Answer:in 2 + in a - in b
Step-by-step explanation: edge 2021
The expanded form is ln(2) + ln(a) - ln(b) of the expression ln(2a/b).
What is Expression?An expression is combination of variables, numbers and operators.
Using the properties of logarithms
log(a/b)=loga-logb
we can expand ln(2a/b) as follows:
ln(2a/b) = ln(2a) - ln(b)
Now we use the property log(ab)=loga+logb
ln(2a) = ln(2) + ln(a)
we can substitute this in the above equation:
ln(2a/b) = ln(2) + ln(a) - ln(b)
Therefore, the expanded form of expression ln(2a/b) is ln(2) + ln(a) - ln(b).
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When you think of a multiplication fact that can help you solve a division problem, the quotient of the division will become what part of the multiplication fact?
Answer:
The quotient of the division will become a factor in a multiplication fact.
Step-by-step explanation:
In division there is a relationship between the dividend, divisor, quotient and remainder. The number which we divide is referred to as the dividend. The number by which we divide is called the divisor. The result obtained is known as the quotient. The number left over is called the remainder.
The dividend, divisor, quotient and remainder will help us to verify the answer of division. Add remainder (if there is any) with the product of divisor and quotient. The sum we get should be equal to the dividend.
The quotient of the division will become a factor in a multiplication fact.
For instance,
18 ÷ 3= 6
Where 3 is the divisor, 6 the quotient and 18 the dividend
3 × 6= 18
The quotient of the division 6 is a factor in the multiplication.
On Thursday, Mme Q answered emails from her students for 5/6 hour. On Friday, she increased her time answering emails by 7/12 hour. On Thursday, Mme F answered emails for 1/2 hour. On Friday, Mme F increased the amount of time answering emails by 3/4 hour.Who spent more time answering emails from students on Friday and by how many minutes?
Answer:
Mme Q spent more time answering emails from students by 10 minutes
Step-by-step explanation:
Here we have
Time spent by Mme Q in answering mails on Friday given by
5/6 Hour = 50 minutes and
7/12 Hour = 35 minutes
Total time spent on Friday = 85 Minutes or
5/6 + 7/12 = 17/12 Hours
Time spent by Mme F in answering mails on Friday given by
1/2 Hour = 30 minutes and
3/4 Hour = 45 minutes
Total time spent on Friday by Mme F = 75 Minutes or
1/2 + 3/4 = 5/4 Hours
Therefore, Mme Q spent more time answering emails from students by 85 - 75 = 10 minutes.
what is 4.5 x 10^6 in standard notation
Answer: 4500000
Step-by-step explanation:
10^6 = 1000000
1000000 x 4.5 = 4500000
Answer = 4500000
Answer:
4500000
Step-by-step explanation:
An isosceles triangle ABC has legs of length 24 and a vertex angle that measures 36º . Determine the length of its base, BC , to the nearest tenth.
Answer: [tex]BC=14.8[/tex]
Step-by-step explanation:
By definition, an Isosceles triangle has two equal sides and its opposite angles are congruent.
Observe the figure attached, where the isosceles triangle is divided into two equal right triangles.
So, in this case you need to use the following Trigonometric Identity:
[tex]sin\alpha =\frac{opposite}{hypotenuse}[/tex]
In this case, you can identify that:
[tex]\alpha =\angle BAD=\angle CAD=18\°\\\\opposite=BD=CD=x\\\\hypotenuse=AB=AC=24[/tex]
Substituting values, and solving for "x", you get:
[tex]sin(18\°)=\frac{x}{24}\\\\24*sin(18\°)=x\\\\x=7.416[/tex]
Therefore, the length of BC rounded to nearest tenth, is:
[tex]BC=2(7.416)=14.8[/tex]
I need help I don’t understand this math
Answer:
I dont understand math either
A cone shaped scoop is being used to fill a
cylindrical bucket of water. The scoop and the
bucket have the same height and radius. How
many scoops of water would it take to fill the
bucket 15 times?
Given a cone and a cylinder with the same radius and height, it would take three scoops (cone volumes) to fully fill the cylinder (bucket). So, to fill it 15 times, it would require 45 scoops.
Explanation:To answer this question, it's critical to understand the concept of volume. The formula for the volume of a cone is 1/3πr²h, and the volume of a cylinder is πr²h. Both the cone and the cylinder have the same radius ('r') and height ('h'), thus the cone's volume is a third of the cylinder's. Hence, it would take three scoops to fill the bucket once.
Since we want to fill the bucket 15 times, we multiply 15 by 3, so it would take 45 scoops of water to fill the bucket 15 times.
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Explain whether y = x2 – 1 is a linear equation
Answer:
Step-by-step explanation:
A linear equation looks like any other equation. It is made up of two expressions set equal to each other. A linear equation is special because: It has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction
The given equation y = x² - 1 is not a linear equation.
What is a linear equation?Linear equations are algebraic equations that have only one constant and are only of the first degree.
Is y = x² - 1 is linear equation?We know that linear equations are of the only first-order(linear) term, but since the given equation has the second-order(linear) term.
Hence, the given equation y = x² - 1 is not a linear equation.
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Sammy and his family took a hiking trip to the mountains. They started out with 20 pounds of food. They plan on eating 4 pounds of food each day. Write a. Equation that relates the remaining food supply r to the number d
Answer:
The answer is r = 20 - 4d
Step-by-step explanation:
They started out with 20 pounds of food and consume 4 pounds each day which implies after d number of days, they would have consumed 4d pounds.
Hence, the remaining amount of food (r) = 20 - 4d
What is 5/6 times 11/12 in fraction form
Answer: 55/72
Step-by-step explanation:
Answer:
55/72
Step-by-step explanation:
5/6×11/12
=5 × 11/6 × 12
=55/72
Estimate the number of cell phone subscribers in 2008. Round to the nearest tenth.
Answer:
For this case we have an exponential function of the form:
Where,
A: initial number of subscribers
b: rate of change
x: number of years
Part A:
The equation modeling the problem is given by:
For the year 2008 we have x = 2.
Substituting values:
Part B:
For the year in which the company reaches 278 million we have
Thus, the company reaches 278 million in the year 2009.
Step-by-step explanation:
Find the value of x.
Answer:
x=136
Step-by-step explanation:
The sum of the angles inside a quadrilateral add to 360, so
79+55+110+x=360
Combine like terms
224+x=360
Subtract 224 from both sides
x=136
Distance, one of the four characteristics of mapping rules, refers to _____.
a) the use of ordered numbers such that two is less than three but greater than one
b) the use of numbers used to group or sort responses when no order to the numbers exists
c) the use of a series of numbers in which each number is an equal distance from the next
d) the use of a series of numbers with a unique origin indicated by the number zero
e) the use of a number that is not used again
Answer:
C. the use of a series of numbers in which each number is an equal distance from the next.
Step-by-step explanation:
The four characteristics of mapping rules are:
1. Classification: This is the grouping of data or information based on given criteria.
2. Order: this is the chronological arrangements of numbers.
3. DISTANCE: This is the range or difference between one unit to the other.
4. Origin
Maria wants to plant grass in her backyard. Her backyard is in the shape of a rectangle. Its length is 30 feet and its width is 21 feet. Suppose each pack of seed covers 15 square feet. How many packs of seed will she need to cover the backyard?
Answer: 42
Step-by-step explanation:
30x21=630
630 divided by 15= 42
42x15= 630
Four students collected data for the length of an object.
Student 1 Student 2 Student 3 Student 4
5.5 5.6 7.8 8.1
Which statement correctly describes the students’ data?
Answer:b
Step-by-step explanation:
I took the text
Answer:
b
Step-by-step explanation:
if 85g = 237ml
20g = ?
Answer:
55 13/17
Or, 55.765 g
Step-by-step explanation:
85 : 237
20 : X
X/237 = 20/85
X = 55 13/17
Or, 55.765 g
I need help with this asap
lani and her friends started a dog walking service after school, they want to know how much money they can earn walking diffrent dogs
The amount of money Lani and her friends can earn walking different dogs depends on a number of factors, including:
The number of dogs they walk each day/weekThe length of each walkThe rates they charge per dog/walkThe demand for dog walking services in their area.Here is an example of how to calculate the potential earnings for Lani and her friends:
Number of dogs walked per day/week: Let's say Lani and her friends walk 5 dogs per day, 5 days per week.
Length of each walk: Let's say each walk is 30 minutes long.
Rates charged per dog/walk: Let's say they charge $20 per dog per walk.
Demand for dog walking services: Let's say there is a high demand for dog walking services in their area.
Based on these assumptions, Lani and her friends could earn up to $250 per day and $1,250 per week walking dogs
Of course, these are just estimates. The actual amount of money they earn will depend on the factors listed above.
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"Suppose that an automobile manufacturer advertises that its new hybrid car has a mean gas mileage of 50 miles per gallon. You take a simple random sample of 30 hybrid vehicles and test their gas mileage. You find that in this sample, the average is x = 47 miles per gallon with a standard deviation of s = 5.5 miles per gallon. Does this indicate that the advertiser’s statement is too high, with = 0.1 ?"
Answer:
We conclude that the new hybrid car has a mean gas mileage of less than 50 miles per gallon which means that the advertiser’s statement is too high.
Step-by-step explanation:
We are given that an automobile manufacturer advertises that its new hybrid car has a mean gas mileage of 50 miles per gallon.
A simple random sample of 30 hybrid vehicles is taken and tested their gas mileage. It was found that in this sample, the average is x = 47 miles per gallon with a standard deviation of s = 5.5 miles per gallon.
Let [tex]\mu[/tex] = mean gas mileage of new hybrid car.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 50 miles per gallon {means that the new hybrid car has a mean gas mileage of more than or equal to 50 miles per gallon}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 50 miles per gallon {means that the new hybrid car has a mean gas mileage of less than 50 miles per gallon}
The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average gas mileage = 47 miles per gallon
s = sample standard deviation = 5.5 miles per gallon
n = sample of hybrid vehicles = 30
So, test statistics = [tex]\frac{47-50}{\frac{5.5}{\sqrt{30} } }[/tex] ~ [tex]t_2_9[/tex]
= -2.988
Now at 0.1 significance level, the t table gives critical value of -1.311 at 29 degree of freedom for left-tailed test. Since our test statistics is less than the critical value of t as -1.311 > -2.988, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the new hybrid car has a mean gas mileage of less than 50 miles per gallon which means that the advertiser’s statement is too high.
In circle O, what is MÃE?
84
0
48°
36
96°
120
1689
Answer:
1689 MAE
Step-by-step explanation:
The measure of the arc AE is 120°
We can solve this with the Intersecting Secant Angles Theorem.
That theorem says that:
∠ACE = (mAE - mBD)/2
so
36 = (mAE - 48)/2
so,
mAE - 48 = 72 => mAE = 72 + 48 = 120°
therefore, the measure of the arc AE is 120°
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Which of the following is the definition of a hypothesis?
A. a testable scientific question
B. an interesting question for further research
C. an informed explanation that can be tested
D. a type of experiment that provides information
Answer:
A. a testable scientific question
Answer:
the answer is A beacuse it is a testable dientific questuon
A bag has 2 blue marbles 3 red marbles and 5 white marbles. Which event has a probability greater than 1/5 select three options
Answer:
all
Step-by-step explanation:
all of them has the probability
Select the correct answer.
An elevator at a department store must carry fewer than 17 people at a time. An elevator operator is present in the elevator at all times. If
x customers can travel in the elevator with the elevator operator, which inequality represents this situation?
A X+1 <17
B. x>18
C. x+1<16
D. X<17
E. x+1 >18
Answer:
a
Step-by-step explanation:
3) Mr Peterson bought a case (24 boxes) of fruit juice. One-third of the drinks were
grape and two-thirds were cranberry How many boxes of each flavor did Mr.
Peterson buy?
Answer:
8 grape and 16 cranberry
Step-by-step explanation:
To find this, we need to know what one-third of 24 boxes are; we'd then do 24 divided by 3, which is equal to 8. One-third of them were grape so we know 8 are grape. Cranberry makes up the other two-thirds; two-thirds is equal to one-third times 2. 8 (one-third) times 2 is 16, giving our answer of 16 cranberry.
Answer:
mr peterson bought 8 boxes of grape juice and he bought 16 boxes of cranberry juice
Step-by-step explanation:
(5 × 4) × (16 ÷ 8) × (24 − 22) =
Answer:
= 80
Step-by-step explanation:
(5 × 4) × (16 ÷ 8) × (24 − 22) =
20 * 2 * 2 =
80
If you place a 29-foot ladder against the top of a 20-foot building, how many feet will the bottom of the ladder be from the bottom of the building?
Answer:
Step-by-step explanation:
20
In a triangle, the first angle is 22⁰ and the second angle is 78⁰. What is the measure of the third angle?
Answer:
80°
Step-by-step explanation:
Hello all triangles equal 180 degrees. So, with that being said to solve this you need to do 180-22-78 Which equals 80
Answer:
The third angle is 80 degrees
Step-by-step explanation:
In math, the rule is such that for all triangles, regardless of what kind they are, whether or not the sides are equal or all not equal to each other, the sum of the interior angles must add up to 180 degrees.
The outdoor temperature was 60 degrees at midnight. The temperature went down 3 degrees each hour for the next 4 hours. What was the temperature at 4 AM
The scale drawing can be used to approximate the area of an LCD television. There are 58,000 pixels in the area shown. What is the density of the pixels on the television
answer: 6,628.6
you do 3.5 x 2.5 and get 8.75
then divide 58,000 by 8.75 to get the answer
To calculate the density of pixels on the television, divide the total number of pixels by the actual area of the television screen. Use the scale drawing to find the actual area of the television screen. In this case, the density of pixels on the television is 5.8 pixels per square unit.
Explanation:The density of pixels on the television can be calculated by dividing the total number of pixels by the total area of the television screen. In this case, the total number of pixels is given as 58,000. To find the area of the television screen, we need to use the scale drawing. Let's say the scale factor is 1:100. If we represent the actual area of the television screen as A, and the area shown on the scale drawing as D, we can set up the equation A/D = 1/100. Rearranging the equation, we have A = D * 100. Now we can substitute the value of D, which is the area shown on the scale drawing, into the equation. So, if the area shown on the scale drawing is 100 square units, the actual area of the television screen would be 100 * 100 = 10,000 square units. Finally, we can calculate the density of pixels by dividing the total number of pixels (58,000) by the actual area of the television screen (10,000). The density of pixels on the television is therefore 5.8 pixels per square unit.
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Find the value of x and y in the diagram below.
In this line equation y=3x+9, you find the values of x and y by plugging in different x-values and calculate corresponding y-values. These (x,y) pairs are points on the line which can be represented on the graph.
The subject of this question is Mathematics, specifically equations of a line. Looking at the initial line equation, the form appears to be y = mx + b, where m is the slope and b is the y-intercept. Based on the given information, m is set to 3 and b to 9.
To find values of x and y, you plug different x-values into the equation and solve for y. For example, if x=1, y would be 3×1+9=12. Thus, for x=1, y=12. This applies on this line for all different x-values.
Remember: different values of x will correspond to different values of y. This relation can be represented graphically by plotting these (x,y) pairs on a graph, and drawing a line through them.
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Work out the length X
Answer:
12.1244 or [tex]\sqrt{147}[/tex]
Step-by-step explanation:
Use the Pythagorean Theorem and solve for b^2:
7^2+b^2= 14^2
Simplify:
49+b^2= 196
Subtract 49 from both sides:
49-49+b^2= 196-49
Simplifly:
b^2= 147
Unsquare both sides:
[tex]\sqrt{b} = \sqrt{147}[/tex]