Demand Function
Price ($) Quantity
45 355
120 330
270 280
(a) Write an equation for the supply function's price p as a function of q.
p =
Write an equation for the demand function's price p as a function of q.
p =
(b)Find the quantity and price that give market equilibrium.
Market equilibrium is achieved with a product quantity of units at a price of $ per unit.
The required supply function is p = 3q - 300 and the required demand function is p = -3q + 1110. The equilibrium quantity is 235 and the equilibrium price is $405.
a) Find an equation for the supply function's price p as a function of q as follows.
Let p = mq + b be the required linear supply function.
From the given information, the supply function passes through points (125, 75) and (150,150).
Find the slope m using the points (125, 75) and (150,150) as shown below.
m = (p2-p1)/(q2-q1)
m = (150-75)/ (150-125) = 75/25 = 3
Now find the value of b using the point (125, 75) and slope m = 3 as follows.
p = mq + b
75 = 3(125) + b
b = - 375 + 75 = -300
Therefore, the required supply function is p = 3q - 300.
b) Find an equation for the demand function's price p as a function of q as follows.
Let p = mq + b be the required linear supply function.
From the given information, the demand function passes through points (355, 45) and (330,120).
Find the slope m using the points (355, 45) and (330,120) as shown below.
m = (p2-p1)/(q2-q1)
m = (120-45)/ (330-355) = 75/-25 = -3
Now find the value of b using the point (355, 45) and slope m = -3 as follows.
p = mq + b
45 = -3(355) + b
b = 1065 + 45 = 1110
Therefore, the required demand function is p = -3q + 1110.
Find the equilibrium quantity and equilibrium price as follows.
In order to find the equilibrium quantity, equate the demand function and supply function and solve the equation solve for q as shown below as p is common.
3q - 300 = -3q + 1110
=> 6q = 1410
=> q = 235
Thus, the equilibrium quantity is 235.
Find the equilibrium price by substituting q = 235 in p = 3q -300.
p = 3 x 235 - 300
p = 705 -300 = 405
Hence, the equilibrium price is $405.
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Suppose that sin(0)=3/9. What cos(0)=____________. (round to 3 decimal
Using trigonometry identity the value of cosθ is 0.942.
What is round to 3 decimal?
Rounding to three decimal places is equivalent to rounding to the closest thousandth. Take 3.3685 as an example and round to the nearest thousandth. It is possible to round up to 3.369 or down to 3.368 because the third digit following the decimal point is 8 instead of 3.
Given that sinθ=3/9
Divide the denominator and numerator by 3:
sinθ=1/3
To find the value of cosθ, use trigonometry identity.
The trigonometry identity is sin²θ + cos²θ = 1
Solve the identity for cosθ:
Subtract both side by sin²θ:
cos²θ = 1 - sin²θ
Take square root on both sides:
cos θ = √(1 - sin²θ)
Putting sinθ = 1/3 in the above equation:
cos θ = √(1 - (1/3)²)
cos θ = √(1 - 1/9)
cos θ = √((9 - 1)/9)
cos θ = √(8/9)
cos θ = 0.9428
cos θ = 0.943 (round to 3 decimal places)
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Which of the following gives the correct matrix for this system of equations in reduced row echelon form? x1-3x2-x3 + 3x4 = 2 -xi-2x2-x3 +4x4 = 2 -2x1+4x2 +4x3 +4x4 =-3 12 5 14 100 17 5 18 001 14 1 -3 -1 32 0 -5 -2 74 00ー36-3 b) 1 0 0 -36 9 1 22 010 001_ -_ 1 22 -1 -3 1 3 2 d 0 1 0 0 0 22 -12 -7 1 0 0 0 e) 25 010 -5 0 0 6 -16 f O None of the above
The correct matrix for this system of equations in row reduced echelon form amongst the given options is none of the above.
The given system of equations to get the reduced row echelon form is:
x1 - 3x2 - x3 +3x4 = 2
-x1 - 2x2 - x3 +4x4 = 2
-2x1 + 4x2 + 4x3 +4x4 = -3
To get the reduced row echelon form we need to form the matrix:
[tex]\left[\begin{array}{ccccc}1&-3&-1&3&2\\-1&-2&-1&4&2\\-2&4&4&4&-3\end{array}\right][/tex]
Row reduced echelon form of a matrix is one in which the pivot points equal 1, go from top left to bottom right, there are 0's above and below each pivot point.
R2-R1:
[tex]\left[\begin{array}{ccccc}1&-3&-1&3&2\\-2&1&0&1&0\\-2&4&4&4&-3\end{array}\right][/tex]
R3-R2 then R2+2R1 then R1+R3 then R2+2R3 then R3-3R2
[tex]\left[\begin{array}{ccccc}1&0&3&6&-1\\0&1&6&13&-2\\0&0&-14&-36&3\\\end{array}\right]\\[/tex]
(-1/14)R3 then R2-6R3 then R1-3R3
[tex]\left[\begin{array}{ccccc}1&0&0&-12/7&-5/14\\0&1&0&-17/7&-5/7\\0&0&1&18/7&-3/14\\\end{array}\right]\\[/tex]
which is the reduced row echelon form of the given system of equations.
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One hundred elk, each 1 year old, are introduced into a game preserve. The number N(t) alive after t years is predicted to be N(t)=100(0.9)^t
(a) Estimate the number alive after 7 years. (Round your answer to the nearest whole number.)
(b) What percentage of the herd dies each year?
a) The number alive after 7 years is given as follows: 48.
b) The percentage of herd that dies each year is of 10%.
What is the exponential function?The exponential function in the context of this problem is defined as follows:
N(t)=100(0.9)^t.
The parameters of the function are defined as follows:
The amount of herd alive after 7 years is found with the numeric value at t = 7, replacing the lone instance of t in the function by 7, hence:
N(7) = 100 x (0.9)^7 = 48.
(rounding to the nearest whole number).
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A customer is buying bath towels and hand towels and can spend no more than $100. Each bath towel costs $8, and each hand towel costs $5. The inequality 8x+5y ≤100 represents all possible combinations of x, the number of bath towels, and y, the number of hand towels the customer can buy.
Which graph best represents the solution set for this inequality?
There is an attachment that includes the graph for the inequality 8x + 5y 100.
How do you calculate the scenario's graph?
The parameters are as follows, taken from the query:
The customer's purchase must not exceed $100.
Each bath towel costs $8.
Each hand towel costs $5.
Inequality among the available combinations is another factor that we have.
8x + 5y ≤ 100
like that
x is the quantity of bath towels, while y is the quantity of hand towels.
Plotting the inequality's graph is the following step.
A graphing tool can be used for this.
In order to attach the graph, we enter the inequality in the graphing tool.
Keep in mind that the inequality is provided as
8x + 5y ≤ 100
See the inequality graph in the attached. 8x + 5y ≤ 100
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let $\mathcal{s}$ be the set of real numbers that can be represented as repeating decimals of the form $0.\overline{abc}$ where $a, b, c$ are distinct digits. find the sum of the elements of $\mathcal{s}.$
The sum of the elements of S is 360
Let S be the set of real numbers that can be represented as repeating decimals
The form of the repeating decimal is 0.abc cap
Where a, b and c are distinct digits
If x = 0.abcabc
1000x = abc.abc
1000x - x = abc
999x = abc
x = abc/999
a, b, c are distinct digits
Number of combinations possible = 10 × 9 × 8
= 720 combinations
Therefore each value appear is each place value = 720/10
= 72
Sum of the digits from 0 to 9 = 45
Sum of the elements of S = (45 × 72 × 111 / 999)
= 360
Therefore, the sum of the element is 360
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A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 414 gram setting. Based on a 8 bag sample where the mean is 407 grams and the standard deviation is 18, is there sufficient evidence at the 0.025 level that the bags are underfilled? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
Question #2:
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.8 parts/million (ppm). A researcher believes that the current ozone level is at an insufficient level. The mean of 26 samples is 4.6 ppm with a standard deviation of 1.2. Does the data support the claim at the 0.025 level? Assume the population distribution is approximately normal.
Step 1 of 5:
State the null and alternative hypotheses.
Step 2 of 5:
Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5:
Specify if the test is one-tailed or two-tailed.
Step 4 of 5:
Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Step 5 of 5:
Make the decision to reject or fail to reject the null hypothesis.
A)
A manufacturer of banana chips would like to know whether its bag-filling machine works correctly at the 414-gram setting.
So, Null hypothesis: [tex]H_{0}[/tex] : μ < 414
It is believed that the machine is underfilling the bags.
So, Alternate hypothesis: [tex]H_{1}[/tex] : μ < 414
Given,
n= 8
Population standard deviation (б) = 18
x= 407
We will use the t-test since n > 8 and we are given the population standard deviation.
t=x-μ / (б/[tex]\sqrt{n-1}[/tex])
t= [tex]\frac{407-414}{\frac{18}{\sqrt{7} } }[/tex]
t= -1.028
Use the t table to find p value
p-value = 12.706
Level of significance α = 0.025
p-value>α
It is a two-tailed test.
So, we fail to reject the null hypothesis.
So, its bag-filling machine works correctly at the 414-gram setting.
B)
Let μ be the population mean amount of ozone in the upper atmosphere.
As per the given, we have
[tex]H_{0}[/tex] : μ = 4.8
[tex]H_{1}[/tex] : μ ≠ 4.8
Sample size: n= 26
Sample mean = 4.6
Standard deviation = 1.2
Since population standard deviation is now given, so we use a t-test.
t= [tex]\frac{4.6-4.8}{\frac{1.2}{\sqrt{25} } }[/tex]
t= -0.2/0.24
t= -0.833
It is a two-tailed test.
We are accepting the null hypothesis.
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Which polynomial represents the difference below?
8x³ + 5x+6-(2x² + 3x)
OA. 10x¹0 + 8x² +6
OB. -2x7 + 8x³ + 8x+6
O C. 6x¹0+2x+6
OD. -2x7 + 8x³ + 2x+6
The difference of the given polynomials 8x³+5x+6 and 2x²+3x is 8x³-2x²+2x+6. So, the correct answer is D.
What is the subtraction of polynomials?To subtract polynomials from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
Given that, 8x³+5x+6-(2x²+3x)
Group the like terms are perform the addition or subtraction
= 8x³+5x+6-2x²-3x
= 8x³+(5x-3x)-2x²+6 (Here, like terms are 5x and 3x)
= 8x³+2x-2x²+6
= 8x³-2x²+2x+6
So, the standard form of obtained polynomial is 8x³-2x²+2x+6.
The polynomials difference is 8x³-2x²+2x+6. Therefore, option D is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Which polynomial represents the difference below?
8x³ + 5x+6-(2x² + 3x)
A. 10x+ 8x² +6
B. -2x² + 8x³ + 8x+6
C. 6x¹⁰+2x+6
D. -2x²+ 8x³+2x+6
Rosa makes candles to sell.
Each candle is in the shape of a cuboid of height 8 cm.
The base of each candle is a square of perimeter 20 cm.
Rosa needs to know the volume of one candle.
Work out the volume of one candle.
Remember to give units with your answer
10 -8 -6 -4
| 10+
8
67
-2
4.2
-2
-4-
-6
-8
-10
2
4 6 8 10
Write an equation for the graph, where y depends on x.
The equation of given graph is y = 2x + 6.
What is equation of line?
The formula for a straight line is y = mx + c where c is the height at which the line intersects the y-axis, also known as the y-intercept, and m is the gradient.
Given:
The graph of the line is given.
From graph we have to find the equation of line.
Let the graph passes through the points (0, 6) and (2, 10).
From these two points to find the slope.
Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here, [tex](x_1, y_1) = (0, 6), (x_2, y_2) = (2, 10)[/tex]
⇒ Slope = m = [tex]\frac{10-6}{2-0}= \frac{4}{2} = 2[/tex]
So, the slope is 2.
Now to find the equation of line.
Consider, the point - slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m = 2, (x_1, y_1) = (0, 6)[/tex]
⇒
[tex]y-6=2(x-0)\\y-6=2x\\y=2x+6[/tex]
Hence, the equation of given graph is y = 2x + 6.
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Write a polynomial function in standard form of 3rd degree with zeros
polynomial function for x = 4, - 1 & 2. are
[tex]x^{3}[/tex] - [tex]x^{2}[/tex] - 10x - 8
What is polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.f(x) = anxn + anxn+1 +... + a2x2 + a1x + a0 is the formula for a polynomial. The greatest power of x in an expression is the polynomial's degree. Polynomials of degree 0, 1, 2, 3, and 4 are constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively.Zero polynomial function, linear polynomial function, quadratic polynomial function, and cubic polynomial function are the four most prevalent forms of polynomials used in precalculus and algebra.Given data :
Given the zeroes (roots) of a polynomial are: 4, - 1 & 2.
Here, we are given three roots of the polynomial. That means, the polynomial must be of third degree.
Also, (x - a) is a factor of the polynomial if and only if x = a is a root of the polynomial.
Here, 4, - 1 & 2. are roots. So, the factors are: ( x - 4 ) ( x + 1 ) ( x - 2 )
Multiplying them will result in the polynomial.
= ( x - 4 ) ( x + 1 ) ( x - 2 )
= ( [tex]x^{2}[/tex] - 3x - 4 ) ( x + 2 )
= Distribute parentheses : [tex]x^{2}[/tex] . x + [tex]x^{2}[/tex] . 2 - 3xx - 3x . 2 - 4x - 4 . 2
= Simplify [tex]x^{2}[/tex] .x - [tex]x^{2}[/tex] . 2 - 3xx - 3x . 2 - 4x - 4 . 2
= [tex]x^{3}[/tex] - [tex]x^{2}[/tex] - 10x - 8
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Select all of the lines of reflection that will carry the rectangle back onto itself.
The lines that carry the rectangle onto itself are x = 0 and y = 1
How to determine the lines that carry the rectangle onto itself?The graph that completes the question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The rectangular graph
The coordinates of one end of the graph are
(-3, 3) and (-3, -1)
Next, we calculate the midpoint of these ends
So, we have
Midpoint = 1/2(x₁ + x₂, y₁ + y₂)
Substitute the known values in the above equation, so, we have the following representation
Midpoint = 1/2(-3 + 3, -1 + 3)
Evaluate the like terms
Midpoint = 1/2(0, 2)
So, we have
Midpoint = (0, 1)
So, we have
x = 0 and y = 1
Hence, the reflection lines are x = 0 and y = 1
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The volume of a rectangular prism is 6,618.375 cm3. If the height is 13.25 cm and the length is 27 cm, what is the value of the width?
A: 18.125 cm
B: 18.5 cm
C: 18.75 cm
D: 18.86 cm
The value of width will be;
⇒ 18.5 cm
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;
The volume of a rectangular prism = 6,618.375 cm³
The height is 13.25 cm and the length is 27 cm.
Now,
We know that,
The volume of rectangular prism = Length x Width x Height
Substitute all the values, we get;
⇒ 6,618.375 = 27 × x × 13.25
⇒ 6,618.375 / 357.75 = x
⇒ x = 18.5 cm
Thus, The value of width = 18.5 cm
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Find X, 50 points if you answer
Answer:
x=38
Step-by-step explanation:
linear par
180-134=46
180-84=96
sum of a triangle is 180
96+46+x=180
142+x=180
x=180-142
x=38
NO LINKS!! Please help me with this problem. Part 8ff
Answer:
[tex]\dfrac{1}{36n^2+6n}[/tex]
Step-by-step explanation:
Given factorial expression:
[tex]\dfrac{(6n-1)!}{(6n+1)!}[/tex]
[tex]\boxed{\begin{minipage}{6cm}\underline{Factorial Rule}\\\\$n!=\:n\cdot \left(n-1\right) \cdot \left(n-2\right) \cdot ... \cdot 3 \cdot 2\cdot 1$\\ \end{minipage}}[/tex]
Apply the factorial rule to the numerator and denominator of the given rational factorial expression:
[tex](6n-1)!=\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1[/tex]
[tex]\left(6n+1\right)!=\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{(6n-1)!}{(6n+1)!}&=\dfrac{\left(6n-1\right)\cdot \left(6n-2\right)\cdot \left(6n-3\right)\cdot... \cdot 3 \cdot 2\cdot 1}{\left(6n+1\right)\cdot \:6n \cdot (6n-1) \cdot...\cdot 3 \cdot 2\cdot 1}\\\\&=\dfrac{1}{(6n+1) \cdot 6n}\\\\&=\dfrac{1}{6n(6n+1)}\\\\&=\dfrac{1}{36n^2+6n}\end{aligned}[/tex]
Answer:
[tex]\cfrac{1}{6n(6n+1)}[/tex]--------------------------------
We know that:
n! = 1·2·3·4·...·nTherefore:
(6n + 1)! = (6n - 1)!·6n·(6n + 1)Therefore:
[tex]\cfrac{(6n-1)!}{(6n+1)!} =\cfrac{(6n-1)!}{(6n-1)!(6n)(6n+1)} =\cfrac{1}{6n(6n+1)}[/tex](-4)(-4)(-4)(-4)(-4)(-4)
The answer is to (-4)(-4)(-4)(-4)(-4)(-4) 4096
ANSWER THIS ASAP! FIRST PERSON TO ANSWER GETS EXTRA 50 POINTS. I KNOW ITS ALOT. BUT I REALLY NEED THIS ANSWER. I WILL ALSO MARK BRAINIEST. ANSWER FAST! DEADLINE IS 11:20.
A student is painting a brick for his teacher to use as a doorstop in the classroom. He is only painting the front of the brick. The vertices of the face are (−4, 2), (−4, −11), (4, 2), and (4, −11). What is the area, in square inches, of the painted face of the brick?
The area of the painted face with vertices at (-4, 2), (-4, -11), (4, 2), and (4, -11) which represents a rectangle is 104 square inches
What is a rectangle?A rectangle is a quadrilateral with the four interior angles that are each right angles, and opposite sides that are congruent and parallel.
The specified vertices of the face of the brick are;
(-4, 2), (-4, -11), (4, 2), and (4, -11)
The graph of the above point used to draw the quadrilateral representing the shape of the face in the question, created with MS Word, is attached
From the attached graph and drawing, we get;
Shape of the face of the doorstop = A rectangle
Length of the sides of the quadrilateral (rectangle)
Length = 2 - (-11) = 13
Width = 4 - (-4) = 8
Area of a rectangle Length × Width
Area of the painted face of the brick, A = 13 × 8 = 104
The area of the rectangular painted face of the brick = 104 square inches
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What is the rate of return when 12 shares of Stock
A, purchased for $22/share, are sold for $465? The
commission on the sale is $9.
Rate of Return
Enter the appropriate value into the
formula to calculate the rate of return.
F
profit or loss
total cost
Total Cost = $273
Profit = $192
Rate of Return = [? ]
Answer:
The Rate of return would then be 192 / 273 ≈ 70.32%
find the probability of rolling a five or six on six sided number cube
Answer:
non-violence and kindness with animals
Step-by-step explanation:
Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) C 540 a 3.0, 4.0, LA = C = Solve triangle ABC. (If an answer does not exist,, enter DNE. Round your answers to one decimal place.) b 69 35, LA 72° C = C = a = Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a 28, b = 39, c 29 LA = Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) = 17, 13, c 22 a = LA= o Sketch the triangle 500 LA B 770 C = 270 c 270 50° 77 50° 770 270 A A A 770 50° 270 270 50° 77 C A Solve the triangle using the Law of Sines. (Round side lengths to the nearest integer.) a = b Sketch the triangle. 100° LA = 270, C=60 C 100° 60 100° 27 27° C 60 C C 270 60 100° 27 100° A 60 A Solve the triangle using the Law of Sines. (Round side lengths to one decimal place.) a = b =
The measures of the lengths of the sides and angles of the triangles found using the law of cosines and the law of sines are presented as follows;
Question 1
∠A = 47.35°
∠B = 78.65°
c = 3.3
Question 2
∠B = 78.24°
∠C = 29.76°
a = 67.03
Question 3
∠A = 45.77°
∠B = 86.417°
∠C = 47.813°
Question 4
∠A = 36.15°
∠B = 60.48°
∠C = 93.37°
Question 5
a = 258.98
b = 327.41
∠C = 53°
Question 6
a = 34.11
b = 73.987
∠C = 53°
What is the law of cosines?The law of cosines is a relationship between two sides (b and c) and the included angle, (∠A) and the third side (a) of the triangle.
Mathematically; a² = b² + c² - 2·b·c·cos(A)
Question 1
The dimensions of the triangle ΔABC are;
a = 3.0, b = 4.0, ∠C = 54°
The law of cosines indicates that we get;
c² = b² + a² - 2·b·a·cos(∠C)
Therefore;
c² = 3.0² + 4.0² - 2 × 3.0 × 4.0 × cos(54°) ≈ 10.893
c ≈ √(10.893) ≈ 3.3The law of sines indicates that we get;
sin(54°)/3.3 = sin(∠A)/3.0
∠A = arcsine(3 × sin(54°)/3.3) ≈ 47.35°∠B = 180° - 54° - 47.35° ≈ 78.65°Question 2
b = 69, c = 35, ∠A = 72°
a² = 69² + 35² - 2 × 69 × 35 × cos(72°) ≈ 4493.45
a ≈ √(4493.45) ≈ 67.03The law of sines indicates that we get;
sin(72°)/67.03 = sin(∠B)/69
∠B = arcsine(69 × sin(72°)/67.03) ≈ 78·24°
∠B ≈ 78.24°∠C = 180° - 72° - 78.24° ≈ 29.76°
∠C ≈ 29.76°Question 3
a = 28, b = 39, c = 29
a² = b² + c² - 2·b·c·cos(A)
cos(A) = (a² - (b² + c²)) ÷ (2·b·c)
Therefore; cos(A) = (28² - (39² + 29²)) ÷ (-2 × 39 × 29) ≈ 0.6976
∠A = arccos(0.6976) ≈ 45.77°sin(45.77)/28 = sin(B)/39
sin(B) = 39 × sin(45.77)/28 ≈ 0.998
∠B = arcsine(0.998) ≈ 86.417°∠C = 180° - 45.77° - 86.417° = 47.813°Question 4
a = 13, b = 17, c = 22
cos(A) = (13² - (17² + 22²)) ÷ (-2 × 17 × 22) ≈ 0.807
∠A ≈ arccos(0.807) ≈ 36.15°sin(36.15)°/13 = sin(∠B)/17
sin(∠B) = 17 × sin(36.15)°/13
∠B =50.48° ∠C = 180° - 36.15° - 50.48° ≈ 93.37°Question 5
The parameters of the triangle are; ∠A = 50°, ∠B = 77°, c = 270
Please find attached the sketch of the triangle in the correct option created with MS Word
∠C = 180° - 50° - 77° = 53°a/sin(50°) = 270/sin(53°)
a = sin(50°) × 270/sin(53°) ≈ 258.98
a = 258.98b = sin(77°) × 270/sin(53°) ≈ 329.41
b ≈ 329.41Question 6
The parameters of the triangle are;
∠A = 27°, ∠B = 100°, c = 60
Please find attached the drawing of the correct triangle
∠C = 180° - 27° - 100° = 53°
∠C = 53°
60/sin(53°) = a/sin(27°)
a = sin(27°) × 60/sin(53°) ≈ 34.11
b = sin(100°) × 60/sin(53°) ≈ 73.987
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The vertices of quadrilateral PQRS are listed.
P(3,7). Q(6,-2), R(0,-4), S(-3,5)
Which of the following is the strongest classification that identifies quadrilateral PQRS?
O A.
Quadrilateral PQRS IS a parallelogram.
O B.
Quadrilateral PQRS is a rectangle.
• c.
Quadrilateral PQRS is a square.
• D.
Quadrilateral PQRS is a trapezoid.
Answer: O B. Quadrilateral PQRS is a rectangle.
Step-by-step explanation: The image should help you picture my answer. Good luck with your end of semester test!
Have a great day! :)
A function is shown in the table below:
What is the average rate of change of the function from X equals -7 to X equals 2?
A. -90/101
B. 101/90
C. -101/90
D. 90/101
The average rate of change of the given function from x equals -7 to x equals 2 is calculated as: B. 101/90.
How to Find the Average Rate of a Function for a Given Interval?If we are given a function, f(x), to find the average rate of change of the function within the interval from a to b, the formula to use is:
Average rate of change = f(b) - f(a) / b - a.
Given the table that represents function, we have the following:
a = -7
b = 2
f(a) = f(-7) = -2.7
f(b) = f(2) = 7.4
Plug in the values into the formula:
Average rate of change = (7.4 - (-2.7)) / (2 - (-7))
= (7.4 + 2.7) / 2 + 7)
= 10.1 / 9
= 101/90
Therefore, the average rate of change is: B. 101/90.
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t²-8t+16 can be factorized to give an expression of the form (t + a)², where a is an integer.
Work out the value of a.
Answer:
a = 4
Step-by-step explanation:
Step 1: Find two numbers that multiply to give 16 and add to give -8.
t²-8t+16 = 0
t² -4t -4t + 16 = 0
The two numbers are 4 and -4.
Step 2: Rewrite the equation in the form (t + 4)(t - 4).
t² - 8t + 16 = (t + 4)(t - 4)
Step 3: Factor the equation to get (t + 4)².
(t + 4)² = (t + 4)(t + 4)
Therefore, a = 4.
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Find the slope of the line graphed below.
Answer:
-2
Step-by-step explanation:
The line appears to cross through (2,3) and (4,-1)
You can subtract the x values and y values to determine the difference:
[tex]2 - 4= - 2 \\ 3 - ( - 1) = 4[/tex]
These can be used as the y and x values in y over x to find the slope:
[tex] \frac{4}{ - 2} = - 2[/tex]
The slope is -2
Sydney went to the store and bought candy that was priced according to the weight in pounds. She purchased 2 1/4 pounds of black licorice, 1 7/8 pounds of red licorice, and 1 1/2 pounds of butterscotch candy. if the candy costs $ 4.00 per pound, how much did Sydney spend on candy?
Answer:
$22.50
Step-by-step explanation:
Solve for x. Triangle stuff
Answer:
x=9
Step-by-step explanation:
these 2 angles are supplementary angles meaning added together they will equal 180 degrees
so we can add them together and set it equal to 180
(8x-3)+(16x-33)=180
combine like terms
(8x+16x)+(-3-33)=180
24x-36=180
+36. +36
24x=216
/24. /24
x=9
hopes this helps
The marketing department of a large chain of automobile tire retail stores would like to pursue consumers interested in all-terrain tires. They wish to investigate the extent to which the amount of money spent on TV advertising (ADV) on Sundays is related to the sales revenue (REV) for the week- from this type of tire. They begin by selecting a random sample of 50 stores in various cities. The analyst looks at the data and notices that 9 of the stores are located in cities with warm climater year-round, and there are no off-road driving possibilities anywhere near these locations. She suggests eliminating these cities from the sample as she feels that money spent advertising these tires will have little, if any, effect on sales. Using the remaining cities, a simple regression model is determined. Regression Analysis 7² 0.862 #41 > 0.929 5, 915.247 Dep. Var. REV Regression output variables std. error Intercept
If a store decides to spend $1500 on Sunday TV ads for all-terrain tires, we can predict that 95% of the values for the revenue in those weeks from the sale of these will be between $21863.59 and $25617.41.
A company can use regression analysis to determine statistical relationships between the total sales of its products and the costs associated with promotions and advertising. The outcomes of these analyses can then be used to determine how best to allocate spending funds among, say, various products or sales regions.
n = 41
df = n - 2
df = 41 - 2 = 39
SSₓₓ = (n - 1)S²ₓ
SSₓₓ = (41 - 1) * (400)²
SSₓₓ = 6400000
y = 15531.3086 + 5.4728 * x
If, x = 1500 then:
y = 15531.3086 + 5.4728 * 1500
y = 23740.51
Prediction range of y at 95% = [tex]y + t_{\frac{0.05}{2},39 } * S_{e} * \sqrt{1 + \frac{1}{n} + \frac{(x - x_{1} )^{2}}{SS_{xx} } }[/tex]
Prediction range of y at 95% = [tex]23740.51 + 2.022691 * 915.247 * \sqrt{1 + \frac{1}{41} + \frac{(1500 - 1700)^{2} }{6400000}[/tex]
Prediction range of y at 95% = (2186.1 , 25619.92)
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and drop each item into the correct column. Order does not matter:
(1, 5); (4, 7) - corresponding, (3, 5) - Alternate Interior, (2, 7); (1, 8) - Exterior
(3, 6) are Consecutive Interior Angles.
Line of transversal:
Any line that crosses two straight lines at different locations is known as a transversal.
Corresponding Angles:
When two parallel lines cross the third one, the angles that are in the same relative position at each junction are referred to as corresponding angles to one another
Alternate Interior Angles:
The alternative interior angles are those that are on the inner side of the parallel lines but on the opposing sides of the transversal.
Alternate Exterior Angles:
Alternate external angles are positioned on the opposing sides of the transversal and are always outside the two lines where the transversal intersects.
Consecutive Interior Angles:
The pair of non-adjacent internal angles that are located on the same side of the transversal are referred to as consecutive interior angles.
Here we have
Two parallel lines intersected and formed the angles, ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.
By the given information,
∠1 and ∠ 5 are corresponding angles
∠4 and ∠ 7 are corresponding angles
∠3 and ∠5 are Alternate Interior Angles
∠2, and ∠7 are Alternate Exterior angles
∠1 and ∠ 8 are Alternative Exterior angles
∠3 and ∠ 6 are Consecutive Interior Angles
Therefore,
(1, 5); (4, 7) - corresponding, (3, 5) - Alternate Interior, (2, 7); (1, 8) - Exterior
(3, 6) are Consecutive Interior Angles.
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(a) You have a 10 inch by 15 inch piece of tin which you plan to form into a box (without a top) by cutting a square from each corner and folding up the sides. How much should you cut from each corner so the resulting box has the greatest volume? (b) If the piece of tin is A inches by B inches, how much should you cut from each corner so the resulting box has the greatest volume?
Resulting box has the greatest volume for the values (25 ± 5√7)/6 .
This is a problem that can be solved using derivatives , maxima & minima and common logic.
Hence , going by logic :
Creating a flap of 'a' inches in width, the base of the box will be
(10 - 2a) by (15 - 2a)
and the depth of the box will be the width of the fold-up flap: a.
Then the volume of the box is
v = [tex]a(10 -2a)(15 -2a) = 150a -50a^2 +4a^3[/tex]
Using the derivative of the volume will be zero at the maximum volume.
0 = [tex]dv/da = 150 -100a +12a^2[/tex]
This has roots at
a = (100 ±√(100² - 4(12)(150)))/(2·12)
a = (100 ± √2800)/24 = (25 ± 5√7)/6
Only the smaller of these solutions gives a maximum volume.
You should cut (5/6)(5-√7) ≈ 1.962 inches to obtain the greatest volume.
Similarly , replacing the values of 10 by A and 15 by B , a generalized solution can be formed .
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Mark is cutting 5.3125 inches from a 13.375-inch plank in order to fit it for a dog house he is building.
long will the new board be when he finishes?
Let the new board after final cutting is x. So the new board that is fit for the house will be x= 8.0625
What is subtraction method?A method for calculating the length of a psychological process that involves timing the reactions to two different tasks—one that involves the psychological process in issue and the other—and then subtracting the second reaction time from the first.
What are three types of subtraction?Taking away, part whole and comparison are three types of subtraction.
Let the old house =y= 13.375 inches
Cutting from old house=z= 5.3125 inches
New board=x= y-z
= 13.375-5.3125
= 8.0625
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Let the new board after final cutting is x. So the new board that is fit for the house will be x= 8.0625
What is subtraction method?
A method for calculating the length of a psychological process that involves timing the reactions to two different tasks—one that involves the psychological process in issue and the other—and then subtracting the second reaction time from the first.
What are three types of subtraction?
Taking away, part whole and comparison are three types of subtraction.
Let the old house =y= 13.375 inches
Cutting from old house=z= 5.3125 inches
New board=x= y-z
= 13.375-5.3125
= 8.0625
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