The solution to the equation log₇343 = 3 is 7³ = 343
What is an equation?An equation is used to show the relationship between numbers and variables.
The logarithm can be defined as the exponent that raises a base to get a particular number. The law of logarithm states:
logₓm = n is the same as xⁿ = m
Given the equation:
log₇343 = 3
Applying the law of logarithm gives:
7³ = 343
The solution to the equation is 7³ = 343
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Which statement about f(x) = 2x2 – 3x - 5 is true?
Answer:
-1, 5/2 ; f(x) = (x+1)(2x-5)
Step-by-step explanation:
2x² - 3x - 5 = 0
2x² - 5x + 2x - 5 = 0
x(2x - 5) +1(2x - 5) = 0
Factors are :
(2x - 5) = 0 ; (x + 1) = 0
2x - 5 = 0
2x = 5
x = 5/2
(x + 1) = 0
x = - 1
Zeros are ; x = 5/2 and x = - 1
The members of a consulting firm rent cars from three rental agencies. It is estimated that 0.42 percent of cars come from agency 1, 0.08 percent of cars come from agency 2, and 0.5 percent of cars come from agency 3. It is also estimated that 0.08 percent of cars from agency 1 need a tune-up, 0.02 percent of cars from agency 2 need a tune-up, and 0.02 percent of cars from agency 3 need a tune-up. Answer the following questions, rounding your answers to two decimal places where appropriate.
The probability that a rental car delivered to the firm will need a tune-up is 0.05% and the conditional probability is 0.04%
How to determine the probabilitiesThe probability that a rental car delivered to the firm will need a tune-up
From the question, we have the following parameters that can be used in our computation:
Agency 1 = 0.42%, Tune up from agency 1 = 0.08%
Agency 2 = 0.08%, Tune up from agency 2 = 0.02%
Agency 3 = 0.5%, Tune up from agency 3 = 0.02%
Using total probability, we have the following equation
P(tune-up) = P(tune-up | agency 1) * P(agency 1) + P(tune-up | agency 2) * P(agency 2) + P(tune-up | agency 3) * P(agency 3)
Substitute the known values in the above equation, so, we have the following representation
P(tune-up) = 0.08% * 0.42% + 0.02% * 0.08% + 0.02% * 0.5%
Evaluate the sum of products
P(tune-up) = 0.000452
Express as percentage and approximate
P(tune-up) = 0.05%
(b) The probability that it came from agency 2
This is a conditional probability, and it calculated as
P(Agency 2| Tune up) = P(Tune up and Agency 2)/P(Tune up)
Substitute the known values in the above equation, so, we have the following representation
P(Agency 2| Tune up) = (0.02% * 0.08%)/0.0452%
Evaluate
P(Agency 2| Tune up) = 0.0003539823
Express as percentage
P(Agency 2| Tune up) = 0.03539823%
Approximate
P(Agency 2| Tune up) = 0.04%
So, the probability is 0.04%
Read more about probability at
https://brainly.com/question/251701
#SPJ1
Complete question
The members of a consulting firm rent cars from three rental agencies. It is estimated that 0.42 percent of cars come from agency 1, 0.08 percent of cars come from agency 2, and 0.5 percent of cars come from agency 3. It is also estimated that 0.08 percent of cars from agency 1 need a tune-up, 0.02 percent of cars from agency 2 need a tune-up, and 0.02 percent of cars from agency 3 need a tune-up. Answer the following questions, rounding your answers to two decimal places where appropriate.
(a) What is the probability that a rental car delivered to the firm will need a tune-up?
(b) If a rental car delivered to the firm needs a tune-up, what is the probability that it came from agency 2?
In a particular year, 68% of online courses taught at a system of community colleges were taught by full-time faculty. To test if 68% also represents a particular state's percent for full-time faculty teaching the online classes, a particular community college from that state was randomly selected for comparison. In that same year, 32 of the 44 online courses at this particular community college were taught by full-time faculty.
Conduct a hypothesis test at the 5% level to determine if 68% represents the state in question.
Answer:
The p-value of the test is 0.5028>0.05, which means that there is sufficient evidence to determine that 68% represents the state in question.
Step-by-step explanation:
Test if 68% represents the state in question.
This means that at the null hypothesis, we test if the proportion is 68%, that is:
[tex]H_0: p = 0.68[/tex]
At the alternate hypothesis, we test if the proportion is different of 68%, that is:
[tex]H_a: p \neq 0.68[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.68 is tested at the null hypothesis:
This means that [tex]\mu = 0.68, \sigma = \sqrt{0.68*0.32}[/tex]
32 of the 44 online courses at this particular community college were taught by full-time faculty.
This means that [tex]n = 44, X = \frac{32}{44} = 0.7273[/tex]
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.7273 - 0.68}{\frac{\sqrt{0.68*0.32}}{\sqrt{44}}}[/tex]
[tex]z = 0.67[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion differing by the population proportion by at least 0.7273 - 0.68 = 0.0473, which is P(|z| > 0.67), which is 2 multiplied by the p-value of z = -0.67.
Looking at the z-table, z = -0.67 has a p-value of 0.2514
2*0.2514 = 0.5028
The p-value of the test is 0.5028>0.05, which means that there is sufficient evidence to determine that 68% represents the state in question.
Locating Fractions on a Number Line
A B
Hot
-2
-1
Intro
C
D
+++++
0 1 2
Use the drop-down menus to label the points on the
number line.
Point A is at
Point B is at
Point C is at
Point D is at
<
Done
On solving the provided question we cans ay that - order when writing it on the number line: = -1.25, -0.75, 0.25, 1.5, 2
what is number line?A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.
The numbers on the number line must be
[tex]6/3 = 2\\-3/4 = -0.75\\1.5 = 1.5\\0.25 = 0.25\\-5.4 = -1.25\\[/tex]
In ascending order, t
[tex]-1.25 = -5/4\\-0.75 = -3/4\\0.25\\1.5\\2 = 6/3[/tex]
order when writing it on the number line:
-1.25, -0.75, 0.25, 1.5, 2
To know more about number line visit:
https://brainly.com/question/13425491
#SPJ1
In 2019, the United States Census Bureau reported the various components of population change as estimated below. ∙ One birth every 8 seconds ∙ One death every 11 seconds ∙ One international migrant (net of immigrants versus emigrants) every 33 seconds ∙ Net gain of one person every 17 seconds During that year, which of the components was having the second largest effect on population growth?
Answer:
The components that was having the second largest effect on population growth was deaths.
Step-by-step explanation:
In this question:
The largest the frequency(less time between each time, larger frequency), the higher effect of the component in population growth.
In this question:
Due to the rates, the effects on population growth, in descending order ir:
Birth - Deaths - Gain of one person - Migrants
So the components that was having the second largest effect on population growth was deaths.
Which of the statements below is true for the following set of numbers? 20, 15, 50, 85, 75, 60
The range is 70 and the midrange 50 is .
The range and the midrange are equal.
The range is 85 and the midrange is 55.
The range is 70 and the midrange is 55.
1: What number must be multiplied by (5x + 6) to result in the expression 20x + 24?
2: On the first day of a road trip, you drive x miles.
On Day 2, you drive 10 more than twice the miles driven on Day 1.
On Day 3, you drive 100 miles less than Day 1.
Write an expression to represent the miles driven on each day of the road trip, then write a final simplified expression representing the total miles driven in three days.
a) Day 1:
b) Day 2:
c) Day 3:
d) Final simplified expression to represent total miles driven in three days:
e) Look at your expression for c) Day 3: "100 miles less than Day 1." Describe a real-word situation to explain why order matters when writing this expression.
1. The number that must be multiplied by (5x + 6) to result in the expression 20x + 24 is 4.
2. An expression representing the miles driven on each day of the road trip and a final simplified expression of the total drives in three days are as follows:
a) Day 1: x
b) Day 2: 2x + 10
c) Day 3: x - 100
d) Final simplified expression to represent total miles driven in three days: 4x + 10 - 100.
e) A real-world situation in which order matters when writing the expression x - 100 is that the value of x is supposed to be more than the value of 100.
What is a mathematical expression?A mathematical expression is the combination of constants, numbers, mathematical operators, and variables without the equation sign (=).
Literarily, a mathematical expression is like a phrase in the English language because it does not make complete sense without the equation sign.
1) Multiplication:
(20x + 24) ÷ (5x + 6) = 4
Check:
4(5x + 6) = 20x + 24
2) Road Trip Expressions:
Day one driving distance = x miles
Day two driving distance = 2x + 10
Day three driving distance = x - 100
Total distance = x + 2x + 10 + x - 100
= 4x + 10 - 100
Learn more about mathematical expressions at https://brainly.com/question/1859113
#SPJ1
Find the difference:
16 16
Answer:
3 3/6 or 3 1/2 or 3.5
Step-by-step explanation:
What type of sequence is this: an = 4 * 3(n-1)
Answer:
geometric sequence.
Step-by-step explanation:
Given the sequence an = 4 * 3(n-1)
The type of sequence written in this form is a geometric sequence. It is expressed Mathematically as;
an = ar^n-1
On comparison, we can see that;
a = 4
r = 3
a is the first term]
r is the common ratio
A pre-paid cell phone company charges $10.35 as a monthly access fee and $0.08 per minute of calling time.
Express the monthly cost C in terms of minutes of call time ?
What will the monthly cost be if you make 280 minutes of calls this month?
Answer: $32.75
Step-by-step explanation:
If each call costs $0.08 and you make 280 minutes worth of calls this month you'll have made $22.04 worth of phone calls plus the monthly access fee ($10.35) if you add both those fees you'll be left with a bill of $32.75.
I hope this answer helped you. :)
Answer:
$32.75
Step-by-step explanation:
10.35 + (0.08×280)
Sam has 6 choices of shirts, 4 choices of pants, 5 choices of socks, and 6 choices of shoes for his working dress. In how many ways Sam can select his outfit?
looooovvvvveeee these kinds of questions :D
anyways, there are 6 × 4 × 5 × 6=720 outfits
Which angle refers to the same angle as DOF?
Answer:
LKS
Step-by-step explanation:
just look at them
Answer:
LOJ is also DOL they the same
HELO WILL GIVE BRANLIEST! No links
Answer:
the answer is
[tex] \sqrt{29} [/tex]
#2 Lauren draws a still life picture of a vase of flowers using a scale where 1 inch= 3 inches. In her drawing, the vase is 6.75 inches tall. What is the actual height?
Answer:
20.25
Step-by-step explanation:
6.75 times by 3 is 20.25
Jose has a points card for a movie theater.
• He receives 50 rewards points just for signing up.
• He earns 3.5 points for each visit to the movie theater.
• He needs at least 85 points for a free movie ticket.
Write and solve an inequality which can be used to determine x, the number of visits
Jose can make to earn his first free movie ticket.
Answer:
x ≥ 10
Step-by-step explanation:
Total Points = 50 + 3.5x
Total Points ≥ 85
50 + 3.5x ≥ 85
3.5x ≥ 35
then divide both sides by 3.5
x ≥ 10
40% of an hour is what
Answer:
24 minutes
Step-by-step explanation:
100% = 60 minutes is 100%
So that means that 40% = 24 minutes.
please help me plsssssssssssssss
Answer:
this should help you out
Population Growth
Using the graph, find the value of 7 when x = 7.
a. = 7 c. y = 2.71
b. y = 6.1 d. y = 4.42
Please select the best answer from the choices provided
Answer:
D. y = 4.42
Step-by-step explanation:
I calculated it logically
help me with this question
Explain the cyclin-dependent regulation
cell cycle
Cyclins drive the events of the cell cycle by partnering with a family of enzymes called the cyclin-dependent kinases (Cdks). A lone Cdk is inactive, but the binding of a cyclin activates it, making it a functional enzyme and allowing it to modify target proteins.
hope this helps!
Answer:
Cyclins drive the events of the cell cycle by partnering with a family of enzymes called the cyclin-dependent kinases (Cdks). A lone Cdk is inactive, but the binding of a cyclin activates it, making it a functional enzyme and allowing it to modify target proteins.
Step-by-step explanation:
How many kilometers long is the perimeter of a square whose area is 25 square kilometers? (A.5) (B.20) (C.10) (D.25)
Answer:d
Step-by-step explanation:
Which TWO scenarios can be represented by a ratio of 4 : 5?
I NEED AN ANSWER ASAP PLEASE
The two scenarios that can be represented by a ratio 4:5 are
1. The ratio of fiction books to the non fiction books, if there are 4 fiction books to 5 non fiction books
2. The ratio of marker to crayon , if there are 4 markers and 5 crayons. ( option A and D)
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
For a scenario that will give ratio of 4:5, it means the first entity will be 4 and the second entity will be 5.
Therefore the two statements that obey this in the option are
1. The ratio of fiction books to the non fiction books, if there are 4 fiction books to 5 non fiction books
2. The ratio of marker to crayon , if there are 4 markers and 5 crayons.
learn more about ratio from
https://brainly.com/question/2328454
#SPJ1
pls help me ☺️!!!!!!!
Let p be the statement "He is tall" and let q be the statement the following statements in symbolic form using p and q. He is handsome". Write each of /1/ He is tall and handsome. /2/ He is tall but not handsome. /3/ He is false that he is short or handsome. /4/ He is neither tall nor handsome. /5/ He is tall, or he is short and handsome /6/ It is not true that he is short or not handsome
On solving the provided question we can say that by logarithm the statement is true he is short.
what is logarithm?The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).
He is tall, or he is short and handsome
It is not true that he is short or not handsome
by logarithm,
the statement is true he is short.
To know more about logarithm visit:
https://brainly.com/question/30085872
#SPJ1
Can someone help me with my last question for my hw plz
answer:
-4
explanation:
when reflected the a will be at -2 in the third quadrant, when moved 2 units to the left you get the y coordinate of -4
hope this helped!
Jason spends no more than 20% of the money he earns at his job each week. He earns $80 each week for 4 weeks. Write an inequality that describes the total amount that Jason spends during this 4-week period.
9514 1404 393
Answer:
s ≤ 4(0.20×80)
Step-by-step explanation:
The maximum Jason spends each week is 0.20 × $80. Then the amount (s) he spends in 4 weeks will be less than or equal to 4 times this product.
s ≤ 4(0.20×80)
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
4.5
Step-by-step explanation:
Answer:
[tex]\sqrt{20}[/tex], calculate this further on calculator if necessary
Step-by-step explanation:
The Pythagorean Theorem states that [tex]a^2 +b^2=c^2[/tex]
Plugged in, we get [tex]2^2+4^2=c^2[/tex]
4 + 16 = c^2
20 = c^2
c = [tex]\sqrt{20}[/tex]
What is the first step in solving this equation ? y + 7 = 18
Answer:
subtract 7
Step-by-step explanation:
y+7=18
You need to get the y by itself, so you subtract 7 to cancel it out.
y+7=18
-7 -7
y=11
---
hope it helps
this isn’t a question but i just wanted to tell everyone you all are doing great. this year has been hard and everyone is working as hard as they mentally can. i’m so proud of all of you. don’t forget to take breaks and rest.
Thank you so much friend.
I think a advantage of this will be that we will be able to tell our grandchildren about how we survived the pandemic, just like our grandparents talk about World War. Lol.
Evaluate -3x³-4x for x = -1.
A)-1
B)7
C)1
Answer:
B) 7
Step-by-step explanation:
-3x³-4x =
-3(-1)³-4(-1) =
-3(-1)+4=
3+4 =7