The linear equation in y=mx+b form that represents this scenario is:
y = -10x + 450.
What is a linear equation?
A linear equation is a mathematical equation in which the highest power of the variable(s) is one.
ax + b = 0
or
y = mx + b
where a, b, and m are constants and x and y are variables. In the first form, x is a variable and a and b are constants. In the second form, x and y are variables, m is the slope of the line, and b is the y-intercept.
Let x be the number of weeks that have passed since Todd started withdrawing money from his savings account. Initially, Todd had $450 in his savings, so the amount of money he has left after x weeks is:
450 - 10x
The rate of change of the amount of money Todd has with respect to time is -10, since he is withdrawing $10 per week. Therefore, the slope of the line that represents this situation is -10.
The y-intercept represents the initial amount of money Todd had in his savings, which is $450. Therefore, the linear equation in y=mx+b form that represents this scenario is:
y = -10x + 450
where y is the amount of money Todd has in his savings after x weeks.
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An isosceles triangle whose sides are 5cm, 5cm and 6cm is inscribed in a circle. Find the radius of the circle.
Answer:
To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:
r = (a/2) * cot(π/n)
where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.
In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:
6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)
36 = 50 - 50cos(x)
cos(x) = (50 - 36)/50
cos(x) = 0.28
x = cos^-1(0.28) ≈ 73.7°
Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:
(5/2)^2 + h^2 = 5^2
25/4 + h^2 = 25
h^2 = 75/4
h = sqrt(75)/2 = (5/2)sqrt(3)
Now we can find the radius of the inscribed circle using the formula:
r = (a/2) * cot(π/n)
where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:
r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm
Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.
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?
Help please I got 5.76 I don’t know if that’s right
Evaluating the linear equation in x = 19 we can see that the temperature was 5.76 degrees, so your answer is correct.
How to predict the temperature?Here we have a linear equation that relates the wind temperature with the wind's velocity.
The linear equation is:
y = -0.36*x + 12.6
Where y is the temperature and x is the wind speed. We want to find the temperature when the speed is 19 miles per hour, to get it, just replace x by 19 in the linear equation above, then we will get:
y = -0.36*19 + 12.6
y = -6.84 + 12.6
y = 5.76
So your answer is correct.
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A normal population has a mean of $76 and standard deviation of $6. You select random samples of 40.
1. What is the probability that a sample mean is less than $75? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
2. What is the probability that a sample mean is between $75 and $77? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
3. What is the probability that a sample mean is between $77 and $78? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
4. What is the probability that the sampling error ( x¯
− μ) would be $1.50 or less? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is used in various fields such as mathematics, statistics, science, and finance to make predictions and analyze data.
Here,
1. The z-score for a sample mean of $75 is calculated as:
z = (75 - 76) / (6 / √(40)) = -2.36
Using a z-table, the probability of a z-score less than -2.36 is 0.0099 (rounded to 4 decimal places).
2. The z-score for a sample mean of $75 is calculated as:
z1 = (75 - 76) / (6 / √(40))
= -2.36
The z-score for a sample mean of $77 is calculated as:
z2 = (77 - 76) / (6 / √(40))
= 0.79
Using a z-table, the probability of a z-score between -2.36 and 0.79 is 0.8669 (rounded to 4 decimal places).
3. The z-score for a sample mean of $77 is calculated as:
z1 = (77 - 76) / (6 / √(40))
= 0.79
The z-score for a sample mean of $78 is calculated as:
z2 = (78 - 76) / (6 / √(40))
= 1.57
Using a z-table, the probability of a z-score between 0.79 and 1.57 is 0.0823 (rounded to 4 decimal places).
4. The standard error of the mean (SEM) is calculated as:
SEM = standard deviation / sqrt(sample size)
SEM = 6 / √(40) = 0.9487
The z-score for a sampling error of $1.50 is calculated as:
z = 1.50 / 0.9487 = 1.58
Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).
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Christy is training for a race in the summer. Every day she jogs the same number of miles. She also rides her bicycle 7.5 miles each day. During a 5-day training period, she jogs and rides a total of 53 miles. How many miles does Christy jog each day during training? Explain how you solved the problem.
5 miles each day so 5×7=35 miles a week
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
I will mark you brainiest!
The value of X is
A) 3
B) 5
C) 9
D) 12
Therefore, the value of x is 9.
What is triangle?A triangle is a closed two-dimensional geometric shape that is formed by connecting three non-collinear points with three-line segments. The three line segments that connect the three points are called sides of the triangle, and the points themselves are called vertices. The angle formed between any two adjacent sides of a triangle is called an interior angle of the triangle. The sum of the interior angles of a triangle is always 180 degrees.
There are many different types of triangles, including equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles. An equilateral triangle is a triangle in which all three sides are equal, an isosceles triangle is a triangle in which two of the sides are equal, and a scalene triangle is a triangle in which none of the sides are equal. An acute triangle is a triangle in which all three interior angles are less than 90 degrees, an obtuse triangle is a triangle in which one of the interior angles is greater than 90 degrees, and a right triangle is a triangle in which one of the interior angles is exactly 90 degrees.
Given by the question.
According to Thel's theorems
[tex]\frac{5}{3} =\frac{15}{x}[/tex]
5x=45
x=9
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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
Help with this trig identities problems.
1) Given csc Φ = 7/3 and cot Φ = - (2√10)/(3), find sec Φ.
2) Given that sec β = 6/5 and sin β > 0, find tan β and sin β.
Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.
1. We can start by using the Pythagorean identity to find the values of sin Φ:
[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1
Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:
1/(7/3) = sin Φ
sin Φ = 3/7
Next, we can use the fact that cot Φ = cos Φ/sin Φ:
cot Φ = cos Φ/(3/7) = - (2√10)/(3)
Simplifying this expression, we get:
cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7
Finally, we can use the fact that sec Φ = 1/cos Φ:
sec Φ = 1/(- 2√10/7) = -7/(2√10)
2. We can use the fact that sec β = 1/cos β to find the value of cos β:
sec β = 6/5
cos β = 5/6
Next, we can use the Pythagorean identity to find the value of sin β:
[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1
sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6
Finally, we can use the fact that tan β = sin β/cos β:
tan β = (√11/6)/(5/6) = √11/5
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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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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
Select the MEAN, MEDIUM, MODE and RANGE for the data below and how you worked it out
Employment status of parents in couple families
Labour force, parents or partners aged 15 years and over in Warragul
Both employed, worked full-time
580
Both employed, worked part-time
134
One employed full-time, one part-time
853
One employed full-time, other not working
471
One employed part-time, other not working
217
Both not working
799
Other (includes away from work)
193
Labour force status not stated (by one or both parents in a couple family)
185
Answer:
Measures of Central Tendancy
Mean: 429
Median: 344
Mode: 134,185,193,217,471,580,799,853
Range: 719
Step-by-step explanation:
Mean:The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is
[tex]\mu = \frac{{\sum}x}{N}[/tex]
The formula for the mean of a sample is
[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]
Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:
[tex]\frac{3432}{8} = 429[/tex]
Median:The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:
[tex]134, 185, 193, 217, 471, 580, 799, 853[/tex]
Since there is an even number of data values in this data set, there are two middle numbers. With 8 data values, the middle numbers are the data values at positions 4 and 5. These are 217 and 471. The median is the average of these numbers. We have
[tex]{\frac{ 217 + 471 }{2}}[/tex]
Therefore, the median is
[tex]344[/tex]
Mode:The mode is the number that appears most frequently. A data set may have multiple modes. If it has two modes, the data set is called bimodal. If all the data values have the same frequency, all the data values are modes. Here, the mode(s) is/are
[tex]134,185,193,217,471,580,799,853[/tex]
Help with math problems
Answer:
13.) y=(x-4)^(2)+3
Step-by-step explanation:
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.
69 POINTS NEED HELP ASAP QUESTION IS DOWN BELOW
Answer:
(a) 22 inches
(b) 770 inches
(c) 26,950 inches
Step-by-step explanation:
(a) To find the perimeter of the drawing, we add up the lengths of all four sides:
Perimeter of drawing = 7 + 4 + 7 + 4 = 22 inches
(b) The length and width of the actual garden are 35 times larger than the dimensions in the drawing. This means that the actual length is 7 x 35 = 245 inches and the actual width is 4 x 35 = 140 inches. To find the perimeter of the actual garden, we add up the lengths of all four sides:
Perimeter of actual garden = 245 + 140 + 245 + 140 = 770 inches
(c) When the dimensions of the garden are multiplied by 35, the perimeter of the garden will also be multiplied by 35. This is because each side will increase by a factor of 35, so the total length of all four sides will increase by a factor of 35 as well. Therefore, the new perimeter will be:
New perimeter = 35 x Perimeter of actual garden = 35 x 770 = 26,950 inches
According to Okun's law, if the unemployment rate goes from 3% to 7%, what
will be the effect on the GDP?
Answer: decrease in the GDP by 2.5%.
Step-by-step explanation:
Please help me w my trig
Answer:
Assuming that the expression is asking for the tangent of 1 radian, we can use the tangent half-angle formula to find an exact value:
tan(1) = 2tan(1/2) / (1 - tan^2(1/2))
To find tan(1/2), we can use the half-angle formula for tangent:
tan(1/2) = sin(1) / (1 + cos(1))
We cannot simplify this expression any further without a calculator. Therefore, the exact value of tan(1) is:
tan(1) = 2sin(1) / (cos(1) - cos^2(1) + 1)
Again, we cannot simplify this expression any further without a calculator.
For the second expression, we are asked to find the value of:
tan(arctan(6/4))
By definition, tan(arctan(x)) = x for all x, so we have:
tan(arctan(6/4)) = 6/4 = 3/2
Therefore, the exact value of the expression tan(6/4) is 3/2.
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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Help with math problems
The vertex form of the quadratic equations in standard form are, respectively:
Case 9: y = 2 · (x + 2)² - 12
Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32
Case 11: y = 3 · (x - 4 / 3)² - 16 / 3
Case 12: y = - 3 · (x - 3)²
Case 13: y = (x - 4)² + 3
Case 14: y = (x - 1)² - 7
Case 15: y = (x + 3 / 2)² - 9 / 4
Case 16: 2 · (x + 1 / 4)² - 1 / 8
Case 17: y = 2 · (x - 3)² - 7
Case 18: y = - 2 · (x + 1)² + 10
How to derive the vertex form of a quadratic equationIn this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.
The two forms are introduced below:
Standard form
y = a · x² + b · x + c
Where a, b, c are real coefficients.
Vertex form
y - k = C · (x - h)²
Where:
C - Vertex constant(h, k) - Vertex coordinates.Now we proceed to determine the vertex form of each quadratic equation:
Case 9
y = 2 · x² + 4 · x - 4
y = 2 · (x² + 2 · x - 2)
y = 2 · (x² + 2 · x + 4) - 12
y = 2 · (x + 2)² - 12
Case 10
y = - (1 / 2) · x² - 3 · x + 3
y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]
y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)
y = - (1 / 2) · (x + 3 / 4)² + 33 / 32
Case 11
y = 3 · x² - 8 · x
y = 3 · [x² - (8 / 3) · x]
y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)
y = 3 · (x - 4 / 3)² - 16 / 3
Case 12
y = - 3 · x² + 18 · x - 27
y = - 3 · (x² - 6 · x + 9)
y = - 3 · (x - 3)²
Case 13
y = x² - 8 · x + 19
y = (x² - 8 · x + 16) + 3
y = (x - 4)² + 3
Case 14
y = x² - 2 · x - 6
y = (x² - 2 · x + 1) - 7
y = (x - 1)² - 7
Case 15
y = x² + 3 · x
y = (x² + 3 · x + 9 / 4) - 9 / 4
y = (x + 3 / 2)² - 9 / 4
Case 16
y = 2 · x² + x
y = 2 · [x² + (1 / 2) · x]
y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)
y = 2 · (x + 1 / 4)² - 1 / 8
Case 17
y = 2 · x² - 12 · x + 11
y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)
y = 2 · (x - 3)² - 7
Case 18
y = - 2 · x² - 4 · x + 8
y = - 2 · (x² + 2 · x - 4)
y = - 2 · (x² + 2 · x + 1) + 2 · 5
y = - 2 · (x + 1)² + 10
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Use the following results from a test for marijuana use, which is provided by a certain drug testing company. Among 145 subjects with positive test results, there are 21 false positive results; among 156 negative results, there are 4 false negative results. If one of the test subjects is randomly selected, find the probability that the subject tested negative or did not use marijuana. (Hint: Construct a table.)
Question content area bottom
Part 1
The probability that a randomly selected subject tested negative or did not use marijuana is enter your response here.
(Do not round until the final answer. Then round to three decimal places as needed.)
Answer:
The probability that a randomly selected subject tested negative or did not use marijuana is 0.589.
Step-by-step explanation:
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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What is the value of the expression below? 34 - 9 x 2
The value of the expression 34 - 9 x 2 is 16.
What is the order of operations?The order of operations is a set of rules that dictate the order in which mathematical operations should be performed in an expression. These rules help to ensure that mathematical expressions are evaluated correctly and consistently. The order of operations is typically summarized by the acronym PEMDAS, which stands for:
Parentheses: Perform operations inside parentheses first.
Exponents: Evaluate exponents (powers and square roots, etc.) next.
Multiplication and Division: Perform multiplication and division, from left to right.
Addition and Subtraction: Perform addition and subtraction, from left to right.
In the given questions,
In this case, there are no parentheses or exponents, so we move on to multiplication before subtraction.
We perform the multiplication first, following the rule of performing multiplication before addition or subtraction.
9 x 2 = 18
Then, we subtract the result from 34:
34 - 18 = 16
Therefore, the value of the expression 34 - 9 x 2 is 16.
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Oliver spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 6900 feet.
Oliver initially measures an angle of elevation of 16° to the plane at point A. At some
later time, he measures an angle of elevation of 27° to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest tenth of a foot if necessary.
The distance the plane traveled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).
What are angles?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 they are used to describe the amount of rotation or turning between two lines or planes. In a two-dimensional plane, angles are usually measured as the amount of rotation required to move one line or plane to coincide with the other line or plane.
Let's first draw a diagram to visualize the problem:
/ |
/ |
/ |P (plane)
/ |
/ |
/ | h = 6900 ft
/
/ θ2. |
/ |
/ |
B ___/θ1__ _|___ A
d
We need to find the distance the plane traveled from point A to point B, which we'll call d. We can use trigonometry to solve for d.
From point A, we have an angle of elevation of 16° to the plane. This means that the angle between the horizontal and the line from point A to the plane is 90° - 16° = 74°. Similarly, from point B, we have an angle of elevation of 27° to the plane, so the angle between the horizontal and the line from point B to the plane is 90° - 27° = 63°.
Let's use the tangent function to solve for d:
x = h / tan(74°) = 19906.5 ft
d - x = h / tan(63°) = 23205.2 ft
So,
d = x + h / tan(63°) ≈ 43111.7 ft ≈ 8.15 miles.
Therefore, the distance the plane travelled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).
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which expression is equivalent to the following 3( 8x - 2y + 7 )
Answer:
24x - 6y + 21
Step-by-step explanation:
3( 8x - 2y + 7 )
Multiply each term in the bracket by 3
= (3 x 8x) - ( 3 x 2y) + (3 x 7)
= 24x - 6y + 21
pls help me with this
Therefore , the solution of the given problem of unitary method comes out to be rectangle's size is 7/12 square inches.
An unitary method is what ?The objective can be accomplished by using what was variable previously clearly discovered, by utilizing this universal convenience, or by incorporating all essential components from previous flexible study that used a specific strategy. If the anticipated claim outcome actually occurs, it will be feasible to get in touch with the entity once more; if it isn't, both crucial systems will undoubtedly miss the statement.
Here,
=> A = L x W,
where A is the area, L is the length, and W is the breadth, is the formula for calculating the area of a rectangle.
Inputting the numbers provided yields:
=> A = (7/4) x (1/3)
These fractions can be made simpler by eliminating any shared variables in the numerator and denominator before being multiplied. Since 7 and 3 are both prime integers in this instance, there are no shared factors to cancel.
The new numerator and denominator can then be obtained by multiplying the numerators and denominators, respectively. Thus, we get:
=> A = (7 x 1) / (4 x 3)
When we multiply the numerator by the remainder, we obtain:
=> A = 7/12
The rectangle's size is 7/12 square inches as a result.
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A standard die is rolled. Find the probability that the number rolled is greater than 3
. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Rolling a number higher than 3 has a 2/6 or 1/3 chance of happening. Another way to say this is to round a decimal to the closest millionth, which is [tex]0.333333[/tex] .
What is the fraction in the lowest terms?A standard die has 6 sides, labelled with the numbers 1 through 6. When the die is rolled, each side has an equal probability of landing face up.
Since we want to find the probability of rolling a number greater than 3, we need to determine the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.
When you roll a standard die, there are six equally likely outcomes: 1, 2, 3, 4, 5, and 6. Since we want to find the probability of rolling a number greater than 3, we need to count how many of these outcomes satisfy that condition.
Therefore, the probability of rolling a number greater than 3 is 2/6 or 1/3. Alternatively, we could express this as a decimal rounded to the nearest millionth, which would be [tex]0.333333[/tex] .
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The vertices of figure PQRS are translated to form figure P'Q'R'S'. Select all the statements that describe the two figures. Q S R P' S' Q' 'R
the anawer choices are : A. P Q R S is the preimage of PQRS, B. the two figures are congruent, C. the two figures are in different positions , but have the same orientation, D. the two figures are in different positions and have oppsoite orientation , E. corresponding angles and sides of the figures have the same measures.
The true statements are:
(B) Both figures are congurent.
(C) The two figures have the same orientation but different positions.
(E) Corresponding angles and sides have the same measures.
What is orientation?In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.
It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.
To get to the current positioning, a rotation might not be sufficient.
It could be required to include a fictitious translation known as the object's location (or position, or linear position).
Together, the position and orientation completely explain where the object is situated in space.
Therefore, the true statements are:
(B) Both figures are congurent.
(C) The two figures have the same orientation but different positions.
(E) Corresponding angles and sides have the same measures.
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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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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]
Limt x tend to π 1-sinx/2(π-x) ²
The value of the limit of the expression Limit x tend to π 1-sinx/2(π-x) ² is infinity (∝)
How to evaluate the limit of the expressionGiven that
Limit x tend to π 1-sinx/2(π-x) ²
To solve this expression, we make use of
If limit of x to a+ of f(x) = limit of x to a- = L, then limit of x to a+ of f(x) = L
The interpretation is that we solve the expression by direct substitution
So, we have
Limit = 1 - sin(π)/2(π - π) ²
Evaluate the difference
Limit = 1 - sin(π)/2(0)²
Evaluate the exponent and the bracket
Limit = 1 - sin(π)/0
Divide
Limit = ∝
Hence, the limit of the expression is ∝
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