From the given information provided, m is multiplied by 6m-7 so that the product is 6m²-7m.
To find what is multiplied by 6m-7 so that the product is 6m²-7m, we can use polynomial long division or factorization. Here's how to do it using factorization:
We need to find two numbers that multiply to give 6m²-7m and add up to -7. We can factor the expression 6m²-7m as:
6m² - 7m = m(6m - 7)
So, we see that 6m-7 is a factor of 6m²-7m. Therefore, to find what is multiplied by 6m-7 to get 6m²-7m, we just need to divide 6m²-7m by 6m-7:
(6m² - 7m) / (6m - 7) = m
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Factor 72 + 32. Write your answer in the form a ( b + c) where a is the gcf of 72 and 32
Factor 72 + 32 in the form of a ( b + c) with A having gcf is 72 + 32 is 8(9 + 4).
To factor 72 + 32, we first need to find the greatest common factor (GCF) of 72 and 32.
The prime factorization of 72 is 2³ x 3², and the prime factorization of 32 is 2⁵.
The common factors of 72 and 32 are 1, 2, 4, 8, and 16. The greatest common factor is 8, since it is the largest factor that they both share.
So, we can write 72 + 32 as:
72 + 32 = 8 x (9 + 4)
Therefore, the factored form of 72 + 32 is 8(9 + 4).
To factor 72 + 32, we need to find the greatest common factor (GCF) of 72 and 32, which is 8. We can then use this GCF to write 72 + 32 in factored form as 8(9 + 4). This expression can also be simplified as 8(13), which equals 104. This means that 72 + 32 can be written as the product of 8 and 13, where 8 is the GCF of 72 and 32, and 13 is the sum of the quotients of 72 and 32 when divided by 8. Factoring expressions is an important skill in algebra and is used in many areas of mathematics and science.
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Given mn, find the value of x.
t
(7x-4)º
(3x+28)°
Hence, the value of variable in the given expression x is 8
What is Angle?An angle is formed when two straight lines meet at a common endpoint.
given:∠1 = 7x - 4
∠2 = 3x + 28
A secant line that crosses two parallel lines produces these angles. After that, these angles were congruent, which means that their measures are equal.
Then, equaling both given expressions and solving for x, we get:
Step1: subtract 3x both sides
7x - 4 = 3x + 28
Step2: add 4 both sides
7x - 3x - 4 = 28
Step2: simplify like terms
7x - 3x = 28 + 4
Step3: divide by 4 both sides
4x = 32
x = 32/4
x = 8
Hence, the value of x is 8.
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Assume that females have pulse rates that are normally distributed with a mean of μ=75.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts (a) through (c) below.
a. The probability that a randomly selected adult female has a pulse rate less than 82 beats per minute is 0.7123.
b. The probability that 25 randomly selected adult females have a pulse rate with a mean less than 82 beats per minute is 0.9974.
c. The normal distribution can be used in part (b), even though the sample size does not exceed 30 as Option D: Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
a. Using the z-score formula, z = (x - μ) / σ, where x = 82, μ = 75, and σ = 12.5, we get -
z = (82 - 75) / 12.5
z = 0.56
Using a standard normal distribution table or calculator, we can find the probability that z is less than 0.56 is 0.7123.
Therefore, the probability value is obtained as 0.7123.
b. The central limit theorem states that as the sample size increases, the distribution of sample means becomes approximately normal, regardless of the shape of the original population distribution.
Therefore, we can use a normal distribution to approximate the sampling distribution of the sample mean, even if the sample size is less than 30.
The mean of the sampling distribution of the sample mean is the same as the mean of the original population, which is 75.
The standard deviation of the sampling distribution of the sample mean, also known as the standard error, can be calculated as σ / sqrt(n), where n = 25 is the sample size.
standard error = 12.5 / √(25) = 2.5
Using the z-score formula again, we can find the z-score for a sample mean of x' = 82 -
z = (x' - μ) / (σ / √(n))
z = (82 - 75) / (2.5)
z = 2.8
Using a standard normal distribution table or calculator, we can find the probability that z is less than 2.8 is 0.9974.
Therefore, the probability value is obtained as 0.9974.
c. The correct answer is the central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.
The requirement of a sample size greater than 30 applies to using a normal distribution to approximate the population distribution, not the sampling distribution of the sample mean.
Therefore, the correct option is D.
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Assume that females have pulse rates that are normally distributed with a mean of μ=75.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts (a) through (c) below.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 82 beats per minute.
The probability is ___.
b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 82 beats per minute.
The probability is ___.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
A. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.
B. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size.
C. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.
D. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.
the university of montana ski team has eight entrants in a men's downhill ski event. the coach would like the first, second, and third places to go to the team members. in how many ways can the eight team entrants achieve first, second, and third places?
There are 336 ways for the 8 team entrants to achieve the desired outcome of first, second, and third place positions.
The problem involves selecting 3 individuals out of 8 to fill the 1st, 2nd, and 3rd place positions. Since the order in which the individuals are selected matters, we need to use the permutation formula to determine the total number of ways to achieve the desired outcome.
The formula for permutation is:
P(n,r) = n! / (n-r)!
Where n is the total number of individuals, and r is the number of positions to be filled.
In this case, we need to select 3 individuals out of 8 to fill the 1st, 2nd, and 3rd place positions. Using the permutation formula, we get:
P(8,3) = 8! / (8-3)!
= 8! / 5!
= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (5 x 4 x 3 x 2 x 1)
= 8 x 7 x 6
= 336
In other words, the coach has 336 possible ways to select three team members for the podium, assuming all team members have an equal chance of winning.
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what is the relationship between the symbol pi and the word pi
The symbol π and the word "pi" are both used to refer to the mathematical constant that represents the ratio of a circle's circumference to its diameter
The symbol π and the word "pi" are both used to refer to the mathematical constant that represents the ratio of a circle's circumference to its diameter. The symbol π is a Greek letter that has been used to represent this constant for centuries, while the word "pi" is the commonly accepted English-language term for this constant.
They are two different representations of the same mathematical concept. The symbol π is used extensively in mathematical formulas, while the word "pi" is used more colloquially to refer to this constant in everyday conversation.
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determine the balance a for p dollars iinvested at a rate r for t years and compunded n times per year
The balance A for P dollars invested at a rate r for t years and compounded n times per year can be calculated using the formula: A = P (1 + r/n)^(n*t)
where:
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
t = the number of years the money is invested
n = the number of times the interest is compounded per year
A = the total amount including principal and interest
To solve for the balance A, simply substitute the given values for P, r, t, and n into the formula and evaluate:
For example, let's say we invest $5000 at an annual interest rate of 4.5% for 3 years, compounded monthly (n=12).
P = $5000
r = 0.045 (4.5% expressed as a decimal)
t = 3 years
n = 12 (compounded monthly)
A = 5000 (1 + 0.045/12)^(12*3)
= 5000 (1.00375)^36
= $5,838.27
Therefore, balance A is $5,838.27 after 3 years of investing $5000 at an annual interest rate of 4.5%, compounded monthly.
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I need help asap please sb
LN/RT = NM/TS is the correct option in congruent triangle .
What in mathematics is congruent?
If two shapes are similar in size and shape, they are said to be congruent. The mirror image of one shape is the same as the other if two shapes are congruent.
Congruent refers to objects that are precisely the same size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.
In ΔLMN ≅ ΔRST
In triangle are congruent .
LN/RT = NM/TS
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I really want this pleaseeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
QS=24
Step-by-step explanation:
QS and QU is the radius of the circle so they well be congruent
using Pythagorean Theorem:
[tex]x^{2} +32^{2} =(x+16)^{2}[/tex]
[tex]x^{2} +1024=x^{2} +32x+256[/tex]
[tex]32x=768[/tex]
[tex]X=24[/tex]
So,
QS=24
this one, i suck at the hypotenuse and i learned it yesterday and this is due today please help break it down for me
The right triangle has a 90-inch perimeter.
Which triangle is on the right?A right triangle is one with a 90 degree inner angle. Its longest side is the hypotenuse, which is also the side of the right triangle that faces the right angle. The two arms of a right angle are made up of height and base.
To get the length of the other right triangle leg, let's apply the Pythagorean theorem: a2 + b2 = c2, where c is the hypotenuse and a and b are the triangle's legs.
We are aware that c = 41 inches and, let's say, a = 40 inches for one of the legs. Hence, we may find b:
40² + b² = 41²
1600 + b² = 1681
b² = 1681 - 1600
b² = 81
b = √81
b = 9
Hence, the other leg is 9 inches long.
We can now determine the triangle's perimeter:
Perimeter = a + b + c
Perimeter = 40 + 9 + 41
Perimeter = 90 inches
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Solve: -6x + 4 = - 4x + 6
Answer:-1
Step-by-step explanation:
in order to solve this type questions you should "orginize" numbers same variables:
-6x+4x=6-4
-2x=2
x=-1
Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0. 2x^2-0. 7x+10. 516, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?
Aki's Bicycle Designs should build 1.75 hundred, or 175, bicycles to minimize the average cost per bicycle.
To find the number of bicycles Aki's Bicycle Designs should build to minimize the average cost per bicycle, we need to find the minimum point of the given quadratic function C(x).
First, we can find the derivative of C(x) concerning x:
C'(x) = 0.4x - 0.7
Then, we can set C'(x) equal to zero and solve for x:
0.4x - 0.7 = 0
0.4x = 0.7
x = 1.75
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What is the measure of <7?
Answer:
120
Step-by-step explanation:
Can someone help I’ll give 10 points
Answer:
Hey Sweetheart!
z=4
4x4x4= 64
Hope this Helps!!!
know what it is but needs to know how to do it
5x+75=180
Answer:21
Step-by-step explanation:
5x=180-75
5x=105
x=105/5
x=21
If two sets of numbers have the same mean, which of the following must always be true: A) The two sets must have the same variance B) The two sets of numbers must have the same standard deviation. C) The two sets of numbers must be identical. D) None of these statements must be true
None of these statements must be true
=========================================
Explanation:
Let's go through the answer choices one at a time.
----------------
A)
Consider the set {4,5,6}. It has a mean of (4+5+6)/3 = 15/3 = 5. We add up the values and then divide by the number of values (3 in this case).
Now consider the set {3,5,7}. I've added 1 to the largest element and subtracted 1 from the smallest. This will spread the data set out further. The mean is still 5 because (3+5+7)/3 = 15/3 = 5. The center hasn't changed. But the data is more spread out so the variance is larger for this new set.
Therefore, the sets {4,5,6} and {3,5,7} do NOT have the same variance. We cross choice A off the list.
----------------
B)
Recall that
[tex]\text{standard deviation} = \sqrt{\text{variance}[/tex]
For example, if the variance is 36 then the standard deviation would be [tex]\sqrt{36} = 6[/tex]
Because of the connection of the standard deviation and variance, both measure how spread out a set is. Furthermore, it means the sets {4,5,6} and {3,5,7} do NOT have the same standard deviation. We can cross choice B off the list.
----------------
C)
This statement is clearly not true because the sets {4,5,6} and {3,5,7} are not the same, but they produce the same mean. We can cross choice C off the list.
Choice D is the only thing left so it must be the final answer.
Ross is trying to make the target number 10. Using the numbers 6,7,8, and 9, how can ross make an equation out of those numbers that equals 10? Each number can be used only once, in any order, with any operations
One possible equation Ross can make is 9 - 7 + 8 = 10
Ross is given the numbers 6, 7, 8, and 9, and is asked to make an equation that equals 10. The equation can use each number only once, and can use any arithmetic operations (such as addition, subtraction, multiplication, and division) in any order.
One way Ross can approach this problem is to first think about what pairs of numbers can be combined to make 10. Ross could quickly see that there are no pairs of numbers that add up to 10, since the highest pair is 8 + 9 = 17.
Next, Ross could think about using subtraction or division to create a 10. However, there are no pairs of numbers that can be subtracted or divided to get 10 either.
Therefore, Ross needs to use a combination of addition, subtraction, and/or multiplication to create an equation that equals 10.
One possible equation Ross can make is:
9 - 7 + 8 = 10
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or
Elmview School has an annual carnival. Each year, the school needs 2b+18 balloons for carnival decorations, where b is the number of booths. Elmview has 12 booths planned for the carnival this year.
How many balloons does the school need to decorate for the carnival this year?
Write your answer as a whole number or decimal.
that's the final answer
11. Rectangles and trapezoids
Sides:
Angles:
Relationship:
12. Squares and rhombi
Sides:
Angles:
Relationship:
13. Squares and trapezoids
Sides:
Angles:
Relationship:
14. Rhombi and trapezoids
Sides:
Angles:
Relationship:
The relationship between the types of quadrilaterals such as rectangles, trapezoids and rhombi can be quantified in terms of sides and angles.
How do quadrilaterals relate ?Rectangles and trapezoids
Sides: A rectangle has two pairs of parallel sides, where both pairs are equal in length. A trapezoid has one pair of parallel sides and the other pair of non-parallel sides are not equal in length.Angles: A rectangle has four right angles, each measuring 90 degrees. A trapezoid has two acute angles and two obtuse angles.Relationship: A rectangle is a special case of a trapezoid, where both pairs of non-parallel sides are equal in length.Squares and rhombi
Sides: A square has four equal sides, where each side intersects at a 90-degree angle. A rhombus has four equal sides, but opposite sides intersect at an acute angle and the other pair at an obtuse angle.Angles: Both a square and a rhombus have four equal angles, each measuring 90 degrees.Relationship: A square is a special case of a rhombus, where all angles are right angles.Squares and trapezoids
Sides: A square has four equal sides, while a trapezoid has two parallel sides of unequal length and two non-parallel sides of unequal length.Angles: A square has four right angles, while a trapezoid has two acute angles and two obtuse angles.Relationship: A square is not a trapezoid since it does not have parallel sides of different lengths.Rhombi and trapezoids
Sides: A rhombus has four equal sides, while a trapezoid has two parallel sides of unequal length and two non-parallel sides of unequal length.Angles: A rhombus has four equal angles, while a trapezoid has two acute angles and two obtuse angles.Relationship: A rhombus is not a trapezoid since it has two pairs of parallel sides, both of which are equal in length.Find out more on trapezoids at https://brainly.com/question/4458080
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x=8 y=2 find x and y
Answer:
y=1/4x
Step-by-step explanation:a direct variation equation is y=kx. if y=1/4x, then when x=8, y=2.
What is the value of p?
answer the question somebody
Answer:
[tex]\large\boxed{\tt m \angle p = 54.7^{\circ}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the value of p.}[/tex]
[tex]\textsf{Note that we are given \underline{Vertical Angles}, and a \underline{perpendicular} set of lines.}[/tex]
[tex]\large\underline{\textsf{What are Vertical Angles?}}[/tex]
[tex]\textsf{Vertical Angles are 2 angles that are opposite from each other, and share a}[/tex]
[tex]\textsf{common vertex point. (center point) Vertical Angles are congruent as they are}[/tex]
[tex]\textsf{formed by the same 2 intersecting lines.}[/tex]
[tex]\large\underline{\textsf{What are Perpendicular Lines?}}[/tex]
[tex]\textsf{Perpendicular Lines are 2 sets of lines that intersect each other with opposite}[/tex]
[tex]\textsf{reciprocal slopes. Perpendicular Lines form 4 right angles that are 90}^{\circ}.[/tex]
[tex]\large\underline{\textsf{Identifying Vertical Angles;}}[/tex]
[tex]\textsf{Remember that vertical angles are opposite from each other, and are congruent.}[/tex]
[tex]\textsf{We are given 1 measure of an angle, and this angle has a measure of 35.3}^{\circ}.[/tex]
[tex]\textsf{The angle opposite to it, (below angle p) is opposite from our angle.}[/tex]
[tex]\textsf{We have identified our vertical angle, now let's identify p.}[/tex]
[tex]\large\underline{\textsf{Identifying m} \tt \angle p;}[/tex]
[tex]\textsf{We should know that we are Perpendicular lines, and angle p is overlapped in one.}[/tex]
[tex]\textsf{This means that these angles are \underline{Complements}, angles that add up to 90}^{\circ}.[/tex]
[tex]\textsf{Because we know that the other angle inside the right angle is 35.3}^{\circ}, \ \textsf{we are}[/tex]
[tex]\textsf{able to set up an equation to find p.}[/tex]
[tex]\tt p = 90^{\circ} - 35.3^{\circ}[/tex]
[tex]\underline{\textsf{Evaluate;}}[/tex]
[tex]\large\boxed{\tt m \angle p = 54.7^{\circ}}[/tex]
A department store is holding a fall clothing sale where $9.99 will be taken off any clothes purchased. If Taylor wants to buy a pair of pants regularly priced $34.99, how much will he spend at the sale?
Kari opened a savings account and deposited $200.00 as principal. The account earns 15% interest, compounded annually. What is the balance after 10 years?
Round to the nearest cent
Answer:
Omg I HATE IXL sm!!
Step-by-step explanation:
$637.51
you work as a cashier in a supermarket. on saturday, you had 135 customers. on sunday, you had 90 customers. what is the approximate percent decrease
The approximate percent decrease in the number of customers from Saturday to Sunday is 33%. Therefore, the answer is option A: 33%
To find the approximate percent decrease in the number of customers from Saturday to Sunday, we first need to calculate the decrease in the number of customers:
Decrease = Saturday customers - Sunday customers
Decrease = 135 - 90
Decrease = 45
The percent decrease can be found by taking the decrease as a percentage of the original value (Saturday customers):
Percent decrease = (Decrease / Saturday customers) x 100%
Percent decrease = (45 / 135) x 100%
Percent decrease = 33.33%
Rounding to the nearest percent, we get that the approximate percent decrease in the number of customers from Saturday to Sunday is 33%. Therefore, the answer is option A: 33%.
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Your question is incomplete, but probably the complete question is :
You work as a cashier in a supermarket. On Saturday, you had 135 customers. On Sunday, you had 90 customers. What is the approximate percent decrease in the number of customers from Saturday to Sunday?
33%
45%
50%
90%
225%
State the coordinates of the point.
A piece of art is in the shape of a rectangular pyramid like the figure shown.
A rectangular pyramid with a base of dimensions 5 feet by 4 feet. The two large triangular faces have a height of 6.8 feet. The two small triangular faces have a height of 7 feet.
How much glass is needed to cover the entire pyramid?
82 ft2
164 ft2
62 ft2
41 ft2
Answer:
82 ft^2
Step-by-step explanation:
To find the amount of glass needed to cover the entire rectangular pyramid, we need to calculate the combined surface area of all its faces.
The rectangular base of the pyramid has an area of 5 feet by 4 feet, or 20 square feet. The two large triangular faces each have an area of (1/2) x base x height = (1/2) x 5 feet x 6.8 feet = 17 ft^2. The two small triangular faces each have an area of (1/2) x base x height = (1/2) x 4 feet x 7 feet = 14 ft^2.
Therefore, the total surface area of the pyramid is:
20 ft^2 (for the base) + 17 ft^2 + 17 ft^2 + 14 ft^2 + 14 ft^2 = 82 ft^2
So, the amount of glass needed to cover the entire pyramid is 82 square feet.
Therefore, the answer is 82 ft^2.
Answer:82 ft2
Step-by-step explanation:
i did it in class
how many batteries n should be in the package in order for the probability to exceed 1%? give the smallest number n which works.
a) The probability that a battery does not reach the milestone in its first 8 hours of usage is 0.014 or 1.4%. b) The probability of this goal being met is 0.002 or 0.2%. c) The smallest value of n that satisfies P(X >= 10) > 0.01 is n = 13.
(a) To calculate the probability that a battery does not reach the milestone in its first 8 hours of usage, we need to calculate the area under the normal curve to the right of 8 hours. We can use the standard normal distribution to do this by first standardizing the value of 8 hours using the formula:
z = (x - mu) / sigma
where x is the value of 8 hours, mu is the mean of the distribution (7.36 hours), and sigma is the standard deviation (0.29 hours). Substituting these values, we get:
z = (8 - 7.36) / 0.29 = 2.21
Using a standard normal table or a calculator, we can find that the area to the right of z = 2.21 is approximately 0.014.
(b) We want to find the probability that at least 10 batteries out of a pack of 12 last until 7.5 hours of usage. This is a binomial distribution with n = 12 and p = the probability that a single battery lasts until 7.5 hours.
To find p, we can use the standard normal distribution again by standardizing the value of 7.5 hours:
z = (7.5 - 7.36) / 0.29 = 0.48
Using a standard normal table or a calculator, we can find that the area to the right of z = 0.48 is approximately 0.316. Therefore, the probability that a single battery lasts until 7.5 hours is 0.316.
Now we can use the binomial distribution formula to calculate the probability that at least 10 batteries out of 12 last until 7.5 hours:
P(X >= 10) = 1 - P(X < 10)
where X is the number of batteries that last until 7.5 hours, and P(X < 10) is the cumulative probability of 9 or fewer batteries lasting until 7.5 hours. Using a binomial calculator or a standard normal table, we can find that:
P(X < 10) = 0.998
Therefore, P(X >= 10) = 1 - 0.998 = 0.002 or 0.2%.
(c) We want to find the smallest value of n such that the probability of at least 10 batteries out of n lasting until 7.5 hours is greater than 1%. This is equivalent to finding the smallest n such that:
P(X >= 10) > 0.01
Using a binomial calculator or a standard normal table, we can find that:
P(X < 10) = 0.989 when n = 10
P(X < 10) = 0.970 when n = 11
P(X < 10) = 0.942 when n = 12
Therefore, the smallest value of n that satisfies P(X >= 10) > 0.01 is n = 13.
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Your question is incomplete, but probably the complete question is :
Suppose that a brand of AA batteries reaches a significant milestone to their death on average after 7.36 hours, with standard deviation of 0.29 hours. Assume that when this milestone occurs follows a normal distribution.
(a) Calculate the probability that a battery does not reach this milestone in its first 8 hours of usage.
(b) Suppose that the company wants to sell a pack of n batteries of which (at least) 10 will last until 7.5 hours of usage. If n 12, what is the probability of this goal being met?
(c) How many batteries n should be in the package in order for the probability to exceed 1%? Give the smallest number n which works.
according to census 2000, asians in the united states represent about what percent of the total population? question 1 options: 16.2 percent 10.5 percent 3.6 percent
Answer: 4.2 percent
Step-by-step explanation: Your welcome
Simplify: 3−5(−3n+5)3−5(−3n+5)
Answer:
[tex]60n - 97[/tex]
Step-by-step explanation:
[tex]3 - 5( - 3n + 5)3 - 5( - 3n + 5)[/tex]
[tex]3 + (15n - 25)3 + 15n - 25[/tex]
[tex]3 + 45n - 75 + 15n - 25[/tex]
[tex]60n - 97[/tex]
Brandon is going to invest in an account paying an interest rate of 4.6% compounded annually. How much would Brandon need to invest, to the nearest ten dollars, for the value of the account to reach $69,000 in 8 years?
A rectangular garden has a walkway around it. The area of the garden is 6(5. 5x+2. 5). The combined area of the garden and the walkway is 6. 5(8x+4). Find the area if the walkway around the garden as the sum of two terms
The area of the walkway can be expressed as the sum of two terms is 9x + 7 and 10x + 4.
We are given that the area of the garden is 6(5.5x + 2.5). This means that the garden has a length of 5.5x + 2.5 units and a width of 6 units (since the problem doesn't specify which side is the length or width, we can assume either). We can use the formula for the area of a rectangle to find the area of the garden:
Area of the garden = length x width = (5.5x + 2.5) x 6 = 33x + 15
Next, we are given that the combined area of the garden and the walkway is 6.5(8x + 4). This means that the garden and the walkway together have a length of 8x + 4 units and a width of 6.5 units. We can again use the formula for the area of a rectangle to find the combined area:
Combined area = length x width = (8x + 4) x 6.5 = 52x + 26
To find the area of the walkway, we need to subtract the area of the garden from the combined area. This will give us the area of the walkway alone.
Area of the walkway = Combined area - Area of the garden
= (52x + 26) - (33x + 15)
= 19x + 11
Finally, we are asked to express the area of the walkway as the sum of two terms. This means we need to find two numbers that add up to 19 and two numbers that add up to 11. We can use trial and error to find these numbers. One possible solution is:
19x + 11 = (9x + 7) + (10x + 4)
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