Cassie wants to buy a shirt for $15. 75 and some shoes for $10. 25. If the sales tax is 8. 25%, what is the TOTAL amount Cassie will pay?

When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

Given,

The cost of Carpet per square foot = $4

Total cost of the carpet = $616

We know

Area of the rectangle = Length × Width

Length = 14 feet

Consider the width of the rectangular room as x

Then the area of the room = 14x

Total cost of carpet = Area of the rectangular room× Cost of carpet per foot

Substitute the values

14x×4=616

14x=154

x=11 feet

Hence, When carpet sells for $4 per square foot and will cost you $616 to carpet your rectangular room, if you room is 14 feet long then the width is 11 feet

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Answer:

D i think

Step-by-step explanation:

Answer: midpoint is 4,5

Step-by-step explanation:

Step-by-step explanation:

You want to demonstrate the identity ...

  (1-tan⁴(A))·cos⁴(A) = 1 -2·sin²(A)

Working with the left side, we have ...

  \((1-\tan^4(A))\cos^4(A)=1-2\sin^2(A)\\\\(1-\dfrac{\sin^4(A)}{\cos^4(A)})\cos^4(A)=1-2\sin^2(A)\qquad\text{use tangent identity}\\\\\cos^4(A)-\sin^4(A)=1-2\sin^2(A)\qquad\text{multiply it out}\\\\(\cos^2(A) +\sin^2(A))(\cos^2(A)-\sin^2(A))=1-2\sin^2(A)\qquad\text{factor}\\\\1((1-\sin^2(A))-\sin^2(A)) = 1-2\sin^2(A)\qquad\text{use $\cos^2$ identity}\\\\1-2\sin^2(A)=1-2\sin^2(A)\qquad\text{Q.E.D.}\)

__

Additional comment

The referenced identities are ...

  tan = sin/cos

  cos² = 1 -sin²

and the factorization of the difference of squares:

  a² -b² = (a +b)(a -b).

An equation is formed of two equal expressions. The length of the sides QT and SV are 21 units and 41 units respectively.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the length of TR is 17 and it is equal to side VR, therefore,

VR = VT

3x + 2 = 17

x = 5

Since the given figure is a kite, therefore,

QT= QV = 4x + 1

QT = 4(5) + 1

QT = 21 units

Similarly, the sides SV will be equal to ST,

SV =ST = 9x - 4

SV = 9(5) - 4

SV = 41 units

Hence, the length of the sides QT and SV is 21 units and 41 units respectively.

The complete question is:

The length of TR is 17 units. What are the lengths of SV and QT?

SV=___ units

QT=___ units

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The choir practice this week for 5 1/4 hours.

On Monday, the choir practiced for 3/4 hour.

On Wednesday, they practiced for 1/2 hour more than on Monday, which is 3/4 + 1/2 = 6/8 + 4/8 = 10/8 = 1 1/4 hours.

On Friday, they practiced twice as long as on both Monday and Wednesday combined, which is 2 * (3/4 + 1 1/4) = 2 * 2 = 4 hours.

To find the total practice time for the week, we can add up the times from each day:

3/4 + 1 1/4 + 4 = 5 + 1/4 = 5 1/4 hours.

Therefore, the choir practiced for 5 1/4 hours in total this week.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The value will be \(\frac{3a}{8}\)

What are arithmetic operations?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

In the following question it is asked to perform three of these operations.

Subtraction, Multiplication, Division are to be performed here.

Difference of \(9\) and \(6\) is \(9-6=3\).

\(a\) times the difference of  \(9\) and \(6\) is \(3a\)

Product of \(3\) and \(4\) is \(12\).

\(a\) times the difference of  \(9\) and \(6\) divided by the Product of \(3\) and \(4\) is \(\frac{3a}{12}\)Since \(3\) is a common factor for both \(3,12\) it gets cancelled out.

So now we can write \(\frac{3a}{12} =\frac{a}{4}\).

Therefore the final answer is \(\frac{a}{4}\).

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer:

D 18

Step-by-step explanation:

Answer: 100 degress

Step-by-step explanation:

35+65=100

180-100

Angle = 80 degrees

x=100

Answer:

A

Step-by-step explanation:

The solution that is not the same as the solutions to the system of equations is 2x - 2y = 5.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

2x + 3y = 1 _____(1)

x - y = 5 _______(2)

From (1) and (2) we get,

x = 5 + y

2 (5 + y) + 3y = 1

10 + 2y + 3y = 1

10 + 5y = 1

5y = -9

y = -9/5

Now,

x = 5 - 9/5

x = (25 - 9)/5

x = 16/5

The solutions are x = 16/5 and y = -9/5.

Now,

(1) 3x + 2y=6

3 x (16/5) + 2 x (-9/5) = 6

48/5 - 18/5 = 6

30/5 = 6

6 = 6

(2) 5y = -9

5 x (-9/5) = -9

-9 = -9

(3) 2x - 2y = 5

2 x (16/5) - 2 x (-9/5) = 5

32/5 + 18/5 = 5

50/5 = 5

10 ≠ 5

(4) 4x + 6y = 2

4 x (16/5) + 6 x (-9/5) = 2

64/5 - 54/5 = 2

10/5 = 2

2 = 2

Thus,

3x+2y=6, 5y=-9, and 4x+6y=2 have the same solutions.

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1) the cross product of R1 and R2 is -4i + 2j + 3k.

2) the inner angle between R1 and R2 is given by:56.35 degrees

3) the area of the triangle OP1P2 is (1/2) sqrt(29).

4)the circumference of the triangle OP1P2 is: C

(1) Cross product of R1 and R2:

The cross product of two vectors R1 and R2 is given by:

R1 × R2 = (R1yR2z - R1zR2y)i - (R1xR2z - R1zR2x)j + (R1xR2y - R1yR2x)k

Substituting the values of R1 and R2, we get:

R1 × R2 = (2×0 - 2×1)i - (1×0 - (-1)×2)j + (1×1 - 2×(-1))k

= -4i + 2j + 3k

Therefore, the cross product of R1 and R2 is -4i + 2j + 3k.

(2) Inner angle between R1 and R2:

The inner angle between two vectors R1 and R2 is given by:

cos θ = (R1 · R2) / (|R1||R2|)

where R1 · R2 is the dot product of R1 and R2, and |R1| and |R2| are the magnitudes of R1 and R2, respectively.

Substituting the values of R1 and R2, we get:

R1 · R2 = 1×(-1) + 2×1 + 2×0 = -1 + 2 = 1

|R1| = sqrt(1^2 + 2^2 + 2^2) = sqrt(9) = 3

|R2| = sqrt((-1)^2 + 1^2 + 0^2) = sqrt(2)

Therefore, the inner angle between R1 and R2 is given by:

cos θ = 1 / (3sqrt(2))

θ = cos^(-1) (1 / (3sqrt(2)))

θ ≈ 56.35 degrees

(3) Area of a triangle OP1P2:

Let R = R2 - R1 be the vector connecting P1 to P2. Then the area of the triangle OP1P2 is given by:

A = (1/2) |R1 × R2|

= (1/2) |(-4i + 2j + 3k)|

= (1/2) sqrt((-4)^2 + 2^2 + 3^2)

= (1/2) sqrt(29)

Therefore, the area of the triangle OP1P2 is (1/2) sqrt(29).

(4) Circumference of the triangle OP1P2:

Let a, b, and c be the side lengths of the triangle OP1P2 opposite to the points O, P1, and P2, respectively. Then the circumference of the triangle is given by:

C = a + b + c

To find the length of side c, we can use the distance formula:

c = |R2 - R1| = sqrt((-1 - 1)^2 + (1 - 2)^2 + (0 - 2)^2) = sqrt(18)

To find the length of sides a and b, we can use the fact that the triangle isisosceles (since the angles at P1 and P2 are equal), so a = b:

a = b = |P1 - O| = sqrt(1^2 + 2^2 + 2^2) = sqrt(9) = 3

Therefore, the circumference of the triangle OP1P2 is:

C

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Answer:

Solutions

Step-by-step explanation:

El ángulo de 45 grados es uno de los ángulos notables en trigonometría. La razón trigonométrica más comúnmente asociada con este ángulo es:

- La razón trigonométrica del seno: sin(45°) = 1/√2 ≈ 0.7071

- La razón trigonométrica del coseno: cos(45°) = 1/√2 ≈ 0.7071

- La razón trigonométrica de la tangente: tan(45°) = sin(45°)/cos(45°) = 1

Recuerda que estas razones trigonométricas se obtienen a partir de la relación entre los lados de un triángulo rectángulo y se utilizan para calcular longitudes, ángulos y relaciones en problemas trigonométricos.

Part a

we have that

the volume of the box is equal to

V=L*W*H

so

In this problem

the height H is equal to H=x

L=(10-2x) in

W=(8-2x) in

substitute in the formula

V=(10-2x)(8-2x)(x) in3

apply distributive property

V=(80-20x-16x+4x^2)(x)

V=(4x^3-36x^2+80x) in3

Part b

For x=0.7 in

V=4(0.7)^3-36(0.7)^2+80(0.7)

V=39.732 in3

For x=2.3 in

V=4(2.3)^3-36(2.3)^2+80(2.3)

V=42.228 in3

so

the change in the box volume increases (42.228-39.732)=2.5 in3

For x=3.2 in

V=4(3.2)^3-36(3.2)^2+80(3.2)

V=18.432 in3

the change in the box volume decreases (42.228-18.432)=23.8 in3

Answer:

The number of times a variable appears in a date set is called a constant.

The area, in square inches, of the larger triangle is 12.

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The value of the expression is 5.

What is order of operations?

The order of operations is a rule that specifies the correct sequence of steps to be taken when evaluating a mathematical equation.

To simplify this expression, we need to follow the order of operations, which is:

Exponents (powers, roots)

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

So, we start with the exponents:

\(3^0+4^{-1} \\= 1 + 1/4 \\= 5/4\)

Now we substitute this value back into the original expression:

\((3^0+4^{-1} )*2^2\\ = (5/4) * 2^2 \\= (5/4) * 4 \\= 5\)

Therefore, the value of the expression is 5.

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When x increases by 1 in the function y=3^x, the value of the function will be multiplied by 3.

Given the function

y = 3^x

An increment in the value of x would make the expression be multiplied by 3

To see why this happens, we can compare the value of the function at x and x+1:

y(x+1) = 3^(x+1)

y(x+1) = 3^x * 3 (by the laws of exponents)

y(x+1) = 3 * 3^x

Therefore, we can see that when x increases by 1, the value of the function is multiplied by 3.

This means that the function grows very quickly as x increases.

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The Bootstrap Method is straightforward and straightforward to comprehend. First, it chooses randomly from the original sample to produce bootstrap samples from our initial sample.

After that, it uses summary statistics like variation, standard deviation, mean, and so on to get replicates, which is how we can calculate a confidence interval from that sample.

Thus, the answer is "Yes."

The bootstrap method is a resampling method that uses replacement sampling to estimate population statistics. It can be used to estimate standard deviation and mean summaries.

Remember that bootstrapping isn't only valuable for computing standard blunders, it can likewise be utilized to build certainty spans and perform speculation testing. When working with data that doesn't seem to lend itself to conventional methods, always remember bootstrapping techniques.

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Full Question = We want to find a 95% confidence interval for the standard deviation of a large dataset, given a sample.

Can the bootstrap method be used?

Group of answer choices

yes

no

Answer: citizen scientists are already providing large amounts of data for monitoring biodiversity, but they could do much more, according to a new study published in the journal Biological Conservation, which suggests that citizen science has the potential to contribute much more to regional and global assessments of biodiversity. Citizen scientists are regular people who provide data or input to science, for example by monitoring species in their community or examining satellite imagery for evidence of deforestation or land use change.

Step-by-step explanation:

Answer: 1/6

Step-by-step explanation:

5/6 - 4/6 = 1/6

Answer:

1

-

6

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

The arrows on lines AB and CD indicate that these 2 shapes are similar and these 2 lines are corresponding so :

Linear scale factor :

12 ÷ 10 = 1.2 or 6/5

Let's use the fraction form

Using the linear scale factor we can make an equation to solve for x :

2x+4 = 6/5(x+8)

Expand the brackets :

2x+4 = 6/5x + 9.6

Subtract 4 from both sides :

2x = 6/5x + 5.6

Subtract 6/5x from both sides :

4/5x = 5.6

Divide both sides by 4/5 :

x = 7

Now substitute this value into the expression for the length of AE :

AE = 2(7) + 4

AE = 14 + 4

AE = 18

Hope this helped and have a good day

Answer:

116 units

Step-by-step explanation:

AE + ED = 180 because they make a straight angle and a straight angle is 180 degrees or half of a circle 360/2.

AE = 2x + 4 and ED = x +8 added together they equal 180

2x + 4 + x + 8 = 180  Combine the like terms

3x + 12 = 180  Subtract 12 from both sides of the equation

3x = 168  Divide both sides by 3

x = 56

Now that we know that x is 56 we can plug that in for AE to find its length

2x + 4

2(56) + 4

112 + 4

116

This graph above portraiture the linear equation

The method for including the garage square footage in the total depends on national standards, with some including it in the total and others excluding it.

When including the garage square footage in the total square footage of a home, there are different ways to do it depending on the national standards used.

Generally speaking, there are two main methods:

Including the garage in the total square footage, or excluding the garage from the total square footage.

If the garage is included in the total square footage, then Bob would add the square footage of the garage (600 square feet) to the square footage of the living spaces in the home (e.g., bedrooms, bathrooms, kitchen, living room, etc.).

This would give him the total square footage of the home, including the garage.

This method is commonly used in some areas of the United States.

On the other hand, if the garage is excluded from the total square footage, then Bob would only count the square footage of the living spaces in the home.

This method is commonly used in other areas of the United States, as well as in other countries.

It is important to note that the method used to calculate the total square footage can affect the perceived value of the home, as well as the taxes and insurance premiums associated with it.

Therefore, it is important for Bob to consult with a local real estate professional or appraiser to determine the most appropriate method for his area.

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Answer:

The area of a parallelogram is given by the formula A = base x height. In this case, the base has a length of x meters, and the height is x - 1 meters. So we can write:

A = x(x - 1)

We are told that the area is 306 square meters, so we can set up an equation:

x(x - 1) = 306

Expanding the left side gives:

x^2 - x = 306

Bringing all the terms to one side gives a quadratic equation:

x^2 - x - 306 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Here, a = 1, b = -1, and c = -306, so:

x = (1 ± sqrt(1 - 4(1)(-306))) / 2(1)

x = (1 ± sqrt(1 + 1224)) / 2

x = (1 ± sqrt(1225)) / 2

x = (1 ± 35) / 2

So x is either (1 + 35) / 2 = 18 or (1 - 35) / 2 = -17/2. Since x represents a length, it cannot be negative, so the value of x is 18 meters.

Therefore, the answer is x = 18.

The solution to the system of equations is x = 1 and y = 1.

To solve the system of equations using substitution, we start by solving one equation for one variable and substituting it into the other equation. Given the system of equations:

1) 4x + 3y = 7

2) 3x + 5y = 8

We can solve equation 1 for x:

4x = 7 - 3y

x = (7 - 3y)/4

Now, substitute this expression for x into equation 2:

3((7 - 3y)/4) + 5y = 8

Simplify the equation:

(21 - 9y)/4 + 5y = 8

Multiply both sides by 4 to eliminate the fraction:

21 - 9y + 20y = 32

Combine like terms:

11y = 11

Divide both sides by 11:

y = 1

Now, substitute the value of y back into equation 1 to solve for x:

4x + 3(1) = 7

4x + 3 = 7

4x = 7 - 3

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = 1.

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Answer: The  real answer is 62 steps per min

Hope this helps!

Robert averaged 62 steps in a minute.

An equation is a mathematical statement formed when two expressions are equated using an equal sign.

The equations are useful in the determination of unknown parameters.

The equations are of various types, such as Trigonometric equations, and quadratic equations.

The number of steps climbed by Robert is 775

The time taken by Robert to climb the steps is 12 1/2 minutes

The time taken by him = 25/2 minutes in fraction form

The time taken by him = 12.5 minutes in decimal form.

The steps he walks in 1 minute have to be determined.

Let x be the number of steps he walks in 1 minute, then the equation formed is,

x  = Total steps  /  Total Time

x = 775/12.5

x = 7750/125

x = 62 minutes.

So, the average number of steps Robert walked is 62 minutes.

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