4. What is the Median of the data set? ( use picture for problem)

The numbers 2/1/3,h,k,7/7/8 firm a geometric progression. find the value of h and of k

taurus [48]

$\text{We have }\ 2\dfrac{1}{3},\ h,\ k,\ 7\dfrac{7}{8}.\\\\\text{Convert the mixed numbers to the improper fractions}\\\\2\dfrac{1}{3}=\dfrac{2\cdot3+1}{3}=\dfrac{7}{3}\\\\7\dfrac{7}{8}=\dfrac{7\cdot8+7}{8}=\dfrac{63}{8}\\\\\text{If}\ a_1,\ a_2,\ a_3,\ a_4\ \text{is a geometric seqence, then:}\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=r\\\\a_2=a_1r\\\\\text{and}\ \dfrac{a_4}{a_1}=r^3\\\\\text{Substitute:}$

$r^3=\dfrac{\frac{63}{8}}{\frac{7}{3}}\\\\r^3=\dfrac{63}{8}\cdot\dfrac{3}{7}\\\\r^3=\dfrac{9\cdot3}{8\cdot1}\\\\r^3=\dfrac{27}{8}\to r=\sqrt[3]{\dfrac{27}{8}}\\\\r=\dfrac{3}{2}\\\\h=2\dfrac{1}{3}\cdot\dfrac{3}{2}=\dfrac{7}{3}\cdot\dfrac{3}{2}=\dfrac{7}{2}\\\\k=\dfrac{7}{2}\cdot\dfrac{3}{2}=\dfrac{21}{4}\\\\Answer:\ \boxed{h=\dfrac{7}{2}=3\dfrac{1}{2}\ and\ k=\dfrac{21}{4}=5\dfrac{1}{4}}$

8 0

2 years ago

Will give brainliest

Sonja [21]

The sum of the two rational equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).

<h3>How to simplify the addition between two rational equations</h3>

In this question we must use algebra definitions and theorems to simplify the addition of two rational equations into a single rational equation. Now we proceed to show the procedure of solution in detail:

(n + 5) / (n² + 3 · n - 10) + 5 / (3 · n²) Given
(n + 5) / [(n + 5) · (n - 2)] + 5 / (3 · n²) x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)
1 / (n - 2) + 5 / (3 · n²) Associative and modulative property / Existence of the multiplicative inverse
[3 · n² + 5 · (n - 2)] / [3 · n² · (n - 2)] Addition of fractions with different denominator
(3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²) Distributive property / Power properties / Result

To learn more on rational equations: brainly.com/question/20850120

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4 0

2 years ago

Can someone give me the correct solution to the inequality of 3x<-21?

Slav-nsk [51]

Answer:

x < -7

Step-by-step explanation:

3x < -21

Step 1: Divide both sides by 3

3x < -21

3x / 3 < -21 / 3

x < -7

Answer: x < -7

8 0

3 years ago

Read 2 more answers

Im so confused pls help!

Digiron [165]

$-\frac{1}{2} *(-\frac{5}{6} )+(-\frac{1}{2} )*\frac{1}{3} \\=\frac{5}{12} -\frac{1}{6} \\=\frac{5}{12} -\frac{2}{12} \\=\frac{3}{12} \\\frac{1}{4}$

7 0

2 years ago

Read 2 more answers

What is the equation of a line that has an x-intercept of -4 and a y-intercept of 8 ?

podryga [215]

Answer:

y=2/-1+8

Step-by-step explanation:

-4= (-4,0) -4=x1 0=y1, 8= (0,8) 0=x2 8=y2
formula is, y2-y1/x2-x1
8-0/0-4=8/-4=4/-2= 2/-1
2/-1 is the slope or (m), use (-4,0) or (0,8) i used (0,8) because its easier.
(0,8), 0=x1 8=y1
formula is y-y1=m(x-x1)
y-8=2/-1(x-0) ---->distribute
y-8=2/-1x-0 --->get y alone

+8 +8

so the answer is y=2/-1+8

7 0

3 years ago