Condensation of left-hand side of the given expression into a single logarithm is :log(4) + log(2) + log(y) = log(8y)
How to condense log?To evaluate logarithmic expressions, methods for condensing logarithms in order to rewrite multiple logarithmic terms into one can be used. it is a useful tool for the simplification of logarithmic terms. To condense logarithms we use the rules of logarithms: the product rule, the quotient rule and the power rule.
According to the product laws of logarithm,
log x+log y = log (xy)
For the given expression,
log(4) + log(2) + log(y) = log(____)
So, after applying the product rule:
log(4) + log(2) + log(y) = log(4×2×y)
log(4) + log(2) + log(y) = log(8y)
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A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than or equal to 10? Express your answer as a fraction or a decimal number rounded to four decimal places.
The probability of rolling a sum greater than or equal to 10 in rolling dice will be 1/6 or 0.1667.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
A standard pair of six-sided dice is rolled.
Since, All the possible outcomes are;
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6, 1), (6, 2), (6, 3), (6, 4), (6,5), (6,6).
So, Total possible outcomes = 6 x 6 = 36
Now, The favorable outcomes which has sum greater than or equal to 10 are;
(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)
So, Number of favorable outcomes = 6
Thus, The probability of rolling a sum greater than or equal to 10 in rolling dice
= 6/36 = 1/6 = 0.1667
Therefore, The probability of rolling a sum greater than or equal to 10 in rolling dice will be 1/6 or 0.1667.
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Which table shows a relationship with a constant rate of change of 9?
Option C
Explanations:The rate of change is given by the equation:
[tex]\text{Rate of change = }\frac{\triangle y}{\triangle x}[/tex]For the rate of change to be constant, Δy / Δx must be the same for all parts of the table.
In table A, the constant rate of change is (9-9)/(4-2) = 0
In table B, the constant rate of change is (13-11)/(4-2) = 2/2 = 1
In table C, the constant rate of change is (36-18)/(4-2) = 18/2 = 9
In table D, the constant rate of change is (10-9) / (4-2) = 1/2
Only table C has a constant rate of change of 9
The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "RightArrow." For example: P(0, 0) RightArrow P′(1, 2).
Triangle ABC has coordinates
A
(
1
,
4
)
;
B
(
3
,
−
2
)
;
and
C
(
4
,
2
)
.
Find the coordinates of the image
A
'
B
'
C
'
after a reflection over the x-axis.
Answer:
Step-by-step explanation:
Given:
Vertices of triangle ABC are A (1,4), B(3,−2) and C(4,2).
Triangle ABC reflected over the x-axis to get the triangle A'B'C'.
To find:
The coordinates of the image A'B'C'.
Solution:
If a figure reflected over the x-axis, then rule of transformation is
Now, using this rule, we get
Therefore, the coordinates of the image A'B'C' after a reflection over the x-axis are A'(1,-4), B'(3,2) and C'(4,-2).
25 less than 4 times a number is 63. What is the number?
The number is 22
What is a number?
A number is a mathematical entity that may be used to count, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original instances. Number words can be used to represent numbers in language. Individual numbers can be represented more generically by symbols known as numerals; for example, "5" is a numeral that represents the number five. Because only a small number of symbols can be memorized, fundamental numerals are often structured in a numeral system, which is a systematic method of representing any number. The most prevalent numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of 10 fundamental numeric symbols known as digits.
4n - 25 = 63
or, 4n = 63 + 25
or, n = 88/4 = 22
Hence, the number is 22
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A sheriff patrols several neighborhoods in her patrol car it requires 3/15 of an hour to patrol an entire neighborhood how many neighborhoods can the sheriff patrol in 5/8 of an hour
Based on the time it takes to patrol one neighborhood, the number of neighborhoods that the sheriff can patrol in 5/8 of an hour is 3.125 neighborhoods
How to find the number of neighborhoods?The number of neighborhoods that the sheriff can patrol in 5/8 hours depends on the number of hours that it takes the sheriff to patrol one neighborhood.
The number of neighborhoods she can patrol can therefore be found by the formula:
= Number of hours sheriff has / Number of hours required to patrol one neighborhood
= 5/8 ÷ 3/15
= 5/8 x 15/ 3
= 75 / 24
= 3.125 neighborhoods
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im having a little trouble understanding the commutative property and closure property, not a specific problem just would like a small explanation thanks!
Commutative property:
For addition and multiplication if you change the order of the addernds or factor is doesn't change the sum or multiplication.
Example:
Addition
[tex]\begin{gathered} a\pm b=b\pm a \\ \\ 5+3=3+5 \\ 8=8 \end{gathered}[/tex]Multiplication:
[tex]\begin{gathered} a\times b=b\times a \\ \\ 5\times3=3\times5 \\ 15=15 \end{gathered}[/tex]Closure property:
When you add or subtract any two intergers, the result will always be an interger.
Example:
[tex]\begin{gathered} a+b=c \\ \\ a,b,c\text{ are intergers} \\ \\ 8+13=21 \\ \end{gathered}[/tex]8, 13 and 21 are intergers
please help me i need it asp
The solution of the system of equation is as follows:
x = 10 / 7y = - 5How to solve system of equation?The system of equation can be solved as follows:
6x + 4y = 10
-7x - 3y = 5
Hence, let's multiply equation(i) by 3 and multiply equation(ii) by 4
Therefore,
18x + 12y = 30
-28x - 12y = 20
add equation(ii) to equation(ii)
-10x = 50
y = 50 / -10
y = -5
Hence,
-7x - 3y = 5
-7x - 3(-5) = 5
-7x + 15 = 5
-7x = 5 - 15
-7x = - 10
x = 10 / 7
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What are the degree and leading coefficient of the polynomial?Y^3+8y+12y^5-6
Solution
- The question asks us for the leading coefficient of the following polynomial
[tex]y^3+8y+12y^5-6[/tex]Explanation
Leading Coefficient:
- The Leading Coefficient is defined as the number multiplying the variable with the highest degree or exponent.
- In the case of this question, the variable is "y".
- The y-variable with the highest power is "y⁵", thus, the Leading coefficient is the number multiplying "y⁵". In this case, that number is 12.
- Thus, the Leading Coefficient is 12
Degree of the Polynomial:
- The degree of a polynomial is the highest power of the variable in the polynomial.
- This variable with the highest number is usually multiplying the Leading Coefficient.
- Thus, the Degree of the Polynomial is 5.
Final Answer
- The Leading Coefficient is 12.
- The Degree of the Polynomial is 5.
What is Pythagoras Theorem? What is the formula for the same?
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem can be expressed as, c2 = a2 + b2; where 'c' is the hypotenuse and 'a' and 'b' are the two legs of the triangle.
Answer:
Pythagoras theorem is a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
The Pythagoras theorem equation is expressed as,
c²=a²+b²
where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two angles(opposite and adjacent)
Step-by-step explanation:
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Find the volume of this cone. Use 3 for TT. V = 7 r26 3 8ft V [?]ft V 1 6ft Enter SRI nhte. Das
The diameter of the cone is d = 6 ft.
The height of cone is h = 8 ft.
Determine the radius of cone.
[tex]\begin{gathered} r=\frac{d}{2} \\ =\frac{6}{2} \\ =3 \end{gathered}[/tex]Determine the volume of cone.
[tex]\begin{gathered} V=\frac{\pi(3)^28}{3} \\ =\frac{\pi\cdot9\cdot8}{3} \\ =3\cdot3\cdot8 \\ =72 \end{gathered}[/tex]So volume of cone is 72 feet cube.
Answer: 72
Harry HAS 1 1/2 KG whole-wheat flour. He uses 3/4 of the flour to bake bread. How much flour did he use?
Given the following parameter
Mass of flour wheat flour = 1 1/2 kg
If Harry used 3/4 of these flour to bake bread, the amount of flour used is expressed as:
[tex]A=\frac{3}{4}\text{ of 1}\frac{1}{2}[/tex]Convert the mixed fraction into an improper fraction to have:
[tex]\begin{gathered} A=\frac{3}{4}\times\frac{3}{2}kg \\ A=\frac{9}{8}kg \\ A=1\frac{1}{8}kg \end{gathered}[/tex]This shows that Harry used 1 1/8kg of the wheat flour to bake the bread
In the figure, CA and CE are opposite rays, CH bisects
Which of the following are linear pairs involving point F? Select all that apply.
last choices are
e)
f)
pls help im crying
The angles that form a linear pair involving point F are:
a. ∠DFC and ∠CFG
d. ∠HFD and ∠CFD
What is the Definition of a Linear Pair?A linear pair can be defined as the set of two angles that are adjacent to each other and share a common vertex and a common side, and also lie on a straight line.
Given the image in the question above, we see that:
Angle DFC and angle CFG share a common side FC and a common vertex point F, hence, they are adjacent angles that lie on a straight line, thus, they are a linear pair.
Angle HFD and angle CFD also share a common side FD and a common vertex point F. This makes them adjacent to each other. Also they are on a straight line. Therefore, angle HFD and angle CFD are a linear pair.
Thus, we can conclude that the angles that form a pair of angles that are classified as a linear pair are:
a. Angle DFC and angle CFG
d. Angle HFD and angle CFD
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Kevin measured how many times he arrived to work late if he took subway. the results are provided in the following table. Find the probability that Kevin will arrive on-time tomorrow if he plans to take subway. (round the answer to 2 decimal places)
ANSWER
86.67%
EXPLANATION
We want to find the probability that Kevin will arrive on time if he plans to take the subway.
To find this, we have to divide the number of times that Kevin was on-time by the total number of times that he took the measurement.
We have that out of 30 days that Kevin was on-time on 26 occasions.
Therefore, the probability that Kevin will arrive on-time the next day is:
[tex]\begin{gathered} P(on-\text{time) = }\frac{26}{30}\text{ = }\frac{13}{15} \\ P(on-\text{time) = 86.67\%} \end{gathered}[/tex]That is the answer.
A visitor in a Las Vegas casino lost $200, won $100, and then lost $50. What was the change in the gambler's net worth (how much did the gambler win or lose overall)?
The gambler in a Las Vegas casino lost $150.
According to the question,
We have the following details:
The visitor lost $200 and $50 in a Las Vegas casino.
The visitor won $100.
So, in total, the visitor lost $250 overall.
Now, compare the amount the gambler lost and the gambler won in the casino. So, we notice that the gambler lost more amount.
Now, we will find the total amount lost:
Gambler's net worth = The amount lost - the amount won
Gambler's net worth = $(250-100)
Gambler's net worth = $150
Hence, the gambler lost $150 overall in the casino.
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A note with a face value of $8200 was discounted at If the discount was $200 find the length of the loan in days.
A note with a face value of $8200 was discounted If the discount was $200, the length of the loan in days will be 178 Days.
A loan is when money is lent to another person with the understanding that it would be repaid, along with interest. Before agreeing to provide a borrower with a loan, lenders will take into account the borrower's income, credit score, and degree of debt.
Let us consider the number of days to be 'D'
8200 * 5% * (D / 365) = $200
D = (200 * 365) / (8200 * 0.05)
D = 7300 / 41
D = 178 Days.
Therefore, the loan's duration in days will be 178 Days.
COMPLETE QUESTION: A note with a face value of $8200 was discounted at 5% If the discount was $200 find the length of the loan in days
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(a) Write the number 302.658 correct to 2 decimal places, (b) Write the number 302.658 correct to 2 significant figures.
The given number is,
302.658
to corrct to 2 decimal places,
302.66.
A gardener makes a new circular flower bed. The bed is ten feet in diameter. Calculate the circumference and the area of the circular flower bed.
Answer:
C = 31.4159
A = 78.5398
Step-by-step explanation:
diameter = 10
radius = 5
plug into formula: C = 2π5
A = π * 5²
Write the correct equation for the following statement and then solve for the given number of
miles.
You decide to rent a limo for prom. The rate is $200 plus $5 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
If you travel 45 miles what will be your total bill at the end
of the evening?
Answer:
$425
Step-by-step explanation:
Equation can be written as follows:
c = 200 + 5m
Plug 45 in for m to get this:
c = 200 + 5(45)
Simplify!
c = 200 + 225
c = 425
Hope this helps :)
Neil and Barry each bought a new phone plan. Neil bought a plan that costs $80 for a new phone and $3per minute of talk, text, or data. Barry bought a plan that costs $230 for a new phone and $2 per minuteof talk, text, or data.7. Write an equation to represent eachfriend's phone plan.8. How much will each friend pay if they eachuse 100 minutes?10. How many minutes would it take for bothplans to cost the same amount?chorar the
7.-
Equation for Neil P = 80 + 3m
Equation for Barry P = 230 + 2m
8.-
Neil P = 80 + 3(100)
P = 80 + 300
P = $380
Barry P = 230 + 2(100)
P = 230 + 200
P = $430
10.-
P = 80 + 3m
P = 230 + 2m
80 + 3m = 230 + 2m
3m + 2m = 230 - 80
m = 150
how do I find the first five terms of the geometric sequence?
To find the next term of a geometric sequence, the previous term is multiplied by the common ratio r.
[tex]\begin{gathered} r=\frac{1}{2} \\ a_{1=}20 \\ a_2=20\times\frac{1}{2}=10 \\ a_3=10\times\frac{1}{2}=5 \\ a_4=5\times\frac{1}{2}=\frac{5}{2} \\ a_5=\frac{5}{2}\times\frac{1}{2}=\frac{5}{4} \end{gathered}[/tex]Please help meeeeeeeeeeeeeeee
Answer:
-2 1/4 or 2.25
Step-by-step explanation:
i hope this helped and ita also self explanitory
how much wood is needed to make the circular bottom of a bird house if the diameter of the bottom is 12 inches
We are asked to find out how much wood is needed to make the circular bottom of a birdhouse if the diameter of the bottom is 12 inches.
Recall that the circumference of a circular shape is given by
[tex]C=2\cdot\pi\cdot r[/tex]Where π is a constant and r is the radius.
The radius and diameter of a circle are related as
[tex]r=\frac{D}{2}[/tex]So, the circumference of the circle becomes
[tex]\begin{gathered} C=2\cdot\pi\cdot r \\ C=2\cdot\pi\cdot\frac{D}{2} \\ C=\pi\cdot D \\ C=\pi\cdot12 \\ C=36.7\: in \end{gathered}[/tex]Therefore, 36.7 inches of wood is needed to make the circular bottom of a birdhouse.
Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.
You need a $140,000 loan.
Option 1: a 30-year loan at an APR of 9%.
Option 2: a 15-year loan at an APR of 8.5%
Monthly payments and total loan costs on a 30-year loan at an APR of 9% are 1027.27 and for a 15-year loan at an APR of 8.5% are 1297.82.
Formula to computer the periodic payment for a loan with principal P, periodic interest rate R, and several payments T:
(P × R)([tex](1-(1+r)) ^{-T}[/tex])
Option 1, there are 30×12=360 monthly payments, and the monthly interest rate is 8%÷12.
By applying all the given values P=140000, R= 8%÷12 and T = 360 in P÷([tex](1-(1+r)) ^{-T}[/tex]),
(140000 × (9% ÷ 12))÷(1 - [tex](1 + \frac{9}{12} )^{-360}[/tex] ) = 1027.27
In option 2, there are 12 × 15 = 180 monthly payments, and the monthly interest rate is 7.5% ÷ 12. Applying the formula (P × R)([tex](1-(1+r)) ^{-T}[/tex]), the monthly payment is:
(140000 × (8.5% ÷ 12))÷(1 - [tex](1 + \frac{8.5}{12} )^{-180}[/tex] ) = 1297.82
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A rectangle's base is 5 cm longer than its height. The rectangle's area is 50 cm². Find this rectangle's dimensions.
The rectangle's height is
The rectangle's base is
Answer:
The rectangle's height is 5 cm,The rectangle's base is 10 cm.Step-by-step explanation:
Let the dimensions be:
Base = b, Height = hGivenb = h + 5,A = 50 cm²The area of rectangle is:
A = bh h(h + 5) = 50h² + 5h = 50h² + 5h - 50 = 0h² - 5h + 10h - 50 = 0h(h - 5) + 10(h - 5) = 0(h - 5)(h + 10) = 0h - 5 = 0 and h + 10 = 0h = 5 and h = - 10The second value of h is negative and therefore discarded.
So we get:
h = 5 cm,b = 5 + 5 = 10 cmAbigail and her friend Jaya are going to a carnival that has games and rides. Abigail played 7 games and went on 2 rides and spent a total of $24.75. Jaya played 3 games and went on 6 rides and spent a total of $33.75. Determine the cost of each game and the cost of each ride.
The cost of each game is $2.25.
The cost of each ride is $4.50.
What is the cost of each game and each ride?Here are the system of linear equations that can be derived from the question:
7g + 2r = 24.75 equation 1
3g + 6r = 33.75 equation 2
Where:
g = price of each game r = price of each rideIn order to determine the value of g, multiply equation 1 by 3:
21g + 6r = 74.25 equation 3
Subtract equation 2 from equation 3:
40.50 = 18g
g = 40.50 / 18
g = 2.25
In order to determine the value of r, substitute for g in equation 1 :
7(2.25) + 2r = 24.75
15.75 + 2r = 24.75
2r = 24.75 - 15.75
2r = 9
r = 9 /2
r = 4.50
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Name: Date: Writing Linear Equations from Word Problems (Page 2) 5) You are planning a class pool party and have reserved the pool for $625. It will cost an additional $11 per person for food. Write a linear equation to represent the total cost of the pool party based on the number of people that will attend. a) If 26 people end up coming to the pool party how much will it cost you?
Consider that the reservation costs $625. Moreover, it is necessary to pay additional $11 per person for food. If x is the number of people, it means that it is necessary to pay 11x dollars for x people.
THen, the total cost is $625 plus 11x dollars. If y is the cost of the class pool party, you have the following algebraic equation which expresses the given situation:
y = 11x + 625
If there are 26 people in the party, that is, if x = 26, the cost is:
y = 11(26) + 625
y = 286 + 625
y = 911
Hence, the cost is $911
A word problem made out of the equation 1/4+3-7/8x<-2
The word problem of the expression is "Seven eighths of a number less three and a quarter is less than 2"
How to determine the word problem?The inequality expression is given as
1/4 + 3 - 7/8x < 2
From the above expression, we can see that:
The right-hand side of the inequality is 2 and the inequality symbol is less than
This means that the word problem must end in "less than 2"
Next, we analyse the left-hand side
1/4 + 3 - 7/8x
A statement that represents the above is
Seven eighths of a number less three and a quarter is less than 2
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Conrad has two willow trees in his backyard. The first tree is 4 feet taller than the second one. If the second one is 28 feet tall, what is the height, in feet, of the first tree?
The first tree is 28ft tall, and the second tree is 4 ft higher than the second one. Then we need to add 4ft to the height of the second tree:
[tex]28ft+4ft=32ft[/tex]The heigh of the first tree is 32ft
A scale drawing for an apartment is shown below. In the drawing, 3cm represents 5m.
7,7,3,6
Actual area of the real back yard is 96 [tex]m^{2}[/tex]
[scale]=[drawing]/[real] —-> [real]=[drawing]/[scale]
scale=4 m/3 cm —> 0.75 cm/m
The backyard's measurements in the drawing are 9 x 6 cm.
Determine the backyard's actual dimensions
[Real]=[Drawing]/[Scale] for 9 cm
[real]=[9]/[0.75]——> 12 m
[Real]=[Drawing]/[Scale] for 6 cm
[real]=[6]/[0.75]——> 8 m
The backyard's actual measurements are 8 m × 12 m, and its actual size is 8 * 12 = 96 [tex]m^{2}[/tex].
Therefore the original area of the rectangle is 96 [tex]m^{2}[/tex].
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The complete question is as follows:
Below is a scale representation of a piece of land. In the illustration, 3 cm stands in for 4 m. Find the actual backyard space assuming the back is rectangular?
The Sanchez family had dinner at their favorite restaurant. A 9% salestax was added to their bill. Amy paid the bill with a $10 gift certificateplus $30.60. How much did the family's dinner cost before tax? Roundyour answer to the nearest penny.Hint: Use the equation P+rP=T,where P is the price before tax, r is the sales tax rate, and T is the totalprice, including tax.
The formula indicates how the price of the meal after taxes is calculated.
[tex]T=P+rP[/tex]Where
T is the total price
P is the price without taxes
r is the tax rate, this value is always expressed as a decimal value.
Amy paid a total of $30.60 plus a $10 gift certificate, the total cost of the bill is:
[tex]\begin{gathered} T=30.6+10 \\ T=40.6 \end{gathered}[/tex]To express the tax rate as a decimal value you have to divide the percentage by 100:
[tex]\begin{gathered} r=\frac{9}{100} \\ r=0.09 \end{gathered}[/tex]Replace both values on the formula:
[tex]P+0.09P=40.60[/tex]Now we have established an equation with one unknown "P", to solve the equation for P, the first step is to simplify both terms on the left side of the equation. To do so, add both terms:
[tex]\begin{gathered} P+0.09P=40.60 \\ 1.09P=40.60 \end{gathered}[/tex]Divide both sides by 1.09 to determine the value of P
[tex]\begin{gathered} \frac{1.09P}{1.09}=\frac{40.60}{1.09} \\ P=37.249\approx37.25 \end{gathered}[/tex]The cost of the family's dinner before taxes w