The length of each side of the square can be represented by the equivalent expressions 30x + 80, 10(3x + 8), and 2(15x) + 2(40), with the first expression being in the simplest form and containing only two terms.
The student is provided with an expression for the side length of a square and is asked to write equivalent expressions representing the lengths of the other three sides. Since all four sides of a square are equal, we simply need to simplify the given expression and use it to represent each side. The given expression is 6(3x+8)+32+12x.
First, we can simplify this by distributing and combining like terms:
6(3x+8) becomes 18x + 48
Adding the 32 gives us 18x + 48 + 32
Finally, add the 12x to get 18x + 12x + 48 + 32
Combining like terms results in 30x + 80.
Now we have our simplified expression, which is 30x + 80, to represent the length of each side of the square. For different but equivalent forms:
As two terms: 30x + 80 (this meets the requirement of containing only two terms)
Factored form: 10(3x + 8)
Expanded form by distributing a common factor: 2(15x) + 2(40)
These are three different equivalent expressions we can use to represent the lengths of each side of the square.
the number of painters p employed to paint a building is inversely proportional to the time taken to paint the building b which equation best models the number of painters required to finish the painting
Answer:
C
Step-by-step explanation:
Let x ∼ bin(9, 0.4). find
a. p(x > 6)
b. p(x ≥ 2)
c. p(2 ≤ x < 5)
d. p(2 < x ≤ 5)
e. p(x = 0) f. p(x = 7) g. μx h. σ2 x
The question involves the properties of a binomial distribution with parameters 9 and 0.4. The properties asked can be calculated using binomial theory, allowing the probability of certain outcomes, the mean and variance of the distribution to be found.
Explanation:The question involves a binomial distribution denoted as x ∼ bin(9, 0.4), where 9 is the total number of trials and 0.4 is the probability of success. The distribution properties desired are:
c. p(2 ≤ x < 5): The probability that x takes a value between 2 and 5, which is found by adding up the probabilities p(x = 2), p(x = 3) and p(x = 4) in the binomial distribution.e. p(x = 0): This is the probability that there are 0 successes, given by (0.6)^9 in this case.f. p(x = 7): The probability of having 7 successes which can be calculated using binomial formula.g. μx: This is the expected value or mean of the distribution, which in binomial distribution is np, so μx = 9 * 0.4 = 3.6.h. σ2 x: This is the variance, calculated as np(1-p), hence σ2x = 9 * 0.4 * (1 - 0.4) = 2.16.Learn more about Binomial Distribution here:https://brainly.com/question/33656163
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joaquin reached the end of the trail in 2 hours and 15 minutes. Write the amount of hours he spent on the trail as a mixed number and as an improper fraction.
Final answer:
Joaquin's time on the trail is represented as the mixed number 2 1/4 hours and the improper fraction 9/4 hours.
Explanation:
Joaquin reached the end of the trail in 2 hours and 15 minutes. To express this amount of time as a mixed number and as an improper fraction, we need to convert the 15 minutes into a fraction of an hour since 60 minutes make up an hour.
First, as a mixed number, 2 hours and 15 minutes can be written as 2 1⁄4 hours because 15 minutes is a quarter (1/4) of an hour.
Next, to express it as an improper fraction, multiply the whole number (2) by the denominator (4) and add the numerator (1) from the mixed number. This gives us 8 + 1 = 9 quarters, hence 9⁄4 hours.
Kiera wanted to find the approximate number of historical books at the library she works at. She used the computer to randomly take a sample of 80 books and found that 6 of them were considered historical books. There are 21,360 books at this library. What is the best estimate of the amount of historical books at this library?
A sample of 80 books was taken randomly using a computer and 6 of them were considered to be historical books.
It means probability of sample would be 6 out of 80 i.e. P = 6 over 80 = 0.075 or 7.5%.
It says there are 21,360 books in the library, so Population would be 21,360 books. We can use outputs of the sample survey to represent complete collection of books in the library.
So best estimate of total historical books in the library would be 7.5% of total population.
Best estimate = 7.5% of 21,360
Best estimate = 0.075 x 21,360
Best estimate = 1602 books.
Hence, there are approximately 1602 historical books in the entire library.
Which statements are true about the polynomial 28vw + 49v + 35w? Check all that apply.
Answer:
There are no common variables among all three terms.
The resulting expression when factoring out the GCF is 7(4vw + 7v + 5w).
Step-by-step explanation:
those r the two answers
Answer:
B & E
Step-by-step explanation:
Edg
Which expression means 9.7 split into a certain number of equal parts? 99pointsQ!!!
Answer:
9.7/n
Step-by-step explanation:
This is correct because i took the quiz and i got it correct :[
how many eggs are there in 4 1/4 dozen eggs?
Find The Equation Of The Line below
A machine that fills bottles with a beverage has a fill volume whose mean is 25.01 ounces, with a standard deviation of 0.02 ounces. a case consists of 24 bottles randomly sampled from the output of the machine. find the standard deviation of the total volume of the beverage in the case.
The standard deviation of the total volume of beverage in a case of 24 bottles, each with a standard deviation of 0.02 ounces, is approximately 0.098 ounces. This is calculated by multiplying the standard deviation of one bottle by the square root of the number of bottles in the case.
Explanation:The question involves finding the standard deviation of the total volume of beverage in a case of 24 bottles, given that each bottle has a fill volume with a mean of 25.01 ounces and a standard deviation of 0.02 ounces. To calculate the standard deviation of the total volume in the case, we multiply the standard deviation of a single bottle by the square root of the number of bottles in the case. This is because the standard deviation of the sum of independent random variables (in this case, the volume of each bottle) is equal to the square root of the sum of their variances.
Step-by-step Solution:
Standard deviation of one bottle = 0.02 ounces.
Number of bottles in a case = 24.
Total standard deviation = 0.02 ounces * √24.
Calculate the square root of 24, which is approximately 4.898.
Multiply the standard deviation of one bottle by this value to get the total standard deviation of the case: 0.02 * 4.898 = 0.098 ounces (approximately).
Therefore, the standard deviation of the total volume of beverage in a case of 24 bottles is approximately 0.098 ounces.
Mrs. reed baked four pans of lasagna for a family party. use the rectangles to represent the pans.
Where is the point of concurrency of the angle bisectors of a triangle?
A) outside the triangle
B) inside the triangle
C) on the triangle
Answer:
B) inside the triangle
Step-by-step explanation:
That point of concurrency is called the "incenter" as it is the center of the largest circle that can be inscribed in the triangle. It is always located inside the triangle.
Each angle bisector must be inside the triangle, so their point of intersection must be inside the triangle.
Final answer:
The point of concurrency of the angle bisectors of a triangle called the incenter, is always located inside the triangle.
Explanation:
The point of concurrency of the angle bisectors of a triangle is known as the incenter. This point is where all three angle bisectors of a triangle intersect, and it is always inside the triangle.
No matter what type of triangle it is—scalene, isosceles, or equilateral—the incenter is always located within the interior of the triangle, serving as the center of the triangle's incircle, which is a circle that is tangent to all three sides of the triangle. Thus , the correct option is B.
herman draws a scale model of one-half of the side house based on hermans scale model,what is the actual area of the entire side of the house?
The actual area of the entire side of the house is four times the area of Herman's scale model, as Herman's model represents only one-half of the side. So, if the area of Herman's model is A, then the actual area is 4A.
To find the actual area of the entire side of the house based on Herman's scale model, we need to follow these steps:
Understand the Scale: If Herman's scale model represents one-half of the side of the house, it means the scale is 1:2. This implies that every unit on the scale model represents two units in reality.
Find the Area of Herman's Model: Let's assume the area of Herman's scale model is A. Since it represents one-half of the side of the house, the actual area of one side of the house (let's call it X) would be 2A.
Calculate the Total Area of the Side of the House: Since there are two sides to a house, we need to double the area of one side: 2 * 2A = 4A.
Finalize the Answer: Therefore, the actual area of the entire side of the house is 4 times the area of Herman's scale model.
In summary, to find the actual area, we first double the area of Herman's scale model (as it represents only one-half of the side), then multiply it by 2 again to account for both sides of the house. This gives us a total of 4 times the area of Herman's model.
Here's the complete question:
"Herman draws a scale model of one-half of the side of a house. Based on Herman's scale model, what is the actual area of the entire side of the house?"
An engineer is planning a new water pipe installation. The circular pipe has a diameter of d=20cm.
What is the area A of the circular cross section of this pipe?
Give your answer in terms of pi.
HELP
Estimate it’s the length in meters for poster. Explain
Convert the following measurements.
a. 2 cubic yards to cubic feet
b. 135 cubic feet to cubic yards
c. 6,912 cubic feet to cubic inches
d. 279,936 cubic inches to cubic feet
Solve the following addition problem. Remember to carry as necessary.
7 cu. yd. 9 cu. ft. 134 cu. in. + 1 cu. yd. 12 cu. ft. 200 cu. in.
Solve the following subtraction problem. Remember to borrow as necessary.
9 cu. yd. 113 cu. in. – 4 cu. ft. 129 cu. in.
Solve the following multiplication problem.
11 cu. yd. 17 cu. in. × 135
What’s the capacity of a 3 cubic foot carton in cubic inches?
The Great Pyramid was built in Egypt more than 4,000 years ago. It was built by King Khufu, or Cheops, who intended to use it as a tomb. The pyramid contains about 2,300,000 blocks of stone, each weighing 2 1⁄2 tons. Can you calculate the approximate total weight of the Great Pyramid, in pounds?
Convert the following liquid measures.
a. 5 gallons to pints
b. 128 tablespoons to fluid ounces
c. 93 pints to quarts
d. 13 quarts to cups
e. 69 teaspoons to tablespoons
f. 112 cups to gallons
g. 18 fluid ounces to teaspoons
h. 3 gallons to fluid ounces
A local dairy farmer collects 490 gallons of milk a day from his cows. He keeps 1⁄35 of the milk for his own use, and sells the rest. Each quart of milk sells for 35 cents. In dollars, how much does he earn from selling his milk each day? (There are 100 cents in a dollar.)
A swimming pool has a capacity of 1,386 cubic feet. One gallon of water will fill 231 cubic inches of space. How many gallons of water will it take to fill the entire pool? (Hint: Convert the capacity of the pool to cubic inches first.)
The instructions on a bottle of laundry detergent tell you to add two capfuls of detergent to each gallon of water. One capful of detergent is equal to about one tablespoon. If your washing machine holds 11 gallons of water, how many tablespoons of detergent will you need to add? How many fluid ounces of detergent?
Convert the following dry measurements.
a. 11 bushels to quarts
b. 3 pecks to pints
c. 97 quarts to bushels
d. 1,120 quarts to pecks
Twelve apple pies can be made from one bushel of apples. How many apple pies can be made from one peck of apples?
Mr. Osaka sprinkles 1.694 pints of dry, powdered plant food on his garden three times a year. In quarts, what’s the total amount of plant food he uses in one year?
What triangle has 0 reflectional symmetries?
Answer:
A. right scalene triangle
A triangle with 0 reflectional symmetries is a scalene triangle. Equilateral triangles, such as those on an icosahedron, have multiple symmetries. Symmetry in different contexts, like physics and chemistry, can result in a net effect of zero.
Explanation:A triangle that has 0 reflectional symmetries is a scalene triangle, where all three sides and all three angles are of different lengths and magnitudes, respectively. An equilateral triangle, like the ones that form the faces of an icosahedron, has multiple lines of symmetry because of its equal sides and angles. On another note, in vector algebra, a null vector has all components equal to zero, which implies it has no direction or magnitude. Similarly, the molecular geometry of BF3 is described as trigonal planar and possesses symmetry, resulting in a net dipole moment of zero despite having polar B-F bonds.
In physics-related symmetry, charges or forces can cancel each other out leading to a net force of zero. For instance, if equal charges are placed at the corners of a square with a charge at the center, the net Coulomb force on the center charge will be zero due to the symmetry. Similarly, in collisions, certain angles or scenarios can result in a term becoming zero, like having a head-on collision where the incoming ball stops (v1 = 0), or the balls deflect at a 90-degree angle resulting in cos(θ1 - θ2) being zero.
Tom Hornet purchases $7,000 of ten-year term life. He is 31 years old
What is his annual premium?
What is his quarterly premium?
The difference between the two payment options?
(Remember to compare annual premium to annual premium!) :
Answer:I can confirm 35.49, 9.23, 1.43
Step-by-step explanation:
If 36 sqrt2 - 24 sqrt2 = sqrtN, what is N?
Find the interest on the loan if you borrowed $2,000 at 8% for 1 year.
Jerry's strips of dry meat joint sells of these two types of dry meat. he sells twice as many bags of dried beef as he does bags of dried turkey . His profit from the dryed beef is a 1.50 per bag while his profit for dryed turkey is a $2 per bag how many bags of each must he sell to profit for $ 500. please help
A farmer wants to fence in a section of land for a horse pasture. Fencing costs $29 per yard. How much will it cost to fence the pasture?
Final answer:
To find the cost of fencing a horse pasture, calculate the total length needed and multiply it by the cost per yard.
Explanation:
A farmer wants to fence in a section of land for a horse pasture. Fencing costs $29 per yard. How much will it cost to fence the pasture?
To calculate the cost of fencing the pasture, you need to determine the total length of the fencing needed in yards. Once you have the total length, you can multiply it by the cost per yard to find the total cost.
Example:
Assuming the total length of fencing needed is 100 yards.Multiply the total length by the cost per yard: 100 yards x $29 = $2900.Therefore, it will cost $2900 to fence the pasture.What is the solution to this inequality 2(x-4)+14<= x-1
How do you write 4.5 with the same number of decimal places as 6.25
A wedding cake has a diameter of 12 inches. The cake decorator needs to know how many strawberries he will need to put around the outside, so he needs the circumference. What is the circumference? Leave the answer in terms of π.
Which statements are true about thecordered pair (7,19) and the system of equations 2x-y=-5
H + 9.7 = -9.7 what is this answer
the graph shows y in direct variation with x. Find the value of Y when X=-15
A.) -30
B.) -24
C.)-18
D.) -12
Answer:
A -30
Step-by-step explanation:
If you pay attention you will see I did this on USATestPrep and I know the answer
Please help me with questions 24, 25, 26
A department store has average daily sales of $29,876.76. The standard deviation of sales is $1000. On Tuesday, the store sold $34,893.71 worth of goods. Find Tuesday's z score.
Answer with explanation:
Mean[tex]\Bar X[/tex] = $ 29,876.76
Standard Deviation[tex]\sigma[/tex] = $1000
[tex]\mu[/tex] =$34,893.71
Z-Score Formula
[tex]Z_{score}=\frac{\Bar X -\mu}{\sigma}\\\\Z_{score}=\frac{29876.76-34893.71}{1000}\\\\=\frac{-5016.95}{1000}\\\\=-5.01695\\\\=-5.02[/tex]
So, Tuesday Z-Score= -5.02
A number devised by six is 306. What is the number?