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2 years ago

10

After six biology tests, Ruben has a mean score of 74. What score does Ruben need on the next test to raise his average (mean) t

o 76?

1 answer:

blondinia [14]2 years ago

4 0

Answer:

88

Step-by-step explanation:

this question is a question that involves the use of the statistical principles of finding average

let the summation of the six scores of the biology test be represented as ∑x

∴ ∑x÷ 6=74

∑x=74 × 6

=444

444 is the summation of all the scores of all the six biology scores reuben had

the next test would be his 7th

let y represent the score for the 7th test

therefore, $\frac{444 + y}{7}$ = 76

444 + y = (76 × 7)

444 + y = 532

y=88

Reuben needs to score 88 to raise his average to 76

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Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

$x = \frac{5}{2}$

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

3 0

3 years ago

Kimora’s cell phone company charges her $35 a month for phone service plus $.05 for each text message sent. How many text messag

professor190 [17]

Given that Kimora’s cell phone company charges her $35 a month for phone service plus $.05 for each text message sent.

Kimora's cell phone bill for one month is $52.

We need to determine the number of text messages Kimora sent for one month.

Also, we need to write and equation and solve it.

<u>The equation:</u>

Let x denote the number of text messages Kimora sent for one month.

Thus, the equation is given by

$35+0.05x=52$

Therefore, the equation for the number of text messages Kimora sent for one month is $35+0.05x=52$

<u>Solving the equation:</u>

We need to solve the equation $35+0.05x=52$

Subtracting both sides of the equation by 35, we get;

$0.05x=17$

Dividing both sides of the equation by 0.05, we get;

$x=340$

Therefore, the number of messages sent is 340.

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3 years ago

Which numerical expression could represent this phrase?

Agata [3.3K]

Answer:

Step-by-step explanation:

63 divided by 9 times 10 minus 2

7 0

3 years ago

Please help me. Factor. 5x^+23x+26

Alexus [3.1K]

<span>Algebra Calculator | Latest | Discuss | About | Help | Translation</span>

20,897,614 solved | 1,346 online

Skip Ad <span> <span> <span> <span> </span> <span>
</span></span></span></span> <span><span> 5x2-23x=-26</span> </span>Two solutions were found :<span><span> x = 2 </span><span> x = 13/5 = 2.600
</span></span>

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

5*x^2-23*x-(-26)=0

Step by step solution :Skip Ad
<span> Step 1 :</span><span>Equation at the end of step 1 :</span><span> (5x2 - 23x) - -26 = 0 </span><span> Step 2 :</span>Trying to factor by splitting the middle term

<span> 2.1 </span> Factoring <span> 5x2-23x+26</span>

The first term is, <span> <span>5x2</span> </span> its coefficient is <span> 5 </span>.
The middle term is, <span> -23x </span> its coefficient is <span> -23 </span>.
The last term, "the constant", is <span> +26 </span>

Step-1 : Multiply the coefficient of the first term by the constant <span> 5 • 26 = 130</span>

Step-2 : Find two factors of 130 whose sum equals the coefficient of the middle term, which is <span> -23 </span>.

<span><span>       -130    +    -1    =    -131 <span>
</span> </span> <span>       -65    +    -2    =    -67 <span>
</span> </span> <span>       -26    +    -5    =    -31 <span>
</span> </span> <span>       -13    +    -10    =    -23    That's it</span></span>

4 0

2 years ago

An equation parallel and perpendicular to 4x+5y=19

UNO [17]

Answer:

Parallel line:

$y=-\frac{4}{5}x+\frac{9}{5}$

Perpendicular line:

$y=\frac{5}{4}x-\frac{1}{2}$

Step-by-step explanation:

we are given equation 4x+5y=19

Firstly, we will solve for y

$4x+5y=19$

we can change it into y=mx+b form

$5y=-4x+19$

$y=-\frac{4}{5}x+\frac{19}{5}$

so,

$m=-\frac{4}{5}$

Parallel line:

we know that slope of two parallel lines are always same

so,

$m'=-\frac{4}{5}$

Let's assume parallel line passes through (1,1)

now, we can find equation of line

$y-y_1=m'(x-x_1)$

we can plug values

$y-1=-\frac{4}{5}(x-1)$

now, we can solve for y

$y=-\frac{4}{5}x+\frac{9}{5}$

Perpendicular line:

we know that slope of perpendicular line is -1/m

so, we get slope as

$m'=\frac{5}{4}$

Let's assume perpendicular line passes through (2,2)

now, we can find equation of line

$y-y_1=m'(x-x_1)$

we can plug values

$y-2=\frac{5}{4}(x-2)$

now, we can solve for y

$y=\frac{5}{4}x-\frac{1}{2}$

4 0

3 years ago