Answer:
6. 7
7. 32
8. -17
9. -24
10. 6 ft
Step-by-step explanation:
6: 2(3) +1
6+1=7
7: 16-4(-4)
16+16=32
8: 12(-2)+7
-24+7=-17
9: -9-3(5)
-9-15=-24
10: 24-3(6)
24-18=6
Lilith is remodeling her bathroom and needs an $8,700 loan to pay for the cost of the remodel. Which loan option will have Lilith pay the most amount in interest?
Answer:
Step-by-step explanation:
Do you have the rest of the question?
Find the slope, x-intercept and y-intercept of the graph of the equation. Write the equation in slope-intercept form. 3x − 4y = 12
Answer:
The equation using slope-intercept form.
y = − 1 cnprt2 xe2 i + b
x = 0.6x + 384 what is x
Answer:
X=960
Step-by-step explanation:
x=0.6X +384
x-0.6X =384
0.4x=384
divide through by 0.4
X=960
If z = 7, what is the value of the equation? ( only write the numeric value for the answer)
4z + 5 = ?
Answer
4z+5=
4*7+5=33
33
Step-by-step explanation:
The volume of a cylinder, (ℎ), is given by the area of the base times the height, ℎ. The base of the cylinder shown below has a diameter of 5 inches. Write the function, (ℎ), that represents the volume of the cylinder. No spaces. ^use for exponents. 3.14 for pi. All lowercase letters. *
Answer:
(h)=h*19.625
Step-by-step explanation:
start by dividing the diameter by 2 to get the radius:
radius=2.5
the area of a circle is calculated with the formula pi*r^2
solve using our radius to get the area:
area of base= 19.625
using this, we can get our function:
(h)=h*19.625
will mark brainlist!!!!
Jenny is making jewelry craft kits. She purchases 3 bags of each color band. She divides the total number of bands equally into 4 kits. How many bands are in each kit?
The number of bands that are in each kit will be 3/4 bands
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Jenny purchases 3 bags of each color band and she divides the total number of bands equally into 4 kits
The bands in the kit will be:
= Total bags / Number of kits
= 3/4
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12 to the power of 2 (9-7) to the power of 3 +6=12 to the power of 2- to the power of 3 + 6
To simplify this expression, we need to follow the order of operations, which is a set of rules that dictate the order in which arithmetic operations should be performed. The order of operations is.
the simplified expression is 1158.
To simplify this expression, we need to follow the order of operations, which is a set of rules that dictate the order in which arithmetic operations should be performed. The order of operations is:
1. Parentheses (simplify expressions inside parentheses first)
2. Exponents (perform all calculations involving exponents)
3. Multiplication and division (perform all multiplication and division, in order from left to right)
4. Addition and subtraction (perform all addition and subtraction, in order from left to right)
Using these rules, we can simplify the given expression as follows:
12^2(9-7)^3 + 6 = 12^2 - 3 + 6
First, we simplify the expression inside the parentheses:
12^2(2)^3 + 6 = 12^2 - 3 + 6
Next, we perform the exponentiation:
12^2(8) + 6 = 144 - 3 + 6
Then, we perform the multiplication:
1152 + 6 = 147
Finally, we perform the addition:
1158 = 1158
Therefore, the simplified expression is 1158.
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Please help this needs to be done by the end of the day
Given: g(x)=3(x-5), find g(-1)
Answer:
45
Step-by-step explanation:
Answer:
-18
Step-by-step explanation:
g(x)=3(x-5)
g(-1)=3(-1-5)
g(-1)=3(-6)=-18
Find the measure of <1Justify your answer.
Answer:
its 75
Step-by-step explanation:
im in highschool and just did this a couple of weeks ago
its called alternate interior or alternate exterior. something like that but i know im right trust me. also pls mark me brainliest
A helicopter flying 3,590 feet above the ground spots the top of a 150-foot tall tower. The angle of depression from the helicopter to the top of the building is 83 degrees. How far must the helicopter fly to be directly over the tower?
Answer:
\(x\approx 422.4\)
Step-by-step explanation:
Assuming 'x' the distance helicopter needs to fly to be directly over the tower.
It is given that a helicopter flying 3590 feet above ground spots the top of a 150-foot tall cell phone tower at an angle of depression of 83°.
From attachment that helicopter, tower and angle of depression forms a right triangle.
As height of tower is 150 feet, so the vertical distance between helicopter and tower will be: 3590-150=3440 feet.
Also, the side with length 3590-150 feet is opposite and side x is adjacent side to 83° angle.
As the tangent relates the opposite side of a right triangle to its adjacent side, so we will use tangent to find the length of x.
\(\text{Tan}=\frac{\text{Opposite}}{\text{Adjacent}}\)
\(\text{Tan}(83^o)=\frac{3590-150}{x}\\\)
\(\text{Tan}(83^o)=\frac{3440}{x}\)
\(x=\frac{3440}{\text{Tan}(83^o)}\)=>\(x=\frac{3440}{8.14434}\)
\(x\approx 422.4\)
Thus, the helicopter must fly approximately 422.4 feet to be directly over the tower.
Suppose that the demand function for a product is given by D(p)=70,000/p and that the price p is a function of time given by p=1.8t+11, where t is in days. a) Find the demand as a function of time t. b) Find the rate of change of the quantity demanded when t=105 days. a) D(t)= (Simplify your answer.) b) What is the approximate rate of change of the quantity demanded when t=105 days? units/day. (Simplify your answer. Round to three decimal places as needed.)
a) To find the demand as a function of time, we substitute the expression for price, p=1.8t+11, into the demand function D(p)=70,000/p.
D(t) = 70,000/(1.8t+11)
Simplifying further, we can write:
D(t) = 70,000/(1.8t+11)
b) To find the rate of change of the quantity demanded when t=105 days, we need to find the derivative of the demand function D(t) with respect to time, and then evaluate it at t=105.
Taking the derivative of D(t) with respect to t, we use the quotient rule:
D'(t) = -70,000(1.8)/(1.8t+11)^2
Substituting t=105 into D'(t), we have:
D'(105) = -70,000(1.8)/(1.8(105)+11)^2
To find the approximate rate of change of the quantity demanded, we can calculate the numerical value of D'(105) using a calculator or computer software. Round the answer to three decimal places for simplicity.
a) The demand function D(p) gives the relationship between the price of a product and the quantity demanded. By substituting the expression for price p in terms of time into the demand function, we obtain the demand as a function of time, D(t).
b) The rate of change of the quantity demanded represents how fast the demand is changing with respect to time. To find this rate, we calculate the derivative of the demand function with respect to time, which measures the instantaneous rate of change. By evaluating the derivative at t=105 days, we can determine the specific rate of change at that particular point in time. This rate gives us insight into how the quantity demanded is changing over time, allowing us to analyze trends and make predictions.
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at a local restaurant, 52% of the employees work both nights and weekends. if 63% of the employees work nights, what percent, to the nearest tenth, of the employees who work nights are working weekends?
The percentage who work nights are working weekends is 82.5%
Calculating the percentage who work nights are working weekends?From the question, we have the following parameters that can be used in our computation:
Nighr and weekend = 52%
Night = 63%
Using the above as a guide, we have the following:
Night wokers on weekend = 52%/63%
Evaluate
Night wokers on weekend = 82.5%
Hence, the percentage who work nights are working weekends is 82.5%
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An ice cream factory makes 330 quarts of ice cream in 5 hours. How many quarts could be made in 36 hours? What was that rate per day?
use the distributive property to simplify (b+13-m) (5)
Answer:
5b-5m+65
Step-by-step explanation:
Write an equation:
"Ehren worked 36 hours last week and earned a total of $500"
Please help me ;-; Thanks!
The correct equation to represent "Ehren worked 36 hours last week and earned a total of $500" is,
⇒ 36x = 500
Where, x represent the amount earn in per hour.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
"Ehren worked 36 hours last week and earned a total of $500"
Let the amount earn in per hour = x
Hence, For Ehren worked 36 hours last week and earned a total of $500, the correct equation is,
⇒ 36x = 500
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if it takes 4 workers 6 hours to paint a fence, how long would it take 8 workers
Answer:
3 workers
Step-by-step explanation:
just divide by 2
. Evaluate the following convolution f(t)∗δ(t−9)+f(t)∗δ(t+9) with F(ω) is f(t)′ s FT a. F(ω+9)+F(ω−9) b. f(t+9)+f(t−9) c. F(t+9)+F(t−9) d. 2f(t−9)
The correct answer for the given convolution is (d) 2f(t-9).
To evaluate the convolution f(t)δ(t−9)+f(t)δ(t+9), let's break it down step by step.
First, let's consider the convolution of f(t) with δ(t-9):
f(t)δ(t-9) = ∫[f(τ)δ(t-9-τ)]dτ
The integral evaluates to f(t-9) because the Dirac delta function δ(t-9) picks out the value of f(τ) at τ = t - 9.
Therefore, the first term simplifies to f(t-9).
Now, let's consider the convolution of f(t) with δ(t+9):
f(t)δ(t+9) = ∫[f(τ)δ(t+9-τ)]dτ
The integral evaluates to f(t+9) because the Dirac delta function δ(t+9) picks out the value of f(τ) at τ = -t - 9.
Therefore, the second term simplifies to f(t+9).
Now, we can combine the two terms:
f(t-9) + f(t+9)
Next, let's consider the Fourier Transform (FT) of f(t), denoted as F(ω).
The Fourier Transform of f(t-9) is F(ω) * \(e^{(-j\omega9)\), where * represents the convolution and j is the imaginary unit.
Similarly, the Fourier Transform of f(t+9) is F(ω) * \(e^{(-j\omega9)\).
Therefore, the overall expression becomes:
F(ω) * \(e^{(-j\omega9)\) + F(ω) * \(e^{(-j\omega9)\)
Factoring out F(ω), we get:
F(ω) * \(e^{(-j\omega9)\) + \(e^{(-j\omega9)\)
Now, simplifying the exponential terms:
\(e^{(-j\omega9)\) + \(e^{(-j\omega9)\) = 2 * cos(ω9)
Finally, substituting it back into the expression:
F(ω) * 2 * cos(ω9)
Therefore, the correct answer is (d) 2f(t-9).
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Identify the inverse operation:r/4
Answer:
The inverse of this expression is the multiplication of 4. Answer: 4r, or 4 times r
Step-by-step explanation:
So first off, multiplication is the inverse of division, therefore, dividing r by 4 is the inverse of multiplying r by 4, so the answer is 4r.
Please provide Guidance ASAP on how to calculate the last question and answer this question.
How many years will it take to reach 50,000 pairs and what unrealistic assumptions were made in prediting the time it would take to reach 50,000 pairs?
Table 7. Analysis of Bald Eagle Recovery
What is the shape of the curve? J-shaped exponential curve
Doubling time from 1,000 to 2,000 4.73 years
Doubling time from 2,000 to 4,000 9.47 years
Doubling time from 4,000 to 8,000 18.94 years
Average doubling time 11.05 years
Doubling time increasing or decreasing? increasing
Starting number of breeding pairs 791 Year 1974
Theoretical prediction to reach 1,582 pairs Year 1979
Theoretical prediction to reach 3,164 pairs Year 1987
Theoretical prediction to reach 6,328 pairs Year 2002
Theoretical prediction to reach 12,636 pairs Year 2030
How many years to reach 50,000 pairs? 235 years
To calculate the time it would take to reach 50,000 pairs, we can use the average doubling time provided in the table. The shape of the curve is a J-shaped exponential curve.
which means that the number of pairs increases at an accelerating rate over time. Since the average doubling time is 11.05 years, we can determine the number of times we need to double the initial number of breeding pairs (791) to reach 50,000 pairs. By successively doubling the number of pairs and keeping track of the years passed, we reach 50,000 pairs in 235 years (as given in the table).
However, there are unrealistic assumptions made in predicting the time to reach 50,000 pairs. The main assumption is that the doubling time remains constant, while in reality, factors such as environmental limitations, availability of resources, and human intervention could cause the rate of growth to change over time.
Additionally, the model assumes that there are no significant negative events (such as disease outbreaks or natural disasters) that could negatively impact the bald eagle population during this period.
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4^x+ 2^(1+2x)= 50
I know what the answer is (about 2.03), but I need help getting there!
Step-by-step explanation:
4ˣ + 2¹⁺²ˣ = 50
Rewrite 4 as a power of 2.
2²ˣ + 2¹⁺²ˣ = 50
Factor out 2²ˣ.
2²ˣ (1 + 2) = 50
2²ˣ = 50/3
Take log of both sides.
ln(2²ˣ) = ln(50/3)
Use exponent property.
2x ln 2 = ln(50/3)
Solve for x.
x = ln(50/3) / (2 ln 2)
Simplify.
x = ln(50/3) / (ln 4)
x ≈ 2.03
A student would like to estimate the height of a statue. The length of the statue's right arm is 45 feet. The stud
right arm is 2 feet long and her height is 5 g
- feet. Use this information to estimate the height of the statue. Hovc-lose
is the approximate height to the statue's actual height of 120 feet, 3 inches from heel to top of head?
Approximate height to the statue's actual height of 120 feet, 3 inches from heel to top of head is 123.75 feet.
To estimate the height of the statue, the student can use the method of similar triangles. Since the length of the statue's right arm is 45 feet and the length of the student's right arm is 2 feet, the ratio of the lengths of the arms is 45/2 = 22.5. If we assume that the ratio of the heights of the statue and the student is also 22.5, then the height of the statue can be estimated as:
height of statue = height of student x ratio of heights
height of statue = 5.5 x 22.5
height of statue = 123.75 feet
This estimated height of the statue is close to the actual height of 120 feet, 3 inches. It should be noted that this method of estimation assumes that the ratio of the heights of the statue and the student is the same as the ratio of the lengths of their arms. This may not be completely accurate, as the proportions of the statue and the student may be different.
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Question 4 (1 point) In how many ways can 4 girls and 3 boys be arranged in a row, such that all 3 boys are not sitting together?
To calculate the number of ways the 4 girls and 3 boys can be arranged in a row such that all 3 boys are not sitting together, we need to subtract the number of arrangements where the boys are sitting together from the total number of arrangements.
Total number of arrangements:
Since we have 7 individuals (4 girls and 3 boys), the total number of arrangements without any restrictions is 7!.
Number of arrangements where the boys are sitting together:
If we consider the 3 boys as a single entity, we have 5 entities to arrange (4 girls + 1 group of boys). The number of arrangements with the boys sitting together is 5!.
To find the number of arrangements where the boys are not sitting together, we subtract the number of arrangements where the boys are sitting together from the total number of arrangements:
Number of arrangements = Total number of arrangements - Number of arrangements where boys are sitting together
= 7! - 5!
Now let's calculate the values:
Total number of arrangements = 7!
= 7 x 6 x 5 x 4 x 3 x 2 x 1
= 5040
Number of arrangements where boys are sitting together = 5!
= 5 x 4 x 3 x 2 x 1
= 120
Number of arrangements where boys are not sitting together.
= 5040 - 120
= 4920
There are 4920 ways to arrange 4 girls and 3 boys in a row such that all 3 boys are not sitting together.
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Find the generating function of the sequence {an}n≥0 determined by an = an−1 + 6an−1 with initial conditions a0 = 1, a1 = 3. You need to find the closed form of the generating function, but you don’t need find the closed form of the coefficients.
The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.
To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.
The given recurrence relation is: an = an-1 + 6an-2
We are also given the initial conditions: a0 = 1 and a1 = 3.
To find the generating function, we define the generating function A(x) as:
a(x) = a0 + a1x + a2x² + a3x³ + ...
Multiplying the recurrence relation by x^n and summing over all values of n, we get:
∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)
Now, let's express each summation in terms of the generating function a(x):
a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾
Simplifying and rearranging the terms, we have:
a(x)(1 - x - 6x²) = a0 + (a1 - a0)x
Using the given initial conditions, we have:
a(x)(1 - x - 6x²) = 1 + 2x
Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):
a(x) = (1 + 2x) / (1 - x - 6x²)
Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).
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Hector is considering joining a video game service in which you can rent different video games. Hector has two options:
Option 1: requires a monthly fee of $7.50 and then $3.50 per game rental fee.
Option 2: provides the following chart to show rental fees
Table is shown in the attached image
If x is the number of games and y is the rental fee, write an equation for both of the relationships in the form y = mx + b.
Option 1: y = ____ x + ____
Option 2: y = ____ x + ____
If Hector wants to rent 5 video games this month, use substitution to find which option would be the least expensive, Option 1 or Option 2.
Option ___ .
Option 1: y = 3.50x + 7.50
Option 2: y = 2.50x + 3.00
If Hector wants to rent 5 video games, Option 2 would be the least expensive at a cost of $15.50.
What does cost mean?Cost is an economic concept that refers to the amount of money, time, or resources that must be expended or sacrificed in order to acquire or produce something. In business and finance, cost typically refers to the total amount of money that is required to purchase or produce goods or services, taking into account all the expenses associated with the process, including direct costs like raw materials and labor, as well as indirect costs like rent, utilities, and administrative expenses. Cost can be influenced by a variety of factors, such as supply and demand, competition, technology, and government regulations, and it is a key consideration for businesses and consumers when making decisions about what to buy or produce.
For option 1, the monthly fee is $7.50, and each game rental costs $3.50. This means that the total cost for renting x games would be:
y = 3.50x + 7.50
For option 2, the rental fees are as follows:
For 0 games: $0
For 1 game: $3.00
For 2 games: $5.50
For 3 games: $8.00
For 4 games: $10.50
For 5 games: $12.50
To find the equation for option 2, look for the pattern in the rental fees. We can see that the rental fee increases by $2.50 for each additional game, starting from $3.00. This means that the equation for option 2 would be:
y = 2.50x + 3.00
Now, if Hector wants to rent 5 video games this month, substitute x = 5 into both equations and see which option is cheaper:
Option 1: y = 3.50(5) + 7.50 = 24.00
Option 2: y = 2.50(5) + 3.00 = 15.50
Therefore, Option 2 would be the least expensive for Hector if he wants to rent 5 video games this month.
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Rita has 1 quarter, 1 dime, and 2 pennies. What is the total value of Rita’s coins?
The total value of Rita's coin is 37cents
What is the relationship between quarter, dime and pennies?Penny, quarter , and dime are currencies used in transacting. They are all related to cent in the following ways;
A penny is worth 1 cent. . A dime is worth 10 cents. A quarter is worth 25 cents.
Therefore converting all the coins to cent
1 quarter = 25cents
1 dime = 10cents
2 pennies = 2× 1 = 2 cents
Therefore the total value of coin= 1 quarter + 1 dime + 2 pennies
= 25 cent + 10cent + 2 cent = 37 cents
Therefore the total value of Rita's coins is 37cents
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Why is (4x-2)(3x+5) not an intelligent
guess for factoring this trinomial even though
4.3=12 and -2.5=-10?
Trinomials are expressions with three terms
The factor is not an intelligent guess, because the expression can be further simplified
Why the factor is not intelligent?
The factor is given as:
(4x - 2)(3x + 5)
The above factor can further be factorized.
This is shown below
(4x - 2)(3x + 5) = 2(2x - 1)(3x + 5)
Hence, the factor is not an intelligent guess, because the factor can still be further simplified
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tim drives at an average speed of 80 km per hour for 3 hours and 45 minutes, work out how many kilometers tim drives
Tim drives a total of 300 kilometers.
To calculate the distance Tim drives, we need to multiply his average speed by the time he spends driving.
First, let's convert the time of 3 hours and 45 minutes to a decimal form. There are 60 minutes in an hour, so 45 minutes is equal to 45/60 = 0.75 hours.
Now, we can calculate the distance Tim drives using the formula:
Distance = Speed × Time
Distance = 80 km/hour × 3.75 hours
Distance = 300 km
Therefore, Tim drives a total of 300 kilometers.
To arrive at this result, we multiplied Tim's average speed of 80 km/hour by the time he spends driving, which is 3.75 hours. This calculation accounts for the fact that Tim maintains a constant speed of 80 km/hour throughout the entire duration of 3 hours and 45 minutes.
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During a fundraiser, Library has a goal to collect 45,000. If the lower collects 300 less than its goal how much does it collect.