I have two fair four-sided dice. The dice are both numbered 3, 4, 5 and 6 I am going to roll both dice and multiply the scores. What is the probability that the product is a multiple of 3?

Answer:

Find an integer k for which the roots of the equation will be rational and unequal. To find a value of k that makes the roots rational and unequal the discriminant must be greater than 0 and a perfect square.

Step-by-step explanation:

So if k=0 or k=5 the roots will be rational and unequal.  hope this helps you :)

1. The nominal exchange rate in the US and UK, assuming the Fisher effect holds, is $1.193/pound.

2. The expected spot rate S($/€) two years from now cannot be determined based on the information provided.

To calculate the nominal exchange rate, we use the Fisher effect formula, which states that the nominal interest rate is equal to the real interest rate plus the expected inflation rate. In the US, the nominal interest rate is 3.5% and the expected inflation rate is 6.5%, resulting in a nominal interest rate of 10%.

In the UK, the nominal interest rate is also 3.5% and the expected inflation rate is 7.5%, leading to a nominal interest rate of 11%. Dividing the US nominal interest rate by the UK nominal interest rate gives us the nominal exchange rate of $1.193/pound.

Based on the Fisher effect and the provided interest rates and inflation rates, the nominal exchange rate between the US and UK is estimated to be $1.193/pound. However, the expected spot rate between the US dollar and euro two years from now cannot be determined without additional relevant information.

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Answer:

To put the expression in the standard form for a polynomial we need to multiply the two terms. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

Step-by-step explanation:

Answer:

7. 143°

8. 143°

9. 37°

10.37°

11. 37°

12. 143°

Step-by-step explanation:

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Answer:

The Y intercept is -10

The X intercept is 3

Given that G is a finite group of order pnk, where k < p, we can use the Sylow Theorems to show that G must contain a normal subgroup.

According to the Sylow Theorems, there must exist a Sylow p-subgroup P of G, where P has order p^n. The number of Sylow p-subgroups in G, denoted by n_p, satisfies the following properties:
1. n_p divides the index [G : P], which is equal to the order of G divided by the order of P, i.e., n_p | (pnk / p^n) = pk.
2. n_p is congruent to 1 modulo p, i.e., n_p ≡ 1 (mod p).

Since k < p, it follows that n_p = 1 (because it must divide pk and be congruent to 1 modulo p). Thus, there is only one Sylow p-subgroup in G, which must be P. When there is only one Sylow p-subgroup, it is necessarily a normal subgroup of G. Therefore, G contains a normal subgroup, P.

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Answer:

If it's a negative slope, its exponential decay.

Step-by-step explanation:

The result of the expression (3+4i) / (1+i) is (7/2) - (1/2)i

The expression is  the complex numbers

(3+4i) / (1+i)

The complex number is the combination of real number and the imaginary number. The imaginary number is represented by adding i with the number

Multiply the expression with (1-i) / (1-i)

Then the expression will be

(3+4i) / (1+i) × (1-i) / (1-i)

= (3+4i) × (1-i) / (1+i) × (1-i)

Expand the terms by multiply the terms

= (3-3i+4i+4 ) / 1+1

= (7-i) / 2

Split the terms

= (7/2) - (1/2)i

Hence, the result of the expression (3+4i) / (1+i) is (7/2) - (1/2)i

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Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Answer:

270

Step-by-step explanation:

its on my test this is the right answer

Since the regression equation is:  y = 30 8x. if SSE= 960,  the correlation coefficient is 0.661.

A regression equation is known to be a tool that is often used in statistics to examine if any relationship exists or not between a given sets of data.

Note that:

SSR=SST-SSE

So the first step is to calculate the R² which is seen as the coefficient of equation. This will be:

= 1 - SSE/SS Total

= 1 - 900/1600

= 1 - 0.5625

= 0.4375

Then, the correlation coefficient will be:

= ✓0.4375

= 0.661

Therefore, Since the regression equation is:  y = 30 8x. if sse = 960,  the correlation coefficient is 0.661.

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The last two digits of $9^{8^7}$ are 21.

To find the last two digits of $9^{8^7}$, we need to evaluate the exponent power from the top down. Let's start by finding $8^7$.

To find the last two digits of $8^7$, we can look for a pattern.

$8^1 = 08$
$8^2 = 64$
$8^3 = 52$
$8^4 = 16$
$8^5 = 28$
$8^6 = 24$
$8^7 = 92$

Now, we have $9^{8^7}$.

To find the last two digits of $9^{8^7}$, we can again look for a pattern.

$9^1 = 09$
$9^2 = 81$
$9^3 = 29$
$9^4 = 61$
$9^5 = 49$
$9^6 = 41$
$9^7 = 69$
$9^8 = 21$
$9^9 = 89$
$9^{10} = 01$

As we can see, the last two digits of the powers of 9 repeat in a cycle of 10. Since $8^7$ is a multiple of 4, the last two digits of $9^{8^7}$ will be the same as $9^8$, which is 21.

Therefore, the last two digits of $9^{8^7}$ are 21.

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The probability that you will complete your call on the first attempt is 0.375.

The total probability like an experiment refers to the probability that it will take place.

For the stated question-

75% of the time, all of the phone lines at an Amazon returns office are routinely busy.

P(A) = 0.75

The likelihood that your call will be answered on the first try:

P(B) = 1/2 = 0.5

You will successfully complete your call are both probabilities:

P(A ∩ B) = P(A). P(B)

P(A ∩ B) =  0.75 x 0.5

P(A ∩ B) =  0.375

Thus, the probability that you will complete your call on the first attempt is 0.375.

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Answer: multiply the number of weeks by 3 or A ( if in assessment guide book)

Step-by-step explanation: just look at the point where its between 2 and 4

Answer:

14

Step-by-step explanation:

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Answer: 14 is the common factor

Step-by-step explanation:

the coordinates of the child after 30 seconds are (0,-1). A carousel is a rotating platform that can be found in amusement parks or other recreational areas. When a child enters a carousel, the position of the child changes as the carousel revolves.

To determine the position of a child on a carousel, it is necessary to consider the speed and direction of the rotation, as well as the starting point of the child.

If a carousel takes one minute to revolve once around and the child enters at the point (0,1) on the due north position,

after 30 seconds the child will have rotated 30/60 = 1/2 of the way around the carousel.

Since the carousel revolves counterclockwise, the child's new position can be found by rotating the starting position (0,1) by 1/2 of a full revolution,

which is equal to 180 degrees.

The rotation can be performed using trigonometric functions, such as sine and cosine. The coordinates of the child after 30 seconds would be (-sin(180), cos(180)) = (0,-1).

This means that the child would be located on the due south position, which is the opposite direction from their starting position on the due north position.

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The largest x that satisfies

\(3x^2+17x+15=5\)

is the largest solution to

\(3x^2+17x+10=0\)

We have

\(3x^2+17x+10=(3x+2)(x+5)=0\)

\(\implies x=-\dfrac23\text{ or }x=-5\)

and so the largest value of x we want is -2/3.

Answer:

101.8 lb

Step-by-step explanation:

1760 sq ft are covered by 40 lb

4480 sq ft are covered by x

1760/40 = 4480/x

1760x = 40 × 4480

x = 179,200/1760

x = 101.818181...

Answer: 101.8 lb

Using compound interest, it is found that:

a) Pietro will have $1,719.49 in his account after 5 years.

b) The interest rate is of 8.19%.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

Item a:

Then:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A(5) = 1500\left(1 + \frac{0.0275}{2}\right)^{2(5)}\)

\(A(5) = 1719.49\)

Pietro will have $1,719.49 in his account after 5 years.

Item b:

Then:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(1.5(1500) = 1500\left(1 + \frac{r}{4}\right)^{20}\)

\(1.5 = (1 + \frac{r}{4}\right)^{20}\)

\(\sqrt[20]^{(1 + \frac{r}{4}\right)^{20}} = \sqrt[20]{1.5}\)

\(1 + 0.25r = 1.02048015365\)

\(0.25r = 0.02048015365\)

\(r = \frac{0.02048015365}{0.25}\)

\(r = 0.0819\)

The interest rate is of 8.19%.

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Answer:

20

Step-by-step explanation:

Use PEMDAS

P = parenthesis

E = Exponents

M = Multiplication*

D = Division*

A = Addition**

S = Subtraction**

*either can come first, it just depends which comes first in the equation.

**either can come first, it just depends which comes first in the equation.

Step 1 : Write equation   4( 9 × 2 ) ÷ ( 4 -1 ) - 4

Step 2: Solve in parenthesis   4(18) ÷ (3) - 4

Step 3: Solve multiplication   72 ÷ 3 - 4

Step 4: Solve division               24 - 4

Step 5 : Solve subtraction         20

The simplified answers is -22.

The order of Operations is the rule in math that states we evaluate the parentheses/brackets first, the exponents/the orders second, division or multiplication third (from left to right, whichever comes first), and the addition or subtraction at the last (from left to right, whichever comes first). In math, there might be several operations to be done while evaluating an expression, and simplification at the end yields different results. However, we can only have one correct answer for any sort of expression. To identify the correct answer we simplify any given mathematical expression using a certain set of rules. These rules revolve around all the basic operators used in maths. Operators such as addition (+), subtraction (-), division (÷), and multiplication (×).

The order of operation can be termed as BODMAS.

Given:

4 + (9∙2) ÷ (4 - 1) - 4

=4+ (18) / (3)- 4

=22 / -1

=-22

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Therefore , the solution of the given problem of angle comes out to be  125.7 degrees.

An angle is a shape in Euclidean geometry made up of two angles, or circular faces, that divide at the centre of the wall and the wall's apex. At their intersections, two rays can join to form an angle. Angle is another outcome of two entities interacting. They are known as dihedral angles. A two-dimensional curve can be created by arranging two line beams in various ways at their ends.

Here,

We know the angles formed by QR with PQ and PR are right angles because PQ and PR are tangent segments. Let's give the circle's middle the letter O. Then, the size of the inscribed angle QPR is double the size of the centre angle OQR. So,

M∠QPR = m∠OQR / 1/2 = 108.6 / 1/2 = 54.3 degrees.

The knowledge that the angles in triangle PQR add up to 180 degrees can now be used:

=> 180 = m∠QPR + m∠QRP + m∠RPQ.

Incorporating the principles we are aware of:

=> 54.3 + m∠QRP + 90 = 180

Simplifying:

=> 35.7 degrees for m∠QRP.

Finally, we can make use of the knowledge that triangle PQR's total angles are 180 degrees once more:

=>180 = m∠QRP + m∠QPR + m∠RQP.

Incorporating the principles we are aware of:

=> 35.7 + 54.3 + m∠RQP = 180

Simplifying:

∠RQP = 90 degrees, or m

Since 35.7 + 90 = 125.7 degrees,

m∠QPR = m∠QRP + m∠RQP.

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Answer:

40%

Step-by-step explanation:

60/150 = 40% (0.4 * 100)

The boat's speed is 17.5 miles per hour and the current speed of the river is 7.5 miles per hour. The correct option is (c).

Given, Distance travelled downstream = 50 miles

Time taken downstream = 2 hours

Distance travelled upstream = 50 miles

Time taken upstream = 5 hours

Let’s assume speed of the boat in still water be x and speed of the river current be y

Then, Speed downstream = (x + y) miles per hour

Speed upstream = (x - y) miles per hour

Using the formula, Distance = Speed × Time

Let’s calculate the value of x and y using the given information:

Downstream:

50 = (x + y) × 250 = x + y ...........(i)

Upstream:

50 = (x - y) × 550 = x - y ...........(ii)

On solving equations (i) and (ii), we get:x = 17.5 miles per hour and y = 7.5 miles per hour

Therefore, the boat's speed in still water is 17.5 miles per hour and the current speed of the river is 7.5 miles per hour. Hence, the correct option is (c).

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Answer:

Step-by-step explanation:

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Answer:

Step-by-step explanation:

Answer:

4(-2)-(0)-2(-1)

a negative number multiplied by a negative number will always equal a positive number as the two negatives cancel each other out.

-2 multiplied by -1 equals positive 2

this is why the 2 is positive.