What is the value of the logarithm below? (Round your answer to two decimalplaces.)
Answers
We are asked to solve this logarithm, so, firstly, we factor the number 12 as (4)(3) in order to apply the property that states that the logarithm of a product is the sum of the logarithms. Therefore:
\(\log_4(12)=\log_4((4)(3))\text{ --> }\log_4(4)+\log_4(3)=1+\log_4(3)=1+0.79=1.79\)Therefore, the correct answer is A
Related Questions
It takes a shipping employee 4.25 min to prepare a package for domestic delivery and 6.5 min to prepare a package for international delivery. Let x represent the number of domestic packages. Let y represent the number of international packages. The employee has no more than 1 h to ship packages. The employee must ship more than 10 packages.
Select all correct choices for the inequalities that model these constraints.
4.25x + 6.25y <= 60
y >= 0
4.25x + 6.25y >= 60
x+y < 10
x+y > 10
x >= 0
Answers
The inequality which best represents the given scenario is 4.25x + 6.5y ≤ 60 and x + y > 10 thus options (A) and (E) will be correct.
What is inequality?A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal.
Given the domestic package takes 4.25 min to prepare and x represents the number of domestic packages so
Time is taken for domestic delivery = 4.25x
The international package takes 6.5 min to prepare and y represents the number of international packages so
Time taken for international delivery = 6.5x
4.25x + 6.5x must be not more than 1 hour or 60 mint so
4.25x + 6.5y ≤ 60
And the employee must ship more than 10 packages so
x + y > 10
Hence "The inequality which best represents the given scenario is 4.25x + 6.5y ≤ 60 and x + y > 10".
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Simplify:
2
(
3
x
)
+
(
x
+
10
)
2(3x)+(x+10)
Answers
Answer:
7x+10
Step-by-step explanation:
2x(3x)+1x(x+10)
6x+1x+10
7x+10
Evaluate the expression when c=12 and d=112.
3(14+c2)+2d
Enter your answer as a mixed number in simplest form in the box.
Answers
Answer:
698 or 338
Step-by-step explanation:
3*(14+\(c^{2}\)) +2d
3*(14+\(12^{2}\))+2*112 = 42+3*\(12^{2}\)+224
42+3*144+224 = 42+432+224 = 698
3*(14+12*2)+2*112
3(14+24)+2*112 = 3*38+224 = 114+224 = 338
Answer:Substitute the value of the variable into the expression and simplify.
698
Step-by-step explanation:
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
100°
Step-by-step explanation:
tThe sum of all arc measures that make up that circle is 360 degrees.
QS + RQ + RS = 360
QS = 360 - 120 - 140 = 100
An arc angle is the degree measurement of that angle inside the circle, opposite the arc
m∠R = arc QS = 100°
Answer:
∠ R = 50°
Step-by-step explanation:
the inscribed angle R is half the measure of its intercepted arc QS
the sum of the arcs on a circle is 360° , that is
RQ + QS + SR = 360°
120° + QS + 140° = 360°
QS + 260° = 360° ( subtract 260° from both sides )
QS = 100°
Then
∠ R = \(\frac{1}{2}\) × 100° = 50°
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A family recipe calls for sauce and oregano. The table below shows the parts of sauce to oregano used to make the recipe.
Servings Sauce (cups) Oregano (tsp)
4 8 one half
6
At this rate, how much sauce and oregano will be needed to make 6 servings?
The recipe will need 12 cups of sauce and three fourths teaspoons of oregano for 8 servings.
The recipe will need 12 cups of sauce and 1 teaspoon of oregano for 8 servings.
The recipe will need 10 cups of sauce and 1 teaspoon of oregano for 8 servings.
The recipe will need 10 cups of sauce and three fourths teaspoons of oregano for 8 servings
Answers
The amounts needed to make 6 servings are given as follows:
Sauce: 12 servings.Oregano: 3/4 teaspoons.How to obtain the amounts?The needed amounts to make 6 servings of the recipe are obtained applying the proportions in the context of the problem.
From the first line of the table, we get the amounts of sauce and oregano per serving are follows:
Sauce: 8/4 = 2 cups.Oregano: 0.5/4 = 1/8 teaspoons per serving.Hence the amounts for six servings are given as follows:
Sauce: 6 x 2 = 12 servings.Oregano: 6 x 1/8 = 6/8 = 3/4 teaspoons.More can be learned about proportions at https://brainly.com/question/24372153
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What’s 123988+81937297+81937192827-29283729?
Answers
Answer:
81989970383
Step-by-step explanation:
What is an equation of the line that passes through the points (-8, 5) and (2, 0)?
Answers
Answer:
\(y=-\frac{1}{2}x+1\)
Step-by-step explanation:
The slope of the line is \(\frac{5-0}{-8-2}=-\frac{1}{2}\).
So, the equation is
\(y=-\frac{1}{2}(x-2) \\ \\ y=-\frac{1}{2}x+1\)
As the degrees of freedom increase, the Chi-square distribution
Select one:
a.
becomes more right-skewed.
b.
becomes more left-skewed.
c.
becomes less skewed.
d.
does not change shape.
Answers
As the degrees of freedom increase, the Chi-square distribution becomes less skewed.
Option C is the correct answer.
We have,
The Chi-square distribution is a probability distribution that is commonly used in statistics.
It is often used in hypothesis testing and in constructing confidence intervals for population variances.
The shape of the Chi-square distribution depends on the degrees of freedom (df). The degrees of freedom represent the number of independent pieces of information used to estimate a parameter or make an inference.
When the degrees of freedom are small, such as 1 or 2, the Chi-square distribution is highly skewed to the right.
This means that the distribution has a long tail on the right side and is concentrated toward the lower values.
However, as the degrees of freedom increase, the Chi-square distribution becomes less skewed.
The distribution becomes more symmetrical and approaches a bell shape, similar to the shape of a normal distribution. This means that the values are more evenly spread out and there is less concentration towards the lower values.
Therefore,
As the degrees of freedom increase, the Chi-square distribution becomes less skewed.
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Which symbol correctly relates 23 ? 16 check all that apply
Answers
Answer:
C and E
Step-by-step explanation:
23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.
The following expression gives an approximate value of the total average credit card debt in a u.s. household (in dollars) t years after 1995. 410t+5690 Use this expression to predict what the total average credit card debt was or will be in the year 1998. answer: in the year 1998, the total average credit card debt for a u.s. household will be (or was) ______dollars.
Answers
In the year 1998, the total average credit card debt for a U.S. household was approximately 6920 dollars.
As per the data given in the questions,
We have,
The expression for calculating the approximate value of the total average credit card debt in a u.s. household (in dollars) t years after 1995 is: 410t+5690
So, first we will calculate the value of t
As we have in the year 1998, t = 1998 - 1995 = 3.
So, for determining the value of the total average credit card debt in a u.s. household, we will simply plug in this value into the expression,
Thus, will get it as
410 * 3 + 5690
= 1230 + 5690
= 6920
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Studies have linked cigarette smoking, exposure to radon gas, and exposure to asbestos fibers with lung cancer. The model here shows the cell cycle of a cancerous cell.
According to the information regarding causes of lung cancer and the model of a cancer cell cycle, what statement describes how these risk factors lead to lung cancer?
A) The risk factors increase the size of lung cells.
B) The risk factors increase the size of the genome in the lung cell.
C) The risk factors cause changes to genes that regulate the cell cycle.
D) The risk factors decrease the ability of the affected cell to divide.
Answers
Answer:
The Answer Is (C.
Step-by-step explanation: I took the test :)
Answer:
c) is the true answer
Step-by-step explanation:
We toss a die 1,000 times. How many times do we expect to have the die land on an even number.about 250about 167about 500about 17
Answers
die tossed 1000 times
die goes through numbers 1 - 6
2 - 4 - 6
2 - 4 - 6 is all even numbers
Which means they're three different sides the die can land on to give a even number
If the die was tossed 1000 times, in order to find how many times the die would land on even numbers we have to...
3 / 6 × 1000
3 = the number of sides it could land on
6 = total sides
1000 = how many times the die was rolled
\(\frac{3}{6}\times1000=3\div6=0.5\times1000=500\)Which means the number of times the die would land on a even number would be able 500 times or option C.
Notation: Segment YQand Notation: Segment XP are altitudes to the congruent sides of isosceles triangle WXY.
Select all the true statements.
Answers
Answer:
Isosceles triangle has two equal sides and two congruent bases.
Step-by-step explanation:
Isosceles triangle has three sides out of which two are equal. It has two congruent sides. The angle opposite to base is vertex. The two sides of the triangle are congruent and the angles opposite to these sides are also congruent. It is a special type of triangle which is also called equilateral triangle.
a) Work out the percentage population increase from 2001 to 2011.
Give your answer to 1 decimal place.
Answers
The percentage population increase from 2001 to 2011 is 50%.
To calculate the percentage population increase from 2001 to 2011, you need the population figures for both years. Let's assume the population in 2001 was 100,000 and in 2011 it was 150,000.
The formula to calculate the percentage increase is:
Percentage Increase = ((New Value - Old Value) / Old Value) * 100
Plugging in the values:
Percentage Increase = ((150,000 - 100,000) / 100,000) * 100 = (50,000 / 100,000) * 100 = 0.5 * 100 = 50%
Therefore, the percentage population increase from 2001 to 2011 is 50%.
Please note that the actual population figures for the respective years need to be used in the calculation to obtain an accurate result. The example above is for illustrative purposes.
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In ∆BCD if BC=BD, m<B=(13x-35)°, m<C=(5x-19)°, and m<D=(2x+14)°, find x and the measure of each angle
Answers
Answer:
Value of x = 11 ° , ∠B = 108° ,∠C = 36° ,∠D = 36°
Step-by-step explanation:
Given :
In ΔBCD , BC = BD And ∠B= (13x-35)° , ∠C= (5x-19)° ,∠D=(2x+14)°
To Find :
value of x and ∠D , ∠B and ∠C
Solution:
∵ BC=BD , So ∠C = ∠D
Therefore 5x-19 = 2x+14
3x = 33 , ∴ x=11°
So, ∠B = (13×11) - 35 = 108°
∠C = (5×11)-19 = 36°
∠D= (2×11) +14 =36°
Easy question for easy points.
Answers
Answer:
Multiply 10 and 2 each by 4 and .07. Then add.
Step-by-step explanation:
Answer:
Multiply 10 and 2 each by 4 and .07. Then add.
Step-by-step explanation:
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 5 + 54x − 2x3, [0, 4]
Answers
Answer:
The absolute maximum and minimum of \(f(x) = 5 + 54\cdot x -2\cdot x^{3}\) on \([0,4]\) are 113 and 5.
Step-by-step explanation:
Let be \(f(x) = 5 + 54\cdot x -2\cdot x^{3}\), the first and second derivatives of the function are, respectively:
\(f'=54-6\cdot x^{2}\)
\(f''=-12\cdot x\)
Now, let equalize the first derivative to zero and solve the resulting expression:
\(54-6\cdot x^{2} = 0\)
\(x^{2} = 9\)
\(x =\pm 3\)
According to the given interval, only \(x=3\) is a valid outcome. Lastly, this is evaluated in the second derivative expression:
\(f''=-12\cdot(3)\)
\(f'' = -36\)
\(x = 3\) leads to an absolute maximum.
\(f(3) = 5 + 54\cdot (3) -2\cdot (3)^{3}\)
\(f(3) = 113\)
The absolute minimum is determined by evaluating at each extreme of the interval:
\(x = 0\)
\(f(0) = 5 + 54\cdot (0) -2\cdot (0)^{3}\)
\(f(0) = 5\)
\(x = 4\)
\(f(4) = 5 + 54\cdot (4) -2\cdot (4)^{3}\)
\(f(4) = 93\)
The absolute maximum and minimum of \(f(x) = 5 + 54\cdot x -2\cdot x^{3}\) on \([0,4]\) are 113 and 5.
I will give brainliest!!!!!!!!!!!!!!!!!
Answers
Step-by-step explanation:
1. 82.5-82.5+2x=338.5-82.5
2x= 256
2. 2x divided by 2=256 divided by 2
x=256/2
x= 128
What is the vertical distance between the points C(2, -0.8) D(2,1.2)
Answers
Answer:
2 units
Step-by-step explanation:
vertical distance will be the magnitude of the difference in the 'y' coordinates
| -.8 - 1.2| = 2 units
find the fifth term in the geometric sequence, given the first term and the common ratio. a1=5 and r=-3
a5=?
Answers
Answer:
405Step-by-step explanation:
The nth term of a geometric sequence is given by the formula
\(Tn=ar^n^-^1\)
Given data
first term a1=5 and
common ratio r=-3
n= 5
\(T5= 5*3^5^-^1\\T5= 5*3^4\\T5=5*81\\T5=405\)
The 5th term is 405
Answer:
a) Explicit Formula : aₙ = 3. (-3)ⁿ⁻¹
b) Fifth term : a₅ = 243
Step-by-step explanation:
i did the test
Talwar wants to invest R5800 at simple interest rate of 12,2% per annum. How many years will it take for the money to grow to R26100
Answers
It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.
To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:
Simple Interest = Principal × Rate × Time
Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:
Time = (Amount - Principal) / (Principal × Rate)
Plugging in the values, we have:
Time = (R26,100 - R5,800) / (R5,800 × 0.122)
= R20,300 / R708.6
≈ 28.67 years
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Let F(x) =( 3x/2) - (14/3) for x = 4. What is the value for F(x)
Answers
Answer:
f(4) = 1.4
Step-by-step explanation:
f(x) = (3x/2) - (14/3)
We are given that x = 4
f(4) = (3(4)/2) - (14/3)
f(4) = (12/2) - (14/3)
f(4) = 6 - (14/3)
14/3 as a decimal is 4.6
f(4) = 6 - 4.6
f(4) = 1.4 (approximately)
The population of a city was 10,000 in 2010. The population increase at an annual rate of 2.5% per year. Is the growth model function that represents the population of the city linear?
Answers
Answer:
The growth model that represents the population of this city is not linear--it is exponential:
\(f(t) = 10000( {1.025}^{t} )\)
\(t = 0 \: represents \: 2010\)
Write answer in Simplest Form
Answers
hope this helps
Six students write an exam. The average score obtained on the exam by the group of students is 71%. If the first two students each obtained a mark of 73%, while the next three students each obtained a mark of 68%, what was the mark obtained by the sixth student?
Answers
The first two students obtained a mark of 73%, which gives us a total of 73 + 73 = 146 marks.
The next three students obtained a mark of 68% each, which gives us a total of 68 + 68 + 68 = 204 marks.
The average score obtained by the group is 71%. Since there are six students, the total marks obtained by all six students would be 6 * 71 = 426 marks.
To find the mark obtained by the sixth student, we can subtract the total marks obtained by the first five students from the total marks obtained by all six students: 426 - (146 + 204) = 76 marks.
Therefore, the mark obtained by the sixth student is 76%.
calculeaza aria unui triunghi cu baza de 20 cm si inaltimea corespunzatoare ei de 12 cm
Answers
Answer:
Aria unui triunghi =120 cm²
Step-by-step explanation:
Folosind formula:
Aria unui triunghi = (baza x înălțimea) / 2
A=(20x12)/2
=240/2 cm²
=120 cm²
Aria unui triunghi =120 cm²
Of the 32 students in a class, 18 play the violin, 16 play the piano, and 7 play neither.
a. Represent this in a Venn Diagram and determine how many play both the violin and
piano.
B.find the probability that the student
I.plays the violin but not the piano
ii.does not play the violin
iii.plays the piano but not the violin
Answers
Answer:
(a)9
(b)I. 0.28125
II. 0.46875
III. 0.25
Step-by-step explanation:
There are a total of 32 students, therefore the number of elements in the Universal set, n(U)=32
\(1$8 play the violin, n(V)=18\\16 play the piano, n(P)=16\\ 7 play neither, n(P \cup V)' =7\)
(a)The Venn diagram is attached below.
\(n(U)=n(V)+n(P)-n(V \cap P)+ n(P \cup V)'\\32=18+16+7-n(V \cap P)\\32=41-n(V \cap P)\\n(V \cap P)=41-32\\n(V \cap P)=9\\\)
Therefore, 9 students play both the violin and piano.
(b)
I. Probability that the student plays the violin but not the piano
Number of Students who play violin only =18-x=18-9=9
\(P(V \cap P') = \dfrac{n(V \cap P')}{n(U)}\\= \dfrac{9}{32}\\=0.28125\)
ii.Probability that the student does not play the violin
Number of Students who does not play violin only =17-x+7=17-9+7=15
P(does not play violin only)
\(= \dfrac{15}{32}\\=0.46875\)
iii.Probability that the student plays the piano but not the violin
Number of Students who play piano only =17-x=17-9=8
\(P(V' \cap P) = \dfrac{n(V' \cap P)}{n(U)}\\= \dfrac{8}{32}\\\\=0.25\)
Malcolm has $50 gift card to a local car wash and order is the ultimate car wash each visit is $8.95
Answers
The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.
The correct answer choice is option B.
How much cheaper is the car washes Malcolm orders than the car washes Martha's order?Malcolm's gift card = $50.
Cost Malcolm's car wash per visit = $7
Martha's gift card = $180
Cost Martha's car wash per visit = Difference between gift card balance of first and second visit
= $180 - $160
= $20
How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7
= $13
Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13
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Jessica is going to multiply two mixed numbers. 2 1/5 x 8 1/3 Which BEST describes the product of the two mixed numbers? The product will be less than 1 The product will be greater that 1, but less than both factors The product will be greater than both factors The product will be greater than one factor and less than the other factor.
Answers
Answer:
less than .1 the product
First thing we do is multiply the mixed numbers.
Let 2 1/5 x 8 1/3 = (11/5)(25/3) = 55/3.
Using a calculator, we know that 55/3 = 18.3333333333 or simply 18.33.
Let's now go to the given choices.
1. The product will be less than 1.
This is not true.
2. The product will be greater that 1, but less than both factors.
This is not true.
3. The product will be greater than both factors.
This is true.
4. The product will be greater than one factor and less than the other factor.
This is not true.
Answer: The product will be greater than both factors.
Write an expression for the cost of a drink and popcorn for one person
Answers
Answer:
popcorn is usually around 5 dollars and a drink is 3 so: 5 x 3
Step-by-step explanation:
Answer:
drink (d) + popcorn (p) = total cost