The length of the given rectangular field is 120 yd while the width is 70 yd.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Let's say the length of a rectangle is L while the width is W
So,
Perimeter 2(L + W) = 380
And,
L = W + 50
By substitution,
W + 50 + W = 190
2W + 50 = 190
2W = 140
W = 70
And
L = 70 + 50 = 120
Hence "The length of the given rectangular field is 120 yd while the width is 70 yd.
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Interest of $1,632 with principal of $16,000 for 306 days(ordinary interest) results in a rate of
A pair of parallel lines is cut by a transversal:
A pair of parallel lines is cut by a transversal. The interior angle made on the left by the intersection of the upper parallel line and the transversal is divided into 2 parts by a slanting line. One part of this angle is labeled as x, and the other part is labeled as 30 degrees. The interior angle made on the right by the intersection of the lower parallel line and the transversal is labeled as 75 degrees.
What is the measure of angle x?
Answer:
x = 45°
Step-by-step explanation:
It a transversal line intersect two parallel lines, then alternative interior angles are congruent.
From the below graph it is clear that the line m and n are two parallel lines and l is a transversal line.
[tex]\angle ABC\cong \angle BCD[/tex] (Alternative interior angles)
[tex]m\angle ABC=m\angle BCD[/tex] (Definition of congruent angles)
[tex]x+30^{\circ}=75^{\circ}[/tex]
Subtract 30° from both sides.
[tex]x+30^{\circ}-30^{\circ}=75^{\circ}-30^{\circ}[/tex]
[tex]x=45^{\circ}[/tex]
Therefore the measure of angle x is 45°.
Which equation represents a linear function? A) y – 2 = –5(x – 2) B) x + 7 = –4(x + 8) C) y – 3 = y(x + 4) D) y + 9 = x(x – 1)
i believe its the option A
The answer because I don’t know it
Brooke bought all seven members of her family a chocolate bar at the chocolate factory in Hershey, Pennsylvania. Each chocolate bar was .8 ounces. How many ounces of chocolate did Brooke buy?
A single 6-sided die is rolled twice. find the probability of getting a 55 the first time and a 11 the second time. express the probability as a simplified fraction.
24 loaves of bread cost 48 dollars how much does 10 loaves cost?
How are the variables on the graph related?
Answer choices:
A. As speed decreases, height stays constant.
B. As speed decreases, height increases.
C. As speed increases, height decreases.
D. As speed increases, height increases.
During the summer months, the prices of nonsmoking rooms with a king-sized bed in hotels in a certain area are roughly normally distributed with a mean of $131.80 and a standard deviation of $29.12. a travel agent randomly selects prices of nonsmoking rooms with a king-sized bed from 15 hotels in the area. what is the probability that their average cost will be more than $150
the probability that the average cost of nonsmoking rooms with a king-sized bed from 15 hotels in the area will be more than $150 is approximately 0.0081, or 0.81%.
To find the probability that the average cost of nonsmoking rooms with a king-sized bed from 15 hotels will be more than $150, we can use the Central Limit Theorem. Here's how:
1. Calculate the standard error of the mean (SEM) which is the standard deviation of the sample mean:
SEM = standard deviation / sqrt(sample size)
SEM = $29.12 / sqrt(15) ≈ $7.52
2. Calculate the z-score for a mean of $150:
z = (sample mean - population mean) / SEM
z = ($150 - $131.80) / $7.52 ≈ 2.41
3. Look up the z-score in the standard normal distribution table to find the probability associated with this z-score. The area to the right of a z-score of 2.41 gives us the probability that the average cost will be more than $150.
4. From the standard normal distribution table, a z-score of 2.41 corresponds to a probability of approximately 0.0081.
Therefore, the probability that the average cost of nonsmoking rooms with a king-sized bed from 15 hotels in the area will be more than $150 is approximately 0.0081, or 0.81%.
Ella has 50 stacks of ten pennies in each stack. Describe how to find how many pennies ella has in all
What is 5 to the power of 2 +2 [73-(4x5)]
Answer:
[tex]5^2+2[73-(4\times 5)]=131[/tex]
Step-by-step explanation:
Given : Expression [tex]5^2+2[73-(4\times 5)][/tex]
To find : What is the solution of the expression ?
Solution :
Expression [tex]5^2+2[73-(4\times 5)][/tex]
Applying BODMAS,
We multiply the term,
[tex]=5^2+2[73-(20)][/tex]
Solve the bracket by subtraction,
[tex]=5^2+2[53][/tex]
Open the bracket and solve quadratic,
[tex]=25+106[/tex]
Add the terms,
[tex]=131[/tex]
Therefore, [tex]5^2+2[73-(4\times 5)]=131[/tex]
clay is reading a map to decide his vacation route. The map has a scale of 1cm equals 18miles. If he estimates the length of his vacation route on a map is 14 centimeters what is the length in miles
Using the map scale of 1cm equals 18 miles, the actual length of Clay's vacation route is calculated as 252 miles by multiplying 14 centimeters (the length on the map) by 18 miles (the scale conversion factor).
Clay is using a map scale to plan his vacation route. The scale of the map is given as 1cm equals 18 miles. To calculate the actual length of Clay's vacation route in miles, we can set up a simple proportion. Since 1cm on the map represents 18 miles in reality, we multiply the length on the map, which is 14 centimeters, by 18 to find out how many miles this length represents:
Length in miles = 14 cm * 18 miles/cm
After performing the multiplication, we get:
Length in miles = 252 miles
Therefore, Clay’s vacation route is 252 miles long according to the map's scale.
a cereal box contains 15 3/4 ounces of cereal. If a bowl holds 2 2/5 ounces of cereal how many bowls are in 1 box
Tom received a coupon in the mail for 30%off one regular priced item for a local sporting goods store He wishes tp purchase a soccer ball for 22.50 and shin guards for 17.00 which item would he use his coupon justify your answer by comparing the discount taken for each item
it should be used on the higher priced item to get a bigger discount.
So it should be used on the soccer ball
soccer ball: 22.50 * 0.30 = 6.75 discount
shin guards: 17.00 * 0.30 = 5.10 discount
6.75 is greater than 5.10
Medical researcher estimates that .00004 of the population has a rare blood disorder. if the researcher randomly selects 100,000 people from the population? appendix a statistical tables (round your answers to 4 decimal places.)
a. what is the probability that seven or more people will have the rare blood disorder?
To solve this problem, we make use of the binomial probability equation.
P = [n! / (n – r)! r!] p^r * q^(n – r)
where,
n is the total number of sample = 100,000
r is the number of people with rare blood disorder = 7 or more
p is success of having a disorder = 0.00004
q is 1- p = 0.99996
But since it is easier to solve for the sum of probabilities with 0 to 6 disorder then deduct it from 1.
So,
=> at r = 0
P (r = 0) = [100,000! / (100,000 – 0)! 0!] (0.00004)^0 * (0.99996)^(100,000 – 0)
P (r = 0) = 0.01831
=> at r = 1
P (r = 1) = [100,000! / (100,000 – 1)! 1!] (0.00004)^1 * (0.99996)^(100,000 – 1)
P (r = 1) = 0.07326
=> at r = 2
P (r = 2) = [100,000! / (100,000 – 2)! 2!] (0.00004)^2 * (0.99996)^(100,000 – 2)
P (r = 2) = 0.14652
=> at r = 3
P (r = 3) = [100,000! / (100,000 – 3)! 3!] (0.00004)^3 * (0.99996)^(100,000 – 3)
P (r = 3) = 0.19537
=> at r = 4
P (r = 4) = [100,000! / (100,000 – 4)! 4!] (0.00004)^4 * (0.99996)^(100,000 – 4)
P (r = 4) = 0.19537
=> at r = 5
P (r = 5) = [100,000! / (100,000 – 5)! 5!] (0.00004)^5 * (0.99996)^(100,000 – 5)
P (r = 5) = 0.15630
=> at r = 6
P (r = 6) = [100,000! / (100,000 – 6)! 6!] (0.00004)^6 * (0.99996)^(100,000 – 6)
P (r = 6) = 0.10420
So the total P is:
P (r = 0 to 6) = 0.01831 + 0.07326 + 0.14652 + 0.19537 + 0.19537 + 0.15630 + 0.10420
P (r = 0 to 6) = 0.88933
=> So the probability that 7 or more people will have the disease is:
P (r ≥ 7) = 1 - 0.88933
P (r ≥ 7) = 0.11067 = 11.067%
There is only 0.11067 or 11.067% probability that 7 or more will have the disorder.
To solve this problem, we can use the binomial probability formula. The probability of exactly x successes in n trials is given by the formula. In this case, the probability of success (p) is 0.00004, and the total number of trials (n) is 100,000. To find the probability that seven or more people will have the rare blood disorder, we need to calculate the sum of the probabilities for x = 7, 8, 9, ..., 100,000.
Explanation:To solve this problem, we can use the binomial probability formula. The probability of exactly x successes in n trials is given by the formula:
P(x) = C(n, x) * p^x * (1 - p)^(n - x)
where:
P(x) is the probability of x successes
C(n, x) is the number of combinations of n trials and x successes
p is the probability of success in a single trial
n is the total number of trials
In this case, the probability of success (p) is 0.00004, and the total number of trials (n) is 100,000.
To find the probability that seven or more people will have the rare blood disorder, we need to calculate the sum of the probabilities for x = 7, 8, 9, ..., 100,000. This can be done using the binomial probability formula or statistical tables.
work out the value of: xy + 5 when x = 2 and y = -3
rewrite 8/9 with a denominator of 63
Final answer:
To rewrite the fraction 8/9 with a denominator of 63, multiply both the numerator and denominator by 7 to get 56/63.
Explanation:
To rewrite 8/9 with a denominator of 63, you need to find a number that you can multiply both the numerator (8) and the denominator (9) of the original fraction by, so that the denominator becomes 63. To do this, divide 63 by the original denominator, 9, which gives you 7. Thus, the number you need to multiply by is 7.
Multiply both the numerator and the denominator by 7:
Numerator: 8 times 7 = 56
Denominator: 9 times 7 = 63
Therefore, the fraction 8/9 with a denominator of 63 is 56/63.
Find the largest odd number that divides the product of 16*24*60 evenly
Find the tangent plane to z 2 = x 3 + 2xy + y 3 at x, y = 1, 1.
he ratio of girls to boys in Liza’s classroom is 55 to 44. How many girls are in her classroom if there is a total of 2727 students?
looks like the numbers doubles in the problem
shouldn't it be 5 girls to 4 boys in a class total of 27??
5+4 =9
27/9=3
5*3 = 15
there are 15 girls in class
For every 6 hotdogs sold at the malt shop there are 7 hamburgers sold.What is the ratio of hotdogs sold to hamburgers sold?
A total of 29,183 votes were casted I’m an election. The winning candidate in the election received 61.3% of the votes. Which of the following is closest to the number of votes received by the winning candidate
Write ratio in simplest form
6:3/5
If a project is handed in late you receive 8/9 of your earned points. You received 72 points on your late project. How many points did you lose
In this situation, because the project was handed in late, you lost a total of 9 points. The full score was 81, and you got 72 after a deduction.
Explanation:The principal in this problem is understanding proportion. Given that handing in a project late results in receiving 8/9, or approximately 88.88%, of the total points, we'll figure out the total possible score by dividing the received points (72) by the portion of the full score you got for handing in the project late, which is 8/9. So, 72 ÷ 8/9 = 81. This would be the original points you could have received. You can then subtract the received points (72) from the original points (81) to ascertain the number of points lost. Therefore, 81 - 72 = 9. Consequently, you lost 9 points because the project was handed in late.
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Find the opposite of −8c3−10c2+6c+5
Final answer:
To find the opposite of the expression [tex]-8c^3-10c^2+6c+5[/tex], change the sign of each term to get [tex]8c^3+10c^2-6c-5.[/tex].
Explanation:
The opposite of any algebraic expression is found by changing the sign of each term within the expression. To find the opposite of the expression [tex]-8c^3-10c^2+6c+5[/tex], simply change the signs of each term:
The opposite of −[tex]8c^3[/tex] is [tex]8c^3[/tex]The opposite of −10[tex]c^2[/tex] is +10[tex]c^2[/tex]The opposite of +6c is −6cThe opposite of +5 is −5Putting it all together, the opposite of the expression [tex]-8c^3-10c^2+6c+5[/tex] is [tex]8c^3+10c^2-6c-5.[/tex]
In essence, each term in the original expression is multiplied by -1 to obtain its opposite. This operation changes all positive terms to negative and all negative terms to positive.
The concept of taking the opposite is fundamental in algebra and is often used in simplifying expressions, solving equations, and manipulating mathematical statements.
Given the functions f(x) = −2x − 1 and g(x) = −3x + 4, which operation results in the smallest coefficient on the x term?
The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 square feet. Let y represent the number of square yards and x the number of square feet. Then y varies directly with x. What is the constant of variation? What is the equation representing the direct variation?
Answer:
Part 1) The constant of variation is [tex]k=1/9[/tex]
part 2) The equation is [tex]y=\frac{1}{9}x[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
Let
x -----> the number of square feet
y -----> the number of square yards
Three square yards are equivalent to 27 square feet
so
we have the point (27,3)
Part 1) What is the constant of variation?
The constant of variation or proportionality is equal to
[tex]k=y/x[/tex]
substitute the values
[tex]k=3/27[/tex]
Simplify
[tex]k=1/9[/tex]
Part 2) What is the equation representing the direct variation?
we know that
[tex]y=kx[/tex]
substitute the value of k
[tex]y=\frac{1}{9}x[/tex]
This equation shows that the number of square yards (y) is directly proportional to the number of square feet (x) with a constant of variation equal to 1/9.
In direct variation, the relationship between two variables can be represented by the formula:
y = kx
Where:
- y represents one variable (in this case, the number of square yards).
- x represents the other variable (in this case, the number of square feet).
- k is the constant of variation, which remains the same for all data points in the direct variation.
In this specific case, you've mentioned that 3 square yards are equivalent to 27 square feet. You can use this information to find the constant of variation (k). You can choose one of the data points to solve for k. Let's use the point (3, 27):
3 = k * 27
Now, solve for k:
k = 3 / 27
k = 1 / 9
So, the constant of variation (k) is 1/9. The equation representing the direct variation is:
y = (1/9)x
This equation shows that the number of square yards (y) is directly proportional to the number of square feet (x) with a constant of variation equal to 1/9.
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a monkeys heart beat beats about 576 times in 3 minutes how many times does a minkeys heart beat in 1 minute
Alex buys 24 apples from the supermarket. When he gets home, he finds that 6 apples are bad. What percentage of the apples are bad? Round your answer to the nearest number
Complete the comparison: 5 + 4 = ?
A. 5 − 4
B. 10 + 0
C. 9 + 1
D. 14 − 5