A population mean is normally distributed with a mean of 56 and a standard deviation of 12.

Answer: Let's call Mary's walking speed "w". Then, her jogging speed is 2w.

The total distance of the trip was 13.5 + 1.5 = 15 miles.

The total time she spent jogging was 1.5 hours, so the time she spent walking was 1.5 - 1.5 = 0 hours.

Her average speed for the whole trip was 15 miles / 1.5 hours = 10 miles per hour.

So, we can set up the equation:

(13.5 miles / 2w) + (1.5 miles / w) = 1.5 hours

We can substitute 2w for jogging speed and w for walking speed, and simplify:

(13.5 miles / 2w) + (1.5 miles / w) = 1.5 hours

13.5 / 2w + 1.5 / w = 1.5

27 / 2w = 1.5

2w = 27 / 1.5

2w = 18

Finally, we can find Mary's jogging speed by dividing the expression for 2w by 2:

w = 18 / 2

w = 9

So, Mary's jogging speed was 9 miles per hour.

Step-by-step explanation:

Answer:

(-9)×(-7/3)=9×7/3=3×7=21

Answer:

21

Step-by-step explanation:

-9 is equal to -9/1

the negative sign on the -7/3 can be put on the top or bottom

-9 -7 63

--- x --- = ---

1 3 3

63 divided by 3 equals 21 and is therefore in the simplest form

Answer:

Step-by-step explanation:

Step 1: Understand the formula for the circumference of a circle

The formula for the circumference of a circle is given by:

C = 2 * π * r

where C is the circumference of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. This formula expresses the relationship between the radius and the circumference of a circle.

Step 2: Substitute the radius of the circle for "r" in the formula

Let's say the radius of the circle is "r". Substitute "r" for "r" in the formula for the circumference:

C = 2 * π * r

Step 3: Divide the circumference by the radius

Now that you have the formula for the circumference, divide the circumference by the radius:

C/r = 2 * π

Step 4: Simplify the expression

The expression on the right side of the equation can be simplified to 2 times pi:

C/r = 2 * π

C/r = 2 * 3.14 = 6.28

Step 5: Conclusion

Therefore, it would take 6.28 radii laid end to end to fit exactly around the circumference of the circle.

Note: This answer is only an approximation, as the value of π is an irrational number that cannot be expressed exactly as a fraction or a decimal.

The solution is, the value of  (f• Hºg)(x) = 4x+2.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

f(x) = x-4

g(x) = x+ 2,

and h(x) = 4x+1

now, (f• Hºg)(x)

= (f•(4(x+2)+1)(x)

=((4x+6)-4)

=4x+2

Hence, The solution is, the value of  (f• Hºg)(x) = 4x+2.

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The 50% of the data lies above is 49.5. it is called the median.

What is the upper quartile?

Assume that Q₃ represents the upper quartile, which is the median of the data set's upper half. In contrast, Q₁ represents the median and lower quartile of the lower half of the data set. The median is Q₂. Consider a data set that contains n items. The quartiles are then provided by:

Q₁ = [(n+1)/4]

Q₂ = [(n+1)/2]

Q₃ = [3(n+1)/4]

this item

The 50% of the data is median.

The formula of median is

(n+1)/2 th term

The given data is 41, 43, 49.5, 56, and 58.

The number of items is n = 5.

The median of the data is (5+1)/2 the term = 3rd term.

The third term of the data is 49.5.

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Answer:

If the ratio of the length to width of the rectangle is 3 to 2, we can write the length and width as:

length = 3x and width = 2x

where x is a common factor that can be determined once we know one of the dimensions.

Since the length of the rectangle is given as 1 3/4 feet, we can set x = 1 3/4:

length = 3x = 3 * 1 3/4 = 5 1/4 feet

width = 2x = 2 * 1 3/4 = 3 1/2 feet

Now that we know the length and width of the rectangle, we can calculate its area in square inches:

area = length * width = 5 1/4 * 3 1/2 = 18 3/8 square feet

To convert from square feet to square inches, we multiply by 12^2 = 144:

area = 18 3/8 * 144 = 2664 square inches

So the area of the rectangle is 2664 square inches.

Answer: Sure! Here is a table showing the value of y for different values of x using the equation y = 1/3x + 2:

x                                y

1                                2.33

2                               2.67

3                               3.00

4                               3.33

5                               3.67

Note that the values of x in the table are just examples, you can use any value of x that you want to find the corresponding value of y.

Step-by-step explanation:

Answer:

0.262

Step-by-step explanation:

1 - 0.738 = 0.262

0, 738 + 0.262 = 1

Answer:

smaller value = 4yd

larger value = 8yd

Step-by-step explanation:

Let's call the garden's width and length W and L respectively.

The area of the garden is 36yd². We can write this mathematically as W*L=36

If 26yd is enough fencing to perfectly enclose the garden, then this must be the garden's perimeter. Written mathematically, this is 2W+2L=26. We can simplify this by dividing each term by two to get W+L=13

If W and L multiply to get 36, they must be both a factor pair of 36. The factor pairs of 36 (the pairs of numbers which multiply to get 36) are '1 and 36', '2 and 18', '3 and 12', '4 and 9', and '6 and 6'.

W and L must also add to 13, and the only factor pairs of 36 which add to 13 are '4 and 9' so these are our dimensions.

Answer:

smaller value = 4yd

larger value = 8yd

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Tone is the feeling the author wants the reader to have when reading his or her work. Anaya employs tone to generate the texts "Take the Tortillas out of your poetry" and "Speaking Arabic."

Both authors explore regional cuisine and make use of terminology from various languages.

While Nye's tone is welcoming of mixed cultures, Anaya's tone is sincere towards culture and indignant towards suppression.

The funny tone of Anaya's writing reflects his intention to draw attention to the subject. The laid-back nature of Anaya's delivery is evident.

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Answer:

1

Step-by-step explanation:

f(x)=x3+2x2-x-2

...................

The Roots of the given polynomials shown below f(x) = x^3+2x^2-x-2 are -1, 1, -2.

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and nonnegative exponentiation of variables involved.

Example: x² + 3x + 3 is a polynomial.

Since, The given polynomials is,

f(x) = x³ + 2x²-x-2

Now, Solve as;

f(x) = x³ + 2x²-x-2

f (x) = x² (x + 2) - 1 (x + 2)

f (x) = (x² - 1) (x + 2)

Hence, The Roots of the polynomials : -1, 1, -2

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The statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.

In relation to the original function f, the inverse function is denoted by the symbol f⁻¹, and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function.

We know that inverse of function is NOT the reciprocal of f. The composition of the function f and the reciprocal function f inverse gives the domain value of x.

Hence, the statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.

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The given expression can be written in a single radical as q³ .   [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]. The solution has been obtained by solving the radical expressions.

What are radical expressions?

An expression which contains a square root is referred to as a radical expression. The 'V'-shaped portion of the radical sign will have a superscript number when it is used to represent any root other than a square root.

We are given √q³ [tex]\sqrt[3]{q^{8} }[/tex].

On simplifying the expression, we get

⇒√q² . q [tex]\sqrt[3]{q^{3} . q^{3} . q^{2} }[/tex]

⇒q . √q . q² .  [tex]\sqrt[3]{ q^{2} }[/tex]

⇒q³ . √q  [tex]\sqrt[3]{ q^{2} }[/tex]

⇒q³ . [tex]\sqrt[]{ q^{\frac{1}{2} + \frac{2}{3} } }[/tex]

⇒q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]

Hence, the given expression can be written  in a single radical as q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex].

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The truth value for the logical proposition is 1) T 2) F 3) T 4) F 5) T

The rules of mathematical logic specify methods of reasoning mathematical statements. Greek philosopher, Aristotle, was the pioneer of logical reasoning. Logical reasoning provides the theoretical base for many areas of mathematics and consequently computer science. It has many practical applications in computer science like the design of computing machines, artificial intelligence, the definition of data structures for programming languages etc.

Propositional Logic is concerned with statements to which the truth values, “true” and “false”, can be assigned. The purpose is to analyze these statements either individually or in a composite manner

the truth value of the following statements if the universe of discourse of each variable is the set of real numbers. Enter your answer as T or F.

1) there exists x for all y xy=0  is true     T

2) there exist x x2=-1                               F

3) for all x2=y                                           T

4) for all x there exist  x=y2                     F

5) for all x not equal to zero xy=1           T                            

The complete question is -

the truth value of the following statements if the universe of discourse of each variable is the set of real numbers. Enter your answer as T or F.

1) there exists x for all y xy=0  is true    

2) there exist x x2=-1                              

3) for all x2=y                                          

4) for all x there exist  x=y2                    

5) for all x not equal to zero xy=1      

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On solving the provided question, we can say that  the linear equation are 3y - 2x = -9 and y = -2x +5 => 3(-2x +5) - 2x = -9 => x = 3

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

the linear equation are

3y - 2x = -9 and y = -2x +5

3(-2x +5) - 2x = -9

-6x + 15 -2x = -9

-8x = -24

x = 3

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The others operate in a similar manner. The following must be done, however, in order to determine the probability of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat:  1 - P(kit-kat)

You only need to multiply the quantity of the selected candy by the total number of candies if you choose to put each piece of candy back after choosing it.

In this case, the desired confectionery is P(snickers). 12 in number.

In total, the bag contains 20 sweets.

P(snickers) = 12/20 = 3/5

The others function in the same way. The following must be done, however, in order to determine the likelihood of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat:

1 - P(kit-kat)

The complete question is:

Suppose a bag of candy contains 12 Snickers, 5 Kit-Kats, and 3 Three Musketeers. Find each probability if you choose one piece of candy at random.

a) P(Snickers) b) P(Kit-Kat) c)P(Three Musketeers) d) P(not Kit-Kat)

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The supportive statement regarding the trapezoid based on the information is m∠WKT ≅ m∠TRW.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

The non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

The missing statement to support all other statements would be that m∠WKT ≅ m∠TRW as the angle formed by the pair of the corresponding sides is equal.

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Answer:

Step-by-step explanation:

Here's a step-by-step solution to finding the probabilities of the time between customer arrivals:

a. less than 20 seconds:

To find the probability that the time between arrivals is less than 20 seconds, we need to find the cumulative distribution function (CDF) of the time between arrivals and evaluate it at 20 seconds. The CDF for a uniform distribution is given by:

F(x) = x/b - a/b, where a is the lower bound and b is the upper bound of the distribution

For this problem, the lower bound a is 0 and the upper bound b is 120, so the CDF of the time between arrivals is:

F(x) = x/120

Now, we can evaluate the CDF at 20 seconds to find the probability that the time between arrivals is less than 20 seconds:

F(20) = 20/120 = 1/6

So, the probability that the time between arrivals is less than 20 seconds is 1/6.

b. between 10 and 30 seconds:

To find the probability that the time between arrivals is between 10 and 30 seconds, we need to find the difference between the CDFs at 30 seconds and 10 seconds:

F(30) - F(10) = 30/120 - 10/120 = 3/12 - 1/12 = 2/12 = 1/6

So, the probability that the time between arrivals is between 10 and 30 seconds is 1/6.

c. more than 35 seconds:

To find the probability that the time between arrivals is more than 35 seconds, we need to subtract the CDF at 35 seconds from 1:

1 - F(35) = 1 - 35/120 = 85/120 = 7/12

So, the probability that the time between arrivals is more than 35 seconds is 7/12.

d. Mean and standard deviation:

The mean of the time between arrivals is given by the average of the lower and upper bounds of the distribution:

mean = (a + b)/2 = (0 + 120)/2 = 60

The standard deviation of the time between arrivals for a uniform distribution is given by:

standard deviation = (b - a)/(2 * sqrt(3))

For this problem, the standard deviation is:

standard deviation = (120 - 0)/(2 * sqrt(3)) = 60/sqrt(3) ≈ 34.64101615

So, the mean time between arrivals is 60 seconds and the standard deviation is approximately 34.64 seconds.

a. The less than 20 seconds 0.1667.

b. The between 10 and 30 seconds 0.1667.

c.  The more than 35 seconds 0.7083.

d.  The mean and standard deviation of the time between arrivals 34.64 seconds.

To solve the probability questions, to find the probability density function (PDF) of the uniform distribution for the time between customer arrivals. In a uniform distribution, the probability density is constant within the given range.

Given:

Time between arrivals follows a uniform distribution between 0 to 120 seconds.

a. Probability of time between arrivals being less than 20 seconds:

Since the probability density is constant within the given range, we can calculate the probability by dividing the time range of interest (20 seconds) by the total time range (120 seconds).

Probability = (Time of interest) / (Total time range) = 20 / 120 = 1/6 ≈ 0.1667

b. Probability of time between arrivals being between 10 and 30 seconds:

Similar to part (a), the probability for this interval can be found by dividing the time range of interest (30 - 10 = 20 seconds) by the total time range (120 seconds).

Probability = (Time of interest) / (Total time range) = 20 / 120 = 1/6 ≈ 0.1667

c. Probability of time between arrivals being more than 35 seconds:

In this case, we need to calculate the probability of the time between arrivals being in the range from 35 to 120 seconds (as it is more than 35 seconds).

Probability = (Time of interest) / (Total time range) = (120 - 35) / 120 = 85 / 120 ≈ 0.7083

d. Mean and standard deviation of the time between arrivals:

In a uniform distribution, the mean (μ) can be calculated as the average of the minimum and maximum values in the range.

Mean (μ) = (Minimum value + Maximum value) / 2 = (0 + 120) / 2 = 60 seconds

The standard deviation (σ) for a uniform distribution can be calculated using the formula:

Standard deviation (σ) = (Maximum value - Minimum value) / √12

Standard deviation (σ) = (120 - 0) / √12 ≈ 34.64 seconds

So, the mean time between arrivals is 60 seconds, and the standard deviation is approximately 34.64 seconds.

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The ration will be sinA =[tex]\frac{P}{H}[/tex] =[tex]\frac{33}{65}[/tex] , cosA = [tex]\frac{B}{H}[/tex]=[tex]\frac{56}{65}[/tex]  & tanA = [tex]\frac{P}{B}[/tex]= [tex]\frac{33}{56}[/tex].

The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question; and its "adjacent" side is the one that faces it. We use particular terminology to define the sides of right triangles. A right triangle's hypotenuse is always side opposite the right angle.

When one of a triangle's angles is exactly 90 degrees, the triangle is said to be right-angled. The remaining two angles together equal 90 degrees.. The sides that make up the right angle are perpendicular and the triangle's base. The third side, also referred to as the hypotenuse, is the longest of the three sides.

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Answer:

Step-by-step explanation:

The balance of the savings account after 48 months can be calculated using the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A is the balance after t years

P is the principal (initial amount)

r is the interest rate (as a decimal)

n is the number of times compounded per year

t is the number of years

Step-by-step, the calculation is as follows:

Convert the interest rate from a percentage to a decimal:

r = 7% = 0.07

Determine the number of times compounded per year:

n = 2 (compounded semi-annually)

Determine the number of years:

t = 48 months / 12 months/year = 4 years

Plug the values into the formula:

A = P * (1 + r/n)^(nt)

A = $3500 * (1 + 0.07/2)^(2 * 4)

Calculate the balance using the formula:

A = $3500 * (1.035)^8

A = $3500 * 1.306769

A = $4588.72

So, the balance in the savings account after 48 months is $4588.72.

Answer:

<1 and <2

Step-by-step explanation:

Adjacent means angles that are next to each other.  This is not the only pair, but <1 and <2  are adjacent.

The requried domain for the given relationship is (0, 12) or 0 ≤ x ≤ 12.

The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.

here,
The domain of a function represents the set of all possible input values. In this case, the function y = 60 - 5x represents the number of gallons of water left in the pool after x minutes of draining.

So the maximum value of water in the pool left is 60 gallons, while the water is draining at the rate of 5 gallons per minute After a certain minute the water will left be zero gallons(y = 0).

0 = 60 - 5x
-5x = -60
x = 12 minutes

Thus, the requried domain for the given relationship is (0, 12) or 0 ≤ x ≤ 12.

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In the algebra on of the form of sequence is arithmetic progression or sequence which is described below.

In the arithmetic sequence  the common difference between any two consecutive terms remains constant .

In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).

Formula for any nth term in AP,

T = a + nd

d = T₂-T₁

Where, a is first term , n is nth term and d is common difference

If aₙ = aₙ₋₁  -4

where aₙ is a nth term and aₙ₋₁ is a (n-1)th term

Now,

a + nd  = a + (n-1-1)d - 4

nd   = (n - 2)d - 4

nd = nd -2d - 4

2d = -4

d = -2

So, aₙ = a -2n

aₙ₋₁ = a -2(n - 2)

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On solving the given system of equations →

Eq { 1 } :  - 3x + y = 11

Eq { 2 } :  4x + 3y = 7

using substitution, we get {x} = -2 and {y} = 5.

In mathematics, a system of equations is a pair of equations which have a common set of solutions.

Given is the system of equations as -

- 3x + y = 11

4x + 3y = 7

The given system of equations is -

- 3x + y = 11

4x + 3y = 7

Now, we can write -

y = 11 + 3x

So -

4x + 3(11 + 3x) = 7

4x + 33 + 9x = 7

16x = - 26

{x} = - 2

Then, we can write -

- 3 x - 2 + y = 11

{y} = 5

Therefore, on solving the given system of equations using substitution, we get {x} = -2 and {y} = 5.

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The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

What is meant by continuous compounding?

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.

Given,

rate per period  = 3%

Principal amount = $1000

Compounding is done after 1,5 and 20 years.

But we are asked to find the amount after continuous compounding after 1 year.

The formula of the amount after continuous compounding is:

[tex]A = Pe^{rt}[/tex]

where A = amount after continuous compounding

        r = rate of period

     t = time period

    P  = principal amount

[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45

Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]

n = times it compounds per year = 365

r = 0.03

AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]

                                  = 3.04%

Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

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Using division operation, the number of containers that Linden would get from his supply of milk is 79 containers.

Division operation involves the dividend divided by the divisor to obtain a result called the quotient.

Division operation is one of the four basic mathematical operations, including multiplication, addition, and subtraction.

Total liters of milk = 237

The content of the liter containers = 3 liters

The number of containers = 79 (237 ÷ 3)

Thus, based on division operation, Linden, who is sharing 237 liters of milk in containers will need 79 3-liter containers.

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Answer:

no solution

Step-by-step explanation:

- (3x + 1) + 7 = 4 - (3x + 2) ← distribute parenthesis on both sides

- 3x - 3 + 7 = 4 - 3x - 2

- 3x + 4 = 2 - 3x ( subtract 4 from both sides )

- 3x = - 2 - 3x ( add 3x to both sides )

0 = - 2 ← false statement

this false statement indicates the equation has no solution

-(3x+1)+7=4-(3x + 2)

-3x-1+7=4-3x-2

-3x+6=-3x+2

-3x+3x=-4

0=-4

no solution

㏒Answer:

Step-by-step explanation: