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dsp73
3 years ago
11

A swimming pool is in the shape of a rectangular prism. If the base measures

Mathematics
1 answer:
-BARSIC- [3]3 years ago
5 0

Answer:

960

Step-by-step explanation:

10x12x8 is 960

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Illene wrapped 5 gifts for her 5 cousins. if she gives them out randomly, what is the probability that every cousin gets the rig
boyakko [2]
The probability is 1/5
7 0
3 years ago
Show your work please and I will see if you are correct I will give you Brainest Solve using elimination (IXL Ski ZQV). Show all
NeTakaya

x=3 and y=−2

Step-by-step explanation:

Solve8x+5y=14for x:

8x+5y=14

8x+5y+−5y=14+−5y(Add -5y to both sides)

8x=−5y+14

8x8=−5y+148(Divide both sides by 8)

x=−58y+74

Step: Substitute−58y+74forxin−4x−5y=−2:

−4x−5y=−2

−4(−58y+74)−5y=−2

−52y−7=−2(Simplify both sides of the equation)

−52y−7+7=−2+7(Add 7 to both sides)

−52y=5

−52y−52=5−52(Divide both sides by (-5)/2)

y=−2

Step: Substitute−2foryinx=−58y+74:

x=−58y+74

x=−58(−2)+74

x=3(Simplify both sides of the equation)

Answer:

x=3 and y=−2

8 0
3 years ago
The graph of y = x^2 -3 is translated in 4 units to the left of the graph to give the graph A
Vedmedyk [2.9K]

Answer:

a) b = 8, c = 13

b) The equation of graph B is y = -x² + 3

Step-by-step explanation:

* Let us talk about the transformation

  • If the function f(x) reflected across the x-axis, then the new  function g(x) = - f(x)
  • If the function f(x) reflected across the y-axis, then the new  function g(x) = f(-x)
  • If the function f(x) translated horizontally to the right  by h units, then the new function g(x) = f(x - h)
  • If the function f(x) translated horizontally to the left  by h units, then the new function g(x) = f(x + h)

In the given question

∵ y = x² - 3

∵ The graph is translated 4 units to the left

→ That means substitute x by x + 4 as 4th rule above

∴ y = (x + 4)² - 3

→ Solve the bracket to put it in the form of y = ax² + bx + c

∵ (x + 4)² = (x + 4)(x + 4) = (x)(x) + (x)(4) + (4)(x) + (4)(4)

∴ (x + 4)² = x² + 4x + 4x + 16

→ Add the like terms

∴ (x + 4)² = x² + 8x + 16

→ Substitute it in the y above

∴ y = x² + 8x + 16 - 3

→ Add the like terms

∴ y = x² + 8x + 13

∴ b = 8 and c = 13

a) b = 8, c = 13

∵ The graph A is reflected in the x-axis

→ That means y will change to -y as 1st rule above

∴ -y = (x² - 3)

→ Multiply both sides by -1 to make y positive

∴ y = -(x² - 3)

→ Multiply the bracket by the negative sign

∴ y = -x² + 3

b) The equation of graph B is y = -x² + 3

4 0
3 years ago
A certain chalkboard manufacturer determines that their largest blackboard model has a mean length of 5.00 m and a standard devi
Igoryamba

Answer:

23 chalkboards

Step-by-step explanation:

Given:

Mean length = 5 m

Standard deviation = 0.01

Number of units ordered = 1000

Now,

The z factor = \frac{\textup{x - Mean}}{\textup{standard deviation}}

or

The z factor = \frac{\textup{4.98 - 5}}{\textup{0.01}}

or

Z = - 2

Now, the Probability P( length < 4.98 )

Also, From z table the p-value = 0.0228

therefore,

P( length < 4.98 ) = 0.0228

Hence, out of 1000 chalkboard ordered (0.0228 × 1000) = 23 chalkboard are likely to have lengths of under 4.98 m.

7 0
3 years ago
Simplify: [5×(25)^n+1 - 25 × (5)^2n]/[5×(5)^2n+3 - (25)^n+1​]​
Alekssandra [29.7K]

\green{\large\underline{\sf{Solution-}}}

<u>Given expression is </u>

\rm :\longmapsto\:\dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }

can be rewritten as

\rm \:  =  \: \dfrac{5 \times  { {(5}^{2} )}^{n + 1}  -  {5}^{2}  \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {( {5}^{2} )}^{n + 1} }

We know,

\purple{\rm :\longmapsto\:\boxed{\tt{  {( {x}^{m} )}^{n}  \: = \:   {x}^{mn}}}} \\

And

\purple{\rm :\longmapsto\:\boxed{\tt{ \:  \:   {x}^{m} \times  {x}^{n} =  {x}^{m + n} \: }}} \\

So, using this identity, we

\rm \:  =  \: \dfrac{5 \times  {5}^{2n + 2}  - {5}^{2n + 2} }{{5}^{2n + 3 + 1}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 4}  -  {5}^{2n + 2} }

can be further rewritten as

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 2 + 2}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2}  - 1)}

\rm \:  =  \: \dfrac{4}{25 - 1}

\rm \:  =  \: \dfrac{4}{24}

\rm \:  =  \: \dfrac{1}{6}

<u>Hence, </u>

\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }  =  \frac{1}{6} }}

4 0
3 years ago
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