The logarithmic expression given as logₙ(1/63) has its value to be -4.143
How to determine the logarithmic expression?From the question, the given parameters are
logₙ(7) = 1.946
logₙ(9) = 2.197
logₙ(16) = 2.773
The logarithmic expression to calculate is given as
logₙ(1/63)
Express 1/63 as 1/7 * 1/9
So, we have the following representation
logₙ(1/63) = logₙ(1/7 * 1/9)
Apply the product of logarithm
This gives
logₙ(1/63) = logₙ(1/7) + logₙ(1/9)
Apply the exponent of logarithm
This gives
logₙ(1/63) = -logₙ(7) - logₙ(9)
Substitute logₙ(7) = 1.946 and logₙ(9) = 2.197 in logₙ(1/63) = -logₙ(7) - logₙ(9)
logₙ(1/63) = -1.946 - 2.197
Evaluate
logₙ(1/63) = -4.143
Hence, the value of the logarithmic expression is -4.143
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Kyle buys $50,000 of company XYZ's shares, at a share price of
$100. A year later, XYZ's share price is $110, and Kyle sells all his
shares. How many dollars did Kyle's investment gain?
The share Kyle sells worth $55000 and Kyle's gain amount is $5000
Given,
The share bought by Kyle of company XYZ = $50,000
The share price = $100
The share price after an year = $110
We have to find the gain amount by Kyle when Kyle sells all his shares.
Here,
We can apply Unitary method;
100 ⇒ 110
50000 ⇒ x
Compute;
100x = 110 x 50000
x = (110 x 50000) / 100
x = 110 x 500
x = $55000
Now,
Kyle gains,
55000 - 50000 = $5000
That is,
The share Kyle sells worth $55000 and Kyle's gain amount is $5000
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33 is 15 less than k
1: A middle School had a school spirit day
In one class the ratio of students who wore
School colors to the number of students who
Didnt was 8 to 5 Ten students didn't wear school
Colors, Determine the number of students who wore School
Colors.
Answer:
The number of students who wore School colors are 8/13. If, Ratio of students who wore School colors to the number of students who didn't are given.
Define ratio.A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division. A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Given,
Ratio of students who wore School colors to the number of students who didn't
8:5
Total number of student = 13
Number of students who wore school colors = 8/13
The number of students who wore School colors are 8/13. If, Ratio of students who wore School colors to the number of students who didn't are given.
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If q is 2.00 what is the distance from C to A?
Answer: 4.00
Step-by-step explanation:
If the q is 2.00 A to C is double the q. So, 2.00x2= 4.00.
Answer:
AC = 4.00Step-by-step explanation:
Given is a parallelogram.
One of the properties of a parallelogram is its diagonals bisect each other.
It gives us:
AC = 2qAC = 2*2.00 = 4.00Which equation represents a line which is parallel to the line y = -2x - 7?
y = -2x is line parallel to given line.
What is line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that are endlessly stretched in the opposing directions.
Main body:
The slope-intercept form is
y=mx+b, where
m is the slope and b is the y-intercept.
y=mx+b
Using the slope-intercept form, the slope is −2.
m=−2
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
Use the slope −2 and a given point (0,0) to substitute for
x₁ and y₁ in the point-slope form
y−y₁=m(x−x₁)
, which is derived from the slope equation
m=(y₂−y₁)/(x₂−x₁).
y−(0)=−2*(x−(0))
Simplify the equation and keep it in point-slope form.
y+0=−2⋅(x+0)
Solve for y.
y=−2x
Hence y = -2x is line parallel to given line.
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Solve the following simultaneous equations using substitution
Answer:
the answer is 18 lol....
When an object is thrown upward, its height (S), in meters, is given (approximately) by the quadratic equation
S = -5t² + vt + h, where v is the upward initial velocity in meters/second, t is the time of flight in seconds, and h is the
height above level ground from which the object is thrown. Johnny is standing on a platform 16 meters high and
throws a ball straight up as high as he can at a velocity of 16 meters/second. At what time t will the ball hit the
ground?
The ball will strike the ground
seconds after it is thrown.
Check the picture below.
[tex]~~~~~~\textit{initial velocity in meters} \\\\ S = -5t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&16\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&16\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ 0=-5t^2+16t+16\implies 5t^2-16t-16=0 \\\\\\ (5t+4)(t-4)=0\implies t= \begin{cases} -\frac{4}{5}\\\\ 4 ~~ \textit{\LARGE \checkmark} \end{cases}[/tex]
the equation for meters is usually as you see in the picture but for this exercise it got rounded from -4.9 to -5, which is fine.
let's notice that "t" has two values, however the seconds cannot be a negative value, so we dismiss that one.
The ball will strike the ground 4 seconds after it is thrown When an object is thrown upward, its height , in meters, is given by the quadratic equation S = -5t² + vt + h
To find the time at which the ball will hit the ground, we need to determine when the height (S) of the ball becomes zero. At that moment, the ball will be at ground level.
The height (S) of the ball is given by the quadratic equation:
S = -5t² + vt + h
where:
S = height of the ball in meters
t = time of flight in seconds
v = initial velocity in meters/second (upward velocity, so it's positive)
h = height above level ground from which the object is thrown
Given that the initial velocity (v) is 16 meters/second, and the height above the ground (h) is 16 meters, we can substitute these values into the equation:
S = -5t² + 16t + 16
Now, to find the time (t) at which the ball hits the ground, we need to solve for t when S = 0:
0 = -5t² + 16t + 16
This is a quadratic equation in standard form (ax² + bx + c = 0), and we can solve it by factoring or using the quadratic formula. In this case, let's use the quadratic formula:
The quadratic formula is given by:
t = (-b ± √(b² - 4ac)) / 2a
In our case, a = -5, b = 16, and c = 16. Plugging these values into the quadratic formula:
t = (-(16) ± √(16² - 4*(-5)16)) / 2(-5)
t = (-16 ± √(256 + 320)) / -10
t = (-16 ± √576) / -10
Now, find the two possible solutions for t:
t₁ = (-16 + √576) / -10
t₁ = (-16 + 24) / -10
t₁ = 8 / -10
t₁ = -0.8 seconds
t₂ = (-16 - √576) / -10
t₂ = (-16 - 24) / -10
t₂ = -40 / -10
t₂ = 4 seconds
We have two solutions for t: t = -0.8 seconds and t = 4 seconds. However, we can disregard the negative value for time, as time cannot be negative in this context.
So, the ball will strike the ground 4 seconds after it is thrown.
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Write one quadratic equation that forms a graph through the points (−4,2) and (2,2) and has a
maximum value at the vertex.
Explain please
Quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.
Given,
Quadratic equation passes through the points (-4,2) and (2,2)
(x₁, y₁) =(-4,2)
(x₂ ,y₂) = (2,2)
Here,
(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)
⇒(y - 2) / (x + 4) = (2 - 2) / (2 + 4)
⇒ (y-2) / (x+4) =0
⇒y -2 =0
⇒y = 2
Quadratic equation formed from the given points (-4,2) and (2,2) is y =2.
Which represents the horizontal line and does not have any vertex.
Therefore, quadratic equation that passes through the points (-4,2) and (2,2) and a form a graph of horizontal line y =2.
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From ratio proportion for the following using
2 different way
45 members of Glee Club to 30 members of Dance
Club
Answer:
see explanation
Step-by-step explanation:
this can be expressed in ratio form and fractional form , that is
45 : 30 ( divide each part by 15 )
= 3 : 2 ← in simplest form
= [tex]\frac{3}{2}[/tex]
Load the GSS14SSDS-B data set in SPSS and use the frequency procedure to investigate the variability of the respondent's current age (AGE). Click on Analyze, Descriptive Statistics, Frequencies, and then Statistics. Select the appropriate measures of variability.
The level of measurement for the variable AGE is ---
The variance is ---
The standard deviation is ---
The mean is ---
The number of valid responses (n) is ---
Choices:
55.11
48.18,
50.12
1500
Ordinal
18.058
17.073
1490
Nominal
276.584
Interval
291.495
16.054
301.498
Jacob held different part-time jobs during his summer holiday. The table below shows the total money he earned for different amounts of time, in hours.
What type of association will the scatter plot for this data represent between the number of hours worked and the total money earned?
1. A positive nonlinear association
2. A positive linear association
3. A negative nonlinear association
4. A negative linear association
Given the table on the total money earned, the type of association the scatter plot would represent is 2. A positive linear association
What is a positive linear association?When two variables are said to have a positive linear association, it means that they move in the same direction together. When one of them increases, the other increases as well. It also means that they are increasing by a uniform amount. For instance, when one variable increases by 3, the other increases by 6, always.
The hours worked here are increasing as well as the money earned by Jacob. The hours worked is increasing by 1, and the money earned is increasing by 4. This is therefore a positive linear association.
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The measure of the largest angle in a triangle is 110° larger than the sum of the measures of the other two angles. The measure of the smallest angle is three-
quarters the measure of the middle angle. Find the measure of each angle.
Measure of largest. smallest and middle angle of a triangle under given conditions is 145°, 15° and 20° respectively.
What is angle sum property of a triangle?
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
According to the given question:
Let the measure of middle angle = x
The measure of the smallest angle is three-quarters the measure of the middle angle.
∴ Smallest angle = (3/4)x
The measure of the largest angle in a triangle is 110° larger than the sum of the measures of the other two angles.
∴ Largest angle = 110° + x + (3/4)x
Now, by Angle sum property of a triangle
x + (3/4)x + 110° + x + (3/4)x = 180°
On solving for the value of x we get
2x + (3/2)x = 70°
7x = 140°
x = 20°
Therefore,
measure of middle angle x = 20°
measure of smallest angle (3/4)x = 15°
measure of the largest angle 110° + x + (3/4)x = 145°
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Two year ago ernest dorsey purchased a used sports coupe for 8000.00 that is now worth 6000.00 last year he drove it 13569 miles and kept a record od all expenses. His variable costs were gasoline $1589.56 oil changes $245.98 and repairs $548.11 his fix costs were insurance $1105.32 and license $85 find de cost per mile
The cost per mile incurred by Ernest Dorsey for driving the sports coupe for last year was $0.41.
How is the cost per mile derived?The cost per mile is the quotient of the division operation involving the total cost incurred and the driving mileage for the year.
To derive the total cost, add up the value of the car consumed (cost - current value), the annual variable, and fixed costs.
Cost of a used sports coupe last year = $8,000
The current value of the car = $6,000
Used value for the year = $2,000.00 ($8,000 - $2,000)
Yearly variable costs:Gasoline $1,589.56
Oil changes $245.98
Repairs $548.11 $2,383.65
Annual fixed Costs:Insurance $1,105.32
License $85.00 $1,190.32
Total cost for the year = $5,573.97
Driven mileage for the year = 13,569 miles
Cost per mile = $0.41 ($5,573.97/13,569)
Thus, the cost per mile is $0.41.
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Draw the line of reflection that reflects ABC onto A'B'C'.
(3^3*6^6)^-3
what is a simplified version of this
The simplified value of the above expression is 5.00248967e-19
we know,'^' this symbol means by times
[tex]3^{3}[/tex] =27
[tex]6^{6}[/tex] =46,656
27 multiplied by 46,656
[tex]27 \times 46,656 = 1,259,712[/tex]
[tex]1,259,712 ^{-3} = 5.00248967e-19[/tex]
if you want you can apply the BODMAS system here.
it is just a fraction try to simplify it.
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What expression is equivalent to -6(t+9)
-6t -54 is the expression equivalent to-6(t+9)
How determine equivalent expressions?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s)
Given: -6(t+9)
First, clear the parenthesis by using -6 to multiply t and 9:
-6(t+9) = (-6 x t) + (-6 x 9)
= -6t + (-54)
= -6t -54
Therefore, the -6t -54 is equivalent to -6(t+9)
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Carl is making accessories for the soccer team. He uses 773.85 inches of fabric on headbands for 29 players and 4 coaches. He also uses 279.56 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Your answer might be 16.31 inches for each headband and wristband for each player.
---------------------------------------
Hope this helps!
Joke: What has ears but can’t hear a thing?
Answer: A cornfield.
Have a great day and God bless! :D
The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).
Find
(a) the co-ordinates of the mid-point of the line PQ,.
The co-ordinates of the mid-point of the line PQ are (6,4).
From the question, we have
The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).
Mid-point of the line PQ =(10+2)/2 , (12-4)/2
= (6,4).
Midpoint:
A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places. When we know the coordinates of two points, we can apply the midpoint formula to get the midpoint between them. If we know the coordinates of the other endpoint and the midpoint, we can use the midpoint formula to obtain the coordinates of the endpoint as well.
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Simplify: 3√50+ √24 - 2√72
A. 3√6 +2√2
B. 3√9+2√5
C. 3√2+2√6
D. 10√2+2√6
Answer:
Step-by-step explanation:
13+(-3)^2+4(-3)+1- {-10-(-6)}
_________________________
[4+5}/ [4^2-3^2(4-3)-8]+12
15/3=5
Select the correct answer.
Consider the function given below.
f(x) = lx-5l +2
Which of the following statements about the y-values of the graph of the function is true?
A. The y-values are all greater than or equal to 5.
B. The y-values are all greater than or equal to 2.
C. The y-values are all less than or equal to 2.
D. The y-values are all less than or equal to 5.
Step-by-step explanation:
the list of your answer options has a different sequence than the picture.
I assume the picture shows us the correct sequence.
the correct answer is
D : the y-values are all greater than our equal to 2
why ?
because the term in absolute value can only go down to 0 but not below. it is an absolute value after all : it is always positive (minimum 0), no matter what.
so, the minimum value of the function is 0 + 2 = 2. it cannot get lower than this.
A hexagon has exterior angle measures of (7n + 3), (10n-17)°,
(8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
Find the value of n.
Using the sum of exterior angle, the value of n is 11.
In the given question,
A hexagon has exterior angle measures of (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
We have to find the value of n.
As we know that the sum of exterior angle of any polygon is equal to 360°.
As the given measures are (7n + 3), (10n-17), (8n - 16), (4n+17), (-n + 16), and (5n - 6)°.
So we can find the value of n by adding the all measures.
So the expression should be
(7n + 3) + (10n-17) + (8n - 16) + (4n+17) + (-n + 16) + (5n - 6)° = 360°
Simplifying the bracket.
7n + 3 + 10n-17 + 8n - 16 + 4n+17 - n + 16 + 5n - 6 = 360°
Solving the expression by solving the same term
(7n+10n+8n+4n-n+5n)+(3-17-16+17+16-6)= 360°
33n-3 = 360°
Add 3 on both side
33n-3+3 = 360°+3
33n = 357°
Divide by 33 on both side
33/33 n= 363°/33
n = 11
Hence, the value of n is 11.
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A drawer of shirts contains 3 solid red, 2 striped red, 4 solid blue, and 3 striped green. What is the probability of picking a shirt that is red or striped?
The probability of picking a shirt that is red or striped is 2/3.
Given, that a drawer of shirts contains 3 solid red, 2 striped red, 4 solid blue, and 3 striped green.
We have to find the probability of picking a shirt that is red or striped,
P(R ∪ S) = P(R) + P(S) - P(R∩S)
where, R be the event that the shirt is red.
and S be the even that the shirt is striped.
P(R) = 5/12 (as, there are 5 red shirts)
P(S) = 5/12 (as, there are 5 striped shirts)
P(R∩S) = 2/12 (as, there are 5 striped red shirts)
P(R ∪ S) = 5/12 + 5/12 - 2/12
P(R ∪ S) = 8/12
P(R ∪ S) = 2/3
The probability of picking a shirt that is red or striped is 2/3.
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Solve for y 4(7y+x)=4
Answer:
Step-by-step explanation:
y= 1/7 - x/7
Answer:
y = 1/7 - x/7
Step-by-step explanation:
4(7y + x) = 4 Distribute the 4 to 7y and x
28y + 4x = 4 Subtract the 4x on both sides
28y = 4 - 4x To get 'y' by itself divide 28 on both sides
y = 4/28 - 4x/28 You can simplify the 4/28 since 4 goes into 28 7 times
y = 1/7 - x/7
12 ^-3 wasnt at school the week we did negative integers help pls
1/1728 is the value of negative integers .
What in math is an integer?
A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.Three sorts of integers exist: 0 (zero), positive integers (natural numbers), and negative integers (Additive inverse of Natural Numbers)= 12⁻³
= 1/12³
= 1/1728
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Tiffany borrows $8,000 to pay for college. The loan has a 7% interest rate that compounds monthly. She plans to pay off the loan in 15 years. How much will she pay in total?
Tiffany needs to pay $8,084.44 in total.
what is Compound Interest?In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest.
Given:
P= 8000
R= 7%= 0.07
Time= 8 years.
Now, Amount = P[tex](1 + r/n)^{nt[/tex]
Amount = 8000 [tex](1 + 0.07/15)^{12 . 15[/tex]
Amount = 8000 x (1 + 5.8333333333333E-5)
amount = $8,084.44
Hence, Tiffany needs to pay $8,084.44 in total
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The face value of a simple discount note is $17,000. The discount is 4% for 160 days. Calculate the following. a. Amount of interest charged for each note. (Round your answer to the nearest cent.) b. Amount borrower would receive. (Round your answer to the nearest cent.)
The amount of interest to be charged on the note, based on the face value of the note, is $302. 22.
The amount the borrower would receive is $16, 697. 78.
How to find the interest charged?The interest charged on the simple discount note can be found by the formula:
= Face value of note x discount rate x number of days / total days in a year
= 17, 000 x 4% x 160 / 360
= $302. 22
The amount that the borrower would receive is then:
= Face value of note - Interest charged on note
= 17, 000 - 302.22
= $ 16, 697. 78
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if Tn =5n +2 which term will have a value of 52
Answer:
10th term
Step-by-step explanation:
given [tex]T_{n}[/tex] = 5n + 2 and [tex]T_{n}[/tex] = 52 , then equate right sides and solve for n
5n + 2 = 52 ( subtract 2 from both sides )
5n = 50 ( divide both sides by 5 )
n = 10
that is the 10th term has a value of 52
Which of the following is a Rational Number? √11 √14 √77 15
Answer:
1/2
Step-by-step explanation:
HELP!! which expression is equivalent to the given expression 2X^2 -11 X -6
Answer: C.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Can you help me with this problems, thank you.
The probability that student will pass the test is 2/7.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.So, the probability that the student will pass the test:
The total number of questions are 50 and 25 questions need to be correct to pass the test.Out of 25, 15 are correct.Out of the remaining 35 questions, 10 questions need to be right to pass the best.Probability Formula: P(E) = Favourable events/Total events
Now, calculate as follows:
P(E) = Favourable events/Total eventsP(E) =10/35P(E) = 2/7Therefore, the probability that student will pass the test is 2/7.
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