Work out m and c for the line: y = 2 x + 5

John is curious how much money he can make in a month. He makes one penny on March 1st. He hopes to double the amount he makes e

KonstantinChe [14]

Answer:

£10,737,418.24

Step-by-step explanation:

<u>Every day amount doubles:</u>

March 1st = 1p= 2^0 p
March 2nd = 2*1p = 2^1 p
March 3rd = 2*2p = 2^2 p
...
March 31st = 2^30 p = 1,073,741,824 p = £10,737,418. 24

4 0

3 years ago

Find the logarithmic function y = logbx that passes through the points

katovenus [111]

$b\in(0,\ 1)\ \cup\ (1,\ \infty)\\x > 0\\y\in\mathbb{R}\\--------------------------\\\\y=\log_bx\\\\For\ (1,\ 0)\to x=1,\ y=0.\ Substitute:\\\\\log_b1=0\to b^0=1\to b\in(0,\ 1)\ \cup\ (1,\ \infty)\\\\For\ (116,\ 2)\to x=116,\ y=2.\ Substitute:\\\\\log_b116=2\to b^2=116\to b=\sqrt{116}\\\to b=\sqrt{4\cdot29}\to b=\sqrt4\cdot\sqrt{29}\to b=2\sqrt{29}\\\\For\ (4,\ -1)\to x=4,\ y=-1.\ Substitute:\\\\\log_b4=-1\to b^{-1}=4\to b=\dfrac{1}{4}$

Different values of b.

<h3>Answer: There is no logarithmic function whose graph goes through given points.</h3><h3 />

Maybe the second point is $\left(\dfrac{1}{16},\ 2\right)$

Substitute:

$\log_b\dfrac{1}{16}=2\to b^2=\dfrac{1}{16}\to b=\sqrt{\dfrac{1}{16}}\to b=\dfrac{1}{4}$

<h3>Then we have the answer:</h3>

$\boxed{y=\log_{\frac{1}{4}}x}$

6 0

3 years ago

Plz help asap for brainiest

Sergio [31]

Answer: x = 16

Step-by-step explanation:

If RQ is the bisector, that means the angle is cut in half. Therefore angles PRQ and QRS are equal to each other.

4x+6 = 7x-42

subtract 7x from both sides

-3x+6 = -42

subtract 6 from both sides

-3x = -48

divide both sides by -3

x = 16

7 0

2 years ago

Read 2 more answers

Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean. See Attached Excel for Da

alexgriva [62]

Answer:

The 99% confidence interval for the mean germination time is (12.3, 19.3).

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.</em>

<em />

We start calculating the sample mean M and standard deviation s:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(18+12+20+17+14+15+13+11+21+17)\\\\\\M=\dfrac{158}{10}\\\\\\M=15.8\\\\\\$

$s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((18-15.8)^2+(12-15.8)^2+(20-15.8)^2+. . . +(17-15.8)^2)}\\\\\\s=\sqrt{\dfrac{101.6}{9}}\\\\\\s=\sqrt{11.3}=3.4\\\\\\$

We have to calculate a 99% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=15.8.

The sample size is N=10.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{10}}=\dfrac{3.4}{3.162}=1.075$

The degrees of freedom for this sample size are:

df=n-1=10-1=9

The t-value for a 99% confidence interval and 9 degrees of freedom is t=3.25.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=3.25 \cdot 1.075=3.49$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 15.8-3.49=12.3\\\\UL=M+t \cdot s_M = 15.8+3.49=19.3$

The 99% confidence interval for the mean germination time is (12.3, 19.3).

8 0

3 years ago

Find x<br><br> x+4+4x-8+7x-35=180

kipiarov [429]

Answer:

x = 73/4

Step-by-step explanation:

Solve for x:

12 x - 39 = 180

Add 39 to both sides:

12 x + (39 - 39) = 39 + 180

39 - 39 = 0:

12 x = 180 + 39

180 + 39 = 219:

12 x = 219

Divide both sides of 12 x = 219 by 12:

(12 x)/12 = 219/12

12/12 = 1:

x = 219/12

The gcd of 219 and 12 is 3, so 219/12 = (3×73)/(3×4) = 3/3×73/4 = 73/4:

Answer: x = 73/4

5 0

3 years ago

Read 2 more answers