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3 years ago

A six-sided number cube is rolled twice.

Mathematics

1 answer:

kondor19780726 [428]3 years ago

5 0

The probability is 1/6, 16%, or 0.16

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John and Ariana bought school supplies, John spent $10.65 on 4 notebooks and 5 pens. Ariana spent $7.50 on 3 notebooks and 3 pen

timurjin [86]

Cost of 1 notebook is $ 1.85 and cost of 1 pen is $ 0.65

<h3><u>Solution:</u></h3>

Let "a" be the cost of 1 notebook

Let "b" be the cost of 1 pen

Given that John spent $10.65 on 4 notebooks and 5 pens

cost of 1 notebook x 4 + cost of 1 pen x 5 = 10.65

4a + 5b = 10.65 ------ eqn 1

Given that Ariana spent $7.50 on 3 notebooks and 3 pens

3a + 3b = 7.50 ----- eqn 2

Let us solve eqn 1 and eqn 2 to get the values of "a" and "b"

Multiply eqn 1 with 3

12a + 15b = 31.95 ---- eqn 3

Multiply eqn 2 with 4

12a + 12b = 30 ------ eqn 4

Subtract eqn 4 from eqn 3

12a + 15b = 31.95

12a + 12b = 30

(-) ---------------------

3b = 1.95

b = 0.65

Substitute b = 0.65 in eqn 1

4a + 5(0.65) = 10.65

4a = 7.4

a = 1.85

Thus cost of 1 notebook is $ 1.85 and cost of 1 pen is $ 0.65

8 0

3 years ago

(A)using geometry vocabulary, describe a sequence of transformations that maps figure P (-1,2)(-1,4) (-4,2) (-4,4) onto figure Q

andrey2020 [161]

Before we proceed on determining the transformation happening on this problem, it's better to see first the location of the figure by drawing it in a cartesian coordinate plane. We have

If we observe the figures and the coordinates of the plot, we can see that there is a difference of 1 on the x coordinates of P and y coordinates of Q. Therefore, the first transformation that we consider here is the movement of figure P by 1 unit to the left. We have

$\begin{gathered} P_1=(-1-1,2_{})=(-2,2) \\ P_2=(-1-1,4)=(-2,4) \\ P_3=(-4-1,2)=(-5,2) \\ P_4=(-4-1,4)=(-5,4) \end{gathered}$

This transformation changes the location of figure P into

The next transformation will be the rotation of the red dotted figure on the figure above by 90 degrees counterclockwise. With this transformation, the coordinates will transform as

$P_{ccw,90}=(-y,x)$

Hence, for the rotation, we have the new coordinates.

$\begin{gathered} P_1^{\prime}=(-2,-2) \\ P_2^{\prime}=(-4,-2) \\ P_3^{\prime}=(-2,-5) \\ P_4^{\prime}=(-4,-5) \end{gathered}$

The transformed image, which is represented as NMPO, will now be at

For the last transformation, we will be reflecting the figure NMPO over the <em>y</em> axis. This changes the coordinates as

$P_{\text{rotation,y}-\text{axis}}=(-x,y)$

We now have the new coordinates:

$\begin{gathered} P^{\doubleprime}_1=(2,-2)=Q_1_{}_{} \\ P_2^{\doubleprime}=(4,-2)=Q_3 \\ P_3^{\doubleprime}=(2,-5)=Q_2 \\ P_4^{\doubleprime}_{}=(4,-5)=Q_4_{} \end{gathered}$

As you can see, they have the same coordinates as figure Q.

The mapping rules for the sequence described above are as follows:

First transformation (moving one unit to the left (x-1,y))

$\begin{gathered} P_1(-1,2)\rightarrow P_1(-1-1,2)\rightarrow P_1(-2,2) \\ P_2(-1,4)\rightarrow P_1(-1-1,4)\rightarrow P_2(-2,4) \\ P_3(-4,2)\rightarrow P_1(-4-1,2)\rightarrow P_3(-5,2) \\ P_4(-4,4)\rightarrow P_1(-4-1,4)\rightarrow P_4(-5,4) \end{gathered}$

Second transformation (rotation counter clockwise (-y,x))

$\begin{gathered} P_1(-2,2)\rightarrow P^{\prime}_1(-2,-2)_{} \\ P_2(-2,4)\rightarrow P^{\prime}_2(-4,-2) \\ P_3(-5,2)\rightarrow P^{\prime}_3(-2,-5)_{} \\ P_4(-5,4)\rightarrow P^{\prime}_4(-4,-5)_{} \end{gathered}$

Third Transformation (reflection over y-axis (-x,y))

$\begin{gathered} P^{\prime}_1(-2,-2)\rightarrow P^{\doubleprime}_1(-(-2),-2)\rightarrow P^{\doubleprime}_1=(2,-2)=Q_1 \\ P^{\prime}_2(-4,-2)\rightarrow P^{\doubleprime}_1(-(-4),-2)\rightarrow P^{\doubleprime}_1=(4,-2)=Q_3 \\ P^{\prime}_3(-2,-5)\rightarrow P^{\doubleprime}_1(-(-2),-5)\rightarrow P^{\doubleprime}_1=(2,-5)=Q_2 \\ P^{\prime}_4(-4,-5)\rightarrow P^{\doubleprime}_1(-(-4),-5)\rightarrow P^{\doubleprime}_1=(4,-5)=Q_4 \end{gathered}$

7 0

1 year ago

The elevation of an underwater cave is -120 feet relative to sea level. A submarine descends to the cave. the submarine rate of

Drupady [299]

Answer:

Time taken by the submarine to reach the cave is 10 seconds.

Step-by-step explanation:

We are given that,

The elevation of the underwater cave = -120 feet.

The rate at which the submarine descends to the cave = -12 feet per second

Thus, we have,

The time taken by the submarine to reach the cave = $\frac{-120}{-12}$ = 10 seconds.

Hence, the time taken by the submarine to reach the cave is 10 seconds.

3 0

3 years ago

Y=3x+1 and y+5=-3(x-2)

In-s [12.5K]

Answer:

X = -2/3 ; Y = -1

Step-by-step explanation:

Y=3x+1-------------------(eqn1)

Y+5= -3(x-2)

Y+5= -3x + 2

Y= -3x+2-5

Y= -3x-3----------------(eqn2)

Equating (eqn1) =(eqn2)

3x + 1 = -3x - 3

3x + 3x = -1-3

6x = -4

X = -4/ 6 = -2/3

From eqn 1 Y = 3( -2/3) + 1 = -2 + 1 = -1

X = -2/3 ; Y = -1

4 0

3 years ago

For which values of x is the expression undefined?

lord [1]

Answer:

-3, -6

Step-by-step explanation:

Any number of x that makes the bottom 0 makes the expression undefined.

Factor the polynomial in the denominator:

(x+3)(x+6)

Values of x that makes the expression undefined are -3 and -6

Support me by choosing my answer as the brainiest :)

5 0

2 years ago