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a) Isaac is purchasing two pairs of shoes—one pair for $37. 00 and the second pair for $42. 0. The state sales tax applied to Isaac’s bill is 7%. How much is Isaac’s total bill? Show your work. (2 points)


b) If Isaac uses a coupon entitling him to a 25% discount off the purchase price before tax, how much will his bill be? Assume that a 7% sales tax is applied to the discounted price. Using words, explain how you found the discounted price. (3 points)

250 milliliters is equal to 0.25 liter

The conversion factor to convert milliliter to liters is 0.001

Therefore, the equation will be,

1  ml = 0.001 liter

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The volume in liters = The volume in ml × conversion factor

Substitute the values in the equation

1 ml = 0.001 liters

250 ml =  0.001 × 250

Multiply the numbers

= 0.25 liters  

Therefore, 250 ml is 0.25 liters

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Answer:The width of the rectangle is 1 unit

Step-by-step explanation:Let the length of the rectangle be x

let the breadth be x-5

Since ,area of rectangle=length*breadth

           area = x*(x-5)

           6=x^2-5x

           x^2-5x-6=0

solving the above equation,

x^2-(6x-x)-6=0

x^2-6x+x-6=0

x(x-6)+1(x-6)=0

(x-6)(x+1)=0

x=6 and x=-1

since the breadth cannot have negative value

Hence ,the breadth of rectangle is 1 unit

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The inverse of the sine can be calculated by using the formula sin^-1(x) = arcsin(x)

To calculate the inverse sine (sin^-1) of a value, you can use a scientific calculator or look up the value in a trigonometric table. However, if you want to understand how to do it manually, follow these steps:

Make sure the value you are calculating the inverse sine of is between -1 and 1, inclusive. If it is not, the inverse sine is undefined.

Write down the value you want to find the inverse sine of.

Use the formula: sin^-1(x) = arcsin(x), where x is the value you wrote down.

Substitute the value of x into the formula and calculate the inverse sine using a calculator or by using a series expansion or Taylor series approximation.

The inverse sine function returns a value in radians, so you may need to convert it to degrees if that's the unit you're working with.

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Answer:

[tex]x=12[/tex], PM = 27, OM = 54

Step-by-step explanation:

To find x, we can notice that MP is similar to OP. Therefore, we can create an equation:

[tex]2x+3=4x-21[/tex]

[tex]2x-4x=-21-3[/tex]

[tex]-2x=-24[/tex]

[tex]x=12[/tex]

To solve for PM, we can plug in x from [tex]2x+3[/tex]:

[tex]2(12)+3[/tex]

= 27

To solve for OM, we will need to add OP and PM values and plug in x:

[tex]4x-21+2x+3[/tex]

Plug in x:

[tex]4(12)-21+2(12)+3[/tex]

= 54

Answer: r = 5.5%

Step-by-step explanation:

6/12 = 0.5 (years)

(I=Prt) || 1375 = 50000 * r * 0.5

1375 = 25000r

1375/25000 = 25000r/25000

0.055 = r

0.055 * 100% = r

5.5% = r

(Please correct me if I'm wrong)

Answer:(10,7)

Step-by-step explanation:

Answer:

(10 , 7)

Step-by-step explanation:

You start at the point (7 , 2)

Moving up 5 units is going up on the y axis, therefore add 5 to 2.

(7 , 7)

Moving to the right 3 times is going to the right on the x-axis, and since moving to the right is positive, add 3 to 7.

[(10 , 7)]

Answer:

2700ft³ or 76455.49 litre

Step-by-step explanation:

Given

Length = 25 feet

Width = 18 feet

Height = 6 feet

Formula for Volume of cuboid = Length×Width×Height

So,

Volume of the pool = 25×18×6 = 2700ft³ or 76455.49 liters aprox.

Hugh made 110 kilograms of 9.1% salt solution.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Hugh poured 100 kilograms of water into 10 kg of salt.

So, the total mass is the sum of the mass of water and the mass of salt.

Thus, 100+10=110 kg.

The ratio between the mass of the salt (10 kg) and the combined mass of the mixture is the concentration.

Now, C=10/110 ×100

= 100/11

= 9.1%

Therefore, Hugh made 110 kilograms of 9.1% salt solution.

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Answer:

42 meters

Step-by-step explanation:

The length of the factory floor will be 42 meters. This is found by multiplying the length of 0.3 meters by the scale factor of 140, which yields 42 meters.

Answer:

42 meters

Step-by-step explanation:

its correct :)

Answer:

$3,096

Step-by-step explanation:

To find the total interest Mr. Quesada will pay, we need to first calculate the total amount he will pay back, and then subtract the original amount borrowed.

The total amount Mr. Quesada will pay back over 24 months is:

$629 x 24 = $15,096

Subtracting the original loan amount, we get:

$15,096 - $12,000 = $3,096

So Mr. Quesada will pay a total of $3,096 in interest over the course of the loan.

Answer:

sum of all side of Pentagon= 540

10x+6x+4x+3x+x=540

According to question

The temperature at half past eleven would be 2 °C.

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations.

Given is that the temperature in Austria one morning was -5 degrees Celsius at eight o clock and increased by 2 degrees Celsius every hour until twelve o clock.

We can write the temperature variation as a function of hour {x} as -

T{x} = (- 5 + 2{x})°C

For half past eleven, we will have -

{x} = 3.5

So, we can write -

T{x} = (- 5 + 2 x 3.5)°C

T{x} = 2 °C

Therefore, the temperature at half past eleven would be 2 °C.

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Note that the prompt is geared at testing the ability of the to understand certain vocabulary terms. The terms are given as follows:

The completed paragraphs are given below.

The first paragraph is completed as follows:

When Dr. Carter is not fulfilling his duties as the professor of paleontology at Ganton College, he is in the jungles of South America supervising excavations of ancient creatures. During the last dig, Dr. Carter recoiled when a poisonous snake tried to bite him. Now he wears tall boots and gloves to obviate the risk of dangerous animals endemic to the region.

He will definitely elicit the need for such safety measures. Some of the incoming scientists will accuse him of self-aggrandizement despite the fact that the sociable doctor always avoids using too much panache when speaking about safety; he'll flaunt his amazing findings when he returns to the campus at the end of the summer. He can put his bombast to better use in the classroom.

The second paragraph is completed as follows:

Baker deigned to give a semi-friendly nod to his Nazi captors, and he immediately suffered the consequences. Baker then endured the loud paroxysm of his cellmates: "What was that? What, are you working for them, too?"

He understood their paranoia. Just weeks before, a(n) mendacious rebel captive had revealed the escape plan to the guard. The prisoners, including Baker, had to abandon months of secrecy and labor that went into the construction of the tunnel. They had not yet regrouped; most of the saturnine prisoners simply lay in their cells, defeated.

Baker sat against the wall and thought about his capture. He had misused the shibboleth that the Nazis used to identify foreign spies. and the lack of orthography on his forged travel documents instantly signaled that he was not the German officer he claimed to have been. They must need information, he reasoned, or they would have executed him by now.

The definition of terms are given as follows:

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Answer:

x = 3, y = 4

Step-by-step explanation:

3x + y = 13

5x - 2y = 7

To solve by substitution, you solve one of the equations for a variable, and then plug it into the other equation.

I'm going to choose to solve the first equation for y, as that will be the easiest.

y = -3x + 13 (subtract 3x from both sides)

Now we plug this equation into the y in the second equation and solve for x.

5x - 2(-3x + 13) = 7 (distribute)

5x + 6x - 26 = 7 (combine like terms)

11x - 26 = 7 (add 26 to both sides)

11x = 33

x = 3

Now that we know x is 3, we can plug it in a solve either equation for y.

y = -3(3) + 13

y = -9 + 13

y = 4

Answer:

x=2sqrt2

Step-by-step explanation:

The legs are equal, thus the sides are x, x, and hypotenuse is 4. This means that x^2+x^2=4^2. Thus, 2x^2=16 => x^2=8 => x= sqrt8 => x=2sqrt2

Sections taken through the narrow width of an entire building are known as transverse sections.

A building is an enclosed structure with a roof and walls standing more or less permanently in one place, such as a house or factory.

Given is a structural analysis blank statement as -

"Sections taken through the narrow width of an entire building are known as __________ sections.

Sections taken through the narrow width of an entire building are known as transverse sections. Those through the long dimension are known as longitudinal sections.

Therefore, Sections taken through the narrow width of an entire building are known as transverse sections.

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The single natural logarithm expression is ln(2). Therefore, correct answer is (a)

The expression in the form [tex]e^a=b[/tex] can also be written as In b = a  which is called as logarithmic expression.

Properties of Logarithms:

1. In (mn) = In m + In n

2. In [tex]a^m =[/tex] m In a

3. In [tex]e^a[/tex] = a.

The natural logarithm expression is:

4 + ln 2 - ln 4

Apply the product and quotient rule of natural logarithm:

4 + ln 2 - ln 4  = In (4 × 2/4)

Evaluate the quotient:

4 + ln 2 - ln 4  = In (2)

Hence, the single natural logarithm expression is ln(2).

The correct option is (a)

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Answer:

B: ln 4.

Step-by-step explanation:

Therefore , the solution of the given problem of linear equation comes out to be conan needs one more tube to put away the remaining 2 tennis balls.

A straightforward regression curve is created using the equation y=mx+b. The y-intercept is m, and the slope is B. The previous line is usually referred to as a "math equation mixing numerous variables," even though y / y represent independent components. Only two variables are present in bivariate linear equations. There are no known solutions to application issues involving linear equations.

Here,

We know that Conan has 5 tubes, and that 2 tennis balls are left unfilled. This means that he has already filled up 5 - 1 = 4 tubes.

Each tube can hold a certain number of tennis balls, so we need to know how many tennis balls each tube can hold. Once we know that, we can figure out how many tubes are needed to hold the remaining 2 tennis balls.

Let's say each tube can hold n tennis balls. Then, the 4 filled tubes have a total capacity of 4n tennis balls. We also know that there are 2 tennis balls left unfilled. Therefore, we can set up the following equation:

4n + 2 = 5n

Simplifying this equation, we get:

2 = n

So each tube can hold 2 tennis balls. Therefore, Conan needs one more tube to put away the remaining 2 tennis balls.

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The points and the vertex are (1, 0), (2, 2), (0, 2), (-1, 8) and (-2, 18)

From the question, we have the following parameters that can be used in our computation:

f(x) = 2(x - 1)²

See attachment for the graph

From the attached, the points are (1, 0), (2, 2), (0, 2), (-1, 8) and (-2, 18)

Where the vertex is (1, 0)

We have

y = x^2

f(x) = 2(x - 1)²

The transformation is described as follows:

The input has no restriction

So, we have

Domain: (-∝, ∝)

The output starts or ends at the vertex

So, we have

Range: [0, ∝)

In (a), we have

vertex is (1, 0)

So, we have

(x, y) = (1, 0)

Remove the y coordinate

x = 1

Hence, the axis of symmetry is x = 1

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The simplified form of sine of x over the quantity 1 plus cosine of x (end quantity)  is 1. Option D

The question can be interpreted as sin(x) / (1 + cos(x))

sin(x) / (1 + cos(x)) = (sin(x) / cos(x)) / (1/cos(x) + cos(x)/cos(x))

                      = tan(x) / (1 + sec(x))

                      = (sin(x)/cos(x)) / (cos(x)/(cos(x)+1))

                      = (sin(x)/cos(x)) / ((cos(x)+1)/cos(x))

                      = sin(x) / (cos(x) + 1)

Therefore, the simplified form of sin(x) / (1 + cos(x)) is:

sin(x) / (1 + cos(x)) = sin(x) / (cos(x) + 1) = 1

Hence, The simplified form of sine of x over the quantity 1 plus cosine of x (end quantity)  is 1

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The amount in the account after 10 years is $4,978.365.

Interest is the sum of money that must be repaid on a loan or received in exchange for a loan. Principle refers to the borrowed or lent funds. The Amount is the total of the principal plus interest. The term "rate of interest" refers to the rate at which interest is applied to the principal.

Given:

P= $450

R= 2.225%

n= 10

So, Amount = d [[tex](1+i)^n[/tex] - 1 ] / i

A = 450 x [[tex](1+0.02225)^{10[/tex] - 1 ] / 0.02225

A = 450 x (1.24615249763-1) / 0.02225

A = 450 x 0.24615249763/ 0.02225

A = 4,978.365

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The measure of the angle of x is 69.

In order to find the measure of one angle, given the measure of the other angle on the same straight line, you must use the relationship between the angles.

When two angles are on the same line and adjacent, they must add up to 180 degrees. This means that the two angles, x degrees and (2x-27) degrees, must add up to 180 degrees. We can use this to solve for x. We can set up an equation to represent this relationship:

x + (2x - 27) = 180

We can now use the distributive property to solve for x.

3x - 27 = 180

Adding 27 to both sides of the equation, we get:

3x = 207

Dividing both sides of the equation by 3, we get:

x = 69

Therefore, the measure of the angle is x = 69 degrees.

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Complete Question:

The measures of two adjacent angles on a straight line are x degrees and (2x-27) degrees. Find x

Yes, you can compare two marginal distributions to see if the corresponding two variables are related. This is done by plotting the two distributions and visually inspecting them for evidence of a relationship. Additionally, you can use statistical tests to measure the strength of the relationship between the two variables.

Comparing two marginal distributions can help you identify if there is a relationship between two variables. You can plot the distributions and look for evidence of a relationship such as a linear trend or a pattern of higher or lower values compared to one another. Additionally, you can use statistical tests such as the Pearson correlation coefficient or Spearman's rank correlation coefficient to measure the strength of the relationship between the two variables.

Yes, you can compare two marginal distributions to see if the corresponding two variables are related. This is done by plotting the two distributions and visually inspecting them for evidence of a relationship. Additionally, you can use statistical tests to measure the strength of the relationship between the two .

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((30$ x4)+40$)-80$=80$

The equation of the plane can be expressed as 3t2x - y - 3t2z = d, where d is a constant.

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.

The equation of the plane that contains the curve with the vector equation r(t) = (t, t3, t) can be found by taking the cross product of two vectors that are on the plane. Let the two vectors be v1 = (1, 0, 1) and v2 = (1, 3t2, 1). Taking the cross product of these two vectors yields v1 x v2 = (3t2, -1, -3t2). This vector is perpendicular to the plane. Therefore, the equation of the plane can be expressed as 3t2x - y - 3t2z = d, where d is a constant.

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Answer:

24km

Step-by-step explanation:

15 min (jogging)

30 min (cycling)

3km/15 min (jogging)

1km/5min (jogging)

4km/5min (cycling)

30÷5= 6

4×6= 24km

Distance covered during riding is 24 km.

Speed of an object is defined as the rate of change of the distance travelled.

Here,

Speed is the distance travelled in a given time.

Total time given, t = 45 minutes

Time taken for jogging, t₁ = 15 minutes

So, time taken for riding, t₂ = t - t₁

t₂ = 45 - 15

t₂ = 30 minutes

Distance covered during jogging, d₁ = 3 km

Therefore speed of jogging, v₁ = d₁/t₁ = 3/15

v₁ = 0.2 km/min

So, speed of riding, v₂ = 4v₁ = 4 x 0.2

v₂ = 0.8 km/min

Therefore distance covered during riding, d₂ = v₂ x t₂

d₂ = 0.8 x 30

d₂ = 24 km

Hence,

Distance covered during riding is 24 km.

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m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.

Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.

To determine the unknown angle measures of △DEF, we can use the fact that the sum of the angles of a triangle is 180°. Thus, if we know two angle measures in the triangle, we can use them to calculate the third.

Let's denote the two known angle measures as m∠D and m∠F. We can use the following equation to solve for the unknown angle measure:

m∠D + m∠F + m∠E = 180°

We can rearrange the equation to solve for m∠E:

m∠E = 180° - m∠D - m∠F

Therefore, once we know the measures of m∠D and m∠F, we can calculate the measure of m∠E.

For example, if m∠D = 40° and m∠F = 65°, then the measure of m∠E would be:

m∠E = 180° - 40° - 65° = 75°

Therefore, m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.

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Answer: the answer is

m∠D = ✔ 46°

m∠F = ✔ 44°

Step-by-step explanation: I got it correct. it will be show below.

Answer:

75.4

Step-by-step explanation:

Volume of cylinder=πr2h

=π·22·6≈75.39822