A type of cracker, rectangular in shape, is stored in a vertical column with all of the crackers stacked directly on top of each other. Each cracker measures 2 inches in length by One and one-half inches in width. The volume of the column is 15 inches cubed. If there are 40 crackers in the column, what is the height of each individual cracker?

Given:

An object is translated from A(-6, -4) to A'(-18,-8)

We need to determine the translation rule.

Translation rule:

The translation rule is given by

[tex]A(x,y)\rightarrow (x+h,y+k)\rightarrow A'(x,y)[/tex]

Substituting the coordinates of A and A', we get;

[tex]A(-6,-4)\rightarrow (-6+h,-4+k)\rightarrow A'(-18,-8)[/tex]

Equating the x and y coordinates, we get;

x - coordinate:

[tex]-6+h=-18[/tex]

        [tex]h=-12[/tex]

Thus, the value of h is -12.

y - coordinate:

[tex]-4+k=-8[/tex]

        [tex]k=-4[/tex]

Thus, the value of k is -4.

Hence, the translation rule is [tex](x,y)\rightarrow (x-12,y-4)[/tex]

Answer:

2 ft³

Step-by-step explanation:

The volume (V) of the triangular pyramid is calculated as

V = [tex]\frac{1}{3}[/tex] Ah ( A is the area of the base and h the perpendicular height )

A = [tex]\frac{1}{2}[/tex] × 2 × 2 = 2 ft² ← area of triangular base and h = 3, thus

V = [tex]\frac{1}{3}[/tex] × 2 × 3 = 2 ft³

Answer:

The missing number is either 1 or 2.

1/6 and 2/6 are both less than 1/2.

Answer:

what was paid exactly per student as entrance fee is $6.25

Step-by-step explanation:

In this question, we are told that some kids went to an excursion with their teachers and paid a certain total bill. we now need to know the amount paid per child as the entrance fee to the zoo.

Firstly, we need to subtract the amount paid by the teachers so we know exactly how much was spent on the students entrance fee alone.

subtracting the $5 from the total we have $530 - $5 = $525

Now to know what was paid as entrance fee per student, we simply divide this by the total number of students. That will be 525/84 = $6.25

This means that what was paid exactly per student as entrance fee is $6.25

The entrance fee per child at the Dallas zoo can be found by subtracting the teachers' payment from the total bill and then dividing it by the number of kids. In this case, the entrance fee per child is $6.31.

The entrance fee for each child can be calculated by subtracting the amount paid by the teachers from the total bill and then dividing it by the number of kids:

Total bill - Teachers' payment = Amount paid by the kids

530$ - (5$ x Number of teachers) = Amount paid by the kids

530$ - (5$ x 0) = Amount paid by the kids

530$ = Amount paid by the kids

To find the entrance fee for each child, divide the amount paid by the number of kids:

Entrance fee per child = Amount paid by the kids / Number of kids

Entrance fee per child = 530$ / 84 kids

Entrance fee per child = $6.31.

Answer:

(Area of circle a)/5

Step-by-step explanation:

(Area of circle b) = (1/5)* (Area of circle a)

What is the area of circle a?  There is not enough given information

Answer:

area of circle a/5

Step-by-step explanation:

The equation: 1/5(a) = b

multiply 1/5(a)

We get the area of circle a/5

Answer:

The true average mileage of the Libra  Using Null hypothesis is as ;

H0:μ≤26

(Ha):μ >26

Step-by-step explanation:

Given:

Libra, will average better than 26 miles per gallon in the city

To Find:

Average mileage of the Libra.

Solution:

This problem is related to the null hypothesis  and alternate hypothesis.

i.e Null Hypothesis is the statement which is true and statement which contradictory is called alternate hypothesis.

“reject H0” if the sample information favors the alternative hypothesis.

“do not reject H0” / “decline to reject H0” if the sample information is insufficient to reject the null hypothesis

So given that condition is libra will have average better than 26

So it will include 26 and above values .

i.e. True  condition is called as null hypothesis (H0)

so true average will be greater than 26

So H0:μ≤26

And the Alternate hypothesis will be the contradictory to true condition

(Ha):μ >26 .

Given:

The coordinates of the triangle ABC are (3,3), (6,5) and (2,1)

We need to determine the vertices of the triangle A'B'C' after reflection across y - axis.

Reflection across y - axis:

The rule to translate the coordinates across y - axis is given by

[tex](x,y)\implies (-x,y)[/tex]

Let us substitute the coordinates.

The coordinates of the point A' are

[tex]A(3,3)\implies A'(-3,3)[/tex]

The coordinates of the point B' are

[tex]B(6,5)\implies (-6,5)[/tex]

The coordinates of the point C' are

[tex]C(2,1)\implies (-2,1)[/tex]

Therefore, the coordinates of the triangle A'B'C' are (-3,3), (-6,5) and (-2,1).

Hence, Option C is the correct answer.

The image of the transformation is the figure represented by graph (b)

How to determine the image of the transformation

from the question, we have the following parameters that can be used in our computation:

The triangle

Also, we have the reflection axis to be

The y-axis

This means that the pre-image and the image of the reflection will be equidistant from the x-axis

Using the above as a guide, we have the following:

The image is (b)

Answer:

9 : 7

Step-by-step explanation:

Given

4.5 : 3 [tex]\frac{1}{2}[/tex]

Multiply both parts of the ratio by 2 to clear the fractions, that is

= 9 : 7 ← in simplest form

Answer:

D=142

Step-by-step explanation:

Answer:

14 degrees?

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

v = the original speed of the cruise

d = 225 km the distance passed

t = d/v = 225/v the total time of the travel

v*1.5 + (v + 10)(d/v - 1.5 - 0.5) = d (using the formula distance = speed*time)

1.5v + (v + 10)(225/v - 2) = 225

Look at the images to see the solved equation

Answer:

b or d

Step-by-step explanation:

they have the same answers bruh

Answer:

800

Step-by-step explanation:

16,000 x 0.05 = 800

Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:right

Answer:

64

Step-by-step explanation:

The first thing we should know is the equivalence between pound and ounce.

1 pound equals 16 ounces. Which means that Rhada has a total of:

3 * 16 = 48 ounces of clay.

We are told that for every 3 ounces of clay you can make 4 ornaments., therefore:

48 * 4/3 = 64 ornaments

Which means that you can with the amount of clay you have can make 64 ornaments.

Answer:

64

Step-by-step explanation:

Answer:

-200,700

Step-by-step explanation:

(-1676+-108)/2 = -892 x 225 = -200,700

225 = number of terms -108 + 1676 / 7

We solve the system of equations -5x - 5y = 0 and y = 8x using the substitution method. Substituting y = 8x into the first equation, then solving for x and y, we find that x = 0, y = 0.

To solve the system of equations -5x - 5y = 0 and y = 8x we will use substitution method. The substitution method involves substituting the expression from one equation into the other equation. Here, we are given that y is equal to 8x, so we can substitute 8x in place of y in the first equation. That gives us:

-5x - 5*(8x) = 0

Solve this equation, we get x = 0. Now, substitute x = 0 in the second equation to find y. That gives us:

y = 8*0

So, y = 0. Therefore, the solution to the system of equations is x = 0, y = 0.

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Answer:

b = 10

Step-by-step explanation:

We know

x^2 / (24^2)  -    y^2/ ( b^2) = 1

equation:  directrix   x  =  a^2 / c  = 576/26

a = 24

24^2/ c =  576/26

c = 26

so     a^2 + b^2 = c^2

so   24^2  + b^2 =  26^2

b^2 =  26^2 - 24^2 =  100

b = 10

Answer:

¢42 per game

¢1.11 per minute

Step-by-step explanation:

Please refer to the attached image for explanations

LeBron James earns approximately $0.42 per game and $0.01 per minute based on the given salary and total games and minutes played for the season.

The student has asked two questions about calculating earnings per game and per minute for LeBron James, based on a given salary for a season and the total number of games and minutes played.

To calculate the earnings per game, we divide the total salary for the season by the number of games played. If LeBron James was paid $31 for the season and played 74 games, his earnings per game would be: $31 ÷ 74 games = $0.4189 per game, which rounds to $0.42 per game to the nearest cent.

For the earnings per minute, we divide the total salary for the season by the total number of minutes played. With $31 for the season and 2,796 minutes played, his pay per minute would be: $31 ÷ 2,796 minutes = $0.0111 per minute, rounding to $0.01 per minute to the nearest cent.

Answer:

a) 1.

Step-by-step explanation:

Supongamos que el primer número entero positivo es a tal que a ∈ Z⁺.

Luego, el conjunto de los cinco enteros positivos se puede expresar como

A = {a; a+1; a+2; a+3; a+4}

Dada la condición del problema, se debe cumplir que

a + (a+1) + (a+2) = (a+3) + (a+4)

⇒  3a + 3 = 2a + 7

Resolviendo la ecuación resulta

a = 4

Luego, el conjunto A nos resulta

A = {4; 5; 6; 7; 8}

Puede concluirse que sólo un conjunto cumple con esta condición.

Answer:

The FCI for tennis league is $ 58.32 and FCI for basketball league is $65.30

Step-by-step explanation:

We have been given the following data:

The FCIs for an independent tennis league and an independent basketball league totaled $123.62

Let the FCI for tennis league be "x" and the FCI for basketball league be "y". Since, the total for both leagues is $ 123.62, this means the sum of x and y must be $ 123.62. Using this we can set up our first equation as:

x + y = 123.62                              Equation 1

The basketball FCI was $ 6.98 more than that of tennis FCI. This means y would be more than x by 6.98. Using this we can set up our second equation as:

y = x + 6.98                                 Equation 2

Substituting the value of y from Equation 2 to Equation 1, gives us:

x + x + 6.98 = 123.62

2x + 6.98 = 123.62

2x = 123.62 - 6.98

2x = 116.64

x = 116.64/2

x = 58.32

Using the value of x in Equation 2 gives us:

y = x + 6.98 = 58.32 + 6.98 = 65.3

Therefore, the FCI for tennis league is $ 58.32 and FCI for basketball league is $65.30

Answer:

It B and C

Step-by-step explanation:

the equation in Pythagorean theorem is  a^2+b^2=c^2

so the answer for B would be 5^2*5^2=50,which is correct sine 5^2=25,and 25+25=50

The answer for C would be like 9^2+12^2=225

the square root of 225 is 15 which is correct.

but A is wrong because 5^2+6^2=31 is wrong.

Answer:

its A and C

Step-by-step explanation:

khan academy

Answer:

the answer is A

Step-by-step explanation:

The volume of the right triangular prism is x³/2 cubic units.

Volume is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Given that in a right triangular prism its height is equal to the leg length of the base.

we need to find the expression for the volume,

The volume of a right triangular prism is:

V = The base area x the height

Therefore,

V = 1/2 · x · x · x

Hence the volume of the right triangular prism is x³/2 cubic units.

Learn more about volumes click;

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The circumference of the circle is approximately 40.8406 m.

The circumference of a circle can be found using the formula C = πd, where C is the circumference and d is the diameter of the circle.

In this case, the diameter of the circle is given as 13 m. So we can substitute this value into the formula to find the circumference:

C = 3.14159… x 13 m = 40.8406 m

Therefore, the circumference of the circle is approximately 40.8406 m.

Final answer:

The circumference of a circle with a diameter of 13 meters is expressed in terms of Pi as 13π meters.

Explanation:

The circumference of a circle is calculated using the formula C = πd, where C is the circumference, π (Pi) is a mathematical constant, and d is the diameter of the circle.

Given that the diameter is provided as 13 meters, we use this formula to find the circumference in terms of π.

Thus, the circumference C is equal to:

C = π × 13 m

Since we are expressing our answer in terms of π, there's no need to calculate the numeric value of π. However, if we need to use a value for practical purposes, π is approximately 3.14.

So for our purposes, the circumference in terms of π is simply 13π meters.

Answer:

step1:add 3y to both sides

step2:add 4 to both sides

step3:multiply both sides by(1/5)

14/15

Step-by-step explanation:

The steps to solve the equation -3y + 2/3 = 2y - 4 are accurate and lead to the conclusion of y = 14/15.

In examining the steps for solving the equation

-3y + 2/3 = 2y - 4

, we can conclude they are correctly performed.

In summary, the steps are correctly structured and the solution to the equation is y = 14/15.

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Answer:

6

Step-by-step explanation:

8(.25)-1+.5(10)

2-1+5

1+5

6

Answer: proportional

Yes the table is proportional because for every 1 increase in x the increase in y is 5. Because the increase for every 1 x is 5 means it is proportional.

Answer:

28.3 square inches

Step-by-step explanation:

In the question, we are asked to calculate the portion of the area of the cake eaten by Ellie’s sister.

To calculate this, the first thing to do is to calculate the area of the cookie cake. Now, since it’s a round cake, then it must be circular in shape.

Hence we calculate the area.

mathematically the area of a circle can be calculated using the formula;

A = pi * r^2

here our r =6 inches

Substituting this, we have

A = 22/7 * 6 * 6 = approximately 113 sq. inches

we now move on to calculate the portion ate, which is a quarter

That would be 1/4 * 113 = 28.3 sq. inches was eaten

Answer:

28 Square inches

Step-by-step explanation:

Since the cookie is round, it is in a circular shape.

Radius of the Cookie Cake, r= 6 Inches

Area of a Circle [tex]=\pi r^2[/tex]

Therefore, the area of the whole cookie cake [tex]=\pi X 6^2 =113.097 \:Square\: Inches[/tex]

Since Ellie's Sister ate 1/4 of the cookie cake,

Area of cake eaten by Ellie's Sister

[tex]\frac{1}{4} X 113.097\\ =28.27[/tex]

Ellie's Sister ate approximately about 28 Square inches of cake.

The rounded number is 0.01.

To round 0.00706 to 2 significant figures, we first need to identify the non-zero digits and any zeros between them. The non-zero digits in this number are 7 and 6. There are no zeros between them.

Since the second significant digit is 6, which is greater than or equal to 5, we round the first significant digit up. Therefore, the rounded number is 0.01.

Here is a table of the rounding rules:

| Digit to the right of the last significant digit |

| Less than 5 | Round the last significant digit down |

| 5 or greater | Round the last significant digit up |

For such more question on number

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Answer:

Step-by-step explanation:

Step 1:we should turn the “facts” into logical expressions.

Step 2:Assign variables

Our variables are: b (for butler), c (for cook), g (for gardener), h (for handyman)

Step 3 . Let the value of true indicate that the person is telling the truth. For example, b = T means the butler is telling the truth. Then we can translate the statements as follows:

Check attachment

Step 4

We know all of these must hold. So we really want to know when (b→c)∧¬(c∧g)∧¬(¬g∧¬h)∧(h → ¬c) is true.

Step 5

Behold, another truth table task! If you work out the truth table, you see that this statement is only true when:

Check attachment

Step 6

Therefore we can say the butler and cook are definitely lying, but we can not determine if the gardener or handyman are lying. However, there are four variables in this problem. Instead, we can do this with some straight reasoning. Notice that:

If the butler is telling the truth, then by (a) the cook is telling the truth.

If the cook is telling the truth, then by (b) the gardener is lying.

If the gardener is lying, then by (c) the handyman is telling the truth.

If the handyman is telling the truth, they by (d) the cook is lying.

This leads to a contradiction (the cook can not be both telling the truth and lying)! Therefore the butler and cook must be lying. What about the gardener and the handyman? We don’t have enough information to figure out if they are lying. Since the cook is lying, we can’t use (b) to come to any conclusions about the gardener. Even if we are able to conclude that the gardener is telling the truth, we can’t use (c) to come to any conclusions about the handyman.