It is true that when difference on dependent variable is attributed to effect of that variable through statistical hypothesis testing then it is unlikely that the difference would occur by chance alone
A formal assertion about the nature of a phenomenon made within the constraints of a statistical model is known as a statistical hypothesis.
Statistical hypothesis is a description of the makeup of a population. A population parameter is frequently used to express it.
There are two statistical hypotheses used in hypothesis testing. The above-described null hypothesis (H0) is the first.
If it turns out that the null hypothesis is statistically invalid, an alternative hypothesis (Ha) for each H0 will be given preference. Depending on the research hypothesis, the Ha may be directed or nondirectional.
About the statement in the question,
It is improbable that an observed difference between two groups on the dependent variable would occur by chance alone when the difference is explained by the effect of the dependent variable through statistical hypothesis testing.
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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
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
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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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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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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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 side of the triangle below has been extended to form an exterior angle of
132°. Find the value of x
Answer:
x = 15°
Step-by-step explanation:
⭐the exterior angle of a triangle is equal to the sum of the angles that is opposite of said exterior angle
Thus, to solve for x, we have to make an equation in regards of the exterior angle.
132° = x° + 117°
∴ 15 = x° . . . . subtract 117 from LHS and RHS
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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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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:
$22.50
Step-by-step explanation:
NO LINKS!! Please help me with this problem. Part 8ff
Answer:
[tex]\dfrac{1}{36n^2+6n}[/tex]
Step-by-step explanation:
Given factorial expression:
[tex]\dfrac{(6n-1)!}{(6n+1)!}[/tex]
[tex]\boxed{\begin{minipage}{6cm}\underline{Factorial Rule}\\\\$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]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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Find the volume of a cone with a radius of 3 feet and a height of 7 feet. Enter
the answer in terms of pie
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%
Can anyone solve I need help urgent thank you
Answer:
Step-by-step explanation:
3.14 x 3=9.42
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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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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Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by
C(p) =
8100p
100 − p
(a) Is C(p) undefined at any p-value? If so, what value? (If an answer does not exist, enter DNE.)
p =
(b) What is the domain of C(p) as given by the equation? (Enter your answer using interval notation.)
(c) What is the domain of C(p) in the context of the application? (Enter your answer using interval notation.)
(d) What happens to the cost as the percent of pollution removed approaches 100%?
The cost increases (bounded by 8100) as p increases.
The cost decreases (bounded by 0) as p increases.
The cost decreases without bound as p increases.
The cost increases without bound as p increases.
The cost remains constant a
(a) C(p) is not defined since we can't divide by 0.
(b) The domain of C(p) as given by the equation is (-∞, 100) ∪ (100, ∞)
(c) The domain of C(p) in the context of the application is [0, 100)
(d) The percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100
Here we have given that Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by
C(p) = 8100p / (100 − p)
And we need to find the following.
(a) In general ma the we know that dividing by zero is not possible one.
Therefore, C(p) is undefined when we try to divide it by 0.
(b) The domain of C(p) is the function is not defined at p =100 the domain would be written as,
=> D = (-∞, 100) ∪ (100, ∞)
(c) The domain of C(p) in the context of the application is calculated as,
=> D = [0, 100)
Therefore, the percentage of particulate pollution removed from an industrial plant can't be negative or higher or equal than 100.
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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:
-x+y≤-1
x + 2y ≥ 4
Graph the system of inequalities.
Answer:
Step-by-step explanation:
[tex]-x+y\leq -1\\x-y\geq 1\\x+2y\geq 4[/tex]
dark blue is the required region.
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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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
1 hour 15 minutes. is what in minutes
Answer:
75
Step-by-step explanation:
I hour and 15 minutes in minutes is 75 minutes
1 hour = 60 minutes
you add 15 and you get
60+15=75
The answer would be 75 Minutes.
1 Hour = 60 Minutes
[tex]60 + 15 = 75[/tex] Minutes.
(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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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
use the mean value theorem to verify that at some time during the first 3 seconds of fall the instataneous velocity equals the average velocity
Verified that during the first 3 seconds of fall the instantaneous velocity equals the average velocity, the time is 1.5 seconds
The height of an object t seconds after it is dropped from a height of 300 meters is
s(t) = -4.9t^2 + 300
The average velocity of object during first 3 seconds
= s(3) - s(0) / 3 - 0
s(3) = -4.9 × (3)^2 + 300
= -44.1 + 300
= 255.9 meters
s(0) = -4.9(0)^2 + 300
s(0) = 300
The average velocity = (255.9 - 300) / 3 - 0
= -44.1 / 3
= -14.7 meter per second
To find instantaneous velocity differentiate the function
= -9.8t
The instantaneous velocity = The average velocity
-9.8t = -14.7
t = -14.7/-9.8
t = 1.5 seconds
Therefore, time is 1.5 seconds
I have answered the question in general, as the given question is incomplete
The complete question is :
The height of an object t seconds after it is dropped from a height of 300 meters is s(t) = -4.9t^2 + 300.
(b) Use the Mean Value Theorem to verify that at some time during the first 3 seconds of fall, the instantaneous velocity equals the average velocity. Find that time.
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1. Using the stopping distance calculator and your internet browser complete the following table to compare stopping distances at various speeds.
2. You overhear your friend say “It is OK to go 10 mph over the speed limit.” Explain why your friend is wrong using your evidence from the table above to support your answer.
The stopping distance table and the analysis of the stopping distance are presented as follows;
1. The stopping distance calculator, an online tool, provides the stopping distance at a specified speed as presented in the table on the following sections.
2. Increasing the vehicle speed by 10 mph, increases the required stopping distance exponentially, which reduces the safety of driving
What is the stopping distance?The stopping distance is the distance traveled by a vehicle, which is the sum of the distance traveled during the reaction time and the distance traveled during braking (the braking distance)
The table in the question using a perception–reaction time of 2.5 seconds, and the online stopping distance calculator is completed as follows;
Speed (mph) [tex]{}[/tex] Speed (m/s) Stopping Distance (m)
60 mph [tex]{}[/tex] 26.82 m/s 119.55 m
50 mph [tex]{}[/tex] 22.35 m/s 92.34 m
40 mph [tex]{}[/tex] 17.88 m/s 68.05 m
30 mph [tex]{}[/tex] 13.41 m/s 46.665 m
20 mph [tex]{}[/tex] 8.94 m/s 28.197 m
10 mph [tex]{}[/tex] 4.47 m/s 12.642 m
2. The details from the above table indicates that as the speed increases, the stopping distance increases exponentially, such that increasing the speed by 10 mph increases the required stopping distance when the vehicle is moving at an already high speed, thereby reducing safety by increasing the speed by 10 mph.
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let $f(x)$ be a polynomial with integer coefficients. suppose there are four distinct integers $p,q,r,s$ such that $$f(p)
The smallest possible value of f ( t ) = 9 based on the values of p , q , r , s.
Given :
Let f ( x ) be a polynomial with integer coefficients. Suppose there are four distinct integers p , q , r , s such that f ( p ) = f ( q ) = f ( r ) =f ( s ) = 5. If t is an integer and f ( t ) > 5,
Let g(x) = f(x) − 5.
g(x) = (x−p)(x−q)(x−r)(x−s)h(x)
The condition f(t) > 5 translates to g(t) > 0.
Since p,q,r,s,t are distinct integers, the smallest possible positive value of (t−p)(t−q)(t−r)(t−s) is 4 :
the four numbers in the parentheses are all distinct integers ≠ 0, so the smallest value we can get from the product (−2)⋅(−1)⋅1⋅2. }
The smallest possible positive value of h(t) is 1, since we must have g(t)≠0.
Thus the smallest possible value of g(t) is 4, and therefore the smallest possible value of f(t) is 9, and it is achieved for t=2 if we have
f(x)=x(x−1)(x−3)(x−4)+5
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Full question ;
Let f(x) be a polynomial with integer coefficients. Suppose there are four distinct integers p,q,r,s such that f(p)=f(q)=f(r)=f(s)=5. If t is an integer and f(t)>5, what is the smallest possible value of f(t)?
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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What is it? I swear I have no idea
By using matrix, it can be calculated that:
[tex]\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]
What is a matrix?The term "matrix" refers to any configuration of numbers in the form of rows and columns. a collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers.
In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics. Solving linear equations is made easier by it. Matrices are incredibly priceless items that are used in a variety of contexts. In addition to mathematical applications, matrices are employed in a wide range of scientific disciplines. Nearly every element of our life uses engineering mathematics.
Here,
[tex]C = \begin{bmatrix} 12 & 16 & -20 \\ 4 & -24 & 28 \end{bmatrix}[/tex]
[tex]\frac{1}{4}C = \begin{bmatrix} 12\times \frac{1}{4} & 16 \times \frac{1}{4} & -20 \times \frac{1}{4} \\ 4 \times \frac{1}{4} & -24 \times \frac{1}{4}& 28 \times \frac{1}{4}\end{bmatrix}\\\\\frac{1}{4}C = \begin{bmatrix}3 & 4 & -5 \\ 1 & -6 & 7\end{bmatrix}[/tex]
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