what does 6 1/5+ (-7 3/5) equal?

The total amount of money that Mavis with 33 nickels, 67 dimes, 19 quarters, and 14 fifty-cent pieces has is C. $20.10.

The total amount that Mavis has can be determined by the multiplication of the cents based on their unit values.

Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

33 nickels = $1.65 (33 x $0.05)

67 dimes = $6.70 (67 x $0.10)

19 quarters = $4.75 (19 x $0.25)

14 fifty-cents = $7.00 (14 x $0.50)

Total amount = $20.10

Thus, Mavis has a total amount of $20.10.

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The expression that is equivalent to 43,450,000 when simplified is 4.345 x 10⁷

43,450,000 is the numerical expression given, and it can be simplified by breaking it down into its factors of 10.

In scientific notation, a number can be expressed in the form of a x 10^b, where a is a number between 1 and 10 and b is an integer that represents the number of places the decimal point has been moved.

To simplify 43,450,000, we can write it as

4.345 x 10⁷

This is because we have moved the decimal point seven places to the left.

So, the expression that is equivalent to 43,450,000 when simplified is

4.345 x 10⁷

This notation is commonly used in science and engineering to represent very large or very small numbers, as it makes it easier to work with such values.

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The area of the parallelogram  will be equal to 60 in²

Since it's a parallelogram so,  area of a parallelogram is the product of the base and the height of the figure.

area of a parallelogram = Base x Height

We are given that area of a parallelogram = Base x Height

A = bh

A =  6×1 0

A = 60 in²

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The vertex of the absolute value function is (-3, 2).

The range of the function is 2 < y < ∞.

Option C is the correct answer.

We have,

To find the vertex of the given absolute value function, we can first find the vertex of the related linear function, which is y = 2x + 6.

The vertex of this linear function is (-3, 0), obtained by setting x = -3 to find the minimum value of the linear function.

Since the given absolute value function has the same shape as the related linear function but is shifted up by 2 units,

The vertex of the absolute value function is (-3, 2).

To find the range of the function, note that the absolute value of 2x + 6 is always non-negative.

Thus, the smallest possible value of the function is 2 (when 2x + 6 = 0) and the function is unbounded above.

Therefore, the range of the function is 2 < y < ∞.

Therefore,

The vertex of the absolute value function is (-3, 2).

The range of the function is 2 < y < ∞.

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Orthogonal matrix A that satisfies the given conditions is:

[3 3 0 ]

[1/√(2) -1/√(2) √(2/9)]

[-√(2)/2 √(2)/2 √(2)/2]

Let's call the first row of matrix A as r1, which is a multiple of (3, 3, 0). Since the length of a row vector of an orthogonal matrix is always 1, we can find a unit vector that is orthogonal to (3, 3, 0).

One such vector is (3, -3, 2), which can be verified by checking that the dot product of (3, 3, 0) and (3, -3, 2) is zero.

To obtain the second row of A, we can normalize the vector (3, -3, 2) to have a length of 1. This gives us:

(3, -3, 2)/√(18) = (1/√(2), -1/√(2), √(2/9))

To obtain the third row of A, we can take the cross product of the first two rows to get a vector that is orthogonal to both. This gives us:

(3, 3, 0) x (1/√(2), -1/√(2), √(2/9)) = (-2√(2)/3, 2√(2)/3, 2√(2)/3)

We can then normalize this vector to obtain the third row of A:

(-2√(2)/3, 2√(2)/3, 2√(2)/3)/√(8/9) = (-√(2)/2, √(2)/2, √(2)/2)

Therefore, the orthogonal matrix A that satisfies the given conditions is:

[3 3 0 ]

[1/√(2) -1/√(2) √(2/9)]

[-√(2)/2 √(2)/2 √(2)/2]

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The required group of friends spent 94% of their total budget on costumes.

To evaluate the percentage of the total budget that was spent on costumes, we can use the formula:
Percentage = (amount spent / total budget) x 100%

In this case, the amount spent on costumes was $658, and the total budget was $700. Substituting these values into the formula, we get:

percentage = (658 / 700) x 100%

Simplifying the fraction, we get:

percentage = 0.94 x 100%

Converting the decimal to a percentage, we get:

percentage = 94%

Thus, the group of friends spent 94% of their total budget on costumes.

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Using Pythagorean's theorem we will see that the length is 41 ft.

We know that the flagpole is 40 feet tall. A rope is tied to the top of the flagpole and secured to the ground 9 feet from the base of the flagpole. We can think of this as a right triangle whose legs are 40ft and 9ft, and the rope is the hypotenuse.

Then we can use Pythagorean's theorem to find the length of the rope L.

L² = (40ft)² + (9ft)²

Solving this for L we will get.

L = √((40ft)² + (9ft)²)

L = 41ft

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Answer:

Step-by-step explanation:

To calculate the rate of inflation, we can use the inflation rate formula:

inflation rate = ((new price - old price) / old price) x 100%

Using the given information, we have:

old price = $64.99

new price = $150.00

inflation rate = ((150.00 - 64.99) / 64.99) x 100%

inflation rate = (85.01 / 64.99) x 100%

inflation rate = 130.81%

Rounding the inflation rate to the nearest whole number, we get:

inflation rate ≈ 131%

Therefore, the rate of inflation from 1985 to today for a pair of Jordans is approximately 131%.

The requried total change to Rob's funds as an integer is -$50, indicating that he spent more than he received and his funds decreased by $50.

Let's break down the different transactions and calculate the total change to Rob's funds:

Bought 5 rabbits for $10 each: 5 x $10 = $50 spent
Returned 2 rabbits: 2 x $10 = $20 received
Found 2 twenty dollars bills: 2 x $20 = $40 received
Bought 2 desks for $30 each: 2 x $30 = $60 spent

To calculate the total change to Rob's funds, we can add up the amounts received and subtract the amounts spent:
$20 + $40 - $50 - $60 = $-50

Therefore, the total change to Rob's funds as an integer is -$50, indicating that he spent more than he received and his funds decreased by $50.

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Answer:

3/5

Step-by-step explanation:

cause it is

Answer:

Height 15 feet

Base 12 Feet

Step-by-step explanation:

The formula to find the area of a triangle is A= (0.5) x base x height, so if the area is 90 then before it was halved it must be 180 so the base x height must equal 180 and the only number that equal 180 when multiplied with a difference of 3 between them is (15,12) so thats are answer. I know this is right because if I put it through the area formula I get 90.

A=(.5) x 12 x 15

A=(.5) x 180

A= 90

The number of  hours it would take 6 pipes to fill 1/4 of the lake is 4.5 hours

Given that

It takes 4 of the pipes 12 hours to fill the lake.

This means that

Rate = 12 hours/4 pipes

So, we have

Rate = 3 hours/ pipe

For 6 pipes to fill 1/4 of the lake. we have

Time = 3 hours *6 * 1/4

Evalaute

Time = 4.5 hours

Hence, the time taken is 4.5 hours

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Answer: BC = 8.94

Step-by-step explanation:

      Since this is a right triangle, we can use the Pythagorean theorem. a and b are the triangle legs and c is the hypotenuse.

a² + b² = c²

19² + b² = 21²

361 + b² = 441

b² = 80

b = [tex]\sqrt{80}[/tex]

b ≈ 8.94

BC = 8.94

Mark sets aside $404 for more supplies.

Mark spent $175 on supplies, so his total cost is $175.

Mark sold 6 pieces of artwork for $70 each, so he earned 6 * $70 = $420 from these pieces.

He sold 15 - 6 = 9 pieces of artwork at $85 each, so he earned 9 * $85 = $765 from these pieces.

His total revenue is $420 + $765 = $1185.

His profit is his revenue minus his cost: $1185 - $175 = $1010.

He plans to set aside 40% of his profit for more supplies, so he will set aside 0.4 * $1010 = $404.

Therefore, Mark sets aside $404 for more supplies.

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Spencer will have spent 56 minutes on the phone in total while routing 28 phone calls.

If Spencer spent 10 minutes while routing 5 phone calls, the unit rate of time spent on the phone per phone call is;

10 minutes ÷ 5 phone calls = 2 minutes/phone call

Therefore, the unit rate tells us that Spencer spent an average of 2 minutes on the phone for each of the 5 phone calls he routed.

To find how much time Spencer will spend on the phone in total while routing 28 phone calls, we can use the unit rate as a conversion factor;

Total time on the phone = (Number of phone calls) x (Time per phone call)

Total time on the phone = 28 phone calls x (2 minutes/phone call)

Total time on the phone = 56 minutes

Therefore, Spencer will have spent 56 minutes on the phone.

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We can use the distributive property and the greatest common factor to write 36 + 4 as 4(9 + 1) or 4(10).

Using the distributive property, we can write:

36 + 4 = 4(9 + 1)

Next, we can identify the greatest common factor (GCF) of 9 and 1, which is 1. Since there are no other common factors between 9 and 1, we can write:

9 + 1 = 10

Therefore, we can express 36 + 4 as:

36 + 4 = 4(9 + 1) = 4(1 × 9 + 1) = 4(10)

So, 36 + 4 can be written as the product of 4 and 10, where 4 is the GCF of 36 and 4, and 10 is the sum of the two terms divided by their GCF. This is an example of factoring by grouping, which can be a useful technique in algebra and other areas of mathematics.

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True. A circular mil is a unit of measurement used in electrical engineering and is defined as the area of a circle with a diameter of one mil (0.001 inch) which is equivalent to a circumference of one mil.

The statement "A circular mil is a circle with a circumference of one mil" is true. A circular mil is a unit of area used to measure wire and cable cross-sectional sizes, and it is defined as the area of a circle with a diameter of one mil (1/1000 of an inch).

Thus, A circular mil is a unit of measurement used in electrical engineering and is defined as the area of a circle with a diameter of one mil (0.001 inch) which is equivalent to a circumference of one mil.

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The probabilities are given as follows -

A) P(X = 11) = 2/36

B) P(X ≤ 6) = 5/12

The probability mass function for the sum X of the two dice is given by table A. See same attached.

The cumulative mass function (CMF) for X is given by the cumulative sum of the probabilities in the probability mass function is given by table B. See same attached.

To draw the probability mass function and the cumulative mass function, we can plot the values of P(X) and P(X <= x) against X, respectively.

The probability of getting a even value is computed as follows

P(X is even) = P(X = 2) + P(X = 4) + P(X = 6) + P(X = 8) + P(X = 10) + P(X = 12)

= 1/36 + 3/36 + 5/36 + 5/36 + 3/36 + 1/36

= 18/36

P(X is even) = 1/2

The probability that for a single roll of the two dice, the sum of the dots is equal to 11   P(X = 11) = 2/36

= 1/18

The probability of obtaining a value of 6 or less is  P(X < = 6) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= 1/36 + 2/36 + 3/36 + 4/36 + 5/36

= 15/36

P(X ≤ 6) = 5/12

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The probability of winning the minimum prize is approximately 0.00014

To calculate the probability of winning this minimum prize, we need to first find out the total number of possible combinations of numbers that can be drawn.

There are 56 white balls, and 5 balls are drawn from them, so the total number of possible combinations of white balls is

56 choose 5 = 56! / (5! (56-5)!) = 3,819,816

There are 46 gold balls, and only 1 is drawn from them. Therefore, the total number of possible combinations of gold balls is simply 46.

To win the minimum prize, we need to correctly match 4 out of the 5 white balls drawn, and we also need to match the gold ball.

The number of ways to choose 4 white balls out of 5 is

5 choose 4 = 5! / (4! (5-4)!) = 5

So, the total number of ways to win the minimum prize is the product of the number of ways to choose 4 white balls and the number of ways to choose 1 gold ball

Total number of ways to win the minimum prize = 5 × 46 = 230

Therefore, the probability of winning the minimum prize is

Probability = number of ways to win the minimum prize / total number of possible combinations

Probability = 230 / (3,819,816 × 46) = 0.00014

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The angle in standard position is  150°

The angle of any position (x, y) on a graph is given by Ф = tan⁻¹(y/x).

Now given the position (-√3, 1) on the graph, to find the angle in standard position, we proceed as follows.

To find the angle, we substitute the values of the variables into the equation. so, we have that

Ф = tan⁻¹(y/x)

Given that

Ф = tan⁻¹(y/x)

Ф = tan⁻¹(1/-√3)

= tan⁻¹(-1/√3)

= 180° - tan⁻¹(1/√3)

= 180° - 30°

= 150°

So, the angle is  150°

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The equation provided is: ρ²(sin²(φ)sin²(θ) + cos²(φ)) = 16, This equation is in spherical coordinates,

where ρ represents the radial distance from the origin, φ is the polar angle (or the angle between the positive z-axis and the vector), and θ is the azimuthal angle (or the angle between the positive x-axis and the projection of the vector onto the xy-plane).

Now, let's analyze the equation further: 1. Divide both sides of the equation by 16 to isolate ρ²: ρ² = 16 / (sin²(φ)sin²(θ) + cos²(φ)) 2. Take the square root of both sides to find ρ: ρ = √(16 / (sin²(φ)sin²(θ) + cos²(φ))).

From this, we can see that the surface is defined by the radial distance ρ, which depends on the angles φ and θ. This indicates that the given equation represents a 3-dimensional surface in spherical coordinates.

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Answer:

-10

Step-by-step explanation:

the explantion is pinned in the photo

please mark me as branliest

1. Identify the curve and the point: The curve is y = sec(x), and the point is (π/6, 2√3/3).

2. Calculate the derivative of the curve: The derivative of y = sec(x) is y' = sec(x)tan(x).

3. Evaluate the derivative at the given point: At x = π/6, we have y' = sec(π/6)tan(π/6). Since sec(π/6) = 2 and tan(π/6) = √3/3, we get y' = 2(√3/3) = 2√3/3.(4). Use the point-slope form of the line equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope (derivative).

5. Plug in the values: y - (2√3/3) = (2√3/3)(x - π/6). This is the equation of the tangent line to the curve y = sec(x) at the point (π/6, 2√3/3).

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The proof is completed using the properties of equality

The two column proof is completed as below

Statement                                              Reason

angle 2 ≅ angle 4                                  Given

angle 1 + angle 2 = 90 deg                   definition of right triangle

angle 3 + angle 4 = 90 deg                  definition of right triangle

angle 1 + angle 2 = angle 3 + angle 4  substitution property of equality

angle 1 + angle 4 = angle 3 + angle 4  substitution property of equality

angle 1 = angle 3                                   addition property of equality

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The measure of angle BAC in the given shaded right triangle is approximately 45 degrees.

Let's start by labeling the sides of the triangle. We are given that BC = 3, AC = 3, and BA = 4.24. We can use the Pythagorean theorem to find the length of the missing side, which is opposite the right angle at C. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have:

BA² = BC² + AC²

Substituting the given values, we get:

4.24² = 3² + 3²

Simplifying and solving for 4.24², we get:

4.24² = 18.0176

Taking the square root of both sides, we get:

4.24 ≈ √18.0176

Now we can use the trigonometric ratio of sine to find the measure of angle BAC. The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In other words:

sin(BAC) = AC / BA

Substituting the given values, we get:

sin(BAC) = 3 / 4.24

Using a calculator to evaluate the right-hand side, we get:

sin(BAC) ≈ 0.7071

Finally, we can use the inverse sine function (also called arcsine) to find the measure of angle BAC. The inverse sine function takes a ratio and gives us the angle whose sine is that ratio. In other words:

BAC = arcsin(sin(BAC))

Substituting the calculated value of sin(BAC), we get:

BAC = arcsin(0.7071)

Using a calculator to evaluate the right-hand side, we get:

BAC ≈ 45°

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The length of line AC of the given quadrilateral ABCD would be = 13.7cm

To calculate the length of line AC is to calculate the length of CE and AE separately and add up the lengths afterwards.

The length of CE can be calculated using Pythagorean formula;

That is C² = a² +b²

where C = 8cm

a = 5cm

b = CE = ?

b² = 8²-5²

b = 64-25

b² = 39

b =√39

b = 6.2

For AE;

b² = AE = 9²-5²

= 81-25

= 56

b = √56

= 7.5

Therefore the length of AC = 6.2+7.5 = 13.7cm

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The value of z is 20 in.

What is triangle?

A polygon that has three sides and three angles is called triangle.

In triangle QWX, we have WX || RS, so by the intercept theorem, we have:

QW/WX = QR/RS

Substituting the given values, we get:

z/(3y) = 20/(20 + y)

Cross-multiplying, we get:

20z + 3y² = 60y

We also know that:

QW + WX = QX

Substituting the given values, we get:

z + 3y = 3y

Simplifying, we get:

z = 0

Substituting this value of z into the equation we derived earlier, we get:

20z + 3y² = 60y

0 + 3y² = 60y

Dividing both sides by 3y, we get:

y = 20

Therefore, the value of z is:

z = QW = QX - WX = 3y - 2y = y = 20

So, z = 20

Therefore required value of z is 20 in.

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Answer:

Given information:

To obtain the equation of the regression line for the given data.

The equation of regression line of y on x is given by:

y

−

¯

y

=

b

y

x

(

x

−

¯

x

)

;

w

h

e

r

e

,

y

=

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

x

=

i

n

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

b

y

x

=

s

l

o

p

e

o

f

r

e

g

r

e

s

s

i

o

n

l

i

n

e

¯

x

=

m

e

a

n

o

f

x

¯

y

=

m

e

a

n

o

f

y

y−y¯=byx(x−x¯);where,y=dependentvariablex=independentvariablebyx=slopeofregressionlinex¯=meanofxy¯=meanofy

The calculations for the equation of regression line is tabulated below:

The regression coefficient of y on x is given by:

b

y

x

=

∑

x

y

−

1

n

∑

x

∑

y

∑

x

2

−

1

n

(

∑

x

)

2

=

1944

−

1

5

×

98

×

69

2580

−

1

5

(

98

)

2

=

591.6

659.2

=

0.898

byx=∑xy−1n∑x∑y∑x2−1n(∑x)2=1944−15×98×692580−15(98)2=591.6659.2=0.898

Mean of x is calculated as:

¯

x

=

1

n

∑

x

=

1

5

×

98

=

19.6

x¯=1n∑x=15×98=19.6

Mean of y is calculated as:

¯

y

=

1

n

∑

y

=

1

5

×

69

=

13.8

y¯=1n∑y=15×69=13.8

The equation of regression line is given as:

y

−

¯

y

=

b

y

x

(

x

−

¯

x

)

y

−

13.8

=

0.898

(

x

−

19.6

)

y

=

0.898

x

−

3.8

y−y¯=byx(x−x¯)y−13.8=0.898(x−19.6)y=0.898x−3.8

Therefore, the required equation of regression line is y = 0.898x - 3.8.