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3 years ago

12

Write the equation in logarithmic form 8^x=64

1 answer:

Alona [7]3 years ago

8 0

Step-by-step explanation:

8^x= 64

8²= 64

In logarithmic form,

log(base 8) 64= 2

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Genesis wants to ride her bicycle 31 miles this week. She has already ridden 7 miles. If she rides for 4 more days, write and so

tensa zangetsu [6.8K]

Since she has already ridden 7 miles out of 31 miles,

remaining miles to be ridden
= 31 - 7
= 24 miles

Let x be the number of miles she has to ride in each of the 4 days left.

4x = 24
x = 6

6 0

2 years ago

A positive integer is twice another.the sum of the reciprocal of the two positive integer is 3/14. Find the integers

icang [17]

Answer:

$\huge\boxed{14\ \text{and}\ 7}$

Step-by-step explanation:

$n,\ m-\text{positive integer}\\\\n=2m-\text{a positive integer is twice another}\\\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}-\text{the sum of the reciprocal of the two positive integer is }\ \dfrac{3}{14}\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}n=2m&(1)\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}&(2)\end{array}\right$

$\text{Substitute (1) to (2):}\\\\\dfrac{1}{2m}+\dfrac{1}{m}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{1\cdot2}{m\cdot2}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{2}{2m}=\dfrac{3}{14}\\\\\dfrac{1+2}{2m}=\dfrac{3}{14}\\\\\dfrac{3}{2m}=\dfrac{3}{14}\Rightarrow2m=14\qquad\text{divide both sides by 2}\\\\\dfrac{2m}{2}=\dfrac{14}{2}\\\\\boxed{m=7}$

$\text{Substitute it to (1):}\\\\n=2\cdot7\\\\\boxed{n=14}$

8 0

2 years ago

Move two choices to the blanks to correctly complete the sentences.

Pavel [41]

Answer:

(A) There should have been 5 outcomes of HT

(B) The experimental probability is greater than the theoretical probability of HT.

Step-by-step explanation:

Given

$S = \{HH,HT,TH,TT\}$ -- Sample Space

$n(S) = 4$ --- Sample Size

Solving (a); theoretical outcome of HT in 20 tosses

First, calculate the theoretical probability of HT

$P(HT) = \frac{n(HT)}{n(S)}$

$P(HT) = \frac{1}{4}$

Multiply this by the number of tosses

$P(HT) * n= \frac{1}{4} * 20$

$P(HT) * n= 5$

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Solving (b); experimental probability of HT

Here, we make use of the table

$P(HT) = \frac{n(HT)}{n(S)}$

$P(HT) = \frac{6}{20}$

$P(HT) = 0.30$ ---- Experimental Probability

In (a), the theoretical probability is:

$P(HT) = \frac{1}{4}$

$P(HT) = 0.25$ ---- Experimental Probability

By comparison;

$0.30 > 0.25$

6 0

3 years ago

ASAP PLEASE HELP! THANK YOUU

mote1985 [20]

The answer to the question is c

4 0

3 years ago

A 20 foot ladder leaning against a wall is used to reach a window that is 17 feet above the ground. How far from the wall is the

Liono4ka [1.6K]

Answer:

The wall is 10.5 foot far from the bottom of the ladder.

Step-by-step explanation:

Given:

Height of the ladder leaning against wall (Hypotenuse) = 20 foot.

Height from where the window is above from the ground (Leg1) = 17 feet.

To find the distance of the bottom of the ladder far from the wall (Leg2) = ?

Now, by using the pythagorean theorem:

$Hypotenuse^{2} = (Leg1)^{2} + (Leg2)^{2}$

$20^{2} =17^{2}+(Leg2) ^{2}$

$400=289+(Leg2)^{2}$

$400-289=(Leg2)^{2}$

$111=(Leg2)^{2}$

by squaring both sides

$Leg2=10.535$

10.535 foot rounded nearest tenth is 10.5 foot.

Therefore, the wall is 10.5 foot far from the bottom of the ladder.

6 0

3 years ago