what is the least common denominator for the fractions 9/14and 2\21
find the missing data item given the following values
25, 28, 21, x, 32
If a baker doubles a recipe that calls for 6 3/4 cups of flour, how many cups of flour will be needed in all
find the pattern of 1, 5, 30, 210, 2680
The sequence provided (1, 5, 30, 210, 2680) does not match typical simple arithmetic or geometric patterns, suggesting it may involve a more complex rule like factorial growth, though a specific pattern cannot be determined with the provided information.
Explanation:The question is about finding the pattern in the sequence 1, 5, 30, 210, 2680. To solve this, observe how each term relates to its predecessor. The sequence does not directly follow an arithmetic or geometric pattern; instead, it seems to involve a factorial or multiplicative pattern with increasing multipliers.
However, the information provided does not directly match the given sequence, suggesting that there might have been a typo in the sequence or additional rules that were not stated. Generally, patterns can be identified through arithmetic (addition/subtraction), geometric (multiplication/division), or more complex operations (such as factorial or combinations), but without the correct sequence or a clear rule, it's challenging to provide a decisive pattern.
For sequences that escalate rapidly like this one, factorial operations or exponential growth with additional manipulations (addition, subtraction) are common, but the specific pattern here is unclear without further clarification or the correct sequence.
Find two consecutive even integers such that the smaller added to four times the larger gives a sum of 48.
The consecutive even integers such that the smaller added to four times the larger gives a sum of 48 are; 8 and 10
What are the consecutive numbers?The consecutive numbers are those numbers that follow each other continuously in the order from smallest to largest numbers.
WE have to determine the two consecutive even integers such that the smaller added to four times the larger gives a sum of 48.
Let the two consecutive even integers are; x and (x+2)
Therefore,
X+4(x+2) = 48
X+4x+8=48
5x=40
X=8
Hence The consecutive even integers are; 8 and 10
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a toy manufacturer estimates that 6% of its products are defective. if it produces 550 toys in one day, how many will be defective?
Answer:
33
Step-by-step explanation:
We need to find 6% of 550.
We can calculate with a direct rule of 3. If the 100% is 550, how much is the 6%?
[tex]100 -\!\!\!-\!\!\!- 550\\ 6 -\!\!\!-\!\!\!- x[/tex]
We use the formula of the direct rule of 3:
[tex]x = \frac {6 * 550}{100} \\ \\ x = \frac {3300}{100}\\ \\ x = 33[/tex]
33 toys will be defective.
If a toy manufacturer produces 550 toys in one day, then the number of toys that would be defective is 33 toys.
Let the defective toys be D.Let the total toys be T.Given the following data:
Total number of toys produced in a day = 550 toys.To find the number of toys that would be defective from a production:
[tex]D = \frac{6}{100}[/tex] × [tex]T[/tex]
Substituting the given parameters into the formula, we have;
[tex]D = \frac{6}{100}[/tex] × [tex]550[/tex]
[tex]D = 0.06(550)[/tex]
Defective toys, D = 33 toys.
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A car decreases in value 10% a year . If it was brought for £5000 , how much will it be worth after 2 years ?
5000 x (1-0.10)^2
5000 x 0.90^2
5000 * 0.81
it is valued at 4,050 after 2 years
Final answer:
After applying a 10% yearly depreciation to the initial value of £5000, the car's value after 2 years will be £3150.
Explanation:
When a car decreases in value by 10% a year, its value after 2 years can be calculated using exponential decay. To compute the value of the car after two years, we start with the initial value of £5000 and apply a 10% decrease for each year. The formula for the value of the car after a certain number of years is given by:
Future Value = Present Value × (1 - rate of depreciation)^number of years
For the first year:
Future Value = £5000 × (1 - 0.10)¹
Future Value = £5000 × 0.90
Future Value = £4500
For the second year, we use the value at the end of the first year:
Future Value = £4500 × (1 - 0.10)¹
Future Value = £4500 × 0.90
Future Value = £3150
Therefore, after 2 years, the car will be worth £3150.
Please help!! Explain how you got the answer!
multiply 3.5 x 3 = 10.5
add -5 +-10 = -15
so you have 10.5 x 10^15
then you need to move the decimal point 1 place to the left to get 1.05
since you move the decimal point 1 place to the left you add 1 to the -15 to get -14
so answer = 1.05 x 10^-14
Dewayne is comparing two checking accounts. One has a monthly fee of $7 and a per-check fee of $0.30, and the other has a monthly fee of $4 and a per-check fee of $0.40. What is the minimum number of checks Dewayne needs to write for the first bank to be a better option?
7 +0.30x = 4 +0.40x
subtract 4 from each side
3+0.30x = 0.40x
subtract 0.3x from each side
3 = 0.10x
divide both sides by 0.10
3 /0.10 = 30
30 checks would make both accounts equal
so he would need to write 31 checks for the first one to be better.
Answer:30
Step-by-step explanation:
it’s right
Constructed Response 1: A student thinks that the sum of 4.3 and 8.4 is 12.7 because 4 + 8 = 12 and 3 + 4 = 7. The student then adds 3.6 and 2.7 and gets 5.13 because 3 + 2 = 5 and 6 + 7 = 13. Identify the mistake in the student’s procedure and explain why this procedure won’t always work. *
Dependent events can best be described as. A= two or more events that have the same probabilities. B= two or more events that do not have the same probabilities. C= a group of events whose later outcomes are not affected by previous outcomes.D= a group of events whose later outcomes are affected by previous outcomes.
Option: D is the correct answer.
D = a group of events whose later outcomes are affected by previous outcomes.
Step-by-step explanation:We know that two events Event A and event B are said to be dependent if the occurrence of one outcome affects the occurrence of the other outcome.
For example--
If we have a bag containing 5 blue marbles, 2 red marbles and 3 green marbles then if we draw first marble and then draw second without replacement.
Then the event of drawing a blue marble first and then a green marble are dependent events.
What is the product of -9x(5-2x)
What is the element a^23 in matrix A?
A=8 -4 -3
3 -9 -5
-8 8 8
Answer:
1. (5,0)
2. 20 of type A;20 of type B
3. no solution
4. -5
5.D
11 -12 7
5 12 -7
6. (-6,8)
100% right i gotchu bbs <3
The element [tex]a_{23[/tex] in matrix A is -5. Therefore, option A is the correct answer.
We need to find the element [tex]a_{23[/tex] in matrix A.
What is the matrix?In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
From the given matrix, the element in the second row and third column is -5.
The element [tex]a_{23[/tex] in matrix A is -5. Therefore, option A is the correct answer.
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For what values of m does the graph of y=3x^2+7x+m have two x-intercepts
Answer:
For all [tex]\frac{49}{12}>m[/tex], the graph of given equation have two x-intercepts if the discriminant is positive.
Step-by-step explanation:
A quadratic equation [tex]y=ax^2+bx+c[/tex] has
1. No x-intercept if [tex](b^2-4ac)<0[/tex].
2.One x-intercept if [tex](b^2-4ac)=0[/tex].
3. Two x-intercept if [tex](b^2-4ac)>0[/tex].
The given equation is
[tex]y=3x^2+7x+m[/tex]
It is a quadratic equation. Here, a=3, b=7 and x=m. The graph of given equation have two x-intercepts if the discriminant is positive.
[tex](b^2-4ac)>0[/tex]
Put a=3, b=7 and x=m in the above inequality.
[tex]7^2-4(3)(m)>0[/tex]
[tex]49-12m>0[/tex]
Add 12m on both the sides.
[tex]49>12m[/tex]
Divide both sides by 12.
[tex]\frac{49}{12}>m[/tex]
For all [tex]\frac{49}{12}>m[/tex], the graph of given equation have two x-intercepts if the discriminant is positive.
find the rate in the following problem Round the answer to the nearest hundredth of a percent. What percent of 85 is 10?
To find the percent of 85 that is 10, divide 10 by 85 and multiply by 100. The answer is 11.76%.
Explanation:To find the percent of 85 that is 10, we divide 10 by 85 and multiply by 100.
10 / 85 = 0.1176
0.1176 * 100 = 11.76%
Roundin the answer to the nearest hundredth of a percent, we get 11.76%.
The baby weighed 7.25 pounds at birth.At the end of 8 months the baby weighed 2 1/2 times its birth weight .How much does the baby weigh at 8 months
i have zero idea.. help please.
HELP PLEASE!!!!!!! 10 POINTS!!!
How do the rules for adding and subtracting signed decimals compare with the rules for adding and subtracting integers? please explain
A freight train travels at 30 mph. If the freight train is 300 miles ahead of an express train traveling at 55 mph, how long will the express train take to overtake the freight train?
Which equation could be used to find the number of miles the trains will travel?
A. 30x = 55(x + 300)
B. x÷30 = (x - 300)÷55
C. x÷30 = (x + 300)÷55
Answer:
The answer is C. x÷30 = (x + 300)÷55
Step-by-step explanation:
The equation that could be used to find the number of miles the trains will travel is C. x÷30 = (x + 300)÷55.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
A freight train travels at 30 mph. If the freight train is 300 miles ahead of an express train traveling at 55 mph.
The equation will be
Total speed = Total distance / time taken
x ÷ 30 = (x + 300) ÷ 55
The equation that could be used to find the number of miles the trains will travel is C. x÷30 = (x + 300)÷55.
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3c+2d=2;d=4 step by step
A table is 3 feet and 2 inches wide and a chair is 25 inches wide how much wider is the table then chair in inches
Answer:
junko enishima
Step-by-step explanation:
Simplify −0.5i−i
Enter your answer in the box.
Answer: -1.5i
Step-by-step explanation: This was correct
Which expression can be used to convert 22 Australian dollars to US dollars?
Assume 1.2 Australian dollars equals 1 US dollar.
$22 AUD ×
$22 AUD ×
$1.20 AUD ×
$1.20 AUD × pls help need awnwer quick
Answer:
[tex]\frac{22\text{ AUD }\cdot 1\text{ USD}}{1.20\text {AUD}}[/tex]
Step-by-step explanation:
We are told that 1.2 Australian dollars equals to 1 US dollar. We are supposed to write an expression that can be used to convert 22 Australian dollars to US dollars.
To find the amount of US dollars in 22 Australian dollars we will divide 22 by amount of Australian dollars that is equal to 1 US dollar (1.2 AUD).
[tex]22\text{ AUD}=\frac{22\text{ AUD }\cdot 1\text{ USD}}{1.20\text{ AUD}}[/tex]
Australian dollars will cancel out with Australian dollars from unit parts and our unit will be in American dollars.
[tex]22\text{ AUD}=\frac{22\cdot 1\text{ USD}}{1.20}[/tex]
Therefore, our desired expression that can convert 22 Australian dollars to US dollars will be [tex]\frac{22\text{ AUD }\cdot 1\text{ USD}}{1.20\text { AUD}}[/tex].
A ski jacket costing $160 is $20 less than twice the cost of the matching ski pants. Find the total cost of the ski jacket and matching ski pants.
The total cost of the ski jacket and matching ski pants is $250.
Given that, a ski jacket costing $160 is $20 less than twice the cost of the matching ski pants.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the cost of matching ski pants be x.
Now, 2x-20=160
⇒ 2x=180
⇒ x=90
So, the cost of the matching ski pants is $90.
Total cost = 160+90 = $250
Therefore, the total cost of the ski jacket and matching ski pants is $250.
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Chris is trying to find the volume of a pool. What unit will he use?
When measuring the volume of a swimming pool, larger units of capacity like liters and gallons are used. For an Olympic-sized pool, the volume is often measured in megaliters or cubic meters.
When measuring the volume of a swimming pool, we are dealing with a very large capacity, therefore using small capacity units like milliliters would not be practical due to the large numbers it would involve. In cases such as filling a pool, larger units of capacity are more appropriate. Common units of measure for such large volumes are liters and gallons. For very large swimming pools, like Olympic-sized ones, volume is often expressed in megaliters (ML) because one megaliter equals one million liters. For instance, an Olympic-sized swimming pool holds about 2,500,000 liters, which can also be expressed as 2.5 megaliters (ML).
Additionally, when working with the volume of a pool, it would also be possible to measure in cubic meters (m³). This is particularly common in scientific contexts or in regions where the metric system is standard for all measurements.
Jason started a hat-making business. He spent $750 to purchase supplies to get started and he uses about $3.50 worth of supplies per hat made. Jason charges $15 for each hat. Let h represent the number of hats.
What is the minimum number of hats Jason will need to sell to make a profit?
Which inequality models this problem?
A.) 15h>750+3.5h
B.) 3.5h>750+15h
C.) 15h<750+3.5h
D.) 3.5h≥750+15h
Answer:
the answer is A. 15h>750+3.5h
Im 100% sure. Good luck!
ZP bisects ∠OZQ so that ∠OZP = 8x – 9 and ∠PZQ = 5x + 18. Find the value of x, and the measure of each angle. You must show all work in order to receive credit!
Write the quadratic function in vertex form. y = x2 + 8x + 18
Pablo simplified the expression(2^-4)^-2 as shown.
(2^-4)^-2=2^-4*^-2=2^-8
Which statement explains Pablo’s error?
A. He should have added the exponents instead of multiplying them.
B. He should have divided the exponents instead of multiplying them.
C. He should have found 8 as the exponent, not –8.
D. He should have written mc014-3.jpg as mc014-4.jpg.
Answer:
C. He should have found 8 as the exponent, not –8.
Step-by-step explanation:
We have been given an expression [tex](2^{-4})^{-2}[/tex]. We are asked to find the Pablo's error in simplifying the expression.
Let us check steps done by Pablo.
In first step Pablo has simplified [tex](2^{-4})^{-2}[/tex] to [tex](2)^{(-2*-4)}[/tex] using power rule property of exponents which states that to raise a power to a power we have to multiply the exponents. Therefore, his first step is correct.
Now let us check Pablo's second step. We can see that Pablo multiplied -2 by -4 and simplified to [tex]2^{-8}[/tex].
Since we know that multiplying a negative number with another negative number gives a positive result, therefore, Pablo made mistake in second step. He should have found 8 instead of -8 as the exponent.
The correct steps for simplifying the given expression will be [tex](2^{-4})^{-2}=2^{(-2*-4)}=2^{8}[/tex].
Upon looking at our given option we can see that option C is the correct statement about Pablo's error.
What is the solution of the system of equations ? 2x-y=7 y=2x+3
Answer:
Step-by-step explanation:
I forgot