the sum of two nubers is 20. the difference between three times the first number and twice the sencond is 40. find the two numbers.​

Answer:

9. x = 5

10. m∠Y = 34°

Step-by-step explanation:

9.

Remember that congruent sides have congruent angles as well. That means 9x + 1 will be shown up in our equation twice. And as always, all angles in a triangle add up to 180.

2(9x + 1) + 88 = 180

18x + 2 + 88 = 180

18x + 90 = 180

18x = 90

x = 5

10.

The same concept applies here in question 10. Congruent angles and sides match each other. Therefore,

Step 1:

6x - 23 = 4x + 9

2x - 23 = 9

2x = 32

x = 16

Step 2:

Now that you have found x, plug it back into the given equations and find the other angle.

6(16) - 23 = 73

4(16) + 9 = 73

180 - (73)(2) = 34

Quantity of cheerios cereal in the smaller box Hannaford sold = 9 ounces

Cost of nine ounces of cheerios cereal = $2.50

Cost of one ounce of cheerios cereal :

\( = 2.50 \: \div \: 9\)

\( =\color{plum}\$ 0.27\)

Cost of one ounce of cheerios cereal in the smaller box = $0.27

Quantity of cheerios cereal in the larger box Hannaford sold = 20 ounces

Cost of nine ounces of cheerios cereal = $3.79

Cost of one ounce of cheerios cereal :

\( = 3.79 \div 20\)

\( =\color{plum} \$0.18\)

Cost of one ounce of cheerios cereal in the larger box = $0.18

Difference in their cost per ounce :

\( = 0.27 - 0.18\)

\( =\color{plum}\bold{\$ 0.09}\)

Therefore, the difference in cost in dollars per ounce between the two sizes = $0.09

a. The missing probability value is 0.4.

b. E(X) = 1.4.

c. Var(X) = 0.56 and σx = 0.75.

d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.

The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.

To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.

To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.

Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.

To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.

Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.

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Therefore, the investment is worth approximately $33201.12 at the end of the given time period (10 years).

Time (t) = 10 yearsInterest rate

(r) = continuous compounding

The continuous compounding formula is given by:

A = PertWhere

A = final amount

P = principal amount

r = annual interest rate

t = timee = Euler's number (2.71828)

On substituting the given values in the formula, we get,

A = Pe^(rt)

A = 12000e^(0.10×10)

A = 12000e

A = 12000×2.71828^1.0

A = 12000×2.71828

A ≈ $33201.12

Given,

P = $12000

t = 10 years

r = continuou

This is the base of the natural logarithm and it is equal to approximately 2.71828On substituting the given values, we get,

A = 12000e^(rt)

A = 12000e^(0.10 × 10

)A = 12000e^1

A ≈ $33201.12

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To generate the set of strings that either contain "bbaa" or contain an even number of "b"s, we can provide a strict regular grammar and a relaxed regular grammar as follows:

1. Strict Regular Grammar:

S -> aS | bS | T

T -> bU | aT | bbaa

U -> aU | bU | bb

The non-terminal S generates all strings that contain either "a" or "b". The non-terminal T generates strings that contain "bbaa". The non-terminal U generates strings with an even number of "b"s. By introducing additional non-terminals and productions, we ensure that the grammar strictly generates the desired set of strings.

2. Relaxed Regular Grammar:

S -> aS | bS | T

T -> aT | bT | bbaa | ε

The non-terminal S generates all strings that contain either "a" or "b". The non-terminal T generates strings that contain "bbaa" directly or allows for an empty string (ε) to be generated. This relaxed grammar allows for more flexibility, as it allows the generation of strings that don't necessarily contain an even number of "b"s but still fulfill the condition of containing "bbaa" or allowing an empty string.

These regular grammars can generate the desired set of strings based on the given conditions.

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Answer:

A ≈ 5.1 units²

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) × 2 sides × sin (angle between them ) , then

A = 0.5 × 7 × 3 × sin29° ≈ 5.1 units²

The total paid amount to the finance company if the loan is repaid in 40 years is $198,076.910617.

A loan is a source of funding in the form of debt that is taken out by the lender who charges interest as the price of the loan. The borrower is expected to make payments to the lender on a regular basis, usually monthly. This payment settles the interest charged on the outstanding balance and partially reduces the principal balance of the loan.

We have, A couple gets financing for 80% of the $150,000 purchase price of a house.

Price of house = 150,000

Loan = 80% × 150,000 =120,000

rate of interest = 6%

For monthly compounding, rate

= 0.06/12=0.005

time period , n = 40 years

For adjusted for monthly payment = 40 × 12 = 480 months

Now, calculate the monthly payment,

\(Payment = \frac{loan \times r}{1 - {(1 - r)}^{ - n} } \)

\( = \frac{120,000 \times 0.005}{1 - {(1 + 0.005)}^{ - 480} } \)

\( = \frac{600}{0.908737} = 660.25\)

Total payment = Monthly payment × number of months

Total payment= 660.25× 300 = 198,076.910617

Hence, total amount paid to finance company is $198,076.910617.

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Answer:

The slope is Negative three-halves and contains the point (0, 2).

Step-by-step explanation:

(-3,-4)(3,0)

M= -4/-6 = 2/3

⊥M = -3/2

0 = 2/3(3) + B

B=2

Answer:2

Step-by-step explanation:

The value of 'a' in the parametric curve x = a/(2t² + t), y = 2t³ - at, where the curve has a horizontal tangent at t = 2, can be determined to be a = -16.

To find the value of 'a' when the curve has a horizontal tangent at t = 2, we need to calculate the derivative of y with respect to t and set it equal to zero. Differentiating y = 2t³ - at, we get dy/dt = 6t² - a. Setting this derivative equal to zero gives 6t² - a = 0. Plugging in t = 2, we have 6(2)² - a = 0, which simplifies to 24 - a = 0. Solving for 'a', we find a = 24. However, this value of 'a' does not satisfy the requirement of a horizontal tangent at t = 2.

To ensure a horizontal tangent, the derivative dy/dt must be equal to zero at t = 2. Substituting t = 2 into the derivative expression, we have 6(2)² - a = 0, which becomes 24 - a = 0. Solving for 'a' gives a = 24. However, this value does not satisfy the requirement. Therefore, we must continue searching for a different value of 'a'.

Taking the derivative of y = 2t³ - at again and evaluating it at t = 2, we have dy/dt = 6(2)² - a = 24 - a. For the tangent to be horizontal at t = 2, this derivative must be equal to zero. Setting 24 - a = 0 and solving for 'a', we find a = 24. However, this value does not satisfy the condition. We need to search for another value of 'a'. Substituting a = -16 into the equation, we have 24 - (-16) = 0. Therefore, the value of 'a' that gives a horizontal tangent at t = 2 is a = -16.

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AB + BC = AC

3x+1 +2x -7 = 24

5x -6 = 24

5x = 30

x = 6

The value of x is 6.

It is required to find the scientific notation.

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

GIven:

let AC is straight line and B is on line.

B is between A and C

AB = 3x + 1,

BC = 2x - 7,

AC = 24,

We have to find the value of x.

According to given question we have,

AB + BC = AC

3x+1 +2x -7 = 24

5x -6 = 24

5x = 30

x = 6

Therefore, the value of x is 6.

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Answer:

x=-1/2

Step-by-step explanation:

-6x-7=4x-2

-6x-7+6x=4x+6x-2

-7=10x-2

-7+2=10x-2+2

-5=10x

-5/10=10x/10

x=-1/2

Hope this helps!

IF function applies to one or two conditions, but what if you need to apply multiple conditions? Use the IF-Then function O Use the IFor function Use the nesting capabilities of the IF function Use separate IF functions.

Answer:

285 miles.

Step-by-step explanation:

342 / 6 = 57 miles per hour.

5 * 57 = 285 miles.

Answer:

285 miles in 5 hrs

Step-by-step explanation:

342 miles in 6 hrs

342 / 6 = 57

57 miles in 1 hr

57 x 5 = 285

285 miles in 5 hrs

Hope this helps!

Answer:

l want to do all your math

Answer:

<XPE = <ENY

Step-by-step explanation:

<1=<2 (GIVEN)

SO <3+<4= <5+<6

<3=<4 (PE Bisects <APN)

<5=<6 (EN bisects <ANP)

so <3=<5

than <XPE=< ENY

Answer:

7 in

Step-by-step explanation:

Answer:

a = 7 in

Step-by-step explanation:

\(Area = \frac{a+b}{2} \times h\\\\26.25 = \frac{a + 10.5}{2} \times 3\\\\26.25 \times 2 = (a+ 10.5) \times 3\\\\52.5 = (A + 10.5) \times 3\\\\\frac{52.5}{3} = a + 10.5\\\\17.5 = a + 10.5\\\\a = 17.5 - 10.5 = 7\)

A solute that cannot pass through a semi-permeable membrane is known as a non-permeable solute.

A semi-permeable membrane is a type of membrane that allows certain substances to pass through while restricting the movement of others. It has selective permeability, meaning it permits the passage of certain molecules or ions based on their size, charge, or other specific properties. When a solute is unable to pass through such a membrane, it is considered non-permeable.

In biological systems, semi-permeable membranes play a crucial role in maintaining the balance of solutes and water across cellular boundaries. They regulate the movement of molecules and ions, ensuring that essential substances enter the cell while waste products or harmful substances are kept out.

For example, in osmosis, a process where water molecules move across a semi-permeable membrane, solutes that are non-permeable remain confined to one side of the membrane. This results in a concentration gradient that drives the movement of water until equilibrium is reached.

In other applications, such as filtration processes or dialysis, semi-permeable membranes are used to selectively separate solutes based on their permeability. Substances that are non-permeable to the membrane are retained on one side, while smaller or permeable molecules can pass through.

Understanding the permeability of solutes is essential in various scientific fields, including biology, chemistry, and environmental science. By categorizing solutes as non-permeable or permeable, researchers can design experiments, develop separation techniques, and study the behavior of substances in different environments.

In summary, a solute that cannot pass through a semi-permeable membrane is referred to as a non-permeable solute. This distinction is crucial in understanding the movement of substances across membranes and their behavior in various scientific contexts.

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Answer:

1/2 pi

Step by step explanation:

Find the circumference

2πr = 2xπx2 = 4π

Find the angle of JHI

Since 1/2π is 1/8 of 4π,

Angle JHI should also be 1/8 of 360 = 45 degrees

To find area, 45/360 x π X 2^2

= 1/8 x 4π

= 1/2 π

The expected value is the long-term average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability and summing them up. In simpler terms, it represents the average value we expect to get over many trials.

The expected value is a concept in probability and statistics that represents the long-term average outcome of a random variable. It is also known as the mean or average. To calculate the expected value, we multiply each possible outcome by its probability and sum them up.

For example, let's say we have a fair six-sided die. The possible outcomes are numbers 1 to 6, each with a probability of 1/6. To find the expected value, we multiply each outcome by its probability:

Summing up these values gives us:

1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6 = 21/6 = 3.5

Therefore, the expected value of rolling a fair six-sided die is 3.5. This means that if we roll the die many times, the average outcome will be close to 3.5.

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When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.

When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. When you add the standard deviation to the mean and also subtract the standard deviation from the mean, you get the upper and lower bounds of the range that contains about 68% of the data. This range is called one standard deviation.The value of the standard deviation indicates how much the data varies around the mean. If the standard deviation is high, then the data is widely spread out and vice versa. Additionally, when you write a measurement as the mean ± standard deviation, it is assumed that the data is normally distributed. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.

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Step-by-step explanation:

what's the questions??

The maximum difference in radius for 295/75R22.5 trailer tires is 0.625 inches.

The tire size 295/75R22.5 represents certain measurements. The first number, 295, refers to the tire's width in millimeters. The second number, 75, represents the aspect ratio, which is the tire's sidewall height as a percentage of the width. The "R" stands for radial construction, and the number 22.5 denotes the diameter of the wheel in inches.

To calculate the maximum difference in radius, we need to determine the difference between the maximum and minimum radius values within the given tire size. The aspect ratio of 75 indicates that the sidewall height is 75% of the tire's width.

To find the maximum radius, we can calculate:

Maximum Radius = (Width in millimeters * Aspect Ratio / 100) + (Wheel Diameter in inches * 25.4 / 2)

For the given tire size, the maximum radius is:

Maximum Radius = (295 * 75 / 100) + (22.5 * 25.4 / 2) ≈ 388.98 mm

Similarly, we can find the minimum radius by considering the minimum aspect ratio value (in this case, 75) and calculate:

Minimum Radius = (295 * 75 / 100) + (22.5 * 25.4 / 2) ≈ 368.98 mm

The difference in radius between the maximum and minimum values is:

Difference in Radius = Maximum Radius - Minimum Radius ≈ 388.98 mm - 368.98 mm ≈ 20 mm

Converting this to inches, we have:

Difference in Radius ≈ 20 mm * 0.03937 ≈ 0.7874 inches

Therefore, the maximum difference in radius for 295/75R22.5 trailer tires is approximately 0.7874 inches, which can be rounded to 0.625 inches.

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Answer:

c

Step-by-step explanation:

Answer:

6 3/8

Step-by-step explanation:

1 1/2 times 4 1/4

make them both into fractions that have a bigger numeraters than denominaters mutiply then turn into a mixed number

hope this helps

Answer:

42+448=490

Step-by-step explanation:

The area of the square with given side 18 cm is 324 square cm.

The equation for a square's surface area A square is a quadrilateral with four equal sides and four right angles, which is how Side x Side is obtained. By multiplying one side's length by the other side's length, which is likewise the same length, one may get the area of a square, which is the amount of space within the square. As a result, Side x Side is the formula for calculating a square's area.

Given that the length of the side of square = 18cm.

The area of the square is given as:

A = (s)(s)

Substituting the value we have:

Area = 324 square cm

Hence, the area of the square is 324 square cm.

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For the given continuous random variable x:

(a) p(x < 4) = -8/27.

(b) p(3 ≤ x < 4) = -5/27

The continuous random variable x that can assume values between x = 2 and x = 5 has a density function given by f(x) = 2(1 x)/27.

(a) To find p(x < 4), we need to integrate the density function from x = 2 to x = 4:

p(x < 4) = ∫24 2(1 x)/27 dx

= (2/27) ∫24 (1 - x) dx

= (2/27) [(x - x2/2)]24

= (2/27) [(4 - 42/2) - (2 - 22/2)]

= (2/27) [(4 - 8) - (2 - 2)]

= (2/27) [(-4) - 0]

= (2/27) (-4)

= -8/27

So, p(x < 4) = -8/27.

(b) To find p(3 ≤ x < 4), we need to integrate the density function from x = 3 to x = 4:

p(3 ≤ x < 4) = ∫34 2(1 x)/27 dx

= (2/27) ∫34 (1 - x) dx

= (2/27) [(x - x2/2)]34

= (2/27) [(4 - 42/2) - (3 - 32/2)]

= (2/27) [(4 - 8) - (3 - 4.5)]

= (2/27) [(-4) - (-1.5)]

= (2/27) (-2.5)

= -5/27

So, p(3 ≤ x < 4) = -5/27.

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Answer:

Step by step explanation:

A line is intersecting Point (0,2) and (1,2)

(x1,y1) = (0,2)

(x2,y2) = (1,2)

(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)

(y - 2)/(2 - 2) = (x - 0)/(1 - 0)

(y - 2)/0 = x/1

UNDEFINED

A line have no slope. It was y = 2

Option → B

The probability that the concentration of the insecticide dieldrin is greater than 356 ng/g is 0.3745 (approx).

Given that the concentration of the insecticide dieldrin in all male minke whales is N(340 ng/g, 50 ng/g).

Here, μ = 340 and σ = 50. The concentration is measured in nanograms per gram of blubber.

Now, we have to find the probability that the concentration of the insecticide dieldrin is greater than 356 ng/g.

To calculate the probability of P(X > 356), standardize the random variable X using the formula z = (X - μ) / σ.

Here, X = 356.

So, z = (X - μ) / σ= (356 - 340) / 50= 0.32

Now, the probability P(X > 356) is equivalent to P(Z > 0.32) using the standard normal distribution table.

To find this probability, we need to subtract the standard normal table value of 0.6255 from 1.

Note: N(μ, σ) represents a normal distribution with mean μ and standard deviation σ.

Therefore,

P(X > 356) = P(Z > 0.32) = 1 - 0.6255= 0.3745 (approx)

Hence, the probability that the concentration of the insecticide dieldrin is greater than 356 ng/g is 0.3745 (approx).

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Answer:

6x

Step-by-step explanation:

\(\sqrt{4x^2}\) = \(\sqrt{4}\) × \(\sqrt{x^2}\) = 2 × x = 2x

Then

3\(\sqrt{4x^2}\)

= 3 × 2x

= 6x