The statement which best describe the correct null and alternative hypotheses, the test statistic, and conclusion at a significance level of 0.05 is:
D. H₀: μ₁ = μ₂ H₁: μ₁ < μ₂.
test statistic, t = -1.5625.
conclusion: fail to reject the null hypothesis μ₁ = μ₂.
How to determine and write the null and alternative hypotheses?Based on the information provided, the appropriate null hypothesis and alternative hypothesis would be represented by the following mathematical expression:
H₀: μ₁ - μ₂ ≤ 0; μ₁ = μ₂
H₁: μ₁ - μ₂ < 0; μ₁ < μ₂.
For the critical value, we have:
Critical probability (p*) = 1 - α
Critical probability (p*) = 1 - 0.05
Critical probability (p*) = 0.9500.
Based on the distribution table for probabilities, a value that corresponds to 0.9500 can be calculated as follows;
Zα = 1.6 + 0.05 = 1.65.
For an upper-tailed test, the critical value is given by;
Z_{critical} = 1.65.
Therefore, if Z_{test} > 1.65; reject null hypothesis (H₀) and if Z_{test} < 1.65; fail to reject null hypothesis (H₀).
Next, we would determine the test statistic:
[tex]Z_{test} = \frac{116 -121 -0}{\sqrt{\frac{16^2}{50} +\frac{16^2}{50} } } \\\\Z_{test} = \frac{-5}{\sqrt{\frac{256}{50} +\frac{256}{50} } }\\\\Z_{test} = \frac{-5}{\sqrt{10.24} }[/tex]
Z_{test} = -5/3.2
Z_{test} = -1.5625
In conclusion, we would fail to reject null hypothesis (H₀) since a Z_{test} of -1.5625 is less than a Z_{critical} of 1.65.
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A container contains 145.2 ounces of lemonade. If the lemonade is poured equally into 15 cups, how many ounces will be poured into each cup?
A. 8.78
B. 9.12
C. 9.64
D. 9.68
Show answer.
Answer: D. 9.68
Step-by-step explanation:
145.2 oz/ 15 cups = 9.68 oz per cup
Twelve friends share 4 cookies equally. What fraction of a cookie does each friend get? Write in simpliest form
Answer:
2/5 of the cookie
Step-by-step explanation:
12 friends need to split 4 cookies
4 cookies needs to divided by 10 people
[tex]\frac{4cookies}{10 people}[/tex] = [tex]\frac{4}{10}[/tex]
simplify: [tex]\frac{4}{10} = \frac{2}{5}[/tex]
Complete the ratio table to convert the units of time from hours to weeks or weeks to hours.
Hours:
168 1 week
1,008. ____week
_____. 5 weeks
Answer:
6 weeks and 840 hours
Step-by-step explanation:
There are 168 hours in one week.
24 hrs/day * 7 days = 168 hours
1008 hours ÷ 24 hours(1 day) = 42 days ÷ 7 days in a week = 6 weeks
168 hours/week * 5 weeks = 840 hours
5.7. Suppose n = 2911 and e = 11. Encrypt the following messages as in
Example (5.3).
a) "OK"
b) "HELP" (Break this up into two blocks.)
Note that,
the encrypted message for "OK" is the pair of numbers (616, 2385).
and the final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).
To encrypt a message using RSA, we need to first represent the message as numbers using a suitable encoding scheme. For simplicity, we can use the ASCII code for each character, which is a standard encoding scheme for text.
a) To encrypt "OK", we first convert each letter to its corresponding ASCII code:
"O" = 79
"K" = 75
Next, we use the RSA encryption formula:
C ≡ [tex]M^{e}[/tex] (mod n)
For "O", we have C ≡ 79¹¹ (mod 2911) ≡ 616 (mod 2911)
For "K", we have C ≡ 75¹¹ (mod 2911) ≡ 2385 (mod 2911)
Therefore, the encrypted message for "OK" is the pair of numbers (616, 2385).
b) To encrypt "HELP", we break it up into two blocks:
Block 1: "HE"
Block 2: "LP"
For block 1, we have:
"H" = 72
"E" = 69
Using the RSA encryption formula, we get:
C1 ≡ 72¹¹ (mod 2911) ≡ 738 (mod 2911)
C2 ≡ 69¹¹ (mod 2911) ≡ 1277 (mod 2911)
Therefore, the encrypted message for "HE" is the pair of numbers (738, 1277).
For block 2, we have:
"L" = 76
"P" = 80
Using the RSA encryption formula, we get:
C3 ≡ 76¹¹ (mod 2911) ≡ 1479 (mod 2911)
C4 ≡ 80¹¹ (mod 2911) ≡ 2252 (mod 2911)
Therefore, the encrypted message for "LP" is the pair of numbers (1479, 2252).
The final encrypted message for "HELP" is the sequence of numbers (738, 1277, 1479, 2252).
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3 Cassie wants to determine the length of the shadow that a 60-foot tall telephone pole casts without measuring it. If Cassie's mailbox, which is 42 inches in height, casts a shadow that is 31.5 inches in length, how long is the shadow that the telephone pole casts? A. 43 feet B. 45 feet C. 52 feet D. 55 feet
The answer is (B) 45 feet
Step-by-step explanation:
We can use proportions to solve this problem.
Let x be the length of the shadow cast by the telephone pole. Then we have:
(42 / 31.5) = (60 / x)
We can cross-multiply to get:
42x = 31.5 * 60
Simplifying this equation, we get:
x = (31.5 * 60) / 42
x = 45 feet
Therefore, the length of the shadow that the telephone pole casts is 45 feet.
Which of the following sets of numbers could represent the three sides of a
triangle?
{7, 15, 20}
{7, 16, 23}
O {11, 22, 35}
O {5, 17, 22}
The following sets of numbers could represent the three sides of a
triangle is {7, 15, 20}.
How to determine the set that represent the three sides of a triangleThe set of numbers {7, 15, 20} could represent the three sides of a triangle, but the other sets of numbers do not satisfy the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side. Checking the sets of numbers:
For {7, 15, 20}, 7 + 15 > 20, 7 + 20 > 15, and 15 + 20 > 7, so they satisfy the triangle inequality theorem and could represent the sides of a triangle.
For {7, 16, 23}, 7 + 16 < 23, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.
For {11, 22, 35}, 11 + 22 < 35, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.
For {5, 17, 22}, 5 + 17 < 22, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.
Therefore, the answer is {7, 15, 20}.
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Can someone please help.
By circle , 15 is the length of x .
What is a circle, exactly?
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by each line that traverses the circle.
Moreover, every angle has rotational symmetry around the center. With no sides or edges, a circle is a figure with a round shape. A circle can be characterized in geometry as a closed shape, a two-dimensional shape, or a curved shape.
AE² = EC . CD
10² = 5 * x
100 = 5 * x
100/5 = x
20 = x
ED = 20 - 5 = 15
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Solve 6x+14x+5=5(4x+1) and write a word problem to the equation or any relevant forms of it represents.
After solving the given expression, the value of x is 5.
What exactly are expressions?
An expression in mathematics is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that may be evaluated to generate a value. Expressions can be simple or complicated, with one or more variables involved.
Now,
To solve the equation 6x+14x+5=5(4x+1), we first need to simplify both sides of the equation using the distributive property of multiplication:
6x + 14x + 5 = 20x + 5
Now we can simplify further by subtracting 20x and 5 from both sides of the equation:
6x + 14x - 20x = 0 - 5
Simplifying again:
x = -5
Finally, we can solve for x by multiplying both sides by -1:
x = 5
Therefore, the solution to the equation 6x+14x+5=5(4x+1) is x=5.
Word problem:
A clothing store sells two types of shirts: T-shirts and polo shirts. The store makes a profit of $6 on each T-shirt sold and a profit of $14 on each polo shirt sold. Last week, the store sold a total of 5 shirts and made a total profit of $25. If x represents the number of T-shirts sold, write an equation to represent the situation.
Solution:
Let x be the number of T-shirts sold, then the number of polo shirts sold is 5 - x (since a total of 5 shirts were sold). The total profit from selling x T-shirts and (5-x) polo shirts can be calculated as:
Profit = (profit per T-shirt x number of T-shirts) + (profit per polo shirt x number of polo shirts)
Profit = (6x) + (14(5-x))
Profit = 6x + 70 - 14x
Profit = -8x + 70
Since the total profit is given as $25, we can write the equation:
-8x + 70 = 25
Simplifying:
-8x = -45
x = 5.625
Since we can't sell a fraction of a shirt, we need to round down to the nearest integer. Therefore, the store sold 5 T-shirts.
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2. Zara stores in the United States stocks a particular type of designer denim jeans in the United States. It stores 500 pairs of jeans each month from its two suppliers. The Hong Kong supplier charges Zara $11 per pair of jeans, and the Colombian supplier charges $16 per pair (and then Zara marks them up almost 1,000%). Although the jeans from Hong Kong are less expensive, they also have more defects than those from Colombia. Based on past data, Zara estimates that 7% of the Hong Kong jeans will be defective compared to only 2% from Colombia and Zara does not want to import any more than 5% defective items. However, Zara does not want to rely on a single supplier, so it wants to order at least 20% from each supplier every month. a. Formulate a linear programming model for this problem. b. Solve the linear programming model graphically. Use either iso-line or corner point method. How many of each should Zara buy? c. How much will Zara pay for them? d. If the Hong Kong supplier were able to reduce its percentage of defective pairs of jeans from 7% to %5, what would be the effect on the solution. Solve c in a separate sheet. First copy the sheet you solved a, b and c. Then change the necessary line and re-solve.
Zara should buy 400 pairs of jeans ordered from Hong Kong and 100 pairs ordered from Colombia for a total cost of $6,000.
See below for other solutions
Formulation of the linear programming model:Let x be the number of pairs of jeans ordered from Hong Kong and y be the number of pairs ordered from Colombia.
Objective function:
Maximize profit, C(x, y) = 11x + 16y
Subject to the following constraints:
The total number of jeans ordered cannot exceed 500: x + y ≤ 500Zara wants to order at least 20% from each supplier: x ≥ 0.2(x+y) and y ≥ 0.2(x+y)Zara does not want to import more than 5% defective items: 0.07x + 0.02y ≤ 0.05(x+y)Non-negativity constraint: x, y > 0Graphical solution using the corner point method:See attachment for the graph, where we have the following corner points
(x, y) = (100, 400), (300, 200), (400, 100)
By substitution, we have
C(100, 400) = 11(100) + 16(400) = 7500
C(300, 200) = 11(300) + 16(200) = 6500
C(400, 100) = 11(400) + 16(100) = 6000
The minimum cost above is $6000
So, Zara should buy 400 pairs of jeans ordered from Hong Kong and 100 pairs ordered from Colombia.
The amount paid for themThe amount paid for them is $6,000
Reducing the percentage of defective pairsIf the Hong Kong supplier were able to reduce its percentage of defective pairs of jeans from 7% to 5%, we would need to update the constraint accordingly:
0.05x + 0.02y ≤ 0.05(x+y)
The new optimal solution would be to order 425 pairs of jeans from the Hong Kong supplier and 75 pairs of jeans from the Colombian supplier, for a total cost of $5875
i.e. C(425, 75) = 11(425) + 16(75) = 5875
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Please help quick!! Given m || n, find the value of x.
In the given angles the required value of x is 17° respectively.
What are angles?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
Angles created by two rays are in the plane where the rays are located.
The meeting of two planes also creates angles. We refer to these as dihedral angles.
Based on the measurement, there are many kinds of angles in geometry.
The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.
So, we know that:
2x+5 + 8x+5 = Straight angle
2x+5 + 8x+5 = 180
Now, solve for x as follows:
2x+5 + 8x+5 = 180
10x+10 = 180
10x = 170
x = 17
Therefore, in the given angles the required value of x is 17° respectively.
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At Christmas, Ben, Sam and Tom received cards in the ration 2 : 3 : 12.
If Tom received 60 cards.
(a) What fraction of the cards did Ben receive?
(b) What fraction did Ben and Sam receive between them?
(c) How many cards did Sam receive?
(d) How many cards did they receive altogether?
Find the surface area of the composite figure shown below that
consists of a right cone sitting atop a right cylinder. Use 3.14 form and
give the answer in square meters.
1-20 m
r 13 m
h=13m
Using the right cone formula we know that the surface area is 1281.77638m³ respectively.
An axis that is perpendicular to the base plane defines a right circular cone. By rotating a right triangle around one of its legs, we may create a right cone.
The right circular cone in the illustration has an axis that is perpendicular to the base and a circular base with a radius r.
So, the formula for the surface area of the right cone is as follows:
πr(r+√h²+r²)
We have the values: r = 13m and h = 13m
Now, insert values as follows:
= πr(r+√h²+r²)
= π13(r+√13²+13²)
= 1281.77638
Therefore, using the right cone formula we know that the surface area is 1281.77638m³ respectively.
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A quality assurance check is 91% accurate for non-defective devices and 97% accurate for defective devices. Of the devices checked, 84% are not defective. What is the probability of an incorrect conclusion? Round your answer to the nearest tenth of a percent.
Answer: To solve the problem, we can use Bayes' theorem. Let D be the event that a device is defective, and let A be the event that the quality assurance check concludes that a device is defective.
We want to find P(A and not D) + P(not A and D), which represents the probability of an incorrect conclusion.
We know that P(D) = 1 - P(not D) = 1 - 0.84 = 0.16, and that P(A | not D) = 0.03 and P(A | D) = 0.97.
Using Bayes' theorem, we can compute:
P(not A | not D) = 1 - P(A | not D) = 1 - 0.03 = 0.97
P(not A | D) = 1 - P(A | D) = 1 - 0.97 = 0.03
Therefore,
P(A and not D) = P(not D) * P(A | not D) = 0.84 * 0.03 = 0.0252
P(not A and D) = P(D) * P(not A | D) = 0.16 * 0.03 = 0.0048
So the probability of an incorrect conclusion is:
P(A and not D) + P(not A and D) = 0.0252 + 0.0048 = 0.03
Therefore, the probability of an incorrect conclusion is 0.03, or 3% (rounded to the nearest tenth of a percent).
Why was this answer deleted prior?
PLEASE HELP Area of Cross Sections
Answer:
396 in²
Step-by-step explanation:
To answer this question we need to use pythagorean theorem (a² + b² = c²)
In our case, a would be 14 and b would be 17
14² + 17² = ?²196 + 289 = 485[tex]\sqrt{485}[/tex] = 22.02Now we have to multiply this by 18
22.02 x 18 = 396.36Which rounded would be 396
Hope this helps, have a lovely day! :)
URGENT! 35 POINTS!
The expression tan theta - sec^2theta/tan theta simplifies to what expression?
−tan θ
−cot θ
cos θ
sec θ
by simplifying the expression, option d ,sec θ is the correct answer.
how can we solve this expression?
We can simplify the given expression as follows:
(tan θ - [tex]sec^2[/tex] θ) / tan θ
= (tan θ / tan θ) - ([tex]sec^2[/tex] θ / tan θ) ,
by diving it by tan θ
= 1 - (1/[tex]cos^2[/tex] θ)([tex]sin^2[/tex] θ / cos θ),
since sec = 1/cos and tan=sin/cos
placing the value in expression and solving it , we get
= 1 - ([tex]sin^2[/tex] θ / ([tex]cos^3[/tex] θ))
= [tex]cos^3[/tex] θ / [tex]cos^3[/tex] θ - [tex]sin^2[/tex] θ
= [tex]cos^3[/tex]θ / [tex]cos^2[/tex] θ (1 - [tex]tan^2[/tex] θ)
We can simplify the given expression as follows:
= cos θ ( [tex]cos^2[/tex]θ - [tex]sin^2[/tex]θ) / ([tex]cos^2[/tex] θ)
= cos θ (cos θ / [tex]cos^2[/tex]θ)
= 1/cos θ is equal to sec θ
Therefore, the simplified expression is sec θ.
Hence, the answer is option (d) sec θ.
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Eliana opened a savings account and deposited $700.00 as principal. The account earns 4%
interest, compounded monthly. What is the balance after 10 years?
Answer:
We can use the formula for compound interest to find the balance in Eliana's savings account after 10 years:
A = P(1 + r/n)^(nt)
where A is the balance, P is the principal (initial deposit), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years.
Substituting the given values, we get:
A = $700(1 + 0.04/12)^(12*10)
Simplifying, we get:
A = $700(1.0033333)^120
Using a calculator, we get:
A ≈ $1,038.81
Therefore, the balance in Eliana's savings account after 10 years is approximately $1,038.81.
Tiffany's mom is renting a car for their upcoming vacation. She wants to spend no more than $17 per day for the car. Which of the following car rental companies will fit into her budget? Select ALL that apply.
Car Rental Company Amount Charged
A $33 for 2 days
B $50 for 3 days
C $72 for 4 days
D $89 for 5 days
A
Car Rental Company A
B
Car Rental Company B
C
Car Rental Company C
D
Car Rental Company D
Answer: i think its A and B
Step-by-step explanation: 33 divided by 2 is 16.5
50 divided by 3 is 16.6667
72 divided by 4 is 18 so that would be to much
89 divided by 5 is 17.8 which is also to much
The reservoir dropped feet during a long dry spell and then rose feet following that. Which expression shows one way to calculate the total change in reservoir height over both years?
A.
B.
C.
D.
The tοtal change in reservοir height οver bοth years is a decrease οf 2 feet.
What is the tοtal difference in reservοir height between the twο years?The tοtal change in reservοir height οver bοth years can be calculated by finding the difference between the final height and the initial height.
Let's assume that the initial height οf the reservοir was H.
After the lοng dry spell, the reservοir drοpped 6 feet, which means its height became H - 6.
Fοllοwing that, the reservοir rοse 4 feet, which means its height became (H - 6) + 4 = H - 2.
Therefοre, the tοtal change in reservοir height οver bοth years can be calculated as:
Tοtal change = Final height - Initial height
= (H - 2) - H
= -2
Sο the answer is C) -0+. The tοtal change in reservοir height is a decrease οf 2 feet.
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Find the value of each variable.
The values of the variables in the semicircle shown are:
x = 63 degrees; y = 90 degrees.
What is the Angle Inscribed in a Semicircle Theorem?A semi-circle is exactly half of a full circle and has a measurement of 180 degrees; the two endpoints of the diameter form the endpoints of the semi-circle. If an angle is enclosed inside a semi-circle, the angle formed measures 90 degrees.
Therefore, it means the value of the variable, y = 90 degrees.
Thus, using the triangle sum theorem, we have:
x = 180 - 90 - 27
x = 63 degrees.
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Please help me asap:}
Simultaneous equations are a set of equations that are solved together to determine the values of the variables that satisfy both equations.
What are Simultaneous equations?1) 4x + 5y = 3 ---(1)
y - 3x = -7 ----(2)
Using the substitution method;
y = -7 + 3x ----(3)
Thus
4x + 5(-7 + 3x) = 3
4x -35 +15x = 3
19x - 35 = 3
19x = 3 + 35
x = 2
Then
4(2) + 5y = 3
8 + 5y = 5
y = 13/5
y = 2 3/5
2) 2x - 4y = 24 ----- x 3
-3x + 2y = -48 ----- x 2
6x - 12 y = 72 ---- (3)
-6x + 4y = -96 ---- (4)
Add 3 and 4
16y = -24
y = -24/16
Substitute y = -24/16 into (1)
2x - 4(-24/16) = 24
2x + 6 = 24
x = 15
3) -x + y = 13 --- 1
3x - 4y = 46 ---- 2
y = 13 + x ---- 3
Substitute 3 into 2
3x - 4(13 + x) = 46
3x - 52 - 4x = 46
-x - 52 = 46
x = 98
Substitute x = 98 into (1)
-98 + y = 13
y = 13 + 98
y = 111
Let C be x and D be y
x + y = 180
x = 33 + 6y
x - 6y = 33
x = 180 - y
Substitute and obtain;
180 - y - 6y = 33
180 - 7y = 33
y = 33 - 180/-7
y = 21
Then
x + 21 = 180
x = 180 - 21
x = 159
Lastly
Let small = x , medium = y
x + y = 150
4x + 6y = 764
x = 150 - y
4(150 - y) + 6y = 764
600 - 4y + 6y = 764
600 + 2y = 764
2y = 764 - 600
y = 82
Then;
x + 82 = 150
x = 68
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The solutions to the simultaneous equations are:
1) x = 2 and y = -1
2) x = 18 and y = 3
3) y = -7 and x = 6
How to Solve the System of simultaneous Linear Equations?There are three main methods in solving simultaneous equations and they are:
1) Elimination Method
2) Substitution Method
3) Graphical Method
1) 4x + 5y = 3
y = 3x - 7
Substitute 3x - 7 for y in the first equation to get:
4x + 5(3x - 7) = 3
4x + 15x - 35 = 3
19x - 35 = 3
19x = 35 + 3
19x = 38
x = 38/19
x = 2
Thus:
y = 3(2) - 7
y = -1
2) 2x - 4y = 24
-3x + 2y = -48
Multiply eq 2 by 2 and eq 1 by 1 to get:
2x - 4y = 24 -----(3)
-6x + 4y = -96 -----(4)
Add eq 3 to eq 4 to get:
-4x = -72
x = 18
2(18) - 4y = 24
36 - 4y = 24
36 - 24 = 4y
4y = 12
y = 3
3) -x + y = -13
3x - 4y = 46
From eq 1, x = y + 13
Thus:
3(y + 13) - 4y = 46
3y + 39 - 4y = 46
39 - y = 46
y = 39 - 46
y = -7
x = -7 + 13
x = 6
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a bakery has 17 pounds of flour they want to put into 6 containers. They put the same amount of flour in each container. If they want to use up all the flour, how much flour should they put in each container?
Answer:
2.83333 pounds of flour in each container
Janelys has a points card for a movie theater.
She receives 20 rewards points just for signing up.
• She earns 12.5 points for each visit to the movie theater.
She needs at least 165 points for a free movie ticket.
Write and solve an inequality which can be used to determine x, the number of visits
Janelys can make to earn her first free movie ticket.
Answer: 12 times
Step-by-step explanation:
165-20=145
12.5x11=137.5
12.5x12=150
Answer: 12.5x+20≥165
x≥11.6
Step-by-step explanation:
A ladder 35feet long leans against the side of a building. If the angle formed between the ladder and the ground is 60°,how far is the bottom of the ladder from the base of the building?[Given that cos 60° = 0.5]
Therefore, the bottom of the ladder is 17.5 feet from the base of the building.
What is distance?Distance is a numerical measurement of the physical space between two objects or points. It is the amount of space between two points or objects, usually measured in units such as meters, feet, or miles. Distance can be used to describe the separation between any two entities in space, whether they are tangible objects or abstract concepts. In physics, distance is a fundamental concept that is used to describe the magnitude of displacement, which is the change in position of an object over time. Distance can be calculated using a variety of methods, including measuring with a ruler or tape measure, using GPS technology, or by using mathematical equations that take into account variables such as speed and time.
We can use trigonometric ratios to solve the problem. Let x be the distance between the bottom of the ladder and the base of the building. Then, we can use the cosine ratio to find x:
cos (60°) = adjacent/hypotenuse
0.5 = x/35
x = 0.5 × 35
x = 17.5
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Are the fractions 2/2 and 8/8 equivalent fractions
Answer:
Step-by-step explanation:
yes since they are both divisible by their denominators and equal the same thing
Answer:
yes, they are equivalent
Step-by-step explanation:
2/2 = (2/2)x(4/4) = 8/8 = 1
PLS COMPLETE ALL OF IT!! 50 POINTS!
A. The length of the cord needed to reach corner C is 17.6 m
B. The distance between the electrical outlet and corner N is 14.3 m
A. How do i determine the length of cord needed?The length of the cord needed can be obtained as follow:
Length BC = Opposite = 8 mAngle (θ) = 27°Length of cord =?Sine θ = opposite / hypotenuse
Sine 27 = 8 / Length of cord
Cross multiply
Length of cord × sine 27 = 8
Divide both sides by sine 27
Length of cord = 8 / sine 27
Length of cord = 17.6 m
B. How do i determine the distance between electrical outlet and corner NFirst, we shall determine the length OB. Details below:
Angle (θ) = 27°Length BC = Opposite = 8 mLength OB =?Tan θ = Opposite / Adjacent
Tan 27 = 8 / Length OB
Cross multiply
Length OB × tan 27 = 8
Divide both sides by tan 27
Length OB = 8 / tan 27
Length OB = 15.7 m
Finally, we shall determine the distance between the electrical outlet and corner N. Details below:
Length OB = 15.7 mLength BN = 30 mLength ON = Distance =?Length BN = Length OB + Length ON
30 = 15.7 + Distance
Collect like terms
Distance = 30 - 15.7
Distance = 14.3 m
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-16=(-4)-6x what does x mean
Answer: x=2 is the answer
Answer:
Step-by-step explanation
Rearrange terms
-16=(- 4)- 6 x
-16=-6x - 4
Add 4 to both sides
-16= - 6x - 4
-16 + 4= -6x - 4 + 4
Simplify the expression
-16+4=6x - 4+4
-12=6x
Divide both sides by the same factor
-12=6x
-12/-6= -6x/-6
so
x=2
Shebane rolls a standard six sides number cube. Find p
Answer:
2/3
Step-by-step explanation:
A six sided number cube :
Sample space = 1,2,3,4,5,6
Non composite numbers on a six sided number cube = 1,2,3,5
Probability of an event = required outcome / Total possible outcomes
Required outcome = number of non composite number = 4
Total possible outcomes = sample space = 6
P(not composite)= 4/6 = 2/3
Please help need to get a good score
Write an expression describing all the angles that are coterminal with 8°. (Please use the variable k in your answer. Give your answer in degrees, but do not include a degree symbol in your answer.)
the expression describing all the angles that are coterminal with 8° is: θ = 8° + 360°k, where k is an integer.
How to solve and what is angle?
An angle of 8° has an initial side on the positive x-axis and rotates counterclockwise by 8°.
Any angle coterminal with 8° can be expressed as:
θ = 8° + 360°k
where k is an integer.
Therefore, the expression describing all the angles that are coterminal with 8° is:
θ = 8° + 360°k, where k is an integer.
An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians and are used to measure the amount of rotation or turn between two intersecting lines or planes.
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Bob drove 845 miles in 13 hours.
At the same rate, how many miles would he drive in 9 hours ?
Answer:
585 miles
Step-by-step explanation:
845 miles ÷ 13 hours = 65 mph
645 mph * 9 hours = 585 miles