If a square has a length of 3x-y, what is its area?

The probability that a randomly chosen card from a standard 52-card deck is either an ace or a heart is approximately 31%.

In a standard deck of 52 cards, there are 4 suits and each suit has 13 cards: hearts, clubs, diamonds, spades. Therefore, the total number of heart cards in the deck is 13 and the total number of aces in the deck is 4 (one for each suit).

To compute the probability P (A or H), the probability that Anthony chooses a card which is either an ace or a heart, we first need to calculate individual probabilities. The probability of drawing a heart P(H) is 13/52 = 0.25, and the probability of drawing an ace P(A) is 4/52 = 0.077. However, as the aces also include one heart (Ace of Hearts), the probabilities overlap.

To correct this, we use the rule of sum for probabilities which says that the probability that A or B will happen is the probability that A will happen plus the probability that B will happen, minus the probability that both A and B will happen. Applying this, P ( A or H) = P(A) + P(H) - P(A and H) = 0.077 + 0.25 - 0.019 = 0.308, or approximately 31%

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Final answer:

The probability of drawing either an ace or a heart from a standard deck of cards is 11/26.

Explanation:

To find the probability of choosing either an ace or a heart card, we need to calculate the individual probabilities of each event and then subtract the probability of neither event happening.

There are 4 aces in a deck of 52 cards, so the probability of picking an ace is 4/52, which simplifies to 1/13.

Similarly, there are 13 hearts in a deck, so the probability of picking a heart is 13/52, which simplifies to 1/4.

Since the events are mutually exclusive (a card can't be both an ace and a heart), we can add the probabilities together to find the probability of either event happening: 1/13 + 1/4 = 4/52 + 13/52 = 17/52.

Finally, to find the probability of either an ace or a heart, we subtract the probability of neither event happening (the probability of picking a card that is neither an ace nor a heart):

P(A or H) = 17/52 - 39/52 = 22/52, which simplifies to 11/26.

Answer:

49.1 cm^2

Step-by-step explanation:

The appropriate area formula is ...

area = (1/2)(side 1)(side 2)(sin(angle between))

= (1/2)(10 cm)(12 cm)·sin(55°) = 60·sin(55°) cm^2

area ≈ 49.1 cm^2

Answer:

  graph D

Step-by-step explanation:

You want to choose the graph with a y-intercept of 70 and an x-intercept of 140. Graph D matches that.

___

Comment on graph D

The horizontal scale is a bit weird in that the numbers don't correspond to hash marks on the horizontal axis. The hash mark between the numbers 120 and 160 will correspond to a distance of 140 ft. That is where the graph touches the horizontal axis, so that is one indication it is the graph you want.

Answer:

6a. -8

8b. 1/125

Step-by-step explanation:

If you know powers of 2 and the squares and cubes of small integers, you can work these in your head. There is no "work" to show. Of course, a calculator can evaluate these easily. (see attached)

___

6a. (-128)^(3/7) = ((-2)^7)^(3/7) = (-2)^3 = -8

___

8b. (27^(2/3) +8^(4/3))^(-3/2) = ((3^3)^(2/3) +(2^3)^(4/3))^(-3/2)

= (3^2 +2^4)^(-3/2) = (9+16)^(-3/2) = 25^(-3/2)

= (5^2)^(-3/2) = 5^(-3) = 1/5^3

= 1/125

100:40

=2.5

1200 : 2.5

=480

About 480 people out of the 1,200 customers are likely satisfied with their service.

To determine how many of the company's customers are likely satisfied with their service based on the survey results, we can use the concept of proportions. This involves simple multiplication and understanding ratios in percentages.

Find the proportion of satisfied customers in the survey:

Number of satisfied customers in the survey: 40

Total number of people surveyed: 100

Proportion of satisfied customers = (Number of satisfied customers) / (Total number of people surveyed)

Proportion of satisfied customers = 40 / 100 = 0.4 or 40%

Apply this proportion to the entire customer base:

Total number of the company's customers: 1,200

Estimate of satisfied customers = Proportion of satisfied customers × Total customers

Estimate of satisfied customers = 0.4 × 1,200 = 480

Answer:

x ≈ -0.93, x ≈ 1.06

Step-by-step explanation:

A graphing calculator can show you the approximate solutions. (It is also capable of refining those solutions to full calculator precision, if you need.)

_____

Comment on the graphical solution

I prefer to have the calculator show me the zeros of a function, where the zeros correspond to solutions of the original equation. For the purpose, it is sufficient to define the function as the difference between the sides of the original equation.

__

The definition of g(x) in the attachment corresponds to the iterator of Newton's Iteration method for finding zeros of a function. When the input and output values of that iteration function match, the value of x is a zero of the function f(x).

Answer:

b

Step-by-step explanation:

100%

The explicit formula for the sequence -5, -3, -1, 1, 3 is a_n = -5 + (n - 1)2.

Each term of an arithmetic sequence can be found using the formula:

a_n = a + (n-1)d

The given sequence is 5, -3, -1, 1, 3.

From this, we can see that the value of:

a = -5

d = -3 - (-5) = -3 + 5 = 2

∴ The explicit formula can be written as:

a_n = -5 + (n - 1)2

Therefore we have found the explicit formula for the sequence -5, -3, -1, 1, 3 as a_n = -5 + (n - 1)2.

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Answer:

(x, y) ⇒ (-x, y)

Step-by-step explanation:

Any transformation that multiplies a variable by something other than ±1 is not a rigid transformation — it involves some sort of dilation. Constants can be added or subtracted to effect translation, but none of the transformations shown here do any translation.

The first transformation is a reflection across the y-axis, hence the rigid transformation you're looking for.

_____

Comment on rotations

A rotation about the origin can be written in the form ...

(x, y) ⇒ (ax -by, bx +ay)

where a^2 +b^2 = 1 and b/a = tan(angle of rotation)

This rigid transformation is an exception to the statement above about multiplication by something other than ±1.

Answer:

1) 17p + 45.99 = 200

2) 200 > 45.99 + 17p

Step-by-step explanation:

Total Budget = $200

Cost of Party Room = $45.99

Cost of movie ticket for one person = $12.50

Cost of one small bag of popcorn = $4.50

Part 1: Possible Equation by Tomas

The possible equation that can be set up will have the total budget equal to total expenses.

So,

200 = Total Cost of party

200 = Cost of Party Room + Cost of Movie Tickets + Cost of popcorns

If p people attend the party, the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.

So, now the equation will be:

200 = 45.99 + 12.50p + 4.50p

200 = 45.99 + 17p

or

17p + 45.99 = 200

This is a possible equation that Tomas might have used to represent the cost of the party.

Part 2: Possible Inequality by Emilio

Emilio might want to keep the cost below $200 of the entire party. So the possible inequality will be of the form:

200 > Total Cost of party

200 > Cost of Party Room + Cost of Movie Tickets + Cost of popcorns

200 > 45.99 + 12.50p + 4.50p

200 > 45.99 + 17p

This is a possible inequality that Emilio might have used to represent the cost of the party.

To find out how many games Natalie and her friends played, we subtracted the total shoe rental cost for 6 people from the $21 spent and divided the remainder by the cost per game, which gave us a result of 3 games played.

The question asks us to solve a real-world math problem where Natalie and her friends go bowling and spend a total of $21. The cost to play one game is $3 and shoe rental is $2 per person.

To determine the number of games they played, we need to calculate the cost of shoe rental for all people and then figure out how much of the $21 was left for the games.

First, we calculate the shoe rental for 6 people (Natalie and her 5 friends):

Next, we subtract the shoe rental cost from the total amount spent to find the amount spent on games:

Finally, we divide the amount spent on games by the cost per game to find the number of games played:

Natalie and her friends played 3 games of bowling.

Answer:

5/2

Step-by-step explanation:

The multiplicative inverse is what me need to multiply by to get 1

2/5 * what = 1

Multiply by the reciprocal

5/2 *2/5 * what = 1 *5/2

what = 5/2

The multiplicative inverse is 5/2

5/2 is the multiplicative inverse

Answer:

option H

457.9 CM squared

Step-by-step explanation:

Given that,

base of parallelogram = 30 cm

side of parallelogram = 18 cm

one of the angle of parallelogram = 58°

Formula to calculate area of parallelogram is

To calculate height we will use trigonometry identity  

sin(58) = height / 18

height = 15.27

Area = 30 x 15.27

         = 457.9 cm²

so the area of parallelogram is 457.9 cm²

Answer: it should be will receive a refund of $278

Step-by-step explanation:

That’s just what was on my test though

Hope that helps somebody

The amount Ms. Wilson will receive after she figures out her tax for the year is; $999.88

The tax bracket Ms. Wilson falls into demands that she pays 12% of her taxable income in tax.

Hence, the tax she's supposed to pay is;

Hence, she will receive after she figures her taxes for the year is; $5344 - $4,344.12 = $999.88

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Answer:

The answer is ⇒ No, because Deon starts with less bacteria,

but it grows at a faster rat than Cameron's bacteria

Step-by-step explanation:

* Lets study the graph and the equation

- At t = 0

# Cameron's population = 200

# Deon population = 100

- At t = 5

# From the equation b(5) = 200(1 + 0.08)^5 ≅ 294

# From the graph b(5) ≅ 200

∴ Cameron's population > Deon's population

- The increase of the Cameron's population ≅ 94

  (294 - 200 = 94)

- The increase of the Deon's population ≅ 100

  (200 - 100 = 100)

∴ The rat of increase of Deon > The rat of increase of Cameron

- At t = 8

# From the equation b(8) = 200(1 + 0.08)^8 ≅ 370

# From the graph b(8) ≅ 300

∴ Cameron's population > Deon's population

- The increase of the Cameron's population ≅ 76

  (370 - 294 = 76)

- The increase of the Deon's population ≅ 100

  (300 - 200 = 100)

∴ The rat of increase of Deon > The rat of increase of Cameron

- At t = 11

# From the equation b(11) = 200(1 + 0.08)^11 ≅ 466

# From the graph b(11) ≅ 500

∴ Cameron's population < Deon's population

- The increase of the Cameron's population ≅ 96

  (466 - 370 = 96)

- The increase of the Deon's population ≅ 200

  (500 - 300 = 200)

∴ The rat of increase of Deon > The rat of increase of Cameron

- At t = 14

# From the equation b(14) = 200(1 + 0.08)^14 ≅ 587

# From the graph b(14) ≅ 700

∴ Cameron's population < Deon's population

- The increase of the Cameron's population ≅ 121

  (587 - 466 = 121)

- The increase of the Deon's population ≅ 200

  (700 - 500 = 200)

∴ The rat of increase of Deon > The rat of increase of Cameron

* From all these calculations the rate of increase of

 Cameron's population is less than the rate of increase

 of Deon's population

∴ Cameron is not right because Deon starts with less bacteria,

   but it grows at a faster rat than Cameron's bacteria

Answer:

The answer is C

Step-by-step explanation:

Answer:

Since 2 inches represent 8 feet then 2.5 would represent x feet so  

2/8 = 2.5/x  

By doing cross multiplication :  

2 x = 20 --> x = 10 feet

Step-by-step explanation:

I think the last one is maybe ten, maybe

Answer:

Step-by-step explanation:

no

Answer: function b has a greater rate of change

Answer:

Step-by-step explanation:

a) The image A'B'C'D' is smaller than the original ABCD, so the dilation is a reduction. The image is reduced in size from the original.

__

b) Each image point is 1/2 the distance of the original point from the origin. Count the grid squares to see this, or compare coordinates:

  A'(-1, 2) = 1/2·A(-2, 4)

Thus the scale factor is 1/2.

Answer:

x = 2

Step-by-step explanation:

The minimum occurs where the value being squared is zero. x-2 = 0 when x=2.

Answer:

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex]

Step-by-step explanation:

We want to evaluate:

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x[/tex]

When x=0, we obtain the first term of the geometric series as

[tex]a_0=2(\frac{1}{3})^0[/tex]

The common ratio of this geometric series is [tex]r=\frac{1}{3}[/tex]

The sum of the first n-terms of a geometric series is

[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]

From x=0 to x=15, we have 16 terms.

The sum of the first 16 terms of the geometric series is

[tex]S_{16}=\frac{a(1-(\frac{1}{3})^{16})}{1-\frac{1}{3}}=2.99999993031[/tex]

[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex] to the nearest tenth.

Answer: c. Exponential

Answer:

 1) Methods:

-  Quadratic formula.

- Factorization.

- Completing the square.

2) If the determinant is less than zero ([tex]D<0[/tex]) then there are two roots that are complex conjugates.

Step-by-step explanation:

 Methods:

-  Quadratic formula

Given the quadratic equation in Standard form [tex]ax^2+bx+c=0[/tex], you can solve it with the quadratic formula:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

- Factorization

You must find two expression that when you multply them, you get the original quadratic equation. For example:

[tex]x^2+6x+8=0[/tex]

Find two number whose sum is 6 and whose product is 8. These are 2 and 4. Then:

[tex](x+2)(x+4)=0[/tex]

When you make the multiplication indicated in [tex](x+2)(x+4)=0[/tex], you obtain [tex]x^2+6x+8=0[/tex]

- Completing the square

Given the quadratic equation in Standard form [tex]ax^2+bx+c=0[/tex],, you must turn it into:

[tex]a(x+d)^2+e=0[/tex]

Where:

[tex]d=\frac{b}{2a}\\\\e=c-\frac{b^2}{4a}[/tex]

Once you get that form, you must solve for x.

You can predict if the quadratic function will have a complex solution with the determinant:

[tex]D=b^2-4ac[/tex]

If [tex]D<0[/tex] then there are two roots that are complex conjugates.

Quadratic equations can be solved by several methods including the quadratic formula. The concept of a discriminant, calculated by b² - 4ac, can indicate if a function has a complex solution. A negative discriminant means the equation will have complex solutions.

Quadratic equations, or second-order polynomials, take on the form ax²+bx+c = 0. There are several methods to solve these equations, for instance, factoring, completing the square, using the quadratic formula or graphically.

The most general method is the quadratic formula: -b ± √b² - 4ac / 2a.

Indicator for a complex solution is called the discriminant(b² - 4ac). If the discriminant is negative, the equation will have complex solutions rather than real ones. This is because you'd be attempting to find the square root of a negative number, which is not possible within the set of real numbers, and hence the answer is in the form of a complex number.

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Answer:

Failing to pay debt

Step-by-step explanation:

Final answer:

Defaulting on a debt, failing to pay debt, and building a credit history are crucial aspects of managing one's financial health.

Explanation:

Defaulting on a debt occurs when a borrower fails to repay the loan according to the terms agreed upon with the lender. This can lead to serious consequences such as damage to one's credit score and possible legal actions taken by the lender.

One of the contributing factors to defaulting is failing to pay debt on time. This affects a person's credit history and the lender's trust in the borrower's ability to repay borrowed money.

It is important to build a credit history by responsibly managing credit accounts, paying bills on time, and avoiding opening too many accounts rapidly to maintain a good credit score and prevent defaulting.

Answer:

C.  Each additional t-shirt being printed will increase the total cost by $11.

Step-by-step explanation:

We know that the total cost of custom t-shirts, y, in dollars, for x t-shirts is given by:

[tex]y = 11x + 25[/tex]

Here 11 is the price of the shirt, x is the number of shirts that are printed and 25 might be some additional charges.

For each additional shirt that is printed, the total price, y, will increase by $11 so the correct answer option is C.

The second value in a set of parenthesis is the y value, so B is true.

If you multiplied each value of W by -2, you would get the values for V, so C is also true.

The answer is B and C.

Answer:

Option B and C are correct.

Step-by-step explanation:

Given the vectors V = (8, -4) and W = (-4,2)

we have to check the following options.

Option A: V x W = 40

[tex]A\times B=\begin{vmatrix}i&j&k\\8&-4&0\\-4&2&0\end{vmatrix}=0i+0j+k(16-16)=0i+0j+0k[/tex]

Hence, not true

Option B: The y-component of W is 2

W = (-4,2)

x-component is -4

y-component is 2

Hence, true

Option C:  V = -2W

W=(-4, 2)

V=-2(-4,2)=(8,-4)

which is true

Option D: The x-component of V is 4

V = (8,-4)

x-component is 8

y-component is -4

which is not true.

hence, the option B and C are correct.

whats the question? ill help you out i just wanna Answer the right question

Answer:

x = 45, y = 24.

Step-by-step explanation:

If the 2 numbers are x and y:

x + y = 69...........(1)

x = 2y - 3

x - 2y = -3...........(2)

Subtract: (1) - (2):

x - x + y - (-2y) = 69 - (-3)

y + 2y = 72

3y = 72

y = 24.

From equation 1:-

x + 24 = 69

x = 45.

The numbers are x = 24 and y = 45 respectively.

An algebraic expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -

2x + 3y + 5

2z + y

x + 3y

Given is that the sum of two numbers is 69. The larger number is three less than twice the smaller number.

Assume that the numbers are {x} and {y}. So, we can write the equations as -

x + y = 69

y = 2x - 3

Rewriting equation {1}, we get -

x + y = 69

x + 2x - 3 = 69

3x = 72

x = 24

and

y = 2 x 24 - 3

y = 45

Therefore, the numbers are x = 24 and y = 45 respectively.

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Answer:

a: 27 apples

b: $0.40 apples

Step-by-step explanation:

a: another way of saying that the price of an apple one-third that of an orange is that you can get 3 apples for the price of 1 orange. If he bought 5 oranges, he could have gotten 15 apples, so 27 apples total.

b:  $10.80/27 = $0.40 per apple

Answer:

6 to the power of 1 over 6

Answer:

The correct option is 4.

Step-by-step explanation:

The given interpretation is square root of the cube root of 6. The mathematical expression is

[tex]\sqrt{\sqrt[3]{6}}[/tex]

It can be written as

[tex]((6)^{\frac{1}{3})^{\frac{1}{2}}[/tex]

Using the property of exponent, we get

[tex](6)^{\frac{1}{3}\times \frac{1}{2}}[/tex]         [tex][\because (x^m)^n=(x)^{mn}][/tex]

Now simplify the power.

[tex](6)^{\frac{1}{6}}[/tex]

The simplified form of given expression is 6 to the power of 1 over 6. Therefore the correct option is 4.

Answer:

5 cm

Step-by-step explanation:

ΔABC is equilateral, so BC = AB = 5 cm.

____

AO is the perpendicular bisector of BC and the angle bisector of angle A, so ∠OAC = ∠OAB = 30°. Then vertex angle BAC of isosceles triangle ABC is 60°, which means all angles in the triangle are 60° and the triangle is equilateral.

The length of BC is 5cm

Given that line AB is tangent to circle K at point B, and line AC is tangent to circle K at point C, we know that the radius of the circle at the point of tangency is perpendicular to the tangent line. Therefore, OB is perpendicular to AB, and OC is perpendicular to AC. This forms two right triangles,[tex]$\triangle OAB$ and $\triangle OAC$.[/tex]

Let's denote OB as the side opposite the 30° angle and OA as the hypotenuse. Then we have:

[tex]OB = $\frac{1}{2}$AB = $\frac{1}{2} \times 5$ cm = 2.5 cm[/tex]

OA = AB = 5 cm (since AB is the hypotenuse of the right triangle)

Now, since the circle is the same, OA is also the radius of the circle, and thus OB = OC = 2.5 cm.

Therefore [tex], $\triangle OBC$[/tex] is an equilateral triangle because all angles are 60° and the sides opposite these angles are equal. Hence, BC = OB = OC = 2.5 cm.

Thus, BC = OB + OC' = 2.5 cm + 2.5 cm = 5 cm.

But this is not the final answer. We have to consider that the length of the chord BC is equal to the diameter of the circle because the tangents from a common external point to a circle are equal in length. Therefore, the diameter of the circle is twice the length of the radius OB (or OC').

Diameter = 2 * OB = 2 * 2.5 cm = 5 cm

BC = 5cm