parallelogram has sides of lengths 35 inches and 75 inches. One angle has measure of140°. Find the length of each diagonal.
The length of diagonal of a parallelogram is 2546 inches.
What is a parallelogram?A quadrilateral with equal pairs of opposing sides and angles is referred to as a parallelogram. It has a pair of opposing sides that are parallel to one another. The inner angles are supplementary in nature, meaning that the sum of them equals 180 degrees. A parallelogram's diagonals are bisected by one another, or divided into two equal portions. A parallelogram's internal angles add up to 360 degrees.
The diagonals of parallelogram are given by:
x = √(a^2 + b^2 – 2ab cos A) = √(a^2 + b^2 + 2ab cos B)
Given the two sides are 35 and 75 inches.
We also know that the adjacent angles of parallelogram are supplementary:
∠A + ∠B = 180
140 + ∠B = 180
∠B = 40
Substitute the value of sides and angle in the equation:
x = √(a^2 + b^2 – 2ab cos A) = √(a^2 + b^2 + 2ab cos B)
x = √((35)^2 + (72)^2 + 2(35)(72) cos 140)
x = 1225 + 5184 + (5040)(-0.766)
x = 1225 + 5184 - 3860
x = 2546 inches
Hence, the length of diagonal is 2546 inches.
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three quantities, the results of measurements, are to be added. they are 2.0800, 2.677, and 1.67. what is their sum to the correct number of significant figures?
Sum to the correct number of significant figures is 6.43
Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.
Significant figures are used to establish the number which is presented in the form of digits. These digits carry a meaningful representation of numbers. The term significant digits are also used often instead of figures. We can identify the number of significant digits by counting all the values starting from the 1st non-zero digit located on the left. For example, 12.45 has four significant digits.
Since the least precise measurement 1.67 is correct to only two decimal place.
2.0800
+ 2.677
+ 1.67
6.427
Therefore, the final result should be rounded off to 6.43 where Significant Figures: 3, Decimals: 2.
The arithmetic addition of given numbers to the correct number of significant figures is 6.43.
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For the shape below, if side BD = 29 and side AC = 3x - 4, find x.
Answer:
x = 11
Step-by-step explanation:
We know that the answer we will get will be the same as BD because BD and AC are congrudent, meaning that they are exactly equal shape and size. To find 'x' our equation would be: 29 = 3x - 4. To figure this out we just add 29 and 4 which gives us 33 and then divide that by 3 which gives us 11 (our answer)
In bags of Happy Trail Mix, the number of raisins is skewed left with a mean of 33. 6 and a standard deviation of 8. 4, while in bags of a generic trail mix, the number of raisins is skewed right with a mean of 28. 8 and a standard deviation of 12. 7. What is the probability in a sample of 17 randomly selected Happy Trail Mix bags and a sample of 17 randomly selected generic bags that the mean number of raisins in the Happy Trail Mix is more than the mean number of raisins in the generic mix?
The probability that the mean number of raisins in the Happy Trail Mix is more than the mean number of raisins in the generic mix is 9.7%.
To solve this problem, we need to use the central limit theorem, which states that the distribution of the sample means approaches a normal distribution as the sample size increases. With a sample size of 17, we can approximate the distribution of the sample means as normal.
Let's call the mean of the Happy Trail Mix sample x and the mean of the generic mix sample y.
Using the formula for the mean of a normal distribution, we can find the mean of x and y:
μx = μ = 33.6
μy = μ = 28.8
Using the formula for the standard deviation of the sample mean, we can find the standard deviation of x and y:
σx = σ/√n = 8.4/√17 = 2.04
σy = σ/√n = 12.7/√17 = 3.08
Now that we have the mean and standard deviation of x and y, we can use a normal distribution calculator or a z-score table to find the probability that x > y.
The z-score is given by:
z = (x - y - μ)/σ = (33.6 - 28.8)/(√(2.04^2 + 3.08^2)) = 1.30
Using a standard normal table, we find that the probability of a z-score being greater than 1.30 is 0.097, or 9.7%.
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evaluate the function f (x) = -3x + 4 when x = -6
Answer:
x=−3⋅−6+4=x=22
Step-by-step explanation:
A. Sketch a cube and label its side length as 4cm (this will be Cube A).
B. Sketch a cube with sides that are twice as long as Cube A and label its side length (this will be Cube B).
C. Find the volumes of Cube A and Cube B.
Answer:
see attached
Step-by-step explanation:
A towns population is expected to grow between 5% and 8% per year for the next 10yr. if the current population is 50,000, write an inequality for the expected population, p, next year.
Answer: An inequality for the expected population, p, next year can be written using the information provided. Since the population is expected to grow between 5% and 8% per year, we can represent that as a range of growth rates: 0.05 <= growth rate <= 0.08
To find the expected population next year, we can use the formula:
p = population * (1 + growth rate)
where "population" is the current population of 50,000 and "growth rate" is the percentage increase. Since the growth rate is expected to be between 0.05 and 0.08, we can write the inequality as:
50,000 * (1 + 0.05) <= p <= 50,000 * (1 + 0.08)
This inequality represents the expected range of population next year, with the lower bound being the population if it grows by 5% and the upper bound being the population if it grows by 8%.
Simplifying the inequality:
52,500 <= p <= 54,000
So the expected population next year, p, is between 52,500 and 54,000.
Step-by-step explanation:
4 painters that have completed 12 rooms in 8 hours. assuming they are working at the same efficiency, how many hours does it take 7 painters to paint 21 rooms?
Answer: We can use the concept of rates to solve this problem.
A rate is a ratio of the amount of work done to the amount of time it takes to do the work. We can find the rate of work for the 4 painters by dividing the number of rooms they painted by the number of hours it took them:
Rate = Rooms painted / Hours
Rate = 12 rooms / 8 hours = 1.5 rooms per hour
Now we can use this rate to find out how long it will take 7 painters to paint 21 rooms. To do this, we'll use the formula:
Time = Rooms / Rate
Time = 21 rooms / 1.5 rooms per hour = 14 hours
So it would take 7 painters working at the same efficiency as the 4 painters 14 hours to paint 21 rooms.
Step-by-step explanation:
I don’t understand how to do this.
Answer:
6000
Step-by-step explanation:
Interest of 3% a year of principal of 200,000 = 6000
monthly payment of 843 also includes a portion of amortization of the principal itself, which you can ignore cause the question only asked for the interest portion.
this is an unclear question cause it didn't say PER YEAR interest paid. you only need to remember interest% * principal = ANNUAL interest payment $. Then you can divide that over 12 months, which is 500$ per month.
If I Got 7 "(tokens or whatever you prefer) a minute for 9 hours/ 540 minutes, how many tokens would I have
Answer:
If you get 7 tokens a minute and you work for 9 hours, or 540 minutes, then you would have:
7 tokens/minute * 540 minutes = 3780 tokens
You would have 3780 tokens in total.
Answer:
3,780
Step-by-step explanation:
7* 540= 3780
because you get 7 every minute and there are 540 minutes
an automobile manufacturer claims that their car has a 55.7 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this car. after testing 91 cars they found a mean mpg of 55.2 with a variance of 3.24 mpg. is there sufficient evidence at the 0.05 level that the cars underperform the manufacturer's mpg rating? state the null and alternative hypotheses for the above scenario.
For the given case the Null hypothesis is The mean mpg of the 91 cars tested is equal to the manufacturer's mpg rating of 55.7 and the Alternative hypothesis is The mean mpg of the 91 cars tested is less than the manufacturer's mpg rating of 55.7.
In order to determine whether the cars underperform the manufacturer's mpg rating, the independent testing firm would need to perform a hypothesis test. To do this, they would need to compare their sample mean of 55.2 mpg with the manufacturer's mpg rating of 55.7. They would also need to know the standard deviation of the sample, which is 3.24.
The independent testing firm would then calculate the z-score by subtracting the manufacturer's rating from the sample mean, and dividing it by the standard deviation. If the z-score is greater than the critical value for a 0.05 level of significance, then there is sufficient evidence to reject the null hypothesis.
In this case, the z-score is -1.51. Since the critical value for a 0.05 level of significance is 1.96, the z-score is less than the critical value. Therefore, there is not sufficient evidence to reject the null hypothesis, and we cannot conclude that the cars underperform the manufacturer's mpg rating.
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what is WD?
what is AB + DC
what is the perimeter of the trapezoid?
Perimeter (P) = AB + BC + CD + DA.
What is perimeter of trapezoid?The perimeter of a trapezoid is the sum of the lengths of each side of the trapezoid. A trapezoid is a quadrilateral that has two sides parallel to each other and two non-parallel sides termed as bases and legs respectively. Let us learn how to calculate the perimeter of the trapezoid in this article.
perimeter of the trapezoid=sum of 4 side
=AB+BC+CD+DA
Perimeter (P) = AB + BC + CD + DA.
It can also be written as a sum of lengths of parallel sides and the sum of lengths of non-parallel sides where AB and CD are the parallel sides and AD and BC are the non-parallel sides.
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Explain your work please.
Evaluate each expression. Show your thinking 7+2^3
[tex]7+2^3[/tex]
[tex]7+(2^3)[/tex]
[tex]7+8[/tex]
[tex]=\fbox{15}[/tex]
Find the balance in the account after the given period. $2,600 deposit earning 4.2% compounded monthly, after 3 years. The balance after 3 years will be $ (Round to the nearest cent as needed.)
To find the balance of the account after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the initial principal is $2,600, the interest rate is 4.2% (expressed as a decimal), the number of times the interest is compounded per year is 12 (monthly), and the number of years is 3.
So, we can plug these values into the formula:
A = 2600(1 + 0.042/12)^(12*3)
A = 2600(1.0035)^36
A = 2600 * 3.876
A = 10,049.6
The balance of the account after 3 years is $10,049.6.
PLS HELP
What is in decimal form?
16
O 0.3125
O 0.6875
O 1.45
OI don't know.
Answer:
decimal form is limited of 3 numbers after the point only.
so it will be 1.45
I hope I help you in this ans and tq.
rosie says she could solve 24*25 with the arry above. do you agree with her why or why not.
She could only solve 24 * 25 if the array has 24 rows and 25 columns or vice versa
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Product expression = 24 * 25
An array is a set of items that has rows and columns
The array is not given
However, the true statement is that: for Rosie to evaluate the expression using an array, then the array must be a 24 x 25 array or 25 x 24 array
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I need help in this problem
Answer:
b
Step-by-step explanation:
the sum of the 3 angles in the triangle = 180°
sum the 3 angles and equate to 180
2x + 1 + 5x + 5 + 90 = 180
7x + 96 = 180 ( subtract 96 from both sides )
7x = 84 ( divide both sides by 7 )
x = 12
A car travels down the road at a constant speed of 120 meters in 5 seconds. What is the velocity of the car
Answer: 17 m/s
Step-by-step explanation:
on Wednesday evening sonto spent one ½ doing doing homework 45 minutes doing housework 1 hour visiting friends and 1 hour ½ watching television . write information in a ratio
If on Wednesday evening sonto spent one ½ doing doing homework 45 minutes doing housework 1 hour visiting friends and 1 hour ½ watching television .This information in a ratio is: 2: 3 : 4 :6.
How to find the ratio?We need to first analyze the details before determining the ratio.
1 hour = 60 minutes
1/2 h = 30 minutes
1 1/2 = 90 minutes
So,
30 : 45 = 60 :90
Reduce the above minutes to ratio
2: 3 : 4 :6
Therefore the ratio of the information is 2: 3 : 4 :6.
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write the expanded form of the expression
4(3x-5)
4 (3x-5)=
One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation. So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.
How do you write in a more detailed format?One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation.
It is also possible to create a mathematical expression using integers that have been divided into distinct place values and decimal places.
5,000 + 300 + 20 + 5 = 5,325 is the expanded notation for the number.
Expanded form of the given expression.
1) We can expand the given term by the direct formula of the algebra
(A-B)³ = A³-B³-3AB(A-B)2)
We have (3x-5)³on comparing with the formula:
A = 3x
B = 5
(3x-5)³
(3x)³-5³-3×3x×5(3x-5)
27x³-125-45x(3x-5) 27x³-125-135x²+225x
So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.
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mary divides a circle into sectors. the central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. what is the degree measure of the smallest possible sector angle?
The measure of the smallest possible sector angle possible is 8°.
Let [tex]$a_1$[/tex] be the first term of the arithmetic progression and [tex]$a_{12}$[/tex] be the last term of the arithmetic progression.
From the formula of the sum of an arithmetic progression, we have -
[tex]$12*\frac{a_1+a_{12}}{2}=360$[/tex]
simplifying we get,
[tex]$a_1 + a_{12} = 60$[/tex]
[tex]$a_{12}$[/tex] is the largest term of the progression and it can also be expressed as-
[tex]a_{12} = $a_1+11d$[/tex]
where d is a common difference.
Since each angle measure must be an integer, d should also be an integer.
[tex]$a_{12}-a_1=a_1+11d-a_1=11d$[/tex]
Since d is an integer, the difference between the first and last terms, 11d, must be divisible by 11.
Since the total difference should be less than 60, let's start checking multiples of 11 less than 60 for the total difference between [tex]$a_1$[/tex] and [tex]$a_{12}$[/tex].
Let us take the largest multiple because the maximum difference will give us the minimum value of the first term.
If the difference is 55, [tex]$a_1=\frac{60-55}{2}=2.5$[/tex], is not an integer.
If the difference is 44, [tex]$a_1=\frac{60-44}{2}= 8[/tex] . It satisfies the given conditions.
Hence, the measure of the smallest possible sector angle possible = 8°.
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Please anwser this...
Check the picture below.
Question 4(Multiple Choice Worth 2 points)
(Slope MC)
A linear relationship is given in the table.
x −2 −1 0 1 2
y −13 −9 −5 −1 3
What is the slope of the relationship?
one fourth
negative one fourth
4
−4
The slope of the relationship is equal to; C. 4.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be calculated by using this mathematical expression;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
From the information provided above, we have the following data points on the line:
Points on x-axis = (-2, -1).Points on y-axis = (-13, -9).Substituting the given points into the slope formula, we have;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-9 + 13)/(-1 - (-2))
Slope (m) = 4/1
Slope (m) = 4
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How many solutions does the equation 6x + 12 = 2(3x + 6)
Answer: Infinite, or unsolvable
Step-by-step explanation:
6x + 12 = 2(3x+6)
6x + 12 = 6x + 12 <-- opening up the bracket
Because both sides of the equation are the same, the answer is either that there are an infinite amount of solutions for x, or that the equation is unsolvable.
Does 4x - 8 = 3x +13 have one solution, no solution or infinite solutions
Answer:
only one solution
Step-by-step explanation:
4x - 8 = 3x + 13
x = 21
Hey there!
Given:
[tex]4x-8=3x+13[/tex]
Solution(s):
One Solution; [tex]x=21[/tex]
Hope this helps!
help pls and thanks
An equation of a circle which represents the picture include the following: A. (x)² + (y)² = 25.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.From the information provided above, we have the following points on this circle:
P(–5, 0)Q(0, 5)R(5, 0)S(0, –5).Radius of the circle (r) = 5 units.Center of the circle (h, k) = (0, 0)Substituting the given points into the equation of a circle, we have the following;
(x - 0)² + (y - 0)² = 5²
(x)² + (y)² = 25.
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To describe a sequence of transformation that maps triangle ABC onto triangle a”b”c” a student starts with a reflection over x-axis
We can write the coordinates after reflection as -
A (x₁, y₁) → A" (x₁, - y₁)
B (x₂, y₂) → B" (x₂, - y₂)
C (x₃, y₃) → C" (x₃, - y₃)
What is reflection of graph?Reflections of graphs involve reflecting a graph over a specific line.Reflecting functions are functions whose graphs are reflections of each other.Given is that to describe a sequence of transformation that maps triangle ΔABC onto triangle ΔA”B”C” a student starts with a reflection over x - axis.
Assume the coordinates of a triangle are -
A (x₁, y₁)
B (x₂, y₂)
C (x₃, y₃)
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.The reflection of point (x, y) across the x-axis is (x, -y).
So after the reflection over the {x} axis, we can write the coordinates as -
A" (x₁, - y₁)
B" (x₂, - y₂)
C" (x₃, - y₃)
Therefore, we can write the coordinates after reflection as -
A (x₁, y₁) → A" (x₁, - y₁)
B (x₂, y₂) → B" (x₂, - y₂)
C (x₃, y₃) → C" (x₃, - y₃)
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Sal received an 8% raise. He now earns $66960. How much did he earn previously? Hint: number only, no symbols, no units
Answer:
Sal previously earned $61640.
Answer:
$62,000.00
Step-by-step explanation:
x + .08x = 66960 Combine like terms
1.08 x = 66960 Divide both sides by 1.08
[tex]\frac{1.08x}{1.08}[/tex] = [tex]\frac{66960}{1.08}[/tex]
x = 62000
Decide whether triangles ABC and DEC are similar. Explain or show your reasoning.
Answer:
AAA similarity
Step-by-step explanation:
Similar triangles:In ΔECD,
∠E + ∠D + ∠ECD = 180° {Angle sum property}
∠E + 36 + 123 = 180°
∠E + 159 = 180
∠E = 180 - 159
∠E = 21°
In ΔACB,
∠A + ∠B + ∠ACB = 180° {Angle sum property}
∠ACB + 36 + 21 = 180°
∠ACB + 57 = 180
∠ACB = 180 - 57
∠ACB= 123°
In ΔECD & ΔBCA,
∠A ≅ ∠D
∠B ≅ ∠A
∠BCA ≅ ∠ECA
ΔECD ~ ΔBCA by Angle Angle Angle similarity.