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A right rectangular prism is packed with cubes of side length fraction 1 over 4 inch. If the prism is packed with 12 cubes along the length, 8 cubes along the width, and 5 cubes along the height, what is the volume of the prism?

fraction 2 and 3 over 4 cubic inches
fraction 3 and 3 over 4 cubic inches
fraction 7 and 1 over 4 cubic inches
fraction 7 and 1 over 2 cubic inches

9514 1404 393

Answer:

Step-by-step explanation:

Let x and y represent the cost of a hot dog and a hamburger, respectively. The the two purchases can be described by ...

  3x +2y -9.75 = 0

  2x +3y -10.25 = 0

We can list the coefficients of these general-form equations in 2 rows, listing the first one again at the end:

  3, 2, -9.75, 3

  2, 3, -10.25, 2

Now, we can form differences of cross-products in adjacent pairs of columns:

  d1 = (3)(3) -(2)(2) = 9 -4 = 5

  d2 = (2)(-10.25) -(3)(-9.75) = -20.50 +29.25 = 8.75

  d3 = (-9.75)(2) -(-10.25)(3) = -19.50 +30.75 = 11.25

Then the solutions are found from ...

  1/d1 = x/d2 = y/d3

  x = d2/d1 = 8.75/5 = 1.75

  y = d3/d1 = 11.25/5 = 2.25

The cost of one hot dog is $1.75; the cost of one hamburger is $2.25.

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Additional comment

This is my simplification of the "cross-multiplication method" of solving a pair of linear equations. That method can be found described on web sites and in videos. This version, and the versions described elsewhere, are variations on Cramer's Rule and on the Vedic Maths method of solving equations. Each of those do similar differences of cross products, perhaps in less-easily-remembered fashion.

For a given pair of columns with coefficients ...

  a b

  c d

The cross-product we form is ad -cb.

Answer:

1

Step-by-step explanation:

1 : 1 :sqrt(2)

The legs are  in the ratio of 1 to 1

tan 45 = opp side / adj side

tan 45 = 1/1

tan 45 =1

Answer:

Step-by-step explanation:

Answer:

0.81

Step-by-step explanation:

Find the point estimate by dividing the number of respondents that thought it was a major economic concern by the total number of people in the survey:

1,620/2,000

= 0.81

So, the point estimate is 0.81

Answer:

x = 5

Step-by-step explanation:

Your goal is to isolate x

3x + 7 = 22

Subtract 7 from both sides and you are left with

3x = 15

In order to isolate x divide both sides by 3

x = 5

9514 1404 393

Answer:

Step-by-step explanation:

The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.

1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)

__

2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)

9514 1404 393

Answer:

  12°

Step-by-step explanation:

We assume you mean ...

  ∠x = 174°

Angle a is supplementary to angle x, so is ...

  ∠a = 180° -174° = 6°

Angle b is a vertical angle with respect to angle 'a', so is the same measure.

  ∠a +∠b = 6° +6° = 12°

Answer:

The y intercept is 1

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = 2x+b

Substitute the point into the equation and solve for y

3 = 2(1)+b

3 =2+b

1 = b

The y intercept is 1

Answer:

6 samples

Step-by-step explanation:

Given :

Sample size, = n

Standard deviation, = 6000

Margin of Error = 2000

Confidence interval, α = 95%

Zcritical at 95% = 1.96

n = (Zcritical * σ) / margin of error

n = (1.96 * 6000) /2000

n = 11760 / 2000

n = 5.88

n = 6 samples

Answer:

OS = 10

Step-by-step explanation:

We can use a ratio to solve

QP     PR

-----  = ------

QO     OS

14          7

-----   = -------

14+6      OS

14          7

-----   = -------

20        OS

Using cross products

14 * OS = 7*20

14 OS = 140

Divide by 14

OS = 140/14

OS = 10

Answer:

3 maybe I'm just guessing.

now thats room for an answer again: yeah, 3 is right. its the x³ that defines the degree, its just the biggest power.

Answer:

3 doors if we are excluding her own. 4 if we are not.

4, 5, 6. she does not pass 7, she enters 7.

3, 4, 5, 6. it could be argued she must first pass her own door.

that context changes the answer.

Answer:

3 e^t/2 + 4 = 27

e^t/2 = 23 / 3

Taking natural log of both sides

t/2 = ln 23/3 = ln 7.667 = 2.037

t = 4.074

Check:

3 e^4.074/2 + 4 = 27

27 = 27

Answer:

2 sqrt(2) = x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 45 = x/4

4 sin 45 = x

4 ( sqrt(2)/2) =x

2 sqrt(2) = x

Answer: D

Use sine to find the x-value:

[tex]sin(45)=\frac{x}{4} \\\\4*sin(45)=x\\\\x=\frac{\sqrt{2} }{2} *4=2\sqrt{2}[/tex]  

Answer:

66

Step-by-step explanation:

let's use x to represent the unknown number

1/2x is 5 more than 6:

↓

1/2x=5+6

solve to find x

1/2x=11

x=22

next, it asks us what is the value of the number when the number is tripled

since we already found what x is equal to, we can multiply that by 3 to figure out its value when it's tripled

3(22)=66

Using mathematical equation to model the scenario, the value of the number when tripled is 66

Let the number = n

0.5n = 5 + 6

0.5n = 11

Divide both sides by 0.5

n = 22

When n is tripled :

n = 22 × 3

n = 66

Hence, the value of the number when tripled is 66

Learn more : https://brainly.com/question/25480062

Answer:

I think the area is 60 but i couldn't figure out the perimeter, sorry.

Step-by-step explanation:

Answer:

perimeter = 36 m

area = 60 m²

Step-by-step explanation:

there is some missing information. for example about the types of the shapes. e.g. if the triangle on the top is an isosceles triangle (2 equal sides). or if the rectangle at the bottom is actually a square with 6 m on all sides. in order to make the sloped side of the top triangle a round, whole number, i assume that the bottom part is a square.

so, the area of this combined shape is the area of the bottom square plus the area of the top triangle.

area square As = 6×6 = 36 m²

so, one side of the triangle is also 6 m, the other is 14-6 = 8 m.

the area of such a right-angled triangle is half of the full rectangle of 6×8.

area triangle At = 6×8/2 = 48/2 = 24 m²

total area = As + At = 36 + 24 = 60 m²

the perimeter of the total shape is the sum of all sides.

so, 14, 6, 6 and ... the baseline/ Hypotenuse of the top triangle.

for that r need the mentioned Pythagoras :

c² = a² + b²

where a and b are the sides, and c is the Hypotenuse (the side opposite of the 90 degree angle).

so, in our case of an isosceles triangle with a 90 degree angle :

c² = 8² + 6² = 64 + 36 = 100

c = 10 m

so, the perimeter is

14+6+6+10 = 36 m

Step-by-step explanation:

One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.

To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140

Answer:

11 /36 of a pound

Step-by-step explanation:

Take the pounds and divide by the number of people

2 3/4 ÷ 9

Change the mixed number to an improper fraction

(4*2+3)/4 ÷9

11/4 ÷9

Copy dot flip

11/4 * 1/9

11/36

9514 1404 393

Answer:

  (6,2)

Step-by-step explanation:

As is often the case with multiple-choice problems, you don't actually need to know the detailed working. You just need to know what the answer looks like.

When point X is dilated by a factor of 2 with point Z as the center of dilation, it will move to a location twice as far from Z. You can tell by looking at the graph that X' will be in the first quadrant, above and to the right of the location of X. The only sensible answer choice is ...

  X' = (6, 2)

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Additional comment

X is a distance of X-Z = (4, 0) -(2, -2) = (2, 2) from Z Doubling that will put the image point a distance of 2(2, 2) = (4, 4) from Z. When this is added to Z, we find ...

  X' = Z + (4, 4) = (2+4, -2+4) = (6, 2)

Answer: The probability would be zero

Step-by-step explanation:

There are two children and one is a boy, so the probability of both being girls is a zero

Answer:

ind the center and radius of the sphere: x2 + y2 +z2-8x + 2y + 62+1 0 2) Find an equation of the sphere that passes through the point (6,-2, 3) and has center (-1,2, 1). Find the curve in which the sphere from #2 intersects the yz-plane. For #4-11, u : ? + j-2k 4) 2u +3v 5) Iv 6) uv and v-3i-2j + k 8) Ivxu 9) comp,v 10) proju 11) Find the angle between u and v 12) Find the scalar triple product of a, b, and c. If a (3, 1,2), b (-1,1,0), and c (0,0,-4) 13) Find the values of x such that (3,2, x) and (2x, 4, x) are orthogonal 14) Find two unit vectors that are orthogonal to both j + 2k and i-2j+3k 15) Find the acute angle between two diagonals of a cube 16) Find a vector perpendicular to the plane through the points A(1,0,0), B(2,0,-1) and C(1,4,3) 17) Find parametric equations for the line through (4,-1, 2) and (1, 1, 5) 18) Find parametric equations for the line through (-2, 2, 4) and perpendicular to the plane 2x-y+5z 12 19) Find an equation of the plane through (2, 1,0) and parallel to x + 4y -3z 1 20) Find an equation of the plane through (3, -1, 1), (4, 0, 2), and (6, 3, 1). 21) Show that the planes x y-z 1 and 2x 3y + 4z 5 are neither parallel nor perpendicular. Find the angle between the planes.

9514 1404 393

Answer:

  x = 36

Step-by-step explanation:

The interior angle at E is (180-2x). The interior angle at F is (180-4x). The sum of the interior angles of the triangle is 180, so we have ...

  (180 -2x) +x +(180 -4x) = 180

  180 = 5x . . . . . . add 5x-180 to both sides

  36 = x . . . . . . . divide by 5

__

Additional comment

This value of x makes the exterior angles at E and F be 72° and 144°, respectively. The internal angles at E, F, G are then 108°, 36°, 36°, making the triangle isosceles with EF = EG.

Answer: B. X It passes the vertical line test :)

Step-by-step explanation:

Answer: 25

Step-by-step explanation:

Answer:

The answer is "[tex]\frac{5\pi}{6}[/tex]"

Step-by-step explanation:

Please find the graph file.

[tex]h= y=2x-x^2\\\\r= x\\\\Area=2\pi\times r\times h\\\\= 2 \pi \times x \times (2x-x^2)\\\\= 2 \pi \times 2x^2-x^3\\\\volume \ V(x)=\int \ A(x)\ dx\\\\= \int^{x=1}_{x=0} 2\pi (2x^2-x^3)\ dx\\\\= 2\pi [(\frac{2x^3}{3}-\frac{x^4}{4})]^{1}_{0} \\\\= 2\pi [(\frac{2}{3}-\frac{1}{4})-(0-0)] \\\\= 2\pi \times \frac{5}{12}\\\\=\frac{5\pi}{6}\\\\[/tex]

Answer:

The value of [tex]x[/tex] is 10.

Step-by-step explanation:

Both angles ABC and CBD are complementary, that is, the sum of the measures of both angles equals 90°, that is:

[tex]\angle ABC + \angle CBD = 90^{\circ}[/tex] (1)

If we know that [tex]\angle ABC = 5\cdot x[/tex] and [tex]\angle CBD = 4\cdot x[/tex], then the value of [tex]x[/tex] is:

[tex]5\cdot x + 4\cdot x = 90^{\circ}[/tex]

[tex]9\cdot x = 90^{\circ}[/tex]

[tex]x = 10[/tex]

The value of [tex]x[/tex] is 10.

Answer:

Here you go

Ans is in pictures.

Answer:

Following are the solution to the given points:

Step-by-step explanation:

Normal Distribution:

[tex]\mu=50\\\\\sigma= 6\\\\Z=\frac{X-\mu}{\sigma} \sim N(O,l)[/tex]

For point a:

[tex]P(X< 56)=\frac{(56-50)}{6}= \frac{6}{6}=1\\\\[/tex]

[tex]=P(Z<1)\ From\ \sigma \ Table=0.8413\\\\P(X>= 56)=(1-P(X< 56))=1-0.8413=0.1587\\\\[/tex]

For point b:

[tex]P(X< 49)=\frac{(49-50)}{6}=-\frac{1}{6} =-0.1667\\\\=P(Z<-0.1667)\ From\ \sigma \ Table\\\\=0.4338[/tex]

For point c:

To Find [tex]P(a\leq Z\leq b)= F(b) - F(a)\\\\[/tex]

[tex]P(X< 45)=\frac{(45-50)}{6}=\frac{-5}{6} =-0.8333\\\\P (Z<-0.8333) \ From \ \sigma \ Table\\\\=0.20233\\\\P(X< 55)=\frac{(55-50)}{6} =\frac{5}{6}=0.8333\\\\P ( Z< 0.8333) \ From \ \sigma\ Table\\\\=0.79767\\\\P(45 < X < 55) =0.79767-0.20233 =0.5953[/tex]

The linear regression model which models the data is :

y = -6.41053X + 103.83509

Obtaining the regression equation could be performed using either the formula method or using technology (excel, calculator, online regression calculators )

Using technology :

• Enter the data into the columns provided ;

The regression equation obtained for the data is : y = -6.41053X + 103.83509

Where ;

Slope = -6.41053

Intercept = 103.83509

X = Rank

y = probability percentage

Hence, from the linear regression equation obtained, we could see that a negative linear relationship exists between rank and probability as implied from it's negative slope value.

Learn more on linear regression : https://brainly.com/question/12164389

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