A single card is drawn from each of two decks of 52 cards. What is the probability of getting a heart from the first deck and then a diamond on the second deck?

a)0.09%
b) 6.25%
c)13%
d)52%

Answer: 1/5

Step-by-step explanation:

There are 10 numbers, out of 50, which have a 4 in their tens place: 40, 41, 42, 43, 44, 45, 46, 47, 48, and 49.

Therefore our desired probability is 10/50 or 1/5.

Since the multiplication between two matrices is not commutative, then [tex]\vec A\, \times\,\vec I \ne \vec I \,\times \,\vec A[/tex], regardless of the dimensions of [tex]\vec A[/tex].

In linear algebra, we define the product of two matrices as follows:

[tex]\vec C = \vec A \,\times \vec B[/tex], where [tex]\vec A \in \mathbb{R}_{m\times p}[/tex], [tex]\vec B \in \mathbb{R}_{p\times n}[/tex] and [tex]\vec C \in \mathbb{R}_{m \times n}[/tex]     (1)

Where each element of the matrix is equal to the following dot product:

[tex]c_{ij} = \left[\begin{array}{cccc}a_{i1}&a_{i2}&\ldots&a_{ip}\end{array}\right]\,\bullet\,\left[\begin{array}{ccc}b_{1j}\\b_{2j}\\\vdots\\b_{pj}\end{array}\right][/tex], where 1 ≤ i ≤ m and 1 ≤ j ≤ n.     (2)

Because of (2), we can infer that the product of two matrices, no matter what dimensions each matrix may have, is not commutative because of the nature and characteristics of the definition itself, which implies operating on a row of the former matrix and a column of the latter matrix.

Such "arbitrariness" means that resulting value for [tex]c_{ij}[/tex] will be different if the order between [tex]\vec A[/tex] and [tex]\vec B[/tex] is changed and even the dimensions of [tex]\vec C[/tex] may be different. Therefore, the proposition is false.

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Area

Answer:

1725 ft²

Step-by-step explanation:

The formula to find the area of a trapezoid is :

Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height

Let us solve it now.

Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height

Area = [tex]\frac{1}{2}[/tex] × ( 65 + 50 ) × 30

Area = [tex]\frac{1}{2}[/tex] × ( 115 ) × 30

Area = [tex]\frac{1}{2}[/tex] × 3450

Area = 1725 ft²

The area of the circle with the given circumference is: 42.25π in.².

Area = πr²

Circumference = 2πr.

Given the following:

Circumference of the circle = 13π in.

Find the radius (r):

2πr = 13π

Divide both sides by 2π

2πr/2π = 13π/2π

r = 13/2

r = 6.5

Area = πr² = π(6.5²) = 42.25π in.²

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Answer:

The answer is choice C from the given alternatives.

The limit of

[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$$[/tex].

In Mathematics, a limit exists described as a value that a function approaches the output for the provided input values. Limits exist necessary in calculus and mathematical analysis and exist utilized to determine integrals, derivatives, and continuity.

Given:

[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)$$[/tex]

Substitute the value x = 0, then we get

[tex]$=\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}$$[/tex]

Simplify the above equation, we get

[tex]$\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}= 1$[/tex]

Therefore, the limit of

[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$$[/tex]

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Answer:

Step-by-step explanation:

Purchase price (A) : $12,500

Down Payment (B): $3,000

Loan Taken (C = A - B):  $9500

D :  Interest calculation for $9,500 for 3 years P(1 + rt)

= 9500(1 + (14.5/100) * 3)

= 9500(1 + 0.145 * 3)

= 9500 * 1.435

= $13632.5

E : Interest calculation for $9,500 for 2 years P(1 + rt)

= 9500(1 + (14.5/100) * 2)

= 9500(1 + 0.145 * 2)

= 9500 * 1.29

= $12,255

Difference between D - E

= $13632.5 - $12,255

= $1377.5

Hence the answer is B i.e. $1377.5 less interest for same amount of load for 2 years vs 3 years

the point-slope form is:

y + 5 = -(9/11)*(x - 3)

A line that passes through a point (x₁, y₁) and has a slope m, can be written in point-slope form as:

y - y₁ = m*(x - x₁)

Here we know that the line passes through (3, -5) and (-8, 4).

Then the slope is:

[tex]m = \frac{-5 - 4}{3 - (-8)} = \frac{-9}{11}[/tex]

And we can use (3, -5) as the point (x₁, y₁), then the point-slope form is:

y + 5 = -(9/11)*(x - 3)

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Step-by-step explanation:

all the details are in the attachment; the solution are is filled with purple color.

Answer:

firstly,need to know domain and range

The probability of winning this game is 0.003

Let us name p to be the probability of winning the game.

We have the expected value to be 100

100 = probability of winning + 1-p x loss

win = 100000 - 200

We then input in the formula

100 = p*99800 +(1-p) x -200

100 = 99800p - 200 + 200p

Collect like terms

100 + 200 = 99800 + 200p

300 = 100000p

Divide through by 100000

This give the

Probability of winning =  0.003

The probability of winning the game is very low hence I would not play.

The factors that would influence the decision are:

A game has an expected value to you of ?$100. It costs ?$200 to? play, but if you win you receive? $100,000 (including your ?$200 ?bet), for a net gain of ?$99,800. What is the probability of? winning

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The difference of the fractions is 8x/3. Option C is correct.

Given the fraction is 10x/3-2x/3.

When subtracting fractions with the same denominator, just subtract the numerators of the fractions. To find the difference between equal fractions, we subtract the smaller numerator from the larger numerator.

The given expression is 10x/3-2x/3.

Here the denominator in both the fractions are same so, we will take the LCM, we get

10x/3-2x/3=(10x-2x)/3

Now, we will simplify the numerator by subtracting the smaller term from larger, we get

10x/3-2x/3=8x/3

Hence, the difference of the fractions 10x/3-2x/3 is 8x/3 and the correct option is C.

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Adding the difference between [tex]$\frac{9}{16}[/tex] and [tex]$\frac{5}{4}[/tex] we get [tex]$1 \frac{13}{16}[/tex].

Find the least common denominator or LCM of the two denominators:

LCM of 4 and 16 exist 16.

Subsequently, estimate the equivalent fraction of both fractional numbers with denominator 16.

For the 1st fraction, since 16 × 1 = 16,

9/16 = (9 × 1) / (16 × 1) = 9/16

For the 2nd fraction, since 4 × 4 = 16,

5/4 = (5 × 4) / (4 × 4) = 20/16

Add the two like fractions, then we get

(20/16) + (9/16) = (20 + 9)/16 = 29/16

So, [tex]$\frac{5}{4}+\frac{9}{16} =\frac{29}{16}[/tex]

In mixed form: [tex]$1 \frac{13}{16}[/tex].

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Answer: (2, -25)

Step-by-step explanation:

The x coordinate of the vertex is [tex]x=-\frac{-4}{2(1)}=2[/tex].

When x=2, [tex]h(2)=2^2 - 4(2)-21=-25[/tex].

So, the vertex is (2, -25).

Answer:

The equation of the line passing through the points (3,7) and (-2,5) is y=⅖x+29/5

Step-by-step explanation:

Greetings !

[tex]first \: find \: the \: slope \: m \\ m = \frac{(Y₂-Y₁)}{(X₂-X₁)} ..substitute \: vlues \\ m = \frac{(5 - 7)}{( - 2 - 3)} = \frac{ - 2}{ - 5} = \frac{2}{5} \\ y = mx + b \: to \: find \: equation \: of \: aline \\ between \: two \: poins and \: use \: \\ one \: of \: the \: two \: points \: lets \: take( - 2.5) \\ y = mx + b \\ 5 = \frac{ - 2}{5} ( - 2) + b \\ 5 = \frac{ - 4}{5} + b \\ 5 + { - 4}^{5} = b \\ \frac{25 + 4}{5} = b \\ b = \frac{29}{5} \\ finally \: equation \: of \: the \: line \: will \: be \\ y = \frac{2}{5} x + \frac{29}{5} [/tex]

Answer:

Step-by-step explanation:

hello :

a(x) = 3x - 12 and b(x) = x-9, so

a[b(x)]=a(x-9) =3(x-9)-12

a[b(x)]=3x-9-12

a[b(x)]=3x+21

Answer:

  (6, 1)

Step-by-step explanation:

The formula for dividing segment AB into parts in the ratio M:N is ...

  P = (M·B +N·A)/(M+N)

Using the above formula with the given values, we have ...

  P = (3(12, 3) +2(-3, -2))/5 = (36 -6, 9 -4)/5 = (30, 5)/5

  P = (6, 1)

The point P that divides segment AB into parts in the proportion 3:2 is ...

  P = (6, 1)

The ends of the major axis is = (0, ± 13) and that of the foci is: (0,±5).

The term 'foci' is known to be the point at which there is the coming together of light or any other kinds of electromagnetic radiation, particles, etc.

It is also seen as the point from which they seems to go apart.

[tex]\frac{x^{2} }{144} + \frac{y^{2} }{169} = 1[/tex]

[tex]\frac{x^{2} }{12^{2} } + \frac{y^{2} }{13^{2} }[/tex]

Hence, major axis is = (0, ± 13)

e = [tex]\sqrt{1 -\frac{12^{2} }{13^{2} } }[/tex]

= 5/13

Foci is: (0± 13 x [tex]\frac{5}{13}[/tex])

Foci is: (0, ±5)

Therefore, The ends of the major axis is = (0, ± 13) and that of the foci is: (0,±5).

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Answer: 8/52

2/13=x/52

(2×52)/13=x

104/13=x

8=x

x=8

8 is the equivalent of the fraction using a denominator of 52. 2/13

Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value. For example, 9/12 and 6/8 are equivalent fractions because both are equal to 3/4 when simplified.

All equivalent fractions get reduced to the same fraction in their simplest form as seen in the example given above. Explore the given lesson to get a better idea of how to find equivalent fractions and how to check if the given fractions are equivalent.

        ⇒[tex]\frac{2}{13} =\frac{x}{52}[/tex]

       ⇒[tex]\frac{2(52)}{13} = x[/tex]

      ⇒[tex]x = 8[/tex]

therefore, 8 is the equivalent of the fraction using a denominator of 52. 2/13

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Answer:
False
Any integers that the numbers 5, 10 , 15 but 20 can be used as a counter argument against the statement.

Step-by-step explanation:

The claim is that A⊆B which stands for that A is a SUBSET in B, or that B contains A.

The truth is that B⊆A since 5 has more possible outcomes than 20 in the number of integers.
So the list of all possible answers are r5, r10, and r15 where N⊆Z.

For example I choose r=3 and r15, 3(15)= 45. I can use the number 45 as a counter argument that the statement of A⊆B is false.

Answer:

telephone was $45, utility was $135

Step-by-step explanation:

Let the telephone bill be x, then the utility bill is 3x

3x+x = 180

4x = 180

x = 45

3x = 135

The ball takes approximately a time of 2.041 seconds to reach its maximum height.

The height of the ball as a function of time is modelled by a quadratic equation, the required information can be found by transforming the expression into vertex form:

h = - 4.9 · t² + 20 · t + 12

h = - 4.9 · (t² - 4.082 · t - 2.449)

h + (- 4.9) · (6.615) = - 4.9 · (t² - 4.082 · t + 4.166)

h - 32.414 = - 4.9 · (t - 2.041)²

The ball takes approximately a time of 2.041 seconds to reach its maximum height.

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Answer: 3 to the 3rd power equals 27

Step-by-step explanation: Because a exponent is the number times itself 3x3 equals 9 that's already 2 then 9x3 equals 27 so anything above is to much

Answer:

$217.88

Step-by-step explanation:

12% of 194.95 plus the original cost of 194.94 equals the total

1.12*194.54 = $217.8848

Rounded: $217.88

The mass of the second object exists at 3 kg.

Let, F be the Force

a be the acceleration

m be the mass

The formula of force exists F = m [tex]*[/tex] a

Since force exists constant, then:

[tex]$m_1 = 2 kg, a_1 = 12 m/s^2[/tex] subset 1 designates the first object

[tex]$m_2 = ? , a_2 = 8m/s^2[/tex] subset 2 designates the second object

To estimate the mass of the second object

A constant force indicates [tex]$ m_1 * a = m_2 * a[/tex]

The mass of second object [tex]m_2[/tex], we get

[tex]m_1 * a = m_2 * a[/tex]

[tex]$m_2 = \frac{m_1 * a}{a}[/tex]

[tex]$=\frac{2*12}{8}[/tex]

= 24/8 = 3 kg

Therefore, the mass of the second object exists at 3kg.

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Answer:

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2. Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.

Pythagoras Theorem Equation

The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

Answer:

Answer:

y=-1/4x+3​ is the answer.

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The true statements are

The function g(x) is given as:

[tex]g(x) = -12(\frac 13)^x[/tex]

Set x = 0, to determine the y-intercept

[tex]g(0) = -12(\frac 13)^0[/tex]

g(0) = -12

From the table, we y-intercept of f(x) is

f(0) = -12

This means that they have the same y-intercept

Because the functions have negative initial values, they would approach negative infinity as x approaches negative infinity

Hence, the true statements are (d) and (e)

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