You have the following expression:
log(z) - log(18)
By the properties of logarithms, consider that the subtraction of two logarithms is equal to the logarithm of the quotient of the arguments:
log(z) - log(18) = log(z/18)
Hence, the answer is log(z/18)
If the proportion of the total disposable income spent on consumer goods and services is 91.6 percent and if consumers spend 82.0
percent of each additional dollar, what is
Instructions: Round your responses to three decimal places.
a. the APC?
b. the APS?
c. the MPC?
d. the MPS?
a) The Average Propensity to Consume (APC), rounded to three decimal places, is 0.916.
b) The Average Propensity to Save (APS), rounded to three decimal places, is 0.084.
c) The Marginal Propensity to Consume (MPC), rounded to three decimal places, is 0.820.
d) The Marginal Propensity to Save (MPS), rounded to three decimal places, is 0.180.
What do these economic indexes mean?The average propensity to consume is the ratio of consumption expenditures to the total consumers' disposable income.
The average propensity to save is the inverse of the APC. It shows the rate of or total disposable income reserved instead of being consumed.
The marginal propensity to consume is the ratio of consumption based on additional income.
The marginal propensity to save is the inverse of the MPC, showing the percentage of the additional income saved instead of being consumed.
APC = 91.6%
= 0.916
APS = 1 - APC
= 0.084 (1 - 0.916)
MPC = 82%
= 0.820
MPS = 1 - MPC
= 0.180 (1 - 0.820)
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A boy gets #2.00 per week as pocket money. His sister gets only #1.60 per week
Find the ratio of the boy's allowance to his sister's. If his sister gets 20 k more per week,what will be the new ratio?
The Ratio of the boy's allowance to his sister's is 5 : 4.
The new Ratio is 1 : 10000.
What is definition of ratio?The quotient of two mathematical expressions, 1a. b: the proportion between two or more items in terms of quantity, amount, or size.What does the arithmetic term "ratio" mean?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, if there is 1 boy and 3 girls, you may express the ratio as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.To learn more about :Ratio
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;
Is -36/6 a integer number
Answer:
Yes
Step-by-step explanation:
-36/6 = -6
Integers are the whole numbers (0.1.2.3.4.5....) and their opposites ...-4,-3,-2,-1
which anwser show the best approximation of [tex] \sqrt[]{53} [/tex]1. 7.72. 8.13. 7.34. 7.1
The Solution:
The given number is
[tex]\sqrt[]{53}[/tex]Finding the best approximation for the above number, we have
[tex]\sqrt[]{53}=7.28\approx7.3[/tex]Therefore, the best approximation of the given number is 7.3 (option 3)
7. 200 is the ? th term of 24, 35, 46, 57, ..
200 is the 17th term of the progression
What is arithmetic progression?
Arithmetic progression or arithmetic sequence (AP) is a numerical series in which the difference between subsequent terms is constant. The sequence 5, 7, 9, 11, 13, 15,..., for example, is an arithmetic progression with a common difference of 2. A finite arithmetic progression, or simply an arithmetic progression, is a finite section of an arithmetic progression. An arithmetic series is the sum of a finite arithmetic progression. An arithmetic series is the sum of the elements of a finite arithmetic progression. A closed expression determines the product of the members of a finite arithmetic progression with a beginning element a1, common differences d, and n elements in total.
This can be solved using arithmetic progression
Aₙ = a + (n - 1)d
where, Aₙ = 24, d = 35 - 24 = 11
so, n = (Aₙ - a)/d + 1 = (200-24)/11 + 1 = 17
Hence, 200 is the 17th term of the progression
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I need help with this questionif a certain piece of music is written in 3/4 time, how many eighth notes are required per measure of music?
Solution
For this case we need to take in count that in music 3/4 time can be grouped into 3 groups of 2 eight notes and then the answer for this case would be:
6/8
Point B is located at (-5, -5) on the coordinate plane. Point B is reflected over thex-axis to create point B'. What ordered pair describes the location of B'?
SOLUTION
If a coordinate is refleted over the x-axis, the formula to apply is
[tex](x,y)\rightarrow(x,-y)[/tex]So for B(-5, -5), this becomes
[tex]\begin{gathered} B\mleft(-5,-5\mright)\rightarrow(-5,-(-5) \\ \\ the\text{ answer becomes } \\ \\ B(-5,-5)\rightarrow B^{\prime}(-5,5) \end{gathered}[/tex]I don’t know how to find the median and the mode HELPP
First, let's write the data set in crescent order:
[tex]35,35,44,50,50,50,56,60,65,70,86,90,110[/tex]The mean is given by the sum of all values divided by the number of values:
[tex]\begin{gathered} mean=\frac{35+35+44+50+50+50+56+60+65+70+86+90+110}{13}\\ \\ mean=\frac{801}{13}\\ \\ mean=61.62 \end{gathered}[/tex]The median is given by the central value of the set in crescent order. Since this set has 13 values, the median is the 7th value:
[tex]median=56[/tex]The mode is the value that repeats the most. Looking at the set, the value that repeats the most (three times) is 50, so the mode is 50.
Solve the problems fill in the blanks show you work I NEED HELP!
The fill in the blanks (that uses division) can be filled as -1.2([tex](\frac{2}{5} )[/tex] ÷ -2, -0.48÷-2 and 0.24.
According to the question,
We have the following information:
-1.2 [tex](\frac{2}{5} )[/tex] ÷ -2
Now, we have to solve this problem and fill the blanks at the same time.
Now, the first step would be to write the question.
So, for the first blank we have:
-1.2 [tex](\frac{2}{5} )[/tex] ÷ -2
Now, the required number is (2/5).
Now, the next step is to multiply -1.2 with 2/5:
-2.4/5
-0.48
So, the second blank can be filled by -0.48.
Now, the third step would be to divide -0.48 by -2:
-0.48÷-2
0.24
So, the next blank can be filled by 0.24.
Hence, the numbers in the blanks are [tex]\frac{2}{5}[/tex], -0.48 and 0.24 respectively.
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Why did the turkey volenteer to be the drummer in the popular bird band? only 2.1 section
Answer:
I eat birds tasty
11 to the power of 2
When a number is raised to a power, it simply refers to the number of times that number is multiplied by itself.
Applying that logic here, 11 to the power of 2 is simply
[tex]11\times11[/tex]and the answer is
[tex]=121[/tex]Therefore, 11 to the power of 2 is 121.
How many gallons of gas will Justin need to drive 120 miles? Use a table or proportionas
As you can see, both variables are directly proportional.
Thus, the given line should have the form:
[tex]y=kx[/tex]Where k is the proportionality constant.
To find the number of gallons of gas needed to drive 120 miles, we should find k first.
Notice that we need 1 gallon of gas to drive 25 miles and 2 gallons of gas to drive 50 miles. The rate of change (k) between these variables is:
[tex]\frac{50-25}{2-1}=25\frac{gallons}{\text{mile}}[/tex]This means that it takes 25 gallons to drive each mile.
Now, we could replace:
[tex]\begin{gathered} 120=25x \\ x=\frac{120}{25}=4.8\text{gallons} \end{gathered}[/tex]Therefore, Justin needs 4.8 gallons to drive 120 miles.
What is the answer to this question?
The probability of drawing a blue socks and white socks is 1/12.
Given that, a drawer contains 10 red socks, 6 white socks and 8 blue socks.
What is probability of an event?Probability is a type of ratio where we compare how many times an outcome can occur compared to all possible outcomes.
As we know the probability of an event = Number of favorable outcomes/Total number of outcomes
Total number of outcomes = 10+6+8=24
Probability of getting blue socks = 8/24 = 1/3
Probability of getting white socks = 6/24 =1/4
Now, probability of an event = 1/3 × 1/4 = 1/12
Therefore, the probability of drawing a blue socks and white socks is 1/12.
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Which expression is equal to log(xy / z) ?
The expression that can be said to as equal to log(xy / z) is the expression logx + logy - logz and this can be found out through the logarithmic identities.
What is the basic log function?The “basic” logarithmic function can be seen as the the function, y=logbx, where x, b>0 and b≠1.
What are the 3 types of logarithms?In the kind of complex analysis that we come across three types of logarithms namely ln, log and Log are used.
In mathematics log tends to always mean the natural log.
Log is often seen as the main and principal branch that comes under the complex logarithm.
Why do we use log functions?Logarithmic functions are said as important only largely because of their relationship to the kind of exponential functions. Logarithms can also be used to solve any kind of exponential equations and thus help to explore the properties of exponential functions.
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If translation T maps point A(-3, 1) onto point A'(5, 5),
which is the translation T?
Answer: [tex](x,y) \to (x+8, y+4)[/tex]
==================================================
Explanation:
The x coordinate of A and A' are -3 and 5 respectively.
This is an increase of +8 since -3+8 = 5
Therefore, we shift the preimage 8 units to the right to get the image point.
That explains how x turns into x+8.
-------------
The y coordinates of A and A' are 1 and 5 respectively.
This is an increase of +4, so we shift the preimage up 4 units.
This signals that y turns into y+4
--------------
To recap we found that,
x becomes x+8y becomes y+4Therefore we get to the answer [tex](x,y) \to (x+8, y+4)[/tex]
--------------
To check the answer, let's apply this translation to point A(-3,1) and we should get (5,5) as the result.
[tex](\text{x},\text{y})\to(\text{x}+8,\text{y}+4)\\\\(-3,1)\to(-3+8,1+4)\\\\(-3,1)\to(5,5)\\\\[/tex]
This confirms the answer is correct.
Solve the trigonometric equation for all values 0 ≤ x < 2π.tan x - 1 = 0
The quadrilateral RSTU is inscribed in the circle shown below. S R U Jake wants to prove the theorem that says that the measure of the quadrilateral's opposite angles add to 180°. He knows that the measure of angle Ris half the measure of are STU and that the measure of angle T is half the measure of arc SRU. Which of the following is an appropriate step to prove that ZR + ZT =180°?
Arc STU and arc SRU can form the complete circle. Therefore
[tex]Therefore,[tex]\begin{gathered} 2R+2T=360^0 \\ \text{factorize left hand side} \\ 2(R+T)=360^0 \end{gathered}[/tex]Dividing both sides by 2, we have
[tex]Hence, the appropriate steps are: Assume that the measure of arcs STU and SRU add up to 360 degreesAlso, substitute 2 m
pick yes in options 2 and 3
pick no in options 1 and 4
Give the standard form of the given equation below. If it is a quadratic equation, then give the a, b, and c coefficients. 3x2-2x-5x(x-7)=(x-2)(x+4)+1
Answer:
[tex]\begin{gathered} -3x^2+31x+7=0 \\ a=-3 \\ b=31 \\ c=7 \end{gathered}[/tex]Step-by-step explanation:
The quadratic equation in standard form is represented by:
[tex]ax^2+bx+c=0[/tex]For the following equation;
[tex]\begin{gathered} 3x^2-2x-5x(x-7)=(x-2)(x+4)+1 \\ 3x^2-2x-5x^2+35x=x^2+4x-2x-8+1 \\ -2x^2-2x+35x=x^2+2x-7 \end{gathered}[/tex]Compute all the terms on the left side, equalizing 0:
[tex]\begin{gathered} -3x^2+31x+7=0 \\ \text{Then, the a,b and c coefficeints would be:} \\ a=-3 \\ b=31 \\ c=7 \end{gathered}[/tex]how do I put 5/7-i in standard form?
To put
[tex]\frac{5}{7-i}[/tex]In the standard form, we must multiply the numerator and denominator by the complex conjugate of (7-i), it means
[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}[/tex]And now we solve it, therefore
[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}=\frac{5(7+i)}{7^2-i^2}[/tex]Remember that
[tex]i^2=-1[/tex]Then
[tex]\begin{gathered} \frac{5(7+i)}{7^2-i^2}=\frac{5(7+i)}{49+1} \\ \\ \frac{5(7+i)}{49+1}=\frac{5(7+i)}{50} \end{gathered}[/tex]Now we can simplify it
[tex]\frac{5(7+i)}{50}=\frac{7+i}{10}[/tex]And we have it in the standard form
[tex]\frac{7}{10}+\frac{1}{10}i[/tex]Find the volume of the following triangular prism. *15 points5 in6,1 in13 in7 in215.5 cubic inches220.5 cubic inches225.5 cubic inches227.5 cubic inches
Given:
The length of the base of the triangular base of the prism, b=7 in.
The altitude of the triangular base, l=5 in.
The height of the prism, h=13 in.
Now, the volume of the prism can be calculated as,
[tex]\begin{gathered} V=\text{ Base Area}\times height \\ =\frac{1}{2}bl\times h \\ =\frac{1}{2}\times7\times5\times13 \\ =227.5\text{ cu. in} \end{gathered}[/tex]Therefore, the volume of the triangular prism is 227.5 cu. in.
please help me work through this if you can, thank you!
Given:
[tex]C=\frac{x^4}{4}-\frac{4}{3}x^3-\frac{35}{2}x^2+150x[/tex]Let's solve for the following:
• (a). Find C'(x).
Here, we are to find the derivative of C(x).
Apply the sum rule:
[tex]\begin{gathered} C^{\prime}=\frac{d}{dx}(\frac{x^4}{4})+\frac{d}{dx}(-\frac{4}{3}x^3)+\frac{d}{dx}(-\frac{35}{2}x^2)+\frac{d}{dx}(150x) \\ \\ C^{\prime}=x^3-4x^2-35x+150 \end{gathered}[/tex]• (b). The critical numbers of C(x).
The critical numbers will be the points where the graph changes direction.
Using the derivative, let's solve for x.
[tex]x^3-4x^2-35x+150=0[/tex]Factor the left side using the rational root test:
[tex](x-5)(x^2+x-30)=0[/tex]Now factor using the AC method:
[tex]\begin{gathered} (x-5)((x-5)(x+6))=0 \\ \\ (x-5)(x-5)(x+6)=0 \end{gathered}[/tex]Equate each factor to zero and solve for x:
[tex]\begin{gathered} x-5=0 \\ \text{ Add 5 to both sides:} \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x-5=0 \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x+6=0 \\ x+6-6=0-6 \\ x=-6 \end{gathered}[/tex]Therefore, the critical numbers of C(x) are:
x = -6, 5
• (C). Increasing interval.
Use the critical points to find the increasing and decreasing intervals.
Using interval notation, the increasing interval is:
[tex](-6,5)\cup(5,\infty)[/tex]• D. Decreasing interval:
Using interval notation, the decreasing interval is:
[tex](-\infty,-6)[/tex]ANSWER:
(a). C'(x) = x³ - 4x² - 35x + 150
(b). x = -6, 5
(c). Increasing: (-6, 5) U (5,∞)
Decreasing: (-∞, -6)
111 pointFind cot(1.570/7.3). Round to 3 decimal places.Type your answer...
An air traffic controller spots two planes flying at the same altitude. Their flight paths form a right angle at point P. One plane is 150 miles from point P and is moving at 440 miles per hour. The other plane is 200 miles from point P and is moving at 440 miles per hour. Write the distance s between the planes as a function of time t.
The distance s as a function of time is s = 50√(162t² -126t +25)
Take miles and hours to be the problem's units.
The distance of the first plane from point p is provided by
x = 150 -450t
The distance of the second plane from point p is given by
y = 200 -450t
The Pythagorean theorem can be used to calculate the distance between them because their flight trajectories are at right angles (s).
s² = x² + y²
s² = (150 -450t) (150 -450t)
² + (200 -450t)² = 22500 -135000t +202500t² +40000 -180000t +202500t²
... s² = 40500t² -315000t +62500 = 2500(162t² -126t +25)
... s = 50√(162t² -126t +25)
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(a) Describe in words a sequence of transformations that maps AABC to
AA"B"C".
(b) Write an ordered-pair rule for each transformation in the sequence.
Answer:
(x, y) ⇒ (-x, -y) . . . . . . . reflection across the origin(x, y) ⇒ (x +3, y +1) . . . translation 3 right a 1 upStep-by-step explanation:
You want a sequence of transformations that maps ∆ABC to ∆A'B'C' where the vertices are A(-5, 3), B(-2, 3), C(-4, 1), A'(8, -2), B'(5, -2), and C'(7, 0).
Orientation and scalingSegment AB is a 3-unit line segment directed to the right. Segment A'B' is a 3-unit line segment directed to the left. This means there is no dilation involved in the transformation. At least, the figure has been reflected left-to-right.
Point C is below segment AB, while point C' is above segment A'B'. This means the figure has also been reflected top-to-bottom.
Together these reflections can be accomplished by either of reflection across the origin, or rotation 180° about the origin.
TranslationThe reflected figure would leave A' at (5, -3). Its location at (8, -2) means the figure has also been translated to the right and up.
Translation to the right has been by 8 -5 = 3 units.
Translation up has been by -2 -(-3) = 1 unit.
(a) Description of transformationsTriangle ABC can be transformed to triangle A'B'C' by ...
reflection across the origintranslation 3 units right and 1 unit up(b) Transformation rulesThe corresponding ordered-pair rules for these transformations are ...
reflection: (x, y) ⇒ (-x, -y)translation: (x, y) ⇒ (x +3, y +1)__
Additional comment
The single transformation that will accomplish the mapping is ...
(x, y) ⇒ (3 -x, 1 -y) . . . . . reflection across the point (3/2, 1/2)
Need some guidance and reassurance because I am not getting full points on my homework. Thanks.
Given the parent function:
[tex]y=x^3[/tex]If y is shifted right by 7 units, we obtain:
[tex]Option\text{ D: }y=(x-7)^3[/tex]If y is compressed horizontally by a factor of 7, we have:
[tex]Option\; E\colon y=(7x)^3=7^3x^3[/tex]If y is stretched vertically by the factor 7, we obtain:
[tex]\text{Option H: }y=7x^3[/tex]A shift downwards by 7 units gives:
[tex]\text{Option A: }y=x^3-7[/tex]Which of the following hypotheses is not a valid null hypothesis?a.H0: µ = 0b.H0: µ ≥ 0c.H0: µ ≤ 0d.H0: µ < 0
Given:
a. H0: µ = 0
b. H0: µ ≥ 0
c. H0: µ ≤ 0
d. H0: µ
Required:
To choose the hypotheses that is not valid.
Explanation:
The null hypothesis: It is a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
Here the option d is not valid.
Final Answer:
The option d is not valid.
H0: µ < 0
The investment you make into a start-up company is also known as ____.
The investment you make into a start-up company is also known as Venture capital.
Answer: Venture capital
. Which units can be used to measure distance?
A. seconds
B. cubic centimeters
C. meters
D. liters
Answer:
c
Step-by-step explanation:
The metre or meter, symbol m, is the primary unit of length in the International System of Units, though its prefixed forms are also used relatively frequently.
Find the solution.7 · x = 8412139177
We need to find the value for x using the inverse operation:
Then:
[tex]\begin{gathered} 7-x=84 \\ \end{gathered}[/tex]Let us solve for x:
The x is subtracting, so it will add up to the other side:
[tex]7=84+x[/tex]Now, the 84 is positive, so it will be negative on the other side:
[tex]\begin{gathered} 7-84=x \\ x=-77 \end{gathered}[/tex]Hence, the solution for x is -77.
What is 3+2? and add 7 then subtract 4
the answer is 8
add 3+2, that gives u 5, add 7+5 which is 12, do 12-4 its equal to 8