Q4. An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated.
(a) Draw the possibility diagram of the product of the two numbers appearing on the die in each throw
(b) Use the possibility diagram to calculate the probability that the product of the two numbers is
I) A prime number
ii) Not a perfect square
iii) A multiple of 5
iv) Less than or equal to 21
v) Divisible by 4 or 6

Answer:

length of C'B' = 15units (B)

Step-by-step explanation:

Original image is ∆ABC

A = (8,15)

B = (12, 13)

C = (8,10)

Scale factor = 3

Since the circle would be dilated by a scale factor of 3 about the origin, Do(x,y) →3(x,y)

Coordinates of ∆A'B'C'

A' = 3(8, 15) = (24, 45)

B' = 3(12, 13) = (36, 39)

C' = 3(8, 10) = (24, 30)

The distance formula = √(x2 - x1)² + (y2-y1)²

Where x2 = x subscript 2, x1 = x subscript 1; y2 = y subscript 2, y1 = y subscript 1

Length C'B' = Distance between B' and C'

See attachment for details

From the solution, length of C'B' = 15units (B)

Answer:

15 units

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

Multiplying 5.1 by 10^1 shifts the decimal point 1 place to the right.  We get 51.

Answer:

[tex]f(x)=6x^2+x-1[/tex]

I hope this help you :)

Answer:

no

Step-by-step explanation:

Lets she how much money she has

1.00   dollars

5 * .25 = 1.25 quarters

4 * .10 = .40 dimes

7 * .01 = .07 pennies

Add it all together

1 + 1.25+ .40 +.07 =2.72

3.50 - 2.72 =.78

She is 78 cents short

Answer:

Jason likely misplaced the decimal, because 3 times 1 = 3, and if the decimal was between the 2 and the 5, the number would be near 3.

Step-by-step explanation:

Jason applied 2 and 82.242 miles

Answer:

b

Step-by-step explanation:

Answer:

There are no solutions.

Step-by-step explanation:

3y - x = - 7

Put y as 1/3x - 4.

3(1/3x - 4) - x = - 7

1x - 12 - x = -7

0 - 12 = -7

-12 = -7

No solutions.

Answer:

[tex]-\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{98} -\sqrt{128}[/tex]

[tex]\sqrt{49 \times 2} -\sqrt{64 \times 2}[/tex]

[tex]\sqrt{49} \sqrt{2} -\sqrt{64} \sqrt{2}[/tex]

[tex]7\sqrt{2}-8\sqrt{2}[/tex]

[tex]=-\sqrt{2}[/tex]

Answer:

Equation given in graph B → y = -3x² + 4

Step-by-step explanation:

Equation of the graph A,

y = 3x² - 3

We have to find the equation of the graph (parabola) given in graph (B).

Parabola given in graph B is the inverted form of graph A with vertex at (0, 4)

Therefore, equation of the parabola given in graph B will be,

y = -a(x - h)² + k

where negative notation of the coefficient a shows the inverted form of the parabola given in graph A and (h, k) will be the vertex.

y = -3(x - 0)² + 4

y = -3x² + 4

Answer:

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

Step-by-step explanation:

Hello!

The equation of a parabola is written as [tex]y = ax^2 + bx + c[/tex].

The [tex]c[/tex] value of the equation determines the y-intercept, or where the graph hits the y-axis (x = 0).

In Graph A we can see that the graph hits the y-axis at -3, showing the y-intercept is also -3. We can use the same logic to determine the y-intercept of Graph B. We can see that it hits the y-axis at 4, so the y-intercept is 4.

The [tex]a[/tex] value determines the direction and width of the graph. If it is positive, it opens up. If it's negative, it opens down.

Since Graph B opens down, we can simply add a negative sign to indicate that it is a negative graph.

We can plug in the values that we solved for [tex]a[/tex] and [tex]c[/tex].

Equation: [tex]y = -3x^2 + 4[/tex]

Answer:

The answer is 2 hours later.

Step-by-step explanation:

In order to find how many hours you and your friend meet, you have to solve the equation to find h :

[tex]50h = 190 - 45h[/tex]

[tex]50h + 45h = 190[/tex]

[tex]95h = 190[/tex]

[tex]h = 190 \div 95[/tex]

[tex]h = 2[/tex]

Answer:

Step-by-step explanation:

The equivalent interest rate is the rate that would have to be applied so it would earn the same amount in 1 year. It is computed from ...

  requiv = (1 +r/n)^n -1

  requiv = (1 +0.07/4)^4 -1 ≈ 7.186%

__

"Compounded quarterly" means interest is compounded 4 times per year. In 4 years, it will be compounded 4·4 = 16 times.

__

The balance in the account after 4 years is ...

  $600·(1 +.07/4)^(4·4) ≈ $791.96

Answer:

Step-by-step explanation:

We have 3 triangles here, all of them right triangles. The first one is the biggest one, triangle ABC. We know the side length AB = 14, and we know the hypotenuse length, BC = 30. We can use that, along with Pythagorean's Theorem, to solve for side length AC:

[tex]30^2=14^2+(AC)^2[/tex] and

[tex]900-196=(AC)^2[/tex] and

[tex]704=(AC)^2[/tex] so

[tex]AC=8\sqrt{11}[/tex]

We also have the smallest right triangle, triangle ABD, which has the base of x, our unknown. Side BD is our unknown, length x; side AD is the height, length y (also unknown); and side AB is the hypotenuse, length 14. We will come up with a system of equations for these 2 right triangles, using Pythagorean's Theorem, and then solve for x using substitution.

For the medium-sized triangle. triangle ADC, the hypotenuse is side AC with a measure of 8√11, the height is side AD length y, and the base is side DC length 30 - x. Putting those values into Pythagorean's Theorem:

[tex](30-x)^2+y^2=(8\sqrt{11})^2[/tex] and

[tex]900-60x+x^2+y^2=704[/tex] and

[tex]x^2-60x+y^2=-196[/tex]***  That's starred because it's important and we will come back to it.

The smallest triangle in Pythagorean's Theorem:

[tex]14^2=x^2+y^2[/tex] and solving that for y-squared:

[tex]y^2=196-x^2[/tex]. We will now sub that value for y-squared into the starred equation for y-squared and solve for x:

[tex]x^2-60x+196-x^2=-196[/tex] and

-60x = -392 so

x = 6.5

Answer:

b = 40

Step-by-step explanation:

Let b= brownies made

b* 2/5 = brownies left over

b*2/5 = 16

Multiply each side by 5/2

b * 2/5 *5/2 = 16*5/2

b = 40

Answer:

40

Step-by-step explanation:

.4/.4 is 1 so 16/.4 is 40

Answer:

Miles

Step-by-step explanation:

Required

Fill in the gap

From the question, we have that

mpg = Miles per gallon

[tex]mpg = \frac{Miles}{Gallon}[/tex]

Suppose a truck has 5 mpg;

This implies that the truck can travel 5 miles using 1 gallon

What if it's 4 mpg?

This implies that the truck can travel 4 miles using 1 gallon

What if it's x mpg?

This implies that the truck can travel x miles using 1 gallon

So, basically mpg represents the number of miles a truck can go for every unit of gallon

Answer:

A. To add like terms, add the coefficients, not the variables.

C. The simplified expression is 4 x + 3 y + 6 z.

D. Only combine terms which contain the same variable.

Facts could be applied to simplify the expression to add like terms, add the coefficients, not the variables.

We have to determine the steps involved to simplify the expression.

An expression is a set of terms combined using the operations addition, subtraction, multiplication, and division.

For simplifying the expression this expression.

A. To add like terms, add the coefficients, not the variables.

C. The simplified expression is 4 x + 3 y + 6 z.

D. Only combine terms which contain the same variable.

Therefore by applying the above steps we can simplify the given expression.

To learn more about the expression visit:

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Answer:

½Log 57 – ½Log 74

Step-by-step explanation:

Logb √(57/74)

We can expand the above expression as follow:

Logb √(57/74)

Logb √57 /√74

Recall:

logM/N = Log M – Log N

Therefore,

Logb √57/√74 = Logb √57 – Logb √74

Recall:

Log √M = Log M^1/2

Therefore,

Logb √57 = Logb 57^1/2

Logb √74 = Logb 74^1/2

Logb √57 – Logb √74 = Logb 57^1/2 – Logb 74^1/2

Recall:

Log M^1/2 = ½Log M

Therefore,

Logb 57^1/2 = ½Log 57

Logb 74^1/2 = ½Log 74

Logb 57^1/2 – Logb 74^1/2 = ½Log 57 – ½Log 74

From the illustrations above, we see that:

Logb √(57/74) = ½Log 57 – ½Log 74

Answer:

the correct answer is

Step-by-step explanation:

= 12 1/2 - (-4 1/2)

=17

hope this helps you!!!!!

Answer:

17

Step-by-step explanation:

12 1/2 - (-4 1/2)

Turn to improper fractions.

25/2 - (-9/2)

Negative times negative is positive.

25/2 + 9/2

Add fractions with common denominators.

34/2

Divide.

= 17

Answer:

768

Step-by-step explanation:

let C represent cost and w weight, then the equation relating them is

C = kw² ← k is the constant of variation

To find k use the condition w = 20, C = 4800, that is

4800 = k × 20² = 400k ( divide both sides by 400 )

12 = k

C = 12w² ← equation of variation

When w = 8, then

C = 12 × 8² = 12 × 64 = 768

Step-by-step explanation:

I hope you understand what I did

Answer:

Angle x measures 64 degrees and Angle y also measures 64 degrees. X is 11. The value of y is also 11.

Step-by-step explanation:

Alright, so this triangle is an isosceles triangle since there are lines on two sides meaning they are congruent to each other. So, if the sides are congruent, then the angles are also congruent. Angle y is congruent to angle x. First, lets find what they measure totally. Since they are congruent, we can write the equation with 2x+angle w which is 52=180 because the sum of all angles in a triangle is 180. Subtract 52 from both sides 2x=132 divide both sides by 2, and you get 64. You found what angle x and y equal. Now you can find what the value of x and y. For finding x, 4x+20=64 and for y, 6y-2=64. Isolate each variable, and you get 11 for both the value of x and y.

Answer:

1. a) SR = 23

b) QV = 25

c) QT = 20

d) PQ = 40

e) VS = 4·√6

2. a) LH = 16

b) EL = 2·√185

c) JG = 30

d) EK = 22

e) KG = 30

3. a) XT = 37

b) TZ = 34

c) ZW = 17

d) XZ = 21

e) SY = 69

Step-by-step explanation:

The circumcenter ΔPQR is the center of the circle that circumscribes ΔPQR

The length of the radius of the circle ≡ VR = VP = QV = 25

a) Given that VR ≅ VP - Radius of circumcircle

VS ≅ VS Reflective property

∠VPS ≅ ∠VRS - Base angles of an isosceles triangle

Right triangle VPS ≅ Right triangle VRS -Hypotenuse and one Leg HL congruency

Therefore, SR ≅ PS -Corresponding parts of congruent triangles are congruent CPCTC

SR + PS = PR = 46

SR + PS = SR + SR = 2·SR = 46

∴ SR = 46/2 = 23

b) QV = VR = 25 = Radius of circumcircle of ΔPQR -Given V = center and Q = vertices of the triangle circumscribed by the circle referred to in the question

c) QT = √(QV² - TV²) = √(25² - 15²) = √400 = 20

d) TV ≅ TV - Reflexive property of congruency

ΔTQV ≅ ΔTVP - Hypotenuse and one Leg (HL) congruency

QT ≅ TP -Corresponding parts of congruent triangles are congruent CPCTC

PQ = QT + TP Given

∴ PQ = QT + QT since QT = TP

PQ = 2·QT = 2 × 20 = 40

e) VS = √(VR² - SR²) = √(25² - 23²) = √96 = 4·√6

2.  The incenter is the center of the incircle of ΔEFG

  a) LH = LK = JL = 16 -Radius of incircle of ΔEFG

b) EL = Hypotenuse of right triangle LHE = √(LH² + EH²) = √(16² + 22²) = √740 = 2·√185

c) JG = Leg length of right triangle JGL = √(LG² - JL²) = √(34² - 16²) = √900 = 30

d) EK = Leg length of right triangle LKE = √(EL² - LK²) = √(740 - 256) = 22

e) KG = Leg length of right triangle LKG = √(LG² - LK²) = √(34²- 16²) = √900 = 30

3. Point Z id the centroid of ΔRST

a) XT = XS - point X on ST bisected by median line RX

ST = XT + XS = XT + XT = 2.XT = 74

XT = 74/2 = 37

b) TZ = 2/3×TW  - Length from a vertex to the centroid on a median line is equal to two third the length of the median line

TZ = 2/3×51 = 34

c) TZ + ZW = TW

∴ ZW = TW - TZ = 51 - 34 = 17

d) RZ = 42 = 2/3×RX - Length from a vertex to the centroid on a median line is equal to two third the length of the median line

∴ RX = 3/2×42 = 63

RZ + XZ = RX - Given

XZ = RX - RZ = 63 - 42 = 21

e) SZ = 2/3×SY - Length from a vertex to the centroid on a median line is equal to two third the length of the median line

SZ + ZY = SY

∴ ZY = SY - SZ = SY - 2/3×SY = 1/3×SY = 23

Which gives;

SY = 3 × 23 = 69.

Answer:

5

Step-by-step explanation:

Work Shown:

L = (0,1)

N = (6,1)

m = slope of LN

m = (y2-y1)/(x2-x1) is the slope formula

m = (1-1)/(6-0)

m = 0/6

m = 0

Points L and N are on the same horizontal level, so line LN is horizontal and completely flat. We can see this by noting the y coordinates are both the same. All horizontal lines have a slope of 0 to indicate no change in y value (ie, no change in rise; no increase nor decrease)

Answer:

35 acres

Step-by-step explanation:

We have 15.8 happys per acre and the we have exactly 553 happys living in happy land.

To calculate the number of acres, we just need to divide the number of happys we have by the number by the number of happys per acre

Mathematically, that would be 553/15.8 = 35 acres

Happyland have 35 acres of Land.

Given to us:

Population of Happyland = 553 Happys

Population of Happyland per acre = 15.8 Happys per acre,

Land with Happyland in acres:

[tex]\rm {Land with Happyland in acres =\dfrac{ Total\ number\ of\ Happys}{Population\ of\ Happyland\ per\ acre}}[/tex]

Putting in the value we get,

[tex]\rm {Land with Happyland in acres =\dfrac{ Total\ number\ of\ Happys}{Population\ of\ Happyland\ per\ acre}}\\\\\rm {Land with Happyland in acres =\dfrac{553}{15.8}}\\\\\rm {Land with Happyland in acres = 35 acres[/tex]

Hence, Happyland have 35 acres of Land.

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Answer:

d.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

just did it

Answer:

[tex](x - 5)^2 + (y - 4)^2 = 14[/tex]

Step-by-step explanation:

Formula: (x - h)² + (y - k)² = r²

You are given h, k, and r. Simply plug those into the equation and you should get your answer.

Answer:

18 feet

Step-by-step explanation:

Your equation for circumference will always be C = 2πr

In that case, you are given C as 36π

Step 1: Replace known variables

36π = 2πr

Step 2: Divide both sides by 2π

18 = r

And you have your final answer.

Answer: B

Step-by-step explanation:

For this problem, we can use Integration by Parts to find f(u).

∫(ln u) du                 x=ln u             dx=1/u du

                               dv=du               v=u

u(ln u)-∫u(1/u)du

u(ln u)-∫1 du

u(ln u)-u+C

Looking at the placement of f(u), we know that f(u) is u (underlined above).

Answer:

seven-eighths of a number minus three

Step-by-step explanation:

the algebraic expression given to us is:

[tex]\frac{7}{8} y-3[/tex]

we have seven-eighths multiplied by a number "y" (this can also be expressed as seven-eighths  of the number) and then, to that we substract 3 (minus three).

With this information we can conclude that the phrase that best describes this expression is:

seven-eighths of a number minus three

which is the first option.

Answer:

a

Step-by-step explanation:

Answer:

The answer is option A.

Hope this helps.

Answer:

its A

Step-by-step explanation:

Answer:

a) y = 5x

b) y = 60

Step-by-step explanation:

y ∝ x

So, y = kx      -----(1)

Where k is the constant of proportionality

Now, y = 30, x = 6

Putting in (1)

30 = k(6)

Dividing both sides by 6, we get

k = 5

Now, Putting k=5 in (1)

So,

a) The equation connecting x and y is :

y = 5x

b) x = 12, Putting in (1)

y = (5)(12)

y = 60

Answer:

a)y=5x

b)60

Step-by-step explanation:

it just is

Answer:

It moves 8 to the right

Step-by-step explanation:

This is in the y axis so it will move 8 on the x axis