a coin is tossed and a number cube is rolled. What is the probability of tossing heads and rolling a 3 or a 5

Use the Chinese remainder theorem.

Start with x = 3×5 + 2×7 = 15 + 14 = 29. Now,

• 29 ≡ 15 ≡ 1 (mod7)

• 29 ≡ 14 ≡ 4 (mod5)

Adjust for this by multiplying the first term in x by 3, and the second term by 3 (because 4×3 ≡ 12 ≡ 2 (mod5)).

So now x = 3×5×3 + 2×7×3 = 45 + 42 = 87, and

• 87 ≡ 45 ≡ 3 (mod7)

• 87 ≡ 42 ≡ 2 (mod5)

The CRT then says that x ≡ 87 (mod(7×5)) ≡ 87 (mod35), which is to say any number x = 87 + 35n satisfies both congruences (where n is any integer).

So there are 3 possible 2-digit numbers that work: {17, 52, 87}.

To confirm:

• 17 ≡ 15 + 2 ≡ 2 (mod5) and 17 ≡ 14 + 3 ≡ 3 (mod7)

• 52 ≡ 50 + 2 ≡ 2 (mod5) and 52 ≡ 49 + 3 ≡ 3 (mod7)

• 87 ≡ 85 + 2 ≡ 2 (mod5) and 87 ≡ 84 + 3 ≡ 3 (mod7)

Answer:

64000

Step-by-step explanation:

The absolute value is the non-negative number

|64000| = 64000

Answer:

C. b2 – 4ac = 4

Step-by-step explanation:

Answer:

The graph is possible for  

Step-by-step explanation:

we know that

The discriminant of a quadratic equation of the form

is equal to

If D=0 the quadratic equation has only one real solution

If D>0 the quadratic equation has two real solutions

If D<0 the quadratic equation has no real solution (complex solutions)

In this problem , looking at the graph, the quadratic equation has two real solutions (the solutions are the x-intercepts)

so

therefore

The graph is possible for

...............................................................................................................................................

Answer:

b^2 – 4ac = 4

...............................................................................................................................................

=======================================================

Explanation:

The inscribed angle 20 degrees doubles to 2*20 = 40 which is the measure of the central angle, and the arc in which the inscribed angle subtends (or cuts off). This is due to the aptly named inscribed angle theorem.

------------

A slightly longer alternative path would be to do this:

The triangle with interior angles 20 and c is isosceles. Note how the missing angle up top is one of the congruent base angles, so the missing angle is 20 degrees. That means angle c is...

20+20+c = 180

40+c = 180

c = 180-40

c = 140

Then angle b is supplementary to this

b+c = 180

b+140 = 180

b = 180-140

b = 40

This path leads to the same answer. It's slightly longer, but it's a path you can take if you aren't familiar with the inscribed angle theorem.

In fact, this line of thinking is effectively how the inscribed angle theorem is proved as shown in the diagram below.

Answer:

b) 27

Step-by-step explanation:

sum of angles in triangle = 180

a + 63 + 90 = 180

a = 27

Answer:

27 degrees

Step-by-step explanation:

since angle B is 68 and you know that angle c is a right angle it is 90. so yhu take 90 and 63 and add them together and subtract that number from 180 and you find angle A

Answer:

are you sure there is no further info

Step-by-step explanation:

Answer:

Points Q, J and M are not collinear

Step-by-step explanation:

Three points cannot be collinear if they are not coplanar (on the same plane), and M is on a different plane than Q. J is located on both planes.

Answer:

hope this help you

have a great day

Answer:

Step-by-step explanation:

Let's do this out as best as we can here. Here's the problem:

2 |  3   1   2   -7

___________

The rule is to bring down the first term, whatever it is (ours is a 3), and multiply it by the number "outside" which is a 2. Put that product up under the number next to the 3:

2 |  3   1   2   -7

          6          

    3

Then add straight down, and multiply that sum by the 2 outside and put that product under the next number (the 2 "inside" the box):

2 |  3   1   2   =7

          6  14      

     3   7

And do the same thing. Add straight down, multiply the sum by 2 and put the product up under the next number, -7, and add again. The final is shown below:

2 |  3     1     2     -7

            6   14     32

    3      7    16    25

The last number in the very bottom row, the depressed polynomial row, is the remainder. Ours is a 25. This is the super easy way to divide polynomials, as long as our divisor is a linear (first degree) term.

Answer:

an obtuse angle is an angle that is more than 90 degrees

Step-by-step explanation:

Answer:

11/18

Step-by-step explanation:

KL + MN = 11

Total = 18

Probability of KL or MN = 11/18

Step-by-step explanation:

x⁵+x-1

(2x-x+1) ( x³+x²-1 )

9514 1404 393

Answer:

  33 11/16 m² = 33.6875 m²

Step-by-step explanation:

The volume of a prism is given by ...

  V = Bh

where B is the area of the base, and h is the height. Solving for B, we find ...

  B = V/h

  B = (539 m³)/(16 m) = 33 11/16 m² = 33.6875 m²

Answer:

11/43

Step-by-step explanation:

A local community college has 860 students

Out of this 860 students, 220students ride bikes

Therefore the fraction of bike riders to the number of students can be calculated as follows

= 220/860

= 11/43

Answer:

[tex]{ \bf{ \green{line \: B}}}[/tex]

It's a direct proportionality

Answer:

11. angles on a straight line add up to 180

so 180 -133 equal to b.b=47

12.Vertical opposite angles are equal.

therefore b=50

Answer:

4

Step-by-step explanation:

Let's simplify step-by-step.

−2z2+4z+2z2

Combine Like Terms:

=−2z2+4z+2z2

=(−2z2+2z2)+(4z)

=4z

Answer:

4z

Hope this helps <3 Need thanks?

Comment /hearthelp

[tex]\\ \sf\longmapsto -2z^2+4z+2z^2[/tex]

[tex]\\ \sf\longmapsto -2z^2+2z^2+4z[/tex]

[tex]\\ \sf\longmapsto (-2+2)z^2+4z[/tex]

[tex]\\ \sf\longmapsto 0z^2+4z[/tex]

[tex]\\ \sf\longmapsto 4z[/tex]

Answer:

answrr

yes ok

Step-by-step explanation:

4+4-4#_44

Answer:

Total amount paid by the sponsor = 175 + 6d

Step-by-step explanation:

You and 5 friends = 6 people

Cost of renting a bus = $75

Team entry fee = $100

Cost of each student t shirts = $d

Cost of 6 student t shirts = $d × 6= $6d

Write an expression for the total amount the sponsor paid.

Total amount paid by the sponsor = Cost of renting a bus + Team entry fee + Cost of 6 student t shirts

= $75 + $100 + $6d

= $175 + $6d

Total amount paid by the sponsor = 175 + 6d

Where,

d = cost of each student t shirts

Answer:

y = 2/3x + 4/3

Step-by-step explanation:

i found the slope using [tex]\frac{rise}{run}[/tex]. so it would be 2/3. next i just kinda tested similar numbers in the graph to find b.

if you aren't allowed to put factions i would say put:

y = 0.67x + 1.33

Answer:

[tex]2x - 3y + 4 = 0[/tex]

Step-by-step explanation:

The formula of finding equation of two different point is

[tex] \frac{x - x1}{x1 - x2} = \frac{y - y1}{y1 - y2} [/tex]

here, x1 =1, x2=4, y1= 2 and y2= 4

hope you can understand.

Answer:

the vertical line is:

x = 5

The horizontal line is:

y = -9

Step-by-step explanation:

A vertical line has a fixed x-value, while a horizontal line has a fixed y-value.

Then we can write a vertical line as:

x = a

and a horizontal line as

y = b

Then, if we want a vertical line that passes through the point (5, -9), remember that the x-vale will be fixed, then we fix the x-value at the same x-value of the point, which we know that is 5, then the vertical line that passes through the point (5, -9) is:

x = 5

While the horizontal line that passes through the point (5, -9) will be a line with the y-value fixed at the y-value of the point, which we know is -9

Then the horizontal line is:

y = -9

Answer:

"A number, y, is equal to the difference of a larger number and 3."

[tex]y=x-3[/tex]

You can rearrange this equation to find the matching answer choice:

[tex]y-x=-3\\x-y=3[/tex]

"The same number is one third of the sum of the larger number and 9."

[tex]y=\frac{1}{3} (x+9)[/tex]

You can rearrange this equation to find the matching answer choice:

[tex]y=\frac{1}{3} x+3\\3y=x+9\\3y-x=9\\x-3y=-9[/tex]

Answer:

AB is not a tangent to the circle

Step-by-step explanation:

The angle between a tangent and the radius at the point of contact = 90°

Using Pythagoras' identity to determine if the triangle is right at A

If the square of the longest side is equal to the sum of the squares on the other 2 sides then A is right.

longest side = 15 , then 15² = 225

8² + 9² = 64 + 81 = 145 ≠ 225

Then AB is not a tangent to the circle

Answer:

The terms are - 1, 7 and 15.

Step-by-step explanation:

Let the terms be a-d, a, a+d.

ATQ, a-d+a+a+d=21, a=7 and a+d-(a-d+a)=9. 2d-a=9, d=8. The terms are - 1, 7 and 15.

The first three terms will be :   -1, 7, 15

We have sum of first three terms of an arithmetic series is 21. It is given that if the sum of the first two terms is subtracted from the third term then it would be 9.

We have to find the three terms of the series.

An arithmetic progression or sequence with common difference [tex]d[/tex] is given as -

a, a + d, a + 2d, a + 3d .....

According to the question -

a + (a + d) + (a + 2d) = 21

3a + 3d = 21

3(a + d)=21

a + d = 7                             (Eqn. 1)

(a + 2d) - (a + a + d) = 9

a + 2d - a - a - d = 9

d - a = 9

a = d - 9

Substituting the value of 'a' in Eqn. 1, we get -

d - 9 + d = 7

2d - 9 = 7

2d = 16

d = 8

Therefore -

a = 8 - 9

a = -1

The three terms are -

a = -1

a + d = -1 + 8 = 7

a + 2d = -1 + 2 x 8 = 15

Hence, the first three terms will be - -1, 7, 15

To solve more questions on Arithmetic Sequences and finding the terms, visit the link below -

https://brainly.com/question/20384906

#SPJ2

Answer:

A^7

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

The diagonals are bisected so DE =EB

67 = 2x+7

Subtract 7

67-7 = 2x+7-7

60 =2x

Divide by 2

60/2 =2x/2

30 = x

Answer:

y=-4+2x

x=(4+y)/2

2x-y=4