If 36 is added to a number, it will be 4 times as large as it was originally. Find the number

Answer: The sales tax is $2.5 and her total cost of the shirt is $47.5.

Step-by-step explanation:

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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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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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:

Step-by-step explanation:

Answer:5.5

Step-by-step explanation:

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.

Answer:

0.262

Step-by-step explanation:

1 - 0.738 = 0.262

0, 738 + 0.262 = 1

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:

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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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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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 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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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:

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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After 40 years, the account has a total balance of $49.450.80.

Any loans or borrowings come with interest. the portion of the loan's value that lenders use to calculate interest. By lending money (via a bond or certificate of deposit, for instance), or by depositing funds into an interest-bearing bank account, consumers can earn interest.

Let's assume that he starts with $0 in the account and makes a monthly contribution of $100 for 40 years, which is equal to 40 x 12 = 480 months.

The total contributions would be $100 x 480 = $48,000.

The interest earned on the account balance can be calculated as follows:

Interest = Account balance * Interest rate

At the end of each year, the interest is added to the account balance. So, after 40 years, the balance would be:

Year 1: $48,000 * 1.5% = $720

Balance = $48,000 + $720 = $48,720

Year 2: $48,720 * 1.5% = $730.80

Balance = $48,720 + $730.80 = $49,450.80

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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 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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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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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:

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.

The magnitude of the sum of these two vectors is 2.9486m

In trigonometry, the law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one of its angles.

The parameters that will help us to find the magnitude are

/OB/ = 3.14m

/OA/ = 2.71 m

Let /AB/= x

Sum of the angles is (-60+30)⁰ = 30⁰

Using cosine rule

x²= 3.14² +2.71² - 2*3.14*2.71 *cos30⁰

x² = 9.8596+7.3441 -8.5094

x²= 17.2037 -8.5094

x²= 8.6943

x = √8.6943

x = 2.9486

Therefore, the magnitude of the sum

of these two vectors is 2.9486m or 2.9m approximately

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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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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: 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:

In the cyclic quadrilateral the value of R and S are

< S = 87 degrees

< R = 216 degrees

In a cyclic quadrilateral, the opposite angles are supplementary hence

< S + < Q = 180

in the problem we have that < Q = 93

< S + 93 = 180

< S = 180 - 93

< S = 87 degrees

Angle R is adjacent angle to angles 126 and 90 hence we have that

< R = 126 + 90

< R = 216 degrees

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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.