The logarithmic form of the equation a^3 = y is log_a(y) = 3
What is a logarithmic equationA logarithmic equation is an equation that involves the logarithm of one or more variables.
How to convert the expression to a logarithmic formFrom the question, we have the following parameters that can be used in our computation:
a^3 = y
Take the logarithm of both sides of the equation
So, we have
3log(a) = log(y)
Divide both side by log(a)
So, we have
3 = log_a(y)
Rewrte as
log_a(y) = 3
Hence, the equation is (b) 3 = log_a(y)
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The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive given that he or she had the disease.
The probability of getting someone who tested positive, given that he or she had the disease, is 0.9.
What is probability?The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
The probability of getting someone who tested positive, given that he or she had the disease, is equal to the probability that the individual has the disease and tests positive ( P(positive | disease) ).
This can be calculated using the formula P(A|B) = P(A∩B) / P(B)
P(positive | disease) = P(positive ∩ disease) / P(disease)
= 141 / (141+16)
= 0.898
Therefore, the probability of getting someone who tested positive, given that he or she had the disease, is 0.898, which is 0.9.
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What is the length of TR?
Answer:
2x + 30
Step-by-step explanation:
assuming there is no other data
4x + 6 + 24 - 2x =
2x + 30
The shape ABC in the quilt block shown is an isosceles triangle, where AB = AC. The perimeter of the triangle is 27.3 inches. Find the values of x and y. Then, find the length of each side of the triangle. Enter the correct answers in the boxes. AB= BC = AC=
The values of the variables and the side lengths are
(x, y) = (3, 5)AB = AC = 8 and BC = 11.3How to determine the values of the variables and the side lengthsFrom the question, we have the following parameters that can be used in our computation:
AB = AC
Perimeter = 27.3
Using the attached figure, we have
6x - 2y = x + 5
Evaluate
5x = 2y + 5
For the perimeter, we have
AC + AB + BC = 27.3
So, we have
6x - 2y + x + 5 + y + 6.3 = 27.3
Simplify
7x = y + 16
Multiply by 2
14x = 2y + 32
Subtract from 5x = 2y + 5
9x = 27
So, we have
x = 3
This means that
2y + 32 = 14 * 3
2y + 32 = 42
Evaluate
2y = 10
y = 5
For the side lengths, we have
AC + AB + BC = 27.3
So, we have
AC = 6(3) - 2(5) = 8
AB = 3 + 5 = 8
BC = 5 + 6.3 = 11.3
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three numbers m,n,p are in the ratio 3:6:4.which of the following is the value
[tex] \frac{4m - n}{n + 2p} [/tex]
Answer:
the value of (4m-n)/(n+2p) is 3/7.
Step-by-step explanation:
Let's substitute the given ratio in terms of a common multiplier, k:
m = 3k
n = 6k
p = 4k
Now we can substitute these values in the expression:
(4m-n)/(n+2p) = (4(3k) - 6k)/(6k + 2(4k)) = (12k - 6k)/(6k + 8k) = 6k/14k = 3/7
Therefore, the value of (4m-n)/(n+2p) is 3/7.
A spinner is divided into 4 equal sections. The probability of landing on A is 1/4. Brandy spins the spinner 24 times. How many times can she expect the spinner to land on A?
Answer:
6 times
Step-by-step explanation:
24/4 = 6
Examples 1 and 2 1 HOTELS The function y = 100(1.05) represents the cost per night at a hotel that cost $100 when the hotel opened and has been increasing by 5% every year since the hotel opened.
a. Graph the function.
Answer:
The graph of the function y = 100(1.05) is shown below.
b. Calculate the cost of the hotel per night after six years.
The cost of the hotel per night after six years is $130.25. This is calculated by plugging in t = 6 into the equation y = 100(1.05)^t and solving for y.
c. What is the overall cost of 7 nights at the hotel in its sixth year of operation?
The overall cost of 7 nights at the hotel in its sixth year of operation is $910.75. This is calculated by multiplying the cost per night after six years ($130.25) by 7 nights.
2 LEARNING RESOURCES
Discuss the advantages of using online learning resources for students.
One of the main advantages of using online learning resources for students is convenience. Online learning resources can be accessed from virtually any location with an internet connection, allowing students to learn from the comfort of their own homes or from mobile devices when they are on the go. Furthermore, online learning resources reduce the need for students to commute to and from a physical school, meaning that students have more time for their studies, hobbies, and other activities.
Another advantage of online learning resources is adaptability. Online learning resources may be tailored to the needs of each individual student and can easily be adjusted should a student’s needs
The table shows the number of minutes in different numbers of days.
Number of days 4 7 11
Number of minutes 5760 10,080 15,840
Which equation expresses the relationship between the number of days, d, and the number of minutes, m?
Responses
m=d1440
m equals frqaction d over 1440 end fraction
A.m = d + 1440
B.m, = , d, + 1440
C.m = 1440d
D.d = 1440m
Answer:
C. m = 1440d
Step-by-step explanation:
You want to know the equation that represents the relationship between days (d) and minutes (m) given the table of values (d, m) = (4, 5760), (7, 10080), or (11, 15840).
Proportional relationshipOn the off chance you don't already know that the number of days must be multiplied by minutes per day to find the number of minutes (m = 1440d), you can always try the table values in the response choices to see what works:
A. 5760 = 4/1440 . . . . . . nope
B. 5760 = 4 + 1440 . . . . . nope
C. 5760 = 1440·4 . . . . . . . yep
D. 4 = 1440·5760 . . . . . . . nope
The equation that works is m = 1440d.
__
Additional comment
Fractions work the same way with units that they do with numbers. Common factors in numerator and denominator cancel.
[tex]\dfrac{2}{3}\times 3=2\\\\\dfrac{\text{minutes}}{\text{day}}\times \text{days}=\text{minutes}[/tex]
How do l do this??? Please help
Answer:
69
Step-by-step explanation:
69
What is the greatest number of unit cubes that would fit in a rectangular prism that is 12 units tall, 5 units long, and 7 units wide?
A 420
B 84
C 60
D 7
Answer:
A or 420
Step-by-step explanation:
Remember Length x Width x Height. 12 * 5 is 60, then 60 * 7 is 420.
I don't know What 5 + x + 3 simplified is, help me please?
Answer:
5+x+3 simplified is x+8
Step-by-step explanation:
when you simplify something, you combine terms and write it in the simplest way you can. So combine 5 and 3 to get 8, and then the final answer of x+8
Answer: x+8
Step-by-step explanation:
"5 + x + 3" can be simplified by combining the numerical terms, which are 5 and 3, to get 8.
Then, just rewrite the expression as "x + 8." Therefore, "5 + x + 3" simplified is just "x + 8".
Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
The area of the figure is obtained to be approximately 74.1 units².
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The rectangle has the length of 6 units.
The rectangle has the breadth of 10 units.
The semicircle has a diameter of 6 units.
The semicircle has the radius of 3 units.
The formula for area of rectangle is -
Area (r) = l × b
Substitute the values into the equation -
Area (r) = 6 × 10
Area (r) = 60 units²
The formula for area of semicircle is -
Area (r) = πr² / 2
Substitute the values into the equation -
Area (s) = [3.14 × (3)²] / 2
Area (s) = 28.26 / 2
Area (s) = 14.13 units²
The total area of the diagram is -
Total Area = Area (r) + Area (s)
Substitute the values into the equation -
Total Area = 60 + 14.13
Total Area = 74.13 units²
Therefore, the area of the figure is 74.1 units².
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You deposit $1,000 into a bank account. The account pays 3.75% annual interest compounded monthly. Find the balance after 6 years.
Your answer:
O $14,162.62
O 1,471.92
O $1,251.88
O $1,018.90
The answer of the given question based on the compound interest is the balance after 6 years is $14,162.62 (option a).
What is Amount?Amount refers to total value of something, usually in terms of a money. It can also be used in context of a quantity of something, such as an amount of the time or an amount of the material.
formula for the compound interest is :
A = P(1 + r/n)^(nt)
Where,
A = final amount
P = principal amount
r = annual interest rate
n = the number of times interest is to be compounded per year
t = time in years
In this case, we have:
P = $1,000
r = 3.75% = 0.0375 (annual interest rate as a decimal)
n = 12 (monthly compounding)
t = 6 years
Substituting the values into formula, we will get:
A = 1000(1 + 0.0375/12)⁽¹²*⁶⁾
A = $1,4162.62
Therefore, the balance after 6 years is $14,162.62 (option a).
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Assume that the data has a normal distribution and the number of observations is
greater than fifty. Find the critical z value used to test a null hypothesis.
a = 0.05 for a two-tailed test.
O±2.575
O±1.764
O±1.645
O±1.96
-1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.
A null hypothesis is what?A null hypothesis is a statistical hypothesis that presupposes that there is no link between two variables in a population or that there is no meaningful difference between two populations. It serves as the beginning point of a statistical hypothesis test and is typically marked as H0. A null hypothesis serves as a reference point against which the alternative hypothesis may be compared. The alternative hypothesis is accepted if there is sufficient evidence from the data to reject the null hypothesis. The null hypothesis is not rejected if there is insufficient evidence in the data to support it.
Using a significance threshold of 0.05, we may use a conventional normal distribution table or calculator to get the essential z value. The value that corresponds to the 0.025 percentile is the crucial z value (or the 0.975 percentile, depending on the direction of the alternative hypothesis).
The z value for the 0.025 percentile, as determined by a typical normal distribution table, is -1.96.
Hence, -1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.
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Which statement describes the relationships between x and y in these two equations?
y = 25x
y = x + 25
Responses
In y = 25x, the value of y is 25 more than the value of x, and in y = x + 25, the value of y is 25 times the value of x.
In y = 25x and y = x + 25, the value of y is 25 more than the value of x.
In y = 25x and y = x + 25, the value of y is 25 times more than the value of x.
In , y, = 25, x, and , y, = , x , + 25, the value of , y, is 25 times more than the value of , x, .
In y = 25x, the value of y is 25 times the value of x, and in y = x + 25, the value of y is 25 more than the value of x.
That statement that best describes the relationship between x and y in the given equations is: d. In y = 25x, the value of y is 25 times the value of x, and in y = x + 25, the value of y is 25 more than the value of x.
How to Interpret the Linear Relationship Equation?In the equation y = 25x, the value of y is directly proportional to x and is 25 times greater than x. This means that as x increases, y increases by a multiple of 25. For example, if x = 2, then y = 50 (25 x 2), and if x = 4, then y = 100 (25 x 4).
In the equation y = x + 25, the value of y is equal to the value of x plus 25. This means that y is always 25 greater than x, regardless of the value of x. For example, if x = 2, then y = 27 (2 + 25), and if x = 4, then y = 29 (4 + 25).
The answer is option d.
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As time, t, passes the value of an investment is modeled by 푉(푡) = 50(0.9)푡. Which of the following statements is supported by the behavior of V(t)?
The value of the investment modeled by the function V(t) = 50(0.9)^t Decreases at a decreasing rate, starting with an initial value of 50.
We are given the investment value function V(t) = 50(0.9)^t. This function describes the value of an investment over time, t. Let's analyze the behavior of V(t) and find a statement that is supported by this function.
1. The initial value of the investment is V(0) = 50(0.9)^0 = 50(1) = 50. So, the investment starts with a value of 50.
2. The function V(t) contains a term (0.9)^t, which indicates that as time passes, the investment value decreases. This is because 0.9 is between 0 and 1, so raising it to a power of t (as t increases) results in a smaller value.
3. The rate of decrease is not constant, as the function is exponential, not linear. This means the value of the investment decreases at a decreasing rate over time.
Based on the behavior of V(t), the following statement is supported:
As time passes, the value of the investment modeled by the function V(t) = 50(0.9)^t decreases at a decreasing rate, starting with an initial value of 50.
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Anjali borrow 19000 rupees at 6% interest for 2 years at the end of 2 years she pays 15000 rupees and a gold ring to the money lender. What is the value of the gold ring
Answer:
Gold ring = 6180
Step-by-step explanation:
Gold ring = ?
I = prt
= 19000 x 6% x 2
= 2180
Amount to be paid= 19000 + 2180
= 21180
gold ring = 21180 - 15000
= 6180
Divide 14x3 − 21x2 − 7x by −7x.
A) −2x2 + 3x + 1
B) −2x2 + 3x − 1
C) −2x3 − 3x2 − x
D) −2x2 + 3x
Answer:
A
Step-by-step explanation:
simply divide each ter by -7x ..
A city has cone-shaped buildings for storing salt and sand for icy roads. Each
building has a radius of 30 feet and a height of 20 feet. Find the volume of the
building. Use 3.14 for π.
OA. 1884 ft³
OB. 18,840 ft³
OC. 628 ft3
OD. 56,520 ft³
The volume of the building is approximately 18,840 cubic feet.
So the answer is (B) 18,840 ft³
What is volume of cone ?
The volume of a cone is a measure of the amount of space that the cone occupies and can be calculated using the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where V is the volume of the cone, r is the radius of the base of the cone, h is the height of the cone, and π is a mathematical constant approximately equal to 3.14.
According to the question:
The volume V of a cone can be calculated using the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where r is the radius of the base of the cone, h is the height of the cone, and π is a constant approximately equal to 3.14.
In this case, the radius r is 30 feet and the height h is 20 feet. Substituting these values into the formula, we get:
[tex]V = (1/3)\pi (30)^2(20)[/tex]
[tex]V = (1/3)\pi (900)(20)[/tex]
[tex]V = (1/3)(56,520)[/tex]
[tex]V = 18,840[/tex]
Therefore, the volume of the building is approximately 18,840 cubic feet.
So the answer is (B) 18,840 ft³.
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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $11.50. The drama club must make at least $980 from ticket sales to cover the show's costs. Write an inequality that could represent the possible values for the number of student tickets sold, � s, and the number of adult tickets sold, � a, that would satisfy the constraint.
Using inequality, x < 63.33, Student take 62 and adult take 68.
By utilizing the "equal tο" symbοl in mathematics, equatiοns are nοt necessarily balanced οn bοth sides. Sοmetimes it can be abοut a "nοt equal tο" relatiοnship, which denοtes that οne thing is better than οr wοrse than anοther.
A relatiοnship between twο numbers οr οther mathematical expressiοns that yields an unfair cοmparisοn is referred tο as an inequality in mathematics. Certain algebraic mathematical expressiοns are referred tο as inequalities.
The student's ticket sells fοr $5,
adult ticket sells fοr $950,
Tοtal auditοrium = 130,
If x represents the number οf student, then adult = 130 - x,
∴ 5x + 9.5y > 950
insert y = 130 - x5x + 9.5(130 - x) > 950,
5x + 1235 - 9.5 x > 950
x < 63.33
∴ Student take 62 and adult take 68.
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someone help pls i’m confused
Answer:
CF = 12
DE = 23
CD = 23
DF = 23.9
Step-by-step explanation:
We can see that there are 2 right-angled triangles: DEF and CDF with common side FD.
They are right angled triangles because the EF and CF are radii of the circle and these segments intersect the tangents at 90°
The common side DF is the hypotenuse for both triangles
The sides EF and CF are radii of the circle so EF = CF
We have two triangles which have two sides equal and one of the angles equal to the corresponding angle of the other
By the SSA theorem, the two triangles are similar
SSA Theorem
if two sides and an angle not included between them are respectively equal to two sides and an angle of the other then the two triangles are equal
Therefore by the law of similar triangles,
CD = EF
Plugging in the expressions we get
13x - 16 = 4x + 11
Subtract 4x from both sides:
13x - 4x - 16 = 11
9x - 16 = 11
Add 16 to both sides:
9x - 16 + 16 = 11 + 16
9x = 27
x = 27/9 = 3
Therefore
ED = 4x + 11 = 4(3) + 11 = 12 + 11 = 23
and this is equal to CD
Using the Pythagorean theorem for right triangles,
For ΔDEF,
DF² = EF² + DE²
DF² = 12² + 23²
= 144 + 529
= 673
DF = √673
= 25.9422
= 25.9 rounded to the nearest tenth
So the measures of the segments are
CF = 12
DE = 23
CD = 23
DF = 23.9
Sharon paid $32,400 in Social Security taxes over a 25-year period. The total contribution to her account is
The total contribution to Sharon's account over the 25-year period is $64,800.
How to solve
To find the total contribution to Sharon's account, we need to consider both her contribution and her employer's contribution.
Social Security taxes are generally split evenly between the employee and the employer, with each paying half of the tax.
Sharon paid $32,400 in Social Security taxes over the 25-year period, which represents her share (half) of the total Social Security taxes paid.
To find the total contribution to her account, we simply need to double her share to include the employer's contribution:
Total contribution = Sharon's contribution + Employer's contribution
Total contribution = $32,400 + $32,400
Total contribution = $64,800
The total contribution to Sharon's account over the 25-year period is $64,800.
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number that multiplys into -144 ans adds into -10
Answer:
-12 and 2
Step-by-step explanation:
1. Notice that both numbers have to be negative. This means that one number has to be negative, and the number with the largest value has to be negative.
2. Think of numbers that multiply to -144
3. Check and see if they add to -10
4. The only numbers that satisfy this are -12 and 2
HELP ME! PLEASE!! . . .
Step-by-step explanation:
that makes ORQ a right-angled triangle, and we can use Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
OQ is the radius of the circle = OM = LM/2 = 20/2 = 10 cm.
RQ = PQ/2 = 16/2 = 8 cm.
so, our Pythagoras equation looks like :
OQ² = RQ² + OR²
10² = 8² + OR²
100 = 64 + OR²
36 = OR²
OR = 6 cm
RM = OM - OR = 10 - 6 = 4 cm
A video company randomly selected 100 of its subscribers and asked them how many hours of shows they watch per week. Of those surveyed, 45 watch more than 10 hours per week. Based on the data, if the company has 2,500 subscribers, then how many watch more than 10 hours per week?
Answer:
11205 is correct answer
I need help answering this
The first five term of the sequence are -12, -24, -36, -48 and -60.
How to find the value of a sequence?A sequence is an enumerated collection of objects that follows are particular pattern.
The explicit formula of the sequence is aₙ = -12n
where
n = number of termsTherefore, let's find the first five terms of the sequence as follows:
a₁ = -12(1) = -12
a₂ = -12(2) = - 24
a₃ = -12(3) = -36
a₄ = -12(4) = -48
a₅ = -12(5) = - 60
Therefore, the sequence are -12, -24, -36, -48 and -60.
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Type the correct answer in each box. Use numerals instead of words. Consider function g. g ( x ) = { 6 , - 8 ≤ x < - 2 0 , - 2 ≤ x < 4 - 4 , 4 ≤ x < 10 What are the values of the function when x = - 2 and when x = 4 ? g ( - 2 ) = g ( 4 ) =
After addressing the issue at hand, we can state that Therefore, function g(-2) = 0 and g(4) = -4.
what is function?Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.
When x = -2, g(x) = 0.
When x = 4, g(x) = -4.
Therefore, g(-2) = 0 and g(4) = -4.
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The line joiningA(1,4)to B(5,p) has a gradient of 1/2. Find
Answer:
p = 6
Step-by-step explanation:
i need help with the question pls
The area of the region bounded by the curves y = x² + 6x + 9 and y = 4 is 16 ² / ₃ square units.
How to find the area of the region?First, we need to find the points of intersection between the two curves. Set y = x² + 6x + 9 equal to y = 4:
x² + 6x + 9 = 4
Now, solve for x:
x² + 6x + 5 = 0
Factor the quadratic equation:
(x + 5)(x + 1) = 0
This gives us the solutions x = -5 and x = -1. These are the x-coordinates of the points of intersection.
Now, to find the area of the region bounded by the curves, we'll integrate the difference between the two functions with respect to x, from x = -5 to x = -1:
Area = ∫[4 - (x² + 6x + 9)]dx from -5 to -1
Area = ∫[5 - x² - 6x]dx from -5 to -1
Now, integrate:
Area = [5x - (x³/3) - 3x²] from -5 to -1
Plug in the limits:
Area = (5(-1) - (-1)³/3 - 3(-1)²) - (5(-5) - (-5)³/3 - 3(-5)²)
Area = (-5 - 1/3 - 3) - (-25 + 125/3 - 75)
Area = (-8 1/3) - (- 25/3)
Area = 16 ² / ₃ square units
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I need help with this please
Answer: A. Nikko by 2 inches
Step-by-step explanation: Because 82 inches = 6ft 10in, which is 2 inches taller than Ricco.
Billy and Joey collect baseball cards. Billy has 25 more cards than Joey.
Write an expression in simplest form to represent the total number of cards
(c) in both collections.