The distance between the foot of the ladder from the bottom of the wall is 40 meters.
What is the Pythagorean theorem?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Here,
The distance between the foot of the ladder from the bottom of the wall can be found by using the Pythagorean theorem.
The ladder is the hypotenuse, with a length of 50m
The distance from the wall to the ground is 30m
The distance from the wall to the foot of the ladder is x
Using the Pythagorean theorem:
x² + 30² = 50²
x² + 900 = 2500
x² = 1600
x = 40
So, the distance between the foot of the ladder from the bottom of the wall is 40 meters.
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A large cheese pizza costs
$
18
$18dollar sign, 18. Each topping you add on costs
$
1.50 dollar sign, 1, point, 50.
How much would it cost to get a large cheese pizza with
cc toppings added?
Write your answer as an expression.
Answer:
A
=
1.50c + 18
where
A
is amount and
c
is toppings added
Step-by-step explanation:
The constant price is
18
dollars, which never changes and for every topping you get, it costs
$
1.50
. If you got no toppings, sub in
0
for
c
to get
$
18
.
Simplifying algebraic radicals. 14 sqrt 320
7. A polygon has vertices at F(-5, 2), G(-3, 2), H(-3, 4), J(1, 4), K(1, 1), L(4, 1), M(4, -2), N(6, -2), P(6, -3), and Q(-5, -3). Graph the figure on the coordinate plane. Then find the area and perimeter of the figure.
The area of the figure is 52 square units
The perimeter of the figure is 36 units
The graph is attached
How to the perimeterThe perimeter of the figure is found by summing the length of the sides
F(-5, 2) - G(-3, 2) = 2 units
G(-3, 2) - H(-3, 4) = 2 units
H(-3, 4) - J(1, 4) = 4 units
J(1, 4) - K(1, 1) = 2 units
K(1, 1) - L(4, 1) = 3 units
L(4, 1) - M(4, -2) = 3 units
M(4, -2) - N(6, -2) = 2 units
N(6, -2) - P(6, -3) = 1 units
P(6, -3) - Q(-5, -3) = 11 units
Q(-5, -3) - F(-5, 2) = 5 units
The perimeter = 2 + 2 + 4 + 2 + 3 + 3 + 2 + 1 + 11 + 5 = 36 units
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Work out the area of the shaded semicircle shown below.
If your answer is a decimal, give it to 2 d.p.
1.68
Step-by-step explanation:
the area of a circle is
pi×r²
r being the radius (1.68 m).
the area of half a circle is therefore
pi×r²/2
in our case
pi× 1.68²/2 = pi× 2.8224/2 = pi×1.4112 =
= 4.433415553... m² ≈ 4.43 m²
The area of the shaded semicircle is 1.11 meters squared.
What is area of shape?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed shape, two-dimensional .
The area of shape is the space enclosed within the perimeter or the boundary of a given shape.
The area of a circle is expressed as ;
A = π[tex]r^{2}[/tex]
where r is the radius of the circle.
Therefore the area of a semi circle will be :
A = 1/2 π[tex]r^{2}[/tex]
r = d/2
r = 1.68/2 =0.84
A = 1/2 × 3.14 × 0.84 ×0.84
= 1.11 meter squared.
Therefore the area of the shaded semi circle is 1.11 meters squared.
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what is the probability that the sample mean annual insurance cost is greater than $620? show your work.
The probability of the sample mean annual insurance cost being greater than $620 is very low, that is 0.00317% which indicating that it is unlikely to happen by chance.
Probability is a branch of mathematics that deals with the likelihood of an event happening. It is used in various fields, such as insurance, finance, and science.
To calculate the probability, we need to use the central limit theorem, which states that the distribution of sample means of a population approaches a normal distribution as the sample size increases. We also need to know the mean and standard deviation of the population.
Assuming that the population is normally distributed, we can use the following formula to calculate the probability:
z = (x - μ) / (σ / √(n))
where z is the z-score, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, we don't know the population mean and standard deviation, but we can use the sample mean and standard deviation as estimates. Let's say we have a sample of 100 insurance costs with a mean of $600 and a standard deviation of $50.
Now, we can calculate the z-score:
z = (620 - 600) / (50 / √(100)) = 4
The z-score of 4 indicates that the sample mean of $620 is 4 standard deviations away from the mean of $600. We can use a standard normal distribution table or a calculator to find the probability of getting a z-score of 4 or higher. The probability is very small, approximately 0.0000317 or 0.00317%.
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12. Natalie is using one box to ship 10 books to a friend. Each book weighs 810 grams. The box weighs 250 grams. Shipping costs $3. 50 per kilogram. How much will it cost Natalie to ship the books?
The cost to ship a box of 250 grams, with 10 books of weight of 8.5kg by natalie is $ 29.75.
The total weight of the books and the box is:
10 books × 810 grams/book + 250 grams = 8,250 grams + 250 grams = 8,500 grams
To convert this to kilograms, we divide by 1000:
8,500 grams ÷ 1000 = 8.5 kg
The cost of shipping will be based on the weight, so we can multiply the weight in kilograms by the shipping cost per kilogram:
8.5 kg × $3.50/kg = $29.75
Therefore, it will cost Natalie $29.75 to ship the books of 8.5 kg
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3²ˣ -3ˣ⁺² = 3ˣ⁺¹ - 3³.
A second hand car dealer bought a car for R85 000. The costs related to the transaction amount R250. He sells the car for R93 000. Calculate the profit he made on the deal
The profit made on the transaction by the dealer was Rs. 7,750.
To calculate the profit made by the second hand car dealer, you can subtract the cost of buying the car and the transaction costs from the selling price.
Profit = Selling Price - Cost of Car - Transaction Costs
Profit = 93,000 - 85,000 - 250
Profit = 7,750
So the dealer made a profit of Rs. 7,750 on the transaction.
Profit and Loss (P&L) is a statement that summarizes a company's revenues and expenses over a specific period of time, typically a quarter or a year. The purpose of a P&L statement is to show a company's ability to generate revenue, as well as the cost of doing so. The difference between a company's total revenue and total expenses is referred to as net profit or net loss
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Use synthetic division to find the quotient and remainder when x³ + 9x² + 12x - 5 is divided by x+7 by completing the parts below.
(a) Complete this synthetic division table.
-7)
19 12 -5
000
OOOO
(b) Write your answer in the following form: Quotient +
3
x³ + 9x² +
+ 9x + 12x-5
x+7
=
x+7
Remainder
x+7
X
The division can be written as: x³ + 9x² + 12x - 5 = (x + 7)(x² + 7x + 10) - 75
What is synthetic division ?
Synthetic division is a simplified method of polynomial division that can be used to divide a polynomial by a linear binomial. It's used to find the quotient and remainder of a polynomial division without having to perform long division.
In synthetic division, the coefficients of the polynomial are arranged in a table along with the coefficients of the divisor, and then divided and multiplied using the same rules as in long division. The remainder of the division is the last entry in the table, and the quotient is the polynomial whose coefficients are the entries in the table, excluding the remainder.
To perform synthetic division, we divide x³ + 9x² + 12x - 5 by x + 7 by dividing each coefficient by x + 7 and then writing the result in a table with the dividend on top and the divisor on the bottom. Here's what the table would look like:
+ 7 | 1 9 12 -5
-------------------
x^3 | x^3 9 12 -5
x^2 | x^2 +7x 3 -35
x | x +7 10 -70
-------------------
10 43 -75
The quotient of the division is x² + 7x + 10, and the remainder is -75.
Therefore, the division can be written as: x³ + 9x² + 12x - 5 = (x + 7)(x² + 7x + 10) - 75
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Diane obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 9.65%. Her loan is for $17,100 for 76 days. Assume
1
365
De not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
each day is
of a year Answer each part below.
(a) And the interest that will be owed after 76 days.
$
(b) Assuming Diane doesn't make any payments, find the amount owed after 76 days.
?
I need help fast
a) The simple interest that will be owed the bank by Diane after 76 days is $343.59.
b) The final amount that Diane will repay the bank after 76 days is $17,443.59.
What is the simple interest?The simple interest is an interest system that does not compound interest.
Compounding interest means that interest is added to the principal before subsequent interests are computed.
But under the simple interest system, interest is based on the principal from one period to the next.
The loan amount = $17,100
Simple interest rate = 9.65%
Loan period = 76 days
Total interest = $17,100 x 9.65% x 76/365 = $343.59
Final amount = $17,443.59 ($17,100 + $343.59)
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There are 15000 average passengers on domestic flights daily. 1/20 of the passengers are tourists and 1/15 of the tourists are travel bloggers. How many tourist passengers on domestic flights are travel bloggers
If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are 15000 * (1/20) = 750 tourists daily.
And if 1/15 of the tourists are travel bloggers, then there would be 750 * (1/15) = 50 travel bloggers daily.
If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are
15000 * (1/20) = 750 tourists daily
So, there would be a total of 50 tourist passengers on domestic flights who are travel bloggers.
It is important to note that these are average numbers and the actual number of tourists and travel bloggers on domestic flights can vary from day to day. However, this calculation provides a general idea of the proportion of tourist passengers who are travel bloggers on domestic flights.
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5843 divided by 11 whth remainders
Answer:
Remainder:
Step-by-step explanation:
Step 1: Divide 5843 by 11.
5843/11 = 530.272727
Step 2: Find the quotient.
Quotient = 530
Step 3: Find the remainder.
Remainder = 3
m varies directly as n, and m=14 when n=7
a) write an equation that relates m and n
b) find m when n = 16
c) find n when m = 30
Answer:
see explanation
Step-by-step explanation:
(a)
given m varies directly as n then the equation relating them is
m = kn ← k is the constant of variation
to find k use the condition m = 14 when n = 7
14 = 7k ( divide both sides by 7 )
2 = k
m = 2n ← equation of variation
(b)
when n = 16 , then
m = 2 × 16 = 32
(c)
when m = 30 , then
30 = 2n ( divide both sides by 2 )
15 = n
Harold lives 70 miles due south of his parents' house and 24 miles west of his grandparents' house. On his birthday, Harold drove from his house to his parents' house. From there, he drove in a straight line to his grandparents' house and then back home. How far did Harold drive on his birthday?
Approximately 70 miles separated Harold's home at his grandparents' home from his own home. Accordingly, Harold travelled the following distance overall on his birthday: 70 + 74.46 + 70 ≈ 214.46
How would you define distance in plain English?What is a distance? . Regardless of the start or end point, distance can be defined as the amount of space object has to cover.
How do you gauge a distance?The metre serves as the SI unit of distance (m). Centimeters (cm) are a common unit of measurement for short distances, whereas kilometres (km) are used for longer distances (km). You could measure a piece of paper's length in centimetres, for instance, by measuring from the bottom to the top.
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1. Find the geometric mean of the
two numbers.
4 and 42.25
Answer:
13
Step-by-step explanation:
Secured loans are less costly than unsecured loans because _________.
They usually have a lower interest rate.
They require collateral.
They are less risky for the financial institution.
All of these are true.
Due to the fact that secured loans often have lower interest rates than unsecured loans, they are less expensive. They require collateral. They are less risky for the financial institution. The correct option is D.
What are secured loans?A secured loan is one in which the borrower pledges an asset as security for the loan, turning the pledged asset into a secured debt owing to the lender (the creditor).
Some loans may be backed by assets other than your house; for instance, they may be backed by your automobile, jewelry, or other possessions. Because lenders can collect the asset in the event of a default on a secured loan, secured loans often have lower interest rates than unsecured loans.
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Given f(x)=(1)/(x), explain the how the graph of the nee function g(x)=(1)/(x-3)-5 transforms from the graph of f(x).
The function f(x) is translated 3 units right and 5 units down then the function f(x) is coincident with the function g(x).
What is a function?A function is an assertion, conception, or regulation that establishes a partnership between two variables.
The functions f(x) and g(x) are given below.
f(x) = 1 / x
g(x) = 1 / (x - 3) - 5
Translate the function 3 units right, then replace x with (x - 3). And translate the function 5 units down, then replace f(x) with (g(x) + 5). Then we have
g(x) + 5 = 1 / (x - 3)
g(x) = 1 / (x - 3) - 5
The function f(x) is translated 3 units right and 5 units down then the function f(x) is coincident with the function g(x).
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A cardboard box in the shape of a rectangular prism has the
dimensions shown.
a. Write a polynomial that represents the volume of the box.
b. The volume of the box is 60 cubic inches. What are the
length, width, and height of the box?
On solving the provided question, we can say that Volume of cuboid - L X B X H=> volume = (x+6)*(x-2)*(x-1) => [tex]V = x^3 + 3x^2 - 16x + 12[/tex]
what is cuboid?A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.
The dimensions are:
Length =(x + 6), Width = (x - 2) and Height = (x -1)
Volume of cuboid - L X B X H
volume = (x+6)*(x-2)*(x-1)
[tex]V = (x+6)(x^2 - 3x +2)[/tex]
[tex]V = x^3 - 3x^2 + 2x + 6x^2 - 18x + 12[/tex]
[tex]V = x^3 + 3x^2 - 16x + 12[/tex]
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PLEASE HELP IS DUE TOMORROW:The average American throws away 2.5 pounds of empty cans a month (mostly during the winter months). At this rate, how many years will it take the average American to throw away a ton of empty cans? (Show work please)
1 ton = 2000 pounds
2000/2.5 = 800 months
800/12 = ~66.67 years
Answer:
your answer would be 66.6: do the math: 2.5 a month times 12 months in a year=30. 1 ton =2000 pounds. 2000 divided by 2.5 =800. 800 divided by 12=66.6
Step-by-step explanation:
a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 430 gram setting. it is believed that the machine is underfilling the bags. a 21 bag sample had a mean of 421 grams with a standard deviation of 15 . assume the population is normally distributed. a level of significance of 0.1 will be used. find the p-value of the test statistic. you may write the p-value as a range using interval notation, or as a decimal value rounded to four decimal places.
A manufacturer working at the 430 gram setting, and a 21 bag sample had a mean of 421 grams with a standard deviation of 15. The p-value of test statistic is 0.0074.
To test whether the bag filling machine works correctly at the 430 gram setting, we can conduct a one-sample t-test. The null hypothesis is that the true mean weight of the bags filled by the machine is equal to 430 grams, and the alternative hypothesis is that the true mean weight is less than 430 grams.
The test statistic is calculated as:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Plugging in the values given in the problem, we get:
t = (421 - 430) / (15 / sqrt(21)) = -2.77
The degrees of freedom for the t-distribution are n - 1 = 20.
Using a t-table or calculator, we can find the p-value associated with a t-score of -2.77 and 20 degrees of freedom. The p-value turns out to be 0.0074 (rounded to four decimal places).
Since the p-value is less than the level of significance of 0.1, we can reject the null hypothesis and conclude that the bag filling machine is underfilling the bags at the 430 gram setting.
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Stevens high school has 800 students every Wednesday 3% of the students stay after for chess club how many students attend chess club on Wednesdays
Answer: To find out how many students attend chess club on Wednesdays, we need to calculate 3% of the 800 students at Steven's high school. To do this, we multiply the number of students by 3% (which is equivalent to 0.03):
800 x 0.03 = 24
So, 24 students attend chess club on Wednesdays.
Step-by-step explanation:
Answer:
Step-by-step explanation:
How would you
write the name of a segment differently than the name of a line? What
symbols would you use?
The primary difference between writing the name of a segment and the name of a line is the use of symbols.
What is symbol?A symbol is an object, image, or action that stands for or represents something else. Symbols can be used to convey a wide variety of ideas and concepts, from the literal, such as a heart to represent love, to the abstract, such as a peace sign to represent a call for world peace. Symbols are often used to communicate complex ideas quickly and easily.
To denote a segment, a line is usually written with two arrows pointing in opposite directions, such as ↔. To denote a line, the line is usually written with a single arrow pointing in one direction, such as →.
For example, if you were writing the name of a segment called "AB", then you would use the symbol ↔ AB. If you were writing the name of a line called "AB", then you would use the symbol → AB.
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2x-y=9,4x+y=21
answer this equation for a bloody cookie mate
Answer:
x=5, y=1
Step-by-step explanation:
2x-y=9
2(5)=10
10-1=9
4x+y=21
4(5)=20
20+1=21
Hope this helps! Please give brainliest!
Represent and Connect Lennon has 3,330 toothpicks. He
wants to use them all to make a floor mat with 18 equal
rows. Use the bar diagram to write a division equation.
Then solve the equation to find how many toothpicks
Lennon should use in each row.
The toothpicks lennon should use in each row is 185.
What is Algebra?Algebra is the study of abstract symbols, and logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction also. This approach is used to answer the given problem correctly and completely.
We are given that;
Total number of toothpicks= 3330
Number of rows= 18
Now,
To find the number of toothpicks in each row
=3330/18
=1665/9
=185
Therefore, by algebra the answer will be 185.
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40° rcm Find the value of z. zem This sector of a circle has radius r and perimeter 20 cm. find the value of z
The value of length of z is 5.06 cm.
What is the value of length z?
The value of length of z is calculated by determining the radius of the sector as shown below;
The formula for the perimeter of a sector is given as;
P = 2r + (θ/360) × 2πr
where;
r is the radius of the sector20 cm = 2r + (40/360) x 2πr
20 = 2r + 0.7r
20 = 2.7r
r = 20/2.7
r = 7.4 cm
A perpendicular bisector of 40⁰ will cut line z into two equal parts, the length of half of z is calculated as;
sin (20) = (z/2) / r
r x sin (20) = (z/2)
2r x sin (20) = z
2 x 7.4 cm x sin(20) = z
5.06 cm = z
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5 3/5 + 1/2 = ? what is the answer
Answer:
61/10
Step-by-step explanation:
Convert the mixed number to an improper fraction
28 / 5 + 1 / 2
= 61/10
Answer:
Simplified form: 6 1/10
Improper form: 61/10
Step-by-step explanation:
5 3/5 + 1/2
= 28/5 + 1/2
Then, you multiply both fractions so that the denominator is the same number. In this case, multiply the fraction (numerator and denominator) on the left by 2 and on the right by 5.
= 56/10 + 5/10
This way, you can add the numbers because they have the same denominator.
=61/10
3. a computer password consists of two lowercase letters followed by a capital letter and four digits. find the total number of possible passwords.
The total number of possible passwords is 17,576,000.
There are several steps involved in calculating the total number of possible passwords.
Step 1: Determine the number of possible choices for the first lowercase letter. Since there are 26 letters in the alphabet, and the password consists of lowercase letters, there are 26 choices for the first letter.
Step 2: Determine the number of possible choices for the second lowercase letter. Since there are 26 letters in the alphabet and repetition is allowed, there are 26 choices for the second letter.
Step 3: Determine the number of possible choices for the capital letter. Since the password requires a capital letter, there are 26 choices for this position.
Step 4: Determine the number of possible choices for the first digit. Since there are 10 digits (0-9), there are 10 choices for the first digit.
Step 5: Determine the number of possible choices for the second digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the second digit.
Step 6: Determine the number of possible choices for the third digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the third digit.
Step 7: Determine the number of possible choices for the fourth digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the fourth digit.
Step 8: Multiply the number of choices for each position together to get the total number of possible passwords.
Using the multiplication rule of counting, we get:
Total number of possible passwords = (Number of choices for the first lowercase letter) x (Number of choices for the second lowercase letter) x (Number of choices for the capital letter) x (Number of choices for the first digit) x (Number of choices for the second digit) x (Number of choices for the third digit) x (Number of choices for the fourth digit)
Total number of possible passwords = 26 x 26 x 26 x 10 x 10 x 10 x 10
Total number of possible passwords = 17,576,000
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Compare the slope and length of segment EF with the slope and length of segment AB. What do you notice? What are you wondering?
The slope of segment EF and AB is same but the length of segment EF is half of the length of segment AB.
What is Line segment ?
An unmoving portion of a line is called a line segment. Two points serve as its ends. By the termination points, it is identified.
Let's assume the length of EF to be "x"
from the figure, we can clearly see that AB is made up of two segments which are of same length as EF.
So, we can say that AB = 2 times of the length of EF
i.e. AB = 2 x
Hence, By comparing, we conclude that AB's length is double of EF.
Now, if we look at slope,
Slope of EF = CE/CF
and, Slope of AB = BC/AC
But, we know that AC = 2 CF and BC = 2 CE
So, Slope of EF = CE/CF
and, Slope of AB = 2 CE / 2 CF
= CE/CF.
Hence, Both segments have same slope direction.
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Mr. Stanley owns a farm measuring 24m long and 40m wide. If he wants to plant in squares, what is the largest sized square he can use?
The largest square that Mr. Stanley can use to plant in his farm is a square with a side length of 8 meters.
To find the greatest common factor of 24 and 40, we can list the factors of both numbers and find the highest factor that they have in common:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The highest factor that 24 and 40 have in common is 8.
Factors are numbers that can be multiplied together to get a given number. For example, the factors of 6 are 1, 2, 3, and 6 because 1 x 6 = 6 and 2 x 3 = 6. Factors can be prime or composite. Prime factors are those that are only divisible by 1 and themselves. Composite factors are those that have more than two factors.
Factors are important in math because they can be used to simplify fractions, find common denominators, and solve equations. They also play a crucial role in number theory and cryptography, where they are used to encrypt and decrypt messages. 150 is a composite number, which means it has factors other than 1 and itself. The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. To find these factors, you can divide 150 by each number smaller than it and see if the remainder is 0.
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The box-and-whisker plot below represents some data set. What percentage of the data values are greater than 24?
The percentage of the data values are greater than 24 is 75%.
What is a box-and-whisker plot?A box and whisker plot is a special type of graph that is used to show groups of number data and how they are spread. It shows the median, which is the middle value of the numbers in your data, the lowest number, the highest number and the quartiles, which divides the data into four equal groups.
So as per the given question box-whisker plot represents some data set. There is a number 24 just corresponding to it there is a vertical line which shows that 24 is the first quartile of the data and here 24 is the 75th percentile.
It means that there is 75% values are greater than 24.
Therefore, the percentage of the data values are greater than 24 is 75%.
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