Round 45.628 to the nearest tenth.

If

Daniel [21]

Answer:

$x=\sqrt{\frac{7(4+\sqrt{15})}{2}}$

Step-by-step explanation:

From the way it is written, the $x$ is outside the square root. I will rewrite it as:

$x\sqrt{5} =x\sqrt{3} +\sqrt{7}$

$x\sqrt{5}-x\sqrt{3}=\sqrt{7}$

$x(\sqrt{5} - \sqrt{3} )=\sqrt{7}$

$x= \frac{\sqrt{7} }{\sqrt{5} - \sqrt{3}} \implies \frac{\sqrt{7}(\sqrt{5} + \sqrt{3}) }{2}$

$x=\frac{1}{2} \sqrt{7} (\sqrt{5} + \sqrt{3} )$

$x=\frac{\sqrt{35}}{2} +\frac{ \sqrt{21}}{2}$

$x=\frac{\sqrt{35}+\sqrt{21}}{2}$

Multiply denominator and numerator by 3

$x=\frac{3\sqrt{35}+3 \sqrt{21}}{6}$

Factor $\sqrt{3}$

$\sqrt{3} (\sqrt{105}+3 \sqrt{7})$

$x=\frac{\sqrt{3} (\sqrt{105}+3 \sqrt{7})}{6}$

Divide denominator and numerator by $\sqrt{3}$

$x=\frac{\sqrt{105}+3 \sqrt{7}}{2\sqrt{3} }$

Let's rewrite it again

$x=\frac{\sqrt{ (\sqrt{105}+3 \sqrt{7})^2}}{\sqrt{12} }$

$x=\sqrt{ \frac{1}{12} \cdot (\sqrt{105}+3 \sqrt{7})^2}$

It is already in the form $\sqrt{\frac{a}{b} }$

Expanding the perfect square, we have

$63+42\sqrt{15}+105$

$\frac{63}{12} +\frac{42\sqrt{15}}{12} +\frac{105}{12}$

$\frac{21}{4} +\frac{7\sqrt{15}}{2} +\frac{35}{4}$

Factor $\frac{7}{2}$

$\frac{7}{2} (4+\sqrt{15} )$

Therefore,

$x=\sqrt{\frac{7}{2} \left(4+\sqrt{15} \right)}$

$x=\sqrt{\frac{7(4+\sqrt{15})}{2}}$

7 0

3 years ago

Read 2 more answers

A student is selling candy bars for a school fundraiser. In 2 hours he sold 116 candy bars, and in 3 hours he sold 198 candy bar

Citrus2011 [14]

290 is how much hes sold in 5 hrs

6 0

3 years ago

Read 2 more answers

How to solve and graph this equation ?

crimeas [40]

Start by adding 2y so that the equation becomes 2y= -3x-4 then divide by 2 on both sides so it cancelled out. (This if for if your trying to get it in y=mx+b form)

6 0

3 years ago

I have a box of chocolates with white, milk and dark chocolate in. The ratio of white to not white is 3:4. The ratio of not dark

Scrat [10]

white : milk : dark

w : m : d

The ratio of white to not white is 3:4

w : (m+d) = 3:4

The ratio of not dark to dark is 17:4.

(w+m) : d = 17:4

---------

We treat the colons as fraction bars and cross multiply.

4w = 3(m+d) = 3m + 3d

4w + 4m = 17 d

Subtracting,

4m = 17d - (3m+3d) = 14d - 3m

7m = 14 d

m/d = 14/7

m:d = 2:1

Since w:(m+d)=3:4 let's make m+d a multiple of 4.

m:d = 8:4

w : (m+d) = 3:4 = 9:12

w:m:d = 9:8:4

Answer: 9:8:4

Check:

white to non white 9 to 8+4=12 = 3:4, good

non dark to dark (9+8):4=17:4, good

8 0

3 years ago

Here are the total scores of 10 students in an introductory statistics course.

cestrela7 [59]

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Mean (m) = 72

Standard deviation (sd) = 10

Grading cutoff policy:

bottom 5% receive F

next 15% receive D

next 35% receive C

next 30% receive B

A) Give the cutoffs for the grades in this course in terms of standardized scores.

Standardized score for grade cutoff:

Locating the Zscore for the proportions on the z table :

Bottom 5% = 0.05 ; corresponding Zscore = - 1.645

next 15% receive D = (5 +15)% 0.20 ; corresponding Zscore = - 0.84

next 35% receive C = (20+35)% = 0.55 ; corresponding Zscore = 0.13

next 30% receive B = (55 + 30)% = 0.85 ; Corresponding Zscore = 1.04

B) Give the cutoffs in terms of actual total scores.

Recall:

Zscore = (x - m) /sd ; where x = actual score

x = sd*z + m

For F:

10*(-1.645) + 72 = 55.55

For D:

10*(-0.84) + 72 = 63.6

For C:

10*(0.13) + 72 = 73.3

For B:

10*(1.04) + 72 = 82.4

C) Do you think that this method of assigning grades is a good one?

Yes, it is good in terms of expressing scores around the mean such that score below are negative and those above are positive. However, it is a little bit ambiguous.

4 0

4 years ago