The correct answer is option C: Laura determines the four arithmetic means to be −7.2, 2.8, 12.6, and 22.2.
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.
To determine the arithmetic means between two numbers, we need to find the common difference between each pair of consecutive means. The common difference is given by:
Common difference = (larger number - smaller number) / (number of means + 1)
In this case, the larger number is 32 and the smaller number is -17. Laura wants to find four means, so the number of means is 4. Therefore, the common difference is:
Common difference = (32 - (-17)) / (4 + 1) = 49 / 5 = 9.8
To find the four arithmetic means, we start with the smaller number and add the common difference successively. Therefore, the four arithmetic means are:
-17 + 9.8 = -7.2
-7.2 + 9.8 = 2.6
2.6 + 9.8 = 12.4
12.4 + 9.8 = 22.2
Therefore, the correct answer is option C: Laura determines the four arithmetic means to be −7.2, 2.8, 12.6, and 22.2.
To learn more about arithmetic sequence from the given link:
https://brainly.com/question/15412619
#SPJ1
help pleaseee
A population of bacteria is growing according to the equation p(t)=1100e^0.12t
Use a graphing calculator to estimate when the population will exceed 2458.
t= -------------
The population will exceed 2458 after approximately 10.1465 units of time, where the time unit depends on the context of the problem (e.g., hours, days, etc.).
What is equation?A statement proving the equality of two expressions is known as an equation. It can include variables, integers, and mathematical operations like addition, subtraction, multiplication, and division. It also incorporates mathematical symbols. In mathematics and science, equations are frequently used to illustrate connections between quantities. The equals sign (=) is typically used in equations to denote that the expressions on each side of the sign have the same value. For instance, the formula 2 + 3 = 5 demonstrates that the total of 2 and 3 equals 5. Equations can be solved to determine a variable's value or to determine if a certain value meets the connection that the equation describes.
To estimate when the population will exceed 2458, we can set up an inequality using the equation for the population growth:
p(t) > 2458
Substituting the given equation for p(t), we get:
[tex]1100e^0.12t[/tex] > 2458
Dividing both sides by 1100, we get:
[tex]e^0.12t > 2.23545[/tex]
Taking the natural logarithm of both sides, we get:
0.12t > ln(2.23545)
Solving for t, we get:
t > ln(2.23545)/0.12
Using a graphing calculator to evaluate this expression, we get:
t > 10.1465
Therefore, the population will exceed 2458 after approximately 10.1465 units of time, where the time unit depends on the context of the problem (e.g., hours, days, etc.).
To know more about equation:
brainly.com/question/29018878
#SPJ1
a jewllery shop is having a sale
The original price of the bracelet was £1400.
What do you mean by Percentage ?Percentage is a way of expressing a proportion or a fraction as a part of 100. It is denoted using the symbol "%". For example, 50% means 50 out of 100, or half, while 25% means 25 out of 100, or one-quarter.
We can start by using the information given to set up an equation that relates the original price of the bracelet with the sale price and the percentage reduction:
original price x (100% - 70%) = sale price
Simplifying the percentage reduction:
original price x 30% = sale price
Substituting the given sale price (£420):
original price x 30% = £420
To solve for the original price, we need to isolate it on one side of the equation. We can do this by dividing both sides by 30% (which is the same as multiplying by 100/30 or 10/3):
original price = sale price / 30% = £420 / 30% = £1400
Therefore, the original price of the bracelet was £1400.
Complete question - A jewelry shop is having a sale. A bracelet is now reduced to £420. This is 70% of the original price. Work out the original price of the bracelet.
Learn more about Percentage here
https://brainly.com/question/29286925
#SPJ1
Find the absolute maximum and minimum values for the given function over the specific domain
Therefore, the absolute maximum value of f(x) over (-2, 3) is 201 and it occurs at x = -2. The absolute minimum value of f(x) over (-2, 3)is -98 and it occurs at x = 3.
We must identify the crucial points of the function within the period in order to determine the function's absolute maximum and minimum values.
Define critical point?
The critical points are those where the function's derivative is zero or undefinable. The function is then assessed at these pivotal points as well as the interval's endpoints.
Absolute maximum and lowest values are represented by the largest and smallest values, respectively.
The derivative of f(x) = 3x⁴ - 4x³ - 12x² + 1 over (-2, 3) is initially found as follows:
f'(x) = 12x³ - 12x²- 24x
If we set f'(x) to 0, we obtain:
12x³ - 12x² - 24x = 0
By multiplying both sides of this equation by 12x, we may simplify it to:
x²- x - 2 = 0
The answer to this quadratic equation is:
x = -1, x = 0, x = 2
Now we evaluate f(x) at these critical points and at the endpoints of the interval:
f(-2) = 201
f(-1) = -6
f(0) = 1
f(2) = 49
f(3) = -98
To know more about critical point visit:
brainly.com/question/31017064
#SPJ1
Submit AnswerWhat is the product of 3 and 10v 40 in simplest radical form?
The product of 3 and 10v√40 in simplest radical form is 30v(2√5).
What is product?
To find the product of 3 and 10v√40 in simplest radical form, we can simplify the radical first.
First, we can simplify 40 by finding its prime factorization:
40 = 2 × 2 × 2 × 5
Next, we can rewrite 10v√40 as 10v√(2 × 2 × 2 × 5) to separate out the perfect squares:
10v√(2 × 2 × 2 × 5) = 10v(√2 × √2 × √2 × √5)
We can then simplify the perfect squares under the radical:
10v(√2 × √2 × √2 × √5) = 10v(2√5)
Now we can multiply 3 and 10v(2√5):
3 × 10v(2√5) = 30v(2√5)
So the product of 3 and 10v√40 in simplest radical form is 30v(2√5).
What is prime factorization?
Prime factorization is the process of expressing a composite number as a product of its prime factors. In other words, it is finding the prime numbers that can be multiplied together to get the original number. For example, the prime factorization of 24 is 2 x 2 x 2 x 3 or 2³ x 3, since 24 can be expressed as a product of the prime numbers 2 and 3, and each of these primes is repeated as many times as necessary to get the original number. Prime factorization is an important concept in mathematics and has many practical applications, including in cryptography, number theory, and computer science.
To know more about prime factorization, visit:
https://brainly.com/question/29763746
#SPJ9
Complete the steps to find 3.18 × 16
The product of 3.18 × 16 is 50.88 in decimal form.
What is number system?A number system is a way to represent numbers using symbols or digits. The most commonly used number system is the decimal or base-10 system, which uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent any quantity.
Other common number systems include:
Binary or base-2 system, which uses two digits (0 and 1) to represent numbers
Octal or base-8 system, which uses eight digits (0, 1, 2, 3, 4, 5, 6, 7) to represent numbers
Hexadecimal or base-16 system, which uses sixteen digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F) to represent numbers
Knowing that;
3.18 × 16
After multiplying, we now have;
3.18 × 16 = 50.88
Thus, the product of 3.18 × 16 is 50.88 in decimal form.
To learn more about number system from given link
https://brainly.com/question/2237143
#SPJ1
HELP! MY ASSIGNMENT IS DUE TOMORROW. REWARD 15 PTS!
Rewrite each equation without absolute value symbols for the given values of x. y=|2x+5|-|2x-5|
if x<-2.5
if x>2.5
if -2.5<=x<=2.5
Answer: For x < -2.5:
y = |2x + 5| - |2x - 5|
y = -(2x + 5) - (-(2x - 5)) (since 2x - 5 < 0 and 2x + 5 < 0 for x < -2.5)
y = -2x - 5 + 2x - 5
y = -10
For x > 2.5:
y = |2x + 5| - |2x - 5|
y = 2x + 5 - (2x - 5) (since 2x - 5 < 0 and 2x + 5 > 0 for x > 2.5)
y = 10
For -2.5 ≤ x ≤ 2.5:
y = |2x + 5| - |2x - 5|
y = 2x + 5 - (-(2x - 5)) (since 2x - 5 < 0 and 2x + 5 > 0 for -2.5 ≤ x ≤ 2.5)
y = 4x
Step-by-step explanation:
Damian invested $81,000 in an account paying an interest rate of 3% compounded
quarterly. Marques invested $81,000 in an account paying an interest rate of 2%
compounded continuously. After 16 years, how much more money would Damian
have in his account than Marques, to the nearest dollar?
Answer: For Damian's investment:
The interest rate is 3%, compounded quarterly, which means the interest rate per quarter is 3%/4 = 0.75%.
The number of quarters in 16 years is 16*4 = 64.
Using the formula for compound interest, the balance after 16 years is:
A = P*(1 + r/n)^(n*t)
where:
P = the principal (initial investment) = $81,000
r = the interest rate per quarter = 0.75%
n = the number of times the interest is compounded per year = 4 (quarterly)
t = the number of years = 16
A = 81000*(1 + 0.0075/4)^(4*16) = $157,222.39
For Marques's investment:
The interest rate is 2%, compounded continuously.
Using the formula for continuous compound interest, the balance after 16 years is:
A = Pe^(rt)
where:
P = the principal (initial investment) = $81,000
r = the interest rate per year = 2%
t = the number of years = 16
A = 81000e^(0.0216) = $131,518.16
Therefore, Damian would have $157,222.39 - $131,518.16 = $25,704.23 more than Marques in his account after 16 years. Rounded to the nearest dollar, this is $25,704.
Step-by-step explanation:
Damian would have approximately $351 more in his account than Marques after 16 years.
What is interest rate?Interest rate is the percentage of a loan or deposit that is charged as interest or earned as interest over a period of time. It is expressed as a percentage of the principal amount borrowed or deposited, and it represents the cost of borrowing or the reward for saving money.
According to question:We can use the compound interest formula to calculate the future value of each investment after 16 years and then subtract to find the difference.
For Damian's investment, the interest rate is 3% per year, compounded quarterly. This means that the quarterly interest rate is r = 0.03/4 = 0.0075, and the number of compounding periods is n = 16 x 4 = 64. The future value of Damian's investment is:
F = 81000 * [tex](1 + r)^n[/tex]
= 81000 * [tex](1.0075)^64[/tex]
= 129,535.28
For Marques's investment, the interest rate is 2% per year, compounded continuously. This means that the continuously compounded interest rate is r = 0.02, and the number of compounding periods is n = 16 x 1 = 16. The future value of Marques's investment is:
F = 81000 * [tex]e^(rn)[/tex]
= 81000 * [tex]e^(0.0216)[/tex]
= 129,183.81
The difference between the two investments is:
129,535.28 - 129,183.81 = 351.47
So Damian would have approximately $351 more in his account than Marques after 16 years. Rounded to the nearest dollar, the difference is $351.
Learn more about interest rate visit:
https://brainly.com/question/30907196
#SPJ1
The coterminal angle of tan(780°) is?
The tangent of 60° is √3, so the coterminal angle of tan(780°) is √3.
What is coterminal angle?Coterminal angles are angles that have the same initial and terminal sides in standard position.
According to given information:To find the coterminal angle of tan(780°), we need to add or subtract multiples of 360° to 780° until we get an angle between 0° and 360°, because angles that differ by a multiple of 360° have the same trigonometric function values.
First, we can subtract 360° from 780°:
780° - 360° = 420°
This is not yet between 0° and 360°, so we can subtract another 360°:
420° - 360° = 60°
Now we have an angle between 0° and 360° that is coterminal with 780°.
The tangent function has a period of 180°, which means that the tangent function has the same value for angles that differ by a multiple of 180°. Since 60° is an acute angle, we can use the tangent of 60° to find the tangent of 780°:
tan(780°) is equivalent to tan(780° - 720°) = tan(60°)
The tangent of 60° is √3, so the coterminal angle of tan(780°) is √3.
To know more about coterminal angle visit:
https://brainly.com/question/23093580
#SPJ9
Identify the solid formed by rotating the two-dimensional shape about the line.
Select Choice
pls help!!!!!
Answer:
Got you bro
Step-by-step explanation:
The two-dimensional shape appears to be a semi-circle, and it is being rotated about a line to form a three-dimensional shape. The resulting shape is a sphere.
Answer:
Step-by-step explanation:
The two-dimensional shape appears to be a semi-circle, and it is being rotated about a line to form a three-dimensional shape.
The resulting shape is a sphere.
A complex number will, in general, have _____ fourth complex roots.
fill in the blank
Answer:A complex number will, in general, have five(5) fifth complex roots./
Step-by-step explanation:
Juan weighs 54,27 kilograms and his older brother weighs 55,895.1 grams. how much heavier is Juans older brother?
A skydiver falls 4,800 feet in 4 seconds. Which graph has a slope that best represents this rate? ILL GIVE 1O POINTS
Answer:
The slope of a line represents the rate of change, which in this case is the rate at which the skydiver is falling. The rate of falling is 4,800 feet in 4 seconds, which simplifies to 1,200 feet per second, therefore, the graph that has a slope of 1,200 best represents this rate.
Using sine tule find Obtuse angle B
[tex]\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(B)}{7}=\cfrac{\sin(30^o)}{6}\implies \sin(B)=\cfrac{7\sin(30^o)}{6} \\\\\\ B=\sin^{-1}\left[ \cfrac{7\sin(30^o)}{6} \right]\implies B\approx 35.69^o[/tex]
Make sure your calculator is in Degree mode.
Write the statement in words. Let p= "The plane is on time." Let q="The sky is clear."
Q<->P
The sky or if the sky
Is or is not
,and or, or, then, if and only if
Is or is not
The required statement is "The sky is clear if and only if the plane is on time."
What does mean by the sign <->?The statement "Q<->P" is a logical statement that uses the biconditional operator "<->" which means "if and only if." This operator connects two propositions in such a way that both propositions are true or false together.
In this case, the propositions are "Q" and "P" which are defined as "The sky is clear" and "The plane is on time," respectively. Therefore, the statement "Q<->P" can be translated into words as "The sky is clear if and only if the plane is on time."
This means that the truth of the proposition "Q" (the sky is clear) is dependent on the truth of proposition "P" (the plane is on time) and vice versa.
If the plane is on time, then the sky must be clear, and if the sky is clear, then the plane must be on time. If either of these propositions is false, then the bi-conditional statement is false as well.
Thus, required statement is "The sky is clear if and only if the plane is on time."
To know more about Plane in geometry visit:
brainly.com/question/2834992
#SPJ1
On the following checking account record, enter the figures and add or subtract them to keep the running total correct.
Balance Forward
Check
No.
Date
3427 2/14
3428 2/15
2/17
3429 2/22
3430 2/22
Checks Issued To
or Description of Deposit
Alfred's Market
Sunnyside Cafe
Deposit (paycheck)
City Water and Power
Amount of Check Amount of Deposit
$90.48
$65.00
$54.47
$375.99
$381.33
$299.88
Check
or Dep.
Balance $
Check
or Dep.
Balance $
Check
or Dep.
Balance $
Check
or Dep.
Balance
Check
or Dep.
The balances and the running total, given the checking account record is :
2 / 14 - $ 209. 402 / 15 - $ 144. 402 / 17 - $ 525.73 2 / 22 - $ 471.26 2 / 22 - $ 95.27How to find the balances ?The balance on the 14 th of February would be:
= Balance forward - Amount of check
= 299. 88 - 90. 48
= $ 209. 40
The balance on 2 / 15 :
= 209. 40 - 65
= $ 144. 40
The balance on 2 / 17 :
= 144. 40 + 381.33 which is a deposit
= $ 525.73
The balance and running total on 2 / 22 :
= 525. 73 - 54.47
= $ 471.26
The balance on 2 / 22 after the National Mortgage deduction is:
= 471. 26 - 375.99
= $ 95.27
Find out more on checking account records at https://brainly.com/question/11704101.
#SPJ1
a book sold 35,800 copies in its first month of release. suppose this represents 9.7% of the numbers of copies sold to date. how many copies have been sold to date?
round answer to nearest whole number
The answer is 369,072. This is the total number of copies sold to date.
What is equation?An expression that uses symbols to represent the relationship between two or more values.
This is calculated by solving the equation 9.7% × x = 35,800, where x is the total number of copies sold to date.
To solve this equation, we first need to convert the percentage to a decimal.
To do this, we divide 9.7 by 100, giving us 0.097.
We can then multiply both sides of the equation by this decimal, giving us 0.097x = 35,800.
We can then solve for x by dividing both sides of the equation by 0.097. This gives us x = 369,072. This is the total number of copies sold to date.
For more questions related to expression
https://brainly.com/question/4344214
#SPJ1
Use a sum or difference identity to find the exact value. sin 10° cos 50° + cos 10° sin 50°
Answer:
√3/2
Step-by-step explanation:
sin(10°) • cos(50°) + cos(10°) • sin(50°)
= sin(10 + 50)
sin(60°) = √3/2
<
8
Which equation could be used to solve for mº?
49⁰
32°
A 49° +32° + m² = 180°
B 49° +32° + m² = 90°
c) 49° +32° = mᵒ
(D) 49 = 32° +m
mº
The correct answer of the following is option A which is 49+32+m =180 because an angle on a straight line is equal to 180 degree.
what is angle?
Angles are an important concept in mathematics, physics, and engineering. An angle is formed by two rays or lines that share a common endpoint called a vertex. The measurement of an angle is usually expressed in degrees or radians.
In geometry, angles are classified according to their measure. An acute angle measures less than 90 degrees, a right angle measures exactly 90 degrees, an obtuse angle measures greater than 90 degrees but less than 180 degrees, and a straight angle measures exactly 180 degrees.
Angles can be formed by lines that intersect or by shapes such as triangles, quadrilaterals, and circles. The study of angles is an important part of trigonometry, which is the branch of mathematics concerned with the relationships between angles and the sides and heights of triangles.
Angles are also used in physics to describe the orientation and motion of objects. For example, the angle between two vectors can be used to calculate the direction of a force or the trajectory of a moving object.
In engineering, angles are used to design structures such as bridges, buildings, and machines. Engineers use trigonometry to calculate the angles and lengths of the various components of these structures to ensure they are safe and structurally sound.
Overall, angles are a fundamental concept in mathematics and have numerous applications in science, technology, and everyday life.
To know more about angles visit :-
https://brainly.com/question/25770607
#SPJ1
the length of an instant message conversation is normally distributed with a mean of 5 minutes and a standard deviation of 0.7 minutes. what is the probability that a conversation lasts longer than 6 minutes?
The probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.
What is probability?
The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.
We can use the standard normal distribution to solve this problem by standardizing the variable using the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability that a conversation lasts longer than 6 minutes, so x = 6, μ = 5, and σ = 0.7. Substituting these values into the formula, we get:
z = (6 - 5) / 0.7 = 1.43
Next, we can use a standard normal distribution table or a calculator to find the probability that a standard normal random variable is greater than 1.43. Using a standard normal distribution table, we find that this probability is approximately 0.0764.
Therefore, the probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.
Learn more about probability on:
https://brainly.com/question/13604758
#SPJ1
Please help me understand how to solve this. I am studying for an exam and I have tried so many different ways and do not understand this.
The width of the coal tray is approximately 16.24 inches.
What is the width of the coal tray?The width of the coal tray is determined as follows:
The given formula is P α 1/(1 + d²).
We can rewrite it as P = k/(1 + d²), where k is a constant of proportionality.
Since the problem states that the width of the coal tray is equal to d, we can assume that the width of the tray is equal to 1 (arbitrary units), without loss of generality.
So, we have P = k/(1 + d²) = k/(1 + (distance from food to coals / 1)²)
P = k/(1 + distance from food to coals²)
When the food is 16 inches above the tray, the distance from food to coals is d = 16/1 = 16.
When P = 0.53, we have:
0.53 = k/(1 + 16²)
k = 0.53(1 + 16²)
k ≈ 139.88
Now we can use the equation P = 0.53 = 139.88/(1 + d²) to solve for d:
0.53(1 + d²) = 139.88
1 + d² = 264.45
d² = 263.45
d ≈ 16.24
Learn more about inverse variation at: https://brainly.com/question/13998680
#SPJ1
Determine whether Rolle’s Theorem can be
applied to on the closed interval If Rolle’s Theorem can
be applied, find all values of in the open interval such
that If Rolle’s Theorem cannot be applied, explain
why not
Rolle’s Theorem can be applied to the closed interval and the value of x = (12 ±√12)/3
What is Rolle's theorem?Rolle's theorem states that "If a function f is defined in the closed interval [a, b] in such a way that it satisfies the following condition: If is continuous οn [a, b], ii) f is differentiable οn (a, b), and iii) f (a) = f (b), then there exists at leastοne value οf x, let us assume this value to be c, which lies between a and b i.e. (a < c < b) in such a way that f'(c) = 0.".
Here, we have
Given: f(x) = (x-1)(x-2)(x-3), [1,3]
We have to determine whether Rolle’s Theorem can be applied to the closed interval.
This function is continuous in [1, 3] and is differentiable everywhere except at the points x = 1, 2, 3.
This point is in the interval [1, 3], and since Rolle's Theorem requires that the function must be differentiable on the open interval (1, 3).
f(x) = (x-1)(x-2)(x-3)
f'(x) = (x-2)(x-3) + (x-1)(x-3) + (x-1)(x-2)
f'(x) = x² - 5x + 6 + x² - 4x + 3 + x² -3x + 2
f'(x) = 3x² -12x + 11
f'(x) = 0
3x² -12x + 11 = 0
x = (12 ±√12)/3
Hence, Rolle’s Theorem can be applied to the closed interval.
To learn more about Rolle’s Theorem from the given link
https://brainly.com/question/30809316
#SPJ1
what is pemdas and how is it used in math
PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations.
PEMDAS rule states that the order of operation starts with the parentheses first or the calculation, which is enclosed in brackets. Then, the operation is performed on exponents(degree or square roots), and later, we do operations on multiplication & division and at last addition and subtraction.
PEMDAS is the order that you solve a problem.
PEMDAS stands for:
Parenthesis
Exponents
Multiplication and Division
Addition and Subtraction
If you have an equation or expression that you need to solve, you solve it in this order. You do the parenthesis first, then you solve the exponents, then you do the multiplication and division from left to right, and last you do addition and subtraction from left to right.
In the equation
2 + 3 * 5,
first you would do 3 * 5 because multiplication is before addition.
2 + 15
Then you would do the addition to get the answer:
17.
Please give brainliest
You deposit $6000 in an account earning 7% interest compounded monthly. How much will you have in the account in 15 years?
Answer:
$67,000 after 15 years.
Step-by-step explanation:
You deposit $6000 in an account earning 7% interest compounded monthly. How much will you have in the account in 15 years? account will have $67,000 in it after 15 years
Can someone please help me here
The antiderivative of the given function is: [tex]-3/x^2 + 8ln|x| + C[/tex], where x is not equal to 0.
What is antiderivative?
Antiderivative is the reverse process of differentiation in calculus. Given a function f(x), an antiderivative of f(x) is another function F(x) whose derivative is equal to f(x).
The given function can be written as:
[tex](9x^3+8x^5)/x^6 = 9/x^3 + 8/x[/tex]
To find the antiderivative, we integrate each term separately using the power rule of integration:
∫(9/[tex]x^3[/tex]) dx = -3/[tex]x^2[/tex] + C1
and
∫(8/x) dx = 8ln|x| + C2
where C1 and C2 are constants of integration.
Therefore, the antiderivative of the given function is:
∫([tex]9x^3+8x^5[/tex])/[tex]x^6 dx[/tex] = ∫([tex]9/x^3[/tex]) dx + ∫(8/x) dx
= ([tex]-3/x^2 + C1[/tex]) + (8ln|x| + C2)
= [tex]-3/x^2[/tex] + 8ln|x| + C
where C = C1 + C2 is a constant of integration. Therefore, the antiderivative of the given function is:
[tex]-3/x^2 + 8ln|x| + C[/tex], where x is not equal to 0.
To learn more about antiderivative visit:
https://brainly.com/question/30397663
#SPJ1
Fine the missing side lengths. Leave your answers as radicals in the simplest form.
Answer:
x = 3√3;
y = 3
Step-by-step explanation:
Use trigonometry:
[tex] \sin(30°) = \frac{y}{6} [/tex]
Cross-multiply to find y:
[tex]y = 6 \times \sin(30°) = 6 \times 0.5 = 3[/tex]
Use the Pythagorean theorem to find x:
[tex] {x}^{2} = {6}^{2} - {y}^{2} [/tex]
[tex] {x}^{2} = {6}^{2} - {3}^{2} = 36 - 9 = 27[/tex]
[tex]x > 0[/tex]
[tex]x = \sqrt{27} = \sqrt{9 \times 3} = 3 \sqrt{3} [/tex]
what is the estimated quotient of 9.6 / 0.91
Answer:
9.6 / 0.91 ≈ 10.55
Step-by-step explanation:
I used a calculator
Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 4, -12, 36, ... Write your answer using decimals and integers. 30-1
Answer:
Step-by-step explanation:
The sequence starts with 4 and each subsequent term is obtained by multiplying the previous term by -3. Therefore, the equation to describe the sequence is:
aₙ = 4(-3)^(n-1)
where aₙ represents the nth term in the sequence.
Using this equation, we can find the values of the first few terms in the sequence as follows:
a₁ = 4(-3)^(1-1) = 4(1) = 4
a₂ = 4(-3)^(2-1) = 4(-3) = -12
a₃ = 4(-3)^(3-1) = 4(9) = 36
and so on.
Note that the index n starts at 1, but in some contexts it may start at 0, in which case we would need to adjust the exponent accordingly.
Please help I’m so confused and my teacher isn’t responding to me
The inverse of the function f(x) is f⁻¹(x) = √(x) - 8
What is the inverse of the function?To find the inverse of the function f(x) = (x + 8)², we need to solve for x in terms of y:
y = (x + 8)²
Taking the square root of both sides, we get:
±√(y) = x + 8
Solving for x, we get:
x = ±√(y) - 8
Since we want the inverse function to be a function (i.e., have a unique output for each input), we must choose the positive square root. Therefore, the inverse function is:
f⁻¹(x) = √(x) - 8
The domain of f⁻¹ is the range of f, which is [0, ∞). Therefore, the domain of f⁻¹ is [0, ∞).
Learn more on inverse of a function here;
https://brainly.com/question/19425567
#SPJ1
Solve the systems by elimination.
15x -4y=-50
3x-2y = -16
Answer:
[tex]x = 4 \frac{2}{3} [/tex]
[tex]y = 5[/tex]
Step-by-step explanation:
Multiply the second equation by -5 to eliminate 15x:
{15x - 4y = -50,
{3x - 2y = -16; / × (-5)
+ {15x - 4y = -50,
{-15x + 10y = 80;
----------------------------
6y = 30 / : 6
y = 5
Make x the subject from the 2nd equation (it doesn't matter, you can do it from the 1st one instead):
15x = -50 + 4y / : 15
[tex]x = 3 \frac{1}{3} + \frac{4}{15} y[/tex]
[tex]x = 3 \frac{1}{3} + \frac{4}{15} \times 5 = \frac{14}{3} = 4 \frac{2}{3} [/tex]
Using an 8 sector spinner, let E be the event of getting an even. What is the probability of getting a perfect square given you got an even, i.e. P(S/E)? Are the two events independent or dependent?
Two events are dependent since the probability of getting a perfect square is affected by the fact that we already know that we got an even number.
Describe Probability?Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. For example, the probability of rolling a 6 on a fair dice is 1/6, or approximately 0.167.
In probability theory, events are often expressed as sets of possible outcomes, and probabilities are calculated based on the number of outcomes in the event relative to the total number of possible outcomes. For example, the probability of rolling an even number on a fair dice is 3/6, or 0.5, because there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
Since the event E is the event of getting an even number, the possible outcomes are 2, 4, 6, or 8.
Out of these, only 4 is a perfect square. Therefore, P(S/E) = 1/4.
These two events are dependent since the probability of getting a perfect square is affected by the fact that we already know that we got an even number.
To know more about sets visit:
https://brainly.com/question/28985761
#SPJ1