Steven is painting walls that are equal in size. He paints 1/6 of a wall in 3/10
of an hour. Using this
information, create an equation for the unit rate, r, that represents how much of a wall Steven paints in 1
hour.
So the equation for the unit rate, r, is:
r = 50/9
What is multiplication?Calculating the sum of two or more numbers is the process of multiplication. 'A' multiplied by 'B' is how you express the multiplication of two numbers, let's say 'a' and 'b'. Multiplication in mathematics is essentially just adding a number repeatedly in relation to another number.
To find the unit rate, we need to determine how much of a wall Steven can paint in one hour. We can start by using the information given to find out how much of a wall he can paint in 1/10 of an hour:
1/6 of a wall in 3/10 of an hour
= (1/6) ÷ (3/10)
= (1/6) × (10/3)
= 10/18
= 5/9
Therefore, Steven can paint 5/9 of a wall in 1/10 of an hour.
To find out how much of a wall he can paint in one hour, we can multiply this by 10:
(5/9) × 10 = 50/9
Therefore, Steven can paint 50/9 of a wall in one hour.
So the equation for the unit rate, r, is:
r = 50/9
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The population P of an organism
is growing exponentially. Select all
the functions that could represent
the population.
A. P = 400(0.85)t
B. P = 2(1.35)t
C. P = 10(1.15)t
D. P = 215(0.95)t
E. P = 75(2.85)t
F. P = 900(0.05)t
Answer: B, C and E
Step-by-step explanation: the term growing means the value is increasing, and a number multiplied by 1 gives the same number; therefore in order for that number to increase, it need to be multiplied by a bigger number which is greater than 1, in this case it can not be a number less than 0 like 0.85, so all the number which are greater than 1 in the bracket are correct.
the number before the bracket is the population before increasing, so you can substitute any value for t and try out different outcomes, you will get only B, C and E as number greater than the original number
Which set of side measures forms a Pythagorean triple
Answer:
D
Step-by-step explanation:
D is the only one where A^2+B^2=C^2. Meaning that when 10=A, 24=B, 24 would be equal to C. 10^2=100 24^2=576, 100+576=676, and the sqrt of 676 is 36.
Answer: D
Step-by-step explanation:
D is the only one where A^2+B^2=C^2. Meaning that when 10=A, 24=B, 24 would be equal to C. 10^2=100 24^2=576, 100+576=676, and the sqrt of 676 is 36.
the average number of flowers visited a day by anna's hummingbirds in isla vista is normally distributed with a known variance of 47.2 flowers. for allen's hummingbirds in isla vista, the number of flowers visited a day is also normally distributed with a known variance of 40.6 flowers. a ucsb student tracks one hummingbird from each species for 30 days and find the sample average for number of flowers visited a day to be 220 for anna's and 196 for allen's. find the upper bound for the 98% confidence interval for the difference in true averages number of flowers visited a day between anna's and allen's hummingbirds. round your answer to 2 decimal places.
The upper bound for the 98% confidence interval for the difference in true averages number of flowers visited a day between anna's and allen's hummingbirds is 28.77.
To find the upper bound for the 98% confidence interval for the difference in true average numbers of flowers visited a day between Anna's and Allen's hummingbirds, we need to use the following formula:
Upper bound = (x1 - x2) + zα/2 * √(s1^2/n1 + s2^2/n2)
where x1 and x2 are the sample means, s1^2 and s2^2 are the sample variances, n1 and n2 are the sample sizes, and zα/2 is the critical value from the standard normal distribution for a 98% confidence interval (which is 2.33).
Plugging in the given values, we get:
Upper bound = (220 - 196) + 2.33 * √(47.2/30 + 40.6/30)
Upper bound = 24 + 2.33 * √(2.84 + 1.35)
Upper bound = 24 + 2.33 * √4.19
Upper bound = 24 + 2.33 * 2.046
Upper bound = 28.77
Therefore, the upper bound for the 98% confidence interval for the difference in true average numbers of flowers visited a day between Anna's and Allen's hummingbirds is 28.77 (rounded to 2 decimal places).
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fill in the power 4 _ =64
Answer:
the 3'd power
Step-by-step explanation:
4x4=16 16x4=64
Answer:
\(\Huge \boxed{\mathrm{3}}\)
Step-by-step explanation:
Let the power be x.
\(\mathrm{4^x=64}\)
Take log of both sides.
\(\mathrm{log(4^x)=log(64)}\)
\(\mathrm{x \cdot log(4)=log(64)}\)
Divide both sides by log(4).
\(\displaystyle \mathrm{x=\frac{log(64)}{log(4)} }\)
\(\mathrm{x=3}\)
Phil received a prize of xxx dollars from a poker tournament. The tournament cost him 100100100 dollars to enter.
What were Phil's net winnings from the tournament?
Answer:
$(x-100)
Step-by-step explanation:
Phil entered the poker tournament with $100.He received a price of $x.His net winnings from the tournament will be the price minus the entry fee.
Therefore:
Phil's net winnings=$(x-100)
Answer:
x - 100
Step-by-step explanation:
Since it costs 100 dollars for Phil to enter the competition, you subtract that from the prize in which he earns (x).
select the equation and solution for the problem. let x represent the unknown number.
a truck carries 12 bags of peaches to a local supermarket.if each bag weighs 6 pounds,what is the total weight of the peaches taken to the supermarket?
options:
Answer: answer is D
Step-by-step explanation:
Write the equation of the line with the given slope and y-intercept
Answer:
A) y = x - 3/4
Step-by-step explanation:
The equation of the line with slope m and intercept b is
y = mx + b
Here were have slope = m = 1.
y-intercept = b = -3/4
Equation:
y = mx + b
y = 1x + (-3/4)
y = x - 3/4
Answer: A) y = x - 3/4
what is 7/9 divided by 6/8
Answer: \(\frac{28}{27}\) or \(1\frac{1}{27}\)
Step-by-step explanation:
\(\frac{7}{9} /\frac{6}{8} = \frac{7}{9}(\frac{8}{6})\)
\(\frac{7}{9} (\frac{8}{6} ) = \frac{28}{27}\)
\(\frac{28}{27} = 1 \frac{1}{27}\)
Prove the vectors m = (0,5) and n = (-2,1) span the vector space R?, or find a vector that cannot be expressed as a linear combination of these vectors.
The vectors m = (0,5) and n = (-2,1) span the vector space ℝ² because every vector in ℝ² can be expressed as a linear combination of these vectors.
To determine if the vectors m = (0,5) and n = (-2,1) span the vector space ℝ², we need to check if every vector in ℝ² can be expressed as a linear combination of m and n.
Let's consider an arbitrary vector v = (x, y) in ℝ². We want to find scalars a and b such that v = am + bn.
Setting up the equations, we have:
x = 0a + (-2)b
y = 5a + 1b
To solve this system of equations, we can rewrite it in matrix form:
[0 -2] [a] [x]
[5 1] [b] = [y]
By row-reducing the augmented matrix [A|B] where A is the coefficient matrix and B is the column vector of constants, we get:
[1 0] [a] [-(2/5)x]
[0 1] [b] = [(1/5)x + (1/5)y]
The matrix is in row-reduced echelon form, and it indicates that for any vector (x, y) in ℝ², we can find scalars a = -(2/5)x and b = (1/5)x + (1/5)y such that v = am + bn.
Therefore, the vectors m = (0,5) and n = (-2,1) span the vector space ℝ². Every vector in ℝ² can be expressed as a linear combination of these vectors.
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Mary takes a math test and receives a grade of 60% which ratio shows the relationship of the amount
The proportion of 60 % is given by the ratio is 3/5
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 60 %
The proportion is given by A = 60/100
A = 60 / 100
On simplifying the equation , we get
A = 6/10
Divide by 2 on the numerator and denominator of the equation , we get
A = 3/5
Therefore , the value of A is 3 : 5
Hence , the proportion is 3 : 5
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the industry in exercise 8.8 modified its retirement policy after obtaining the results of the survey. it now wants to estimate the proportion of employees in favor of the modified policy. how many plants should be sampled to have a bound of 0.08 on the error of estimation? use the data from exercise 8.8 to approximate the results of the new survey.
By using the formula for sample size with a 95% confidence interval and a proportion of 0.6 we find that bound of 0.08 on the error of estimation, the industry should sample at least 558 plants.
In Exercise 8.8, the sample size was 2500, and the proportion of employees in favor of the policy was 0.64. We need to estimate the sample size required to have a bound of 0.08 on the error of estimation. Using the formula for the margin of error, we get:
ME = z * sqrt(p * q / n)
0.08 = z * sqrt(0.64 * 0.36 / n)
Assuming a 95% confidence interval, we have z = 1.96. Solving for n, we get:
n = (z / ME)^2 * p * q
n = (1.96 / 0.08)^2 * 0.64 * 0.36
n ≈ 558. So, we need to sample at least 558 plants to have a bound of 0.08 on the error of estimation.
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Calculate the average rate of change of the function
f(x)=8-5x^2 on the interval [a,a+h] (assuming h>0)
The average rate of change of the function f(x) = 8 - 5x^2 on the interval [a, a + h] is -10ah - 5h^2.
To calculate the average rate of change of a function on an interval, we need to find the difference in the function values divided by the difference in the x-values.
Let's first find the function values at the endpoints of the interval:
f(a) = 8 - 5a^2
f(a + h) = 8 - 5(a + h)^2
Next, we calculate the difference in the function values:
f(a + h) - f(a) = (8 - 5(a + h)^2) - (8 - 5a^2)
= 8 - 5(a + h)^2 - 8 + 5a^2
= -5(a + h)^2 + 5a^2
Now, let's find the difference in the x-values:
(a + h) - a = h
Finally, we can determine the average rate of change by dividing the difference in function values by the difference in x-values:
Average rate of change = (f(a + h) - f(a)) / (a + h - a)
= (-5(a + h)^2 + 5a^2) / h
= -5(a^2 + 2ah + h^2) + 5a^2 / h
= -10ah - 5h^2 / h
= -10ah - 5h
Thus, the average rate of change of the function f(x) = 8 - 5x^2 on the interval [a, a + h] is -10ah - 5h^2.
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If a figure is a square, its diagonals divide it into isosceles triangles.
p: A figure is a square.
q: A figure's diagonals divide into isosceles triangles.
Which represents the converse of this statement? Is the converse true?
The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:
"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."
The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.
Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.
In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.
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Zappy Electronics manufactures audio components such as speakers, furntables, and XV receivers. Zappy has worked hard to build a dominant position in the AV receiver market with a 7 cht market share. As they expanded their hold on the category, they sold more and more units. They noticed that for each additional thousand receivers they sold, their unit cost of production decreased by 20%. This allowed them to price their receivers lower than those of comparable competitors. further ensuring their dominance. Zappy's observation directly reflects which of the following marketing concepts?
Zappy Electronics' observation that their unit cost of production decreases as they sell more units reflects the marketing concept known as the experience curve.
The experience curve, also known as the learning curve, refers to the idea that as a company gains experience in producing and selling a particular product, its costs decrease and efficiencies improve. This concept is based on the observation that the more a company produces and sells a product, the more it learns about the most efficient ways to manufacture and distribute it.
In the case of Zappy Electronics, as they sold more AV receivers, they experienced a decrease in unit production costs. This implies that they were able to achieve economies of scale and operational efficiencies. For every additional thousand receivers sold, their unit production cost decreased by 20%. This cost advantage allowed Zappy Electronics to price its receivers lower than its competitors, which contributed to its dominance in the AV receiver market.
Therefore, Zappy Electronics' observation aligns with the concept of the experience curve, as they benefited from lower costs due to increased production and sales volume.
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What is 33% of 171? how did you get it
Answer:
56.43
Step-by-step explanation:
= 33/100×171
=56.43
A state offers specialty license plates that contain 5 numbers followed by 2 letters. License plates are assigned randomly. All license plates are equally likely. Findthe number of possible license plates that can be issued using this system.O1.188,137,600 possible license platesO 12,500 possible license platesO 67,600,000 possible license plates039,917,124 possible license plates
Given:
There are 5 numbers followed by 2 letters.
Solution:
To find the answer, we will have a plate number that consists of 5 numbers followed by 2 letters. In that 5 numbers, each place has 10 choices-from 0 to 9. It will be: 10 * 10 * 10 * 10 * 10 = 100,000 .
Now, for the letters, there are 26 letters in the alphabet. We have two places for the letters and each place have 26 choices-from A to Z that will give us: 26 * 26 = 676
We will now multiply the acquired data for both the numbers and letters to arrive at the correct answer.
100,000 * 676 = 67,600,000
ANSWER: 67,600,000 possible license plates
PLEASE HELP ME!!!!!!!Which expression is equivalent to 6x2−(4x+10)−3+(4x2−5x)?
10x2−9x+7
10x2−9x−13
2x2−x+7
2x2−x−13
Answer:
10(-4x+10)-3 +(8-5x)
-40x+100-3+8-5x
-40x-5x+105
-45x+105
-45x+105=0
-45x=-105
x=-105/-45
x=7/3
Step-by-step explanation:
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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How many hours must you drive if you drive 643 miles at 65 mph on the interstate? Round to the nearest tenth hour
Answer:
9.9 hours, rounded to the nearest tenth hour.
Step-by-step explanation:
To calculate the time of travel, we must first divide the distance by the speed. Why, you ask? Because of this equation:
\(Speed\=\ \frac{distance}{time}\)
Therefore, with a little bit of arrangement, we get:
\(Time\=\ \frac{distance}{speed}\)
So, let's get on with it.
\(Time\=\ \frac{643 \ miles}{65 \ mph}\)
\(Time\=\ 9.9 \ hours \)
Finally, we have our answer: 9.9 hours, rounded to the nearest tenth.
Hope this helped!
Please answer correctly !!!!!!!! Will mark brianliest !!!!!!!!!!!!!
Answer:
So since the ball is at x=0 at the end.
We plug in it.
h(x) = 16 if you simplify it
what can i add 1.2 with to get 11.2
23.f(s) = Vs - 1 ÷Vs + 1 .Find the derivatives.
Answer:The derivative of f(s)
Step-by-step explanation:
The derivative of f(s) = (Vs - 1)/(Vs + 1) with respect to s is
df/ds = (V(Vs + 1) - (Vs - 1)V)/(Vs + 1)^2
= (V^2 -1)/(Vs + 1)^2
Brainlest- Pls help me pls thank you sm In advance
a small ferry boat is 4m wide and 6m long
The weight of the truck, When a loaded truck pulls onto it, the boat sinks an additional 5.00cm into the river is 11,788 N.
To discover the weight of the truck, we ought to utilize the concept of buoyancy.
When the truck pulls onto the vessel, it uproots a sum of water that breaks even with its claimed weight. The weight of this uprooted water makes an upward buoyant constraint on the pontoon.
The watercraft sinks an extra 5.00 cm, which suggests that the buoyant constraint breaks even with the weight of the truck furthermore the weight of the uprooted water, and this adds up to the weight causing the boat to sink assist.
Let's accept that the thickness of water is 1000 kg/m³ (this can be ordinary esteem for new water). The volume of water uprooted by the pontoon is rise to its length times its width times the profundity it sinks into the water:
V = (6.00 m)(4.00 m)(0.05 m) = 1.20 m³
The weight of this uprooted water is:
Wwater = Vρg = (1.20 m³)(1000 kg/m³)(9.81 m/s²) ≈ 11,788 N
where ρ is the thickness of water and g is the speeding up due to gravity.
Since the buoyant drive is broken even with the weight of the truck furthermore the weight of the uprooted water, we have:
Wtruck + Wwater = Fbuoyant
where Wtruck is the weight of the truck and Fbuoyant is the buoyant drive. Ready to improve this condition to illuminate for the weight of the truck:
Wtruck = Fbuoyant - WWater
The buoyant drive is broken even with the weight of the water uprooted by the watercraft, which we calculated prior to being around 11,788 N. In this manner:
Wtruck = 11,788 N - 0
Wtruck ≈ 11,788 N
So, the weight of the truck is around 11,788 N.
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The full question is
A small ferryboat is 4.00m wide and 6.00m long. When a loaded truck pulls onto it, the boat sinks an additional 5.00cm into the river. What is the weight of the truck?
Kanya makes and sells jewellery items. In one week she sells earrings, bracelets and necklace in the ratio of 13:24:15
What fraction of the total items sold were bracelets?
Give your answer in simplest form
The ratio shows how many times one value is contained in another value.
The fraction of the bracelets from the total items is 6/13.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of earrings, bracelets, and necklace is 13:24:15.
This means,
Earrings = 13x
Bracelets = 24x
Necklace = 15x
The fraction of the bracelets from the total items.
= 24x / (13x + 24x + 15x)
= 24x / 52x
= 24/52
= 12/26
= 6/13
Thus,
The fraction of the bracelets from the total items is 6/13.
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A 0.5-pound bunch of bananas costs $0.22, and 1 pound of oranges cost $2.39. if a person has $20, which expression could be used to determine how much change the person would get after purchasing the 0.5-pound bunch of bananas and 3.25 pounds of oranges?
The expression that can determine the change the person would get after purchasing the 0.5-pound bunch of bananas and 3.25 pounds of oranges is Total cost = 1×0.22 + 7.8
cost of 1 pound of oranges = 2.39
Cost of 3.25 pounds of oranges = 2.39 × 3.25
Performing multiplication
Cost of 3.25 pounds of oranges = $7.8
Forming the expression -
Total cost = cost of 0.5 pound bunch of bananas + cost of 3.25 pound of oranges
Total cost = 1×0.22 + 7.8
Performing multiplication
Total cost = 0.22 + 7.8
Performing addition
Total cost = $8.02
Remaining amount = 20 - 8.02
Performing subtraction
Remaining amount = $11.98
Thus, $11.98 will be the remaining amount.
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Tail length in a population of peacocks has a phenotypic variance
of 2.56 cm2 and an environmental variance of 1.14 cm2. What is the
broad sense heritability (H2)?
The broad sense heritability (H2) for tail length in the population of peacocks is approximately 0.5547, indicating that genetic factors contribute to about 55.47% of the observed phenotypic variance in tail length.
The broad sense heritability (H2) is defined as the proportion of phenotypic variance that can be attributed to genetic factors in a population. It is calculated by dividing the genetic variance by the phenotypic variance.
In this case, the phenotypic variance is given as 2.56 cm², which represents the total variation in tail length observed in the population. The environmental variance is given as 1.14 cm², which accounts for the variation in tail length due to environmental factors.
To calculate the genetic variance, we subtract the environmental variance from the phenotypic variance:
Genetic variance = Phenotypic variance - Environmental variance
= 2.56 cm² - 1.14 cm²
= 1.42 cm²
Finally, we can calculate the broad sense heritability:
H2 = Genetic variance / Phenotypic variance
= 1.42 cm² / 2.56 cm²
≈ 0.5547
Therefore, the broad sense heritability (H2) for tail length in the population of peacocks is approximately 0.5547, indicating that genetic factors contribute to about 55.47% of the observed phenotypic variance in tail length.
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-26 - 4m = -2(2m + 13)
Answer:
Your answer would equal the same on the other side.
-26-4m=-4m-26
if you minus 26 from both sides youll have -4m on both sides also. So it would equal. So you have an Equaled equation if that makes sense.
Mark is 8 inches shorter than two times the height of his little brother bryan. If mark is 52 inches tall , how tall is bryan?
Answer:
60 inches
Step-by-step explanation:
Mark: 52 inches
Bryan: x Inches
X: 52 + 8
52 + 8 = 60
x= 60
Bryan: 60 inches
because mark is 8 inches shorter so bryan is 8 inches taller.