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

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