The answer of the given question based on expression is the value of p that satisfies the given condition is -2.
What is Binomial theorem?The binomial theorem is a fundamental concept in algebra that provides a formula for expanding expressions of the form (a + b)ⁿ, where n is a non-negative integer and a and b are real numbers. The formula is as follows:
(a + b)ⁿ = C(n, 0)aⁿ b⁰ + C(n, 1)a⁽ⁿ⁻¹⁾ b¹ + ... + C(n, r)a⁽ⁿ⁻r⁾ b^r + ... + C(n, n)a⁰bⁿ
The binomial theorem states that the nth power of a binomial can be expanded as the sum of the products of each term in the binomial raised to a power and the corresponding binomial coefficient. The binomial coefficient represents the number of ways of choosing r objects from a set of n objects, and is often denoted by "n choose r" or written as a combination symbol, (nCr).
We can use the binomial theorem to expand the given expression as:
(2-3px) (4x⁴ + 5x₃ - x) = 8x⁴ + 10x³ - 2x - 12px⁵ - 15px⁴ + 3px²
To find the coefficient of x⁴ in this expansion, we need to look at the terms that contain x⁴. There are two such terms: 8x⁴ and -15px⁴. Therefore, the coefficient of x⁴ is 8 - 15p.
We are given that this coefficient is 38, so we can set up the equation:
8 - 15p = 38
Solving for p, we get:
-15p = 30
p = -2
Therefore, the value of p that satisfies the given condition is -2.
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volume of a cylinder geometry problems
Answer:
81
Step-by-step explanation:
For 1 rod:
V = πr²h
V = 3.14 × (3 cm)² × 20 cm
V = 565.2 cm³
Total volume of steel used: 45,781.2 cm³
45,781.2 cm³ / 565.2 cm³ = 81
Answer: 81
Question 3(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru is able to estimate their wait time more consistently and why?
Burger Quick, because it has a smaller IQR
Burger Quick, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
Burger Quick's box plot has a larger IQR than Super Fast Food's, hence Super Fast Food is better able to predict their wait time
Define IQR?
A measurement of statistical dispersion, or the spread of the data, is the interquartile range (IQR). It is described as the variation between the data's 75th and 25th percentiles. The fourth spread, middle 50%, midspread, or H-spread1 are further names for the IQR.
The dataset is displayed using a box plot, which is a standardized method based on the five-number summary of the minimum, maximum, sample median, and first and third quartiles
The box plot displays measurements made from data acquired from interviews with 20 people on how long they waited at a drive-through restaurant window.
Burger Quick's box plot has a larger IQR than Super Fast Food's, hence Super Fast Food is better able to predict their wait time.
A data set is divided into quartiles to calculate the IQR (Interquartile Range), which is a measure of variability. The first quartile (Q1) is subtracted from the third quartile (Q3) to determine it.
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Help ASAP
Which of these cylinders has the same volume as one with a radius of 4 ft and a height of 9 ft?
Select one:
a cylinder with a radius of 9 ft and a height of 16 ft
a cylinder with a radius of 3 ft and a height of 4 ft
a cylinder with a radius of 3 ft and a height of 16 ft
a cylinder with a radius of 9 ft and a height of 4 ft
A cylinder with a radius of 3 ft and a height of 4 ft has the same volume as one with a radius of 4 ft and a height of 9 ft.
Explain about the cylinders:We can determine how much interior room a cylinder has by measuring its volume. The volume would be the same as how much material would fill the full can if you had one.
Volume of cylinder = π*r²*h
r is the radius and h is the height.
For given cylinder:
r = 4 ft and h = 9 ft
Volume of given cylinder = π*4²*9
Volume of given cylinder = 144π cu. ft.
Now, from the options:
As, its is clear from formula of cylinder that there is a square of radius.
Thus,
take radius r = 3 ft such that r² = 9 ft and height h = 4 ft.
These are the same dimensions as the given cylinder.
Thus, a cylinder with a radius of 3 ft and a height of 4 ft has the same volume as one with a radius of 4 ft and a height of 9 ft.
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Please what’s 7 divided by 70.85 please show work
Answer:
0.098
Step-by-step explanation:
a pollster wishes to estimate the true proportion of u.s. voters who oppose capital punishment. how many voters should be surveyed in order to be 95% confident that the true proportion is estimated to within 2%?
To be 95% confident that the true proportion of U.S. voters who oppose capital punishment is estimated to within 2%, the pollster should survey 2401 voters.
The pollster wants to estimate a proportion, so we will use the formula for sample size for proportions:
[tex]n=\frac{z^2 * p * (1 - p)}{(E^2}[/tex])
where:
n = sample size
z = the z-score associated with the desired confidence level (95% confidence level corresponds to z = 1.96)
p = an estimate of the true proportion (we don't know this yet, so we will use 0.5 as a conservative estimate that gives the largest sample size)
E = the desired margin of error (2% = 0.02)
Substituting the values into the formula, we get:
[tex]n = \frac{(1.96^2 * 0.5 * (1 - 0.5))} {(0.02^2} = 2401[/tex]
Therefore, the pollster should survey 2401 voters to be 95% confident that the true proportion of U.S. voters who oppose capital punishment is estimated to within 2%.
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Order the steps to solve the equationlog(x2 - 15) = log(2x) form 1 to 5.x2 - 2x - 15 = 0Potential solutions are -3 and 510.00x2 - 15 = 2xX-5 = 0 or x +3=0(x - 5)(x + 3) = 0
To solve the equation \begin{equation}-\log{\left(x^2 - 15\right)} = \log{\left(2x\right)}\end{equation}, the following steps can be taken:
Apply the logarithmic identity log(a) = log(b) if and only if a = b to obtain the equation x^2 - 15 = 2x.
Move all the terms to one side of the equation to get x^2 - 2x - 15 = 0.
Factor the quadratic expression to obtain (x - 5)(x + 3) = 0.
Use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero, to get x - 5 = 0 or x + 3 = 0.
Solve for x in each equation to obtain x = 5 or x = -3.
Therefore, the steps to solve the equation log(x^2 - 15) = log(2x) from 1 to 5 are:
Apply the logarithmic identity to get x^2 - 15 = 2x.
Move all the terms to one side of the equation to get x^2 - 2x - 15 = 0.
Factor the quadratic expression to obtain (x - 5)(x + 3) = 0.
Use the zero product property to get x - 5 = 0 or x + 3 = 0.
Solve for x in each equation to obtain x = 5 or x = -3.
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Combine the like terms to create an equivalent expression.
4n + 11 + 2n =
Answer:
To combine like terms, we add the coefficients of the variable n. Therefore, we can combine the two terms with n: 4n + 2n = 6n The expression becomes: 6n + 11
Question 1
What is the approximate circumference of a plate with a diameter of 11 inches? Use 3.14 for . Round to the nearest
hundredth if necessary.
Answer:
34.54 in
Step-by-step explanation:
The approximate circumference of a plate with a diameter of 11 inches can be calculated using the formula C = πd, where C is the circumference and d is the diameter .
So, substituting the given value of diameter d = 11 inches and taking π to be approximately 3.14, we get:
C = πd = 3.14 x 11 = 34.54 inches (approx.)
Therefore, the approximate circumference of the plate is 34.54 inches.
Since it is required to round the answer to the nearest hundredth, we get the rounded answer as 34.54 rounded off to two decimal places, which is 34.54 (no rounding needed).
Answer: For circumference, you simply multiply the diameter by pi, so the answer you are looking for is 34.54
Step-by-step explanation:
the weights of steers in a herd are distributed normally. the variance is 40,000 and the mean steer weight is 1100lbs . find the probability that the weight of a randomly selected steer is between 1000 and 1520lbs . round your answer to four decimal places.
The probability that the weight of a randomly selected steer is between 1000 and 1520lbs is approximately 0.9192, or 91.92%.
How the probability is between 1000 and 1520lbs is approximately 0.9192, or 91.92%?We are given the variance of the population as 40,000. The standard deviation is the square root of the variance, so we can calculate it as follows:Standard deviation = sqrt(variance) = sqrt(40,000) = 200
We want to find the probability that a randomly selected steer has a weight between 1000 and 1520lbs. We need to standardize these values using the formula:z = (x - μ) / σ
where z is the standardized value, x is the value of interest, μ is the mean, and σ is the standard deviation.
For x = 1000:
z1 = (1000 - 1100) / 200 = -0.5
For x = 1520:
z2 = (1520 - 1100) / 200 = 2.1
Now that we have the standardized values, we can use a standard normal distribution table or a calculator to find the area under the normal curve between z1 and z2.Using a calculator, we can use the normal cdf function with the z-scores to find the area between z1 and z2:
P(z1 < z < z2) = normal cdf(-0.5, 2.1) ≈ 0.9192
Rounding to four decimal places, we get:
P(1000 < x < 1520) ≈ 0.9192
Therefore, the probability that the weight of a randomly selected steer is between 1000 and 1520lbs is approximately 0.9192, or 91.92%.
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Evaluate each determinant
The determinant of the given matrix is -51.
What is determinant?A square matrix's related scalar value is known as a determinant. It is calculated based on the matrix's components using a specified formula. The determinant has several uses in linear algebra, including the resolution of systems of linear equations, the discovery of eigenvalues and eigenvectors, and the assessment of invertibility. If and only if a matrix's determinant is nonzero, the matrix is invertible. The determinant is also employed in other branches of mathematics, such as differential geometry and the determination of the volume of parallelepipeds.
The determinant of the matrix is calculated using the formula:
D = a(ei - fh) - b(di - fg) + c(dh - eg)
Substituting the values we have:
3(-20 - 5(-1)) - (-1)(20 - 54) + 4(2*(-1) - (-2)*(-1)) = -51
Hence, the determinant of the given matrix is -51.
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Sandra uses the formula, P = DB, to find her approximate six-month premium when her driver risk factor, D, is 1.0 and the basic six-month premium is $567.
What will her monthly premium be?
A. $170.00
B. $177.50
C. $94.50
D. $201.15
What are the coordinates of A9-5,2) after the following series of transformations?
a reflection across the x-axis followed by a translation of the rule (x-3, y+4)
Group of answer choices
(-8,6)
(8,6)
(-8,-6)
(8,-6)
The coordinates of the image point A" after the given series of transformations are (6,9,2), which corresponds to answer choice (b) (8,6).
What is series of transformations?A series of transformations is a sequence of two or more geometric transformations applied one after the other to a given figure or object, to produce a new transformed figure or object.
Each transformation in the sequence modifies the position, shape, or orientation of the figure or object in some way.
To find the image of point A(9,-5,2) after the given series of transformations, we can apply them one by one.
Reflection across the x-axis:
1. The reflection of point across the x-axis is obtained by changing the sign of its y-coordinate while keeping the x and z coordinates the same. Therefore, the image of A after reflection across the x-axis is A'(9,5,2).
2. Translation by the rule (x-3, y+4):
This transformation moves the point A' 3 units to the left and 4 units up. Therefore, the coordinates of the image point A" are obtained by subtracting 3 from the x-coordinate and adding 4 to the y-coordinate of A', i.e.,
A" = (9-3, 5+4, 2) = (6,9,2)
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help, how would i solve this if x = 6
x = 6 is a valid solution to the equation 3x + 5 = 23.
However, we can give you some general tips on how to approach a math problem when given a specific value of a variable like x = 6:1. Identify the equation or problem that involves x.2.
Replace every instance of x in the equation with the given value, which in this case is 6.3.
Simplify the equation by performing any necessary operations (addition, subtraction, multiplication, division, etc.)4. Solve for the unknown value if possible.
For example, if the equation is 3x + 5 = 23 and x = 6, we would replace every instance of x with 6:
3(6) + 5 = 23
Simplify by multiplying 3 and 6 and adding 5:
18 + 5 = 23
Simplify further by adding 18 and 5: 23 = 23.
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the student breaks taken during a class session are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes. find the probability that a student break lasts more than 7 minutes.
To find the probability that a student break lasts more than 7 minutes, we can use the z-score formula to standardize the break time and then use the standard normal distribution table or a calculator to find the probability. The probability that a student break lasts more than 7 minutes is approximately 0.3745 or 37.45%.
Step 1: Calculate the z-score.
The z-score formula is given by:
z = (X - μ) / σ
where X is the break time, μ is the mean, and σ is the standard deviation. In this case, X = 7 minutes, μ = 6.3 minutes,
and σ = 2.2 minutes. Plugging in these values:
z = (7 - 6.3) / 2.2 ≈ 0.32
Step 2: Find the probability using the standard normal distribution table or a calculator.
Now that we have the z-score, we can find the probability that a student break lasts more than 7 minutes. We want to find the area to the right of the z-score (0.32) since we are interested in break times longer than 7 minutes.
Using a standard normal distribution table or a calculator, we find that the area to the left of z = 0.32 is approximately 0.6255. However, we want the area to the right of z = 0.32, which is given by:
Area to the right of z = 1 - Area to the left of z
Area to the right of z ≈ 1 - 0.6255 ≈ 0.3745.
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Line segment has end points what is the length of the line segment
With given coordinates of the endpoints of line, the length is 17.75 units.
What are coordinates ?
Coordinates are a set of numbers that describe the position or location of a point in space. In a two-dimensional plane, coordinates are typically represented by two values, an x-coordinate and a y-coordinate, which describe the horizontal and vertical position of a point, respectively.
Now,
The length of a line segment in a two-dimensional plane can be calculated using the distance formula:
d=√[(x₂ - x₁)² + (y₂ - y₁)²]
where (x₁, y₁) and (x₂, y₂) = coordinates of the endpoints of the line segment
In this case, the coordinates of the endpoints are (4.25, 6.25) and (22, 6.25)
d = √[(22 - 4.25)² + (6.25 - 6.25)²]
= √[(17.75)² + (0)²]
= √(315.0625)
= 17.75
Therefore,
the length will be 17.75 units.
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multiple regression is a technique which? allows researchers to predict a criterion variable through a single predictor. indicates the strength of a correlation between variables. indicates the percentage of different quotas in a population. allows researchers to explain a criterion variable through an accurate combination of two or more predictor variables
Multiple regression is a technique which allows researchers to explain a criterion variable through an accurate
combination of two or more predictor variables.
Regression is a statistical measure used in finance, investing and other disciplines that attempts to determine the
strength of the relationship between one dependent variable (usually denoted by Y) and a series of other changing
variables (known as independent variables).
Multiple regression is a statistical method used to analyze the relationship between a dependent variable and multiple
independent variables.
It is often used to estimate the effect of a single independent variable on a dependent variable while controlling for
other independent variables.
Multiple regression is a technique that allows researchers to explain a criterion variable through an accurate
combination of two or more predictor variables.
In summary, multiple regression is a technique that allows researchers to explain a criterion variable through an
accurate combination of two or more predictor variables.
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Which two expressions are
equivalent?
A 8 Divided by 3 and 3/8
B 4 divided by 1 and 1/4
C 6 divided by 7 and 6/7
D 9 divided by 2 and 2/9
Answer:
The two expressions that are equivalent are:
B) 4 divided by 1 and 1/4,
D) 9 divided by 2 and 4/9
Answer: i believe its c
Step-by-step explanation: a division symbol and a fractions bar can mean the same thing.
b. using the random table to obtain a systematic sample: 1. list the steps for using the random number table to obtain a systematic sample. 2. what would be the nth value?
1. To get a systematic sample with a random number table, divide the population size by the desired sample size to obtain the sampling interval, select a random starting point from the first n values where n is the sampling interval, and choose every nth value until the sample size is reached.
2. The nth value is found by dividing the population size by the desired sample size.
Determine the total number of items in the population (N) that you want to sample from. Decide on the desired sample size (n) that you want to obtain from the population.
Calculate the sampling interval (k) by dividing the population size by the desired sample size: k = N / n. Choose a random starting point between 1 and k.
Select every kth item in the population from the starting point until the desired sample size is reached. If the last selection exceeds the population size, start again from the beginning.
The nth value would be the sampling interval (k), which is calculated by dividing the population size by the desired sample size.
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1) What was the interest rate if Nick's balance on an investment of $74,460 at
the end of nine years was $97,153.41 and the interest was compounded
annually? Round your answer to the nearest tenth of a percent.
The interest rate of Nick's investment is 3% per year.
What was the interest rate of Nick's balance on the investment?We can use the formula for compound interest to solve for the interest rate r:
A = P(1 + r/n)^(nt)
r = n[ (A/P)^(1/nt) - 1 ]
Given that:
A = final amount = $97,153.41
P = principal amount = $74,460
n = number of times compounded annually = 1 (compounded annually)
t = time in years = 9
r = annual interest rate r = ?
Solving for rate r as a decimal
r = n[ (A/P)^(1/nt) - 1 ]
r = 1 × [ (97153.41/74640)^(1/1×9) - 1]
r = 0.0297237
Then convert r to R as a percentage
R = r × 100%
R = 0.0297237 × 100%
R = 3% per year.
Therefore, the interest rate is 3%.
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why would you multiply in this problem?
jasper's lawn is 3/4 of an acre is size. the fertilizer bag states that 5 1/2 bags are required for 1 acre. how many bags does jasper need to fertilize his lawn.
the fertilizer bag states that 5 1/2 bags are required for 1 acre. then Jasper needs 33/8 bags of fertilizer to fertilize his lawn.
To solve this problem, you need to find out how many bags of fertilizer Jasper needs to fertilize his lawn, which is 3/4 of an acre in size.
To do this, you need to use the information given on the fertilizer bag, which states that 5[tex]\frac{1}{2}[/tex] bags are required for 1 acre of land.
You can then set up a proportion to find out how many bags Jasper needs. Since Jasper's lawn is 3/4 of an acre in size, you can set up the proportion as follows:
5 [tex]\frac{1}{2}[/tex] bags / 1 acre = x bags / 3/4 acre
To solve for x, you can cross-multiply and simplify:
5 1/2 bags * 3/4 acre = x bags * 1 acre
(11/2) * (3/4) = x
(33/8) = x
Therefore, Jasper needs 33/8 bags of fertilizer to fertilize his lawn. You would multiply in this problem to solve for the unknown variable, x, which represents the number of bags of fertilizer that Jasper needs.
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HELP ME PLEASE! I NEED TO KNOW WHAT FUNCTION THAT IS!
The equation representing the total number of pages read by Victor is: p = 9 + 2m.
Explain about the rate of change:An indicator of how some quantity changes in proportion to another is called a rate of change.
Positive or negative change rates are possible. This reflects a change in the mathematical model -value between the two points of information. Zero change rate refers to a quantity that does not fluctuate over time.
You can determine the amount of change that has occurred over this time period if you have data at two points in time. The outcome is known as the rate of change, sometimes known as the percentage change, and is represented by a percentage (in absolute numbers, it really is merely a difference).
Given data:
Initial number of pages read = 9per minute pages read by Victor = 2Let 'm' be the total number of minute.
Let 'p' be the total number of pages read after 'm' minutes.
p = 9 + 2m
Thus, the equation representing the total number of pages read by Victor is: p = 9 + 2m.
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Length ams breadth and height of rectangle block. Ratio is 4:3:5 and its volume is 3840 cm3 calculate length, breadth, height
The length, breadth, and height of the rectangular block are 256 cm, 192 cm, and 320 cm respectively.
To calculate the length, breadth, and height of a rectangular block whose ratio is 4:3:5 and its volume is 3840 cm3,
follow the steps below:
The ratio of length, breadth, and height is 4:3:5 respectively.
Therefore, assume the length to be 4x, the breadth to be 3x, and the height to be 5x, where x is the common factor.
Then, the volume of the block is calculated as:
Volume = length × breadth × height= 4x × 3x × 5x= 60x³
Since the volume of the block is 3840 cm³, we can equate the equation above to 3840 and solve for x, then find the
length, breadth, and height.
60x³ = 3840 x³ = 3840/60 x³ = 64
Length = 4x = 4 × 64 = 256 cm
Breadth = 3x = 3 × 64 = 192 cm
Height = 5x = 5 × 64 = 320 cm
Therefore, the length, breadth, and height of the rectangular block are 256 cm, 192 cm, and 320 cm respectively.
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rick earns 8.50 per hour at his mothers office he plans on working 12.5 hours this week how much money wil rick earn
Answer:
106.25
Step-by-step explanation:
Answer: The answer is 106.25
Step-by-step explanation: I used a calculator and just multiplied them both.
PLEASE HELP
Use your knowledge of the customary system to circle all the quantities that are less than 16 cups.
A. 6 pints
B. 1 gallon
C. 5 quarts
D. 8 pints
E. 3 quarts
The quantities that are less than 16 cups are: 6 pints (A) and 3 quarts (E).
let's convert each option to cups:
A. 6 pints: There are 2 cups in a pint, so 6 pints × 2 cups/pint = 12 cups.
B. 1 gallon: There are 16 cups in a gallon, so 1 gallon = 16 cups.
C. 5 quarts: There are 4 cups in a quart, so 5 quarts × 4 cups/quart = 20 cups.
D. 8 pints: There are 2 cups in a pint, so 8 pints × 2 cups/pint = 16 cups.
E. 3 quarts: There are 4 cups in a quart, so 3 quarts × 4 cups/quart = 12 cups.
Now, let's see which options are less than 16 cups:
A. 6 pints: 12 cups (less than 16 cups)
B. 1 gallon: 16 cups (not less than 16 cups)
C. 5 quarts: 20 cups (not less than 16 cups)
D. 8 pints: 16 cups (not less than 16 cups)
E. 3 quarts: 12 cups (less than 16 cups)
So, the quantities that are less than 16 cups are: 6 pints (A) and 3 quarts (E).
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which fractions are equivalent to 14? response - incorrect responses 516 5 over 16 36 3 over 6 316 3 over 16 28 2 over 8 520 5 over 20 416 4 over 16
The fractions that are equivalent to 14 are 28 2 over 8 520 5 over 20 416 4 over 16.
To find the fraction = 14, multiply or divide both the numerator and denominator of 14 by the same number.
The fraction 14 can be written as 14/1.
Multiplying the numerator and denominator of 14/1 by 2 gives:
28/2 = 14
Multiplying the numerator and denominator of 14/1 by 3 gives:
42/3 = 14
Multiplying the numerator and denominator of 14/1 by 4 gives:
56/4 = 14
28/2 = 14
70/5 = 14
So the fraction corresponding to 14 is:
28/2
42/3
56/4
70/5
Of the choices given in the question, only 28 equals 2/8, and 56 equals 4/16 14. Any other option is wrong.
So the correct answer is:
28 2/8
56 4/16 .
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PLEASE HELPP
Darci works part-time at a bakery earning $12.10 an hour. In the last five days, her time card shows that she worked 4.7, 7.3, 6.4, 5.8, and 5.1 hours. What is her gross pay for the five days?
A)$451,00
B)$531.80
C)$354.53
D)$56.87
Answer:
Option C.
Step-by-step explanation:
Gross pay = (total hours works) * pay rate
= (4.7 + 7.3 + 6.4 + 5.8 + 5.4) * 12.1
= 29.6 * 12.1
= $358.16
This number is closest to 354.53, so C is the correct answer.
How do you turn 3y+3x=2y-2 into a y=mx+b equation?
Accοrding tο the given infοrmatiοn, the equatiοn y = -3x - 2 represents the same line as the equatiοn 3y+3x=2y-2.
What is an equatiοn?An equatiοn is a mathematical assertiοn that prοves the equality οf twο expressiοns. The equals sign (=) separates the twο sides, which make up the οbject. The expressiοns in the equatiοn's twο sides may include numerical values, variables, and mathematical οperatiοns like additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Tο turn the equatiοn 3y+3x=2y-2 intο the y=mx+b fοrm, yοu need tο isοlate y οn οne side οf the equatiοn.
First, simplify the left-hand side οf the equatiοn by cοmbining the like terms οf 3y and 3x:
3y + 3x = 2y - 2
3y - 2y = -3x - 2
y = -3x/1 - 2/1
Nοw, the equatiοn is in the y=mx+b fοrm, where m is the slοpe and b is the y-intercept. In this case, the slοpe m is -3 and the y-intercept b is -2.
Therefοre, the equatiοn y = -3x - 2 represents the same line as the equatiοn 3y+3x=2y-2.
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The number of bacteria in a test tube is increasing by 25% every hour.
f(1)=4.0 billion
f(n)=f(n−1)+0.25f(n−1)
What will be the value of f(3)?
A. 5.25 billion
B. 6.25 billion
C. 6.0 billion
D. 5.0 billion
The value of f(3) is 6.25 billion, which is option B.
What is Function ?
In mathematics, a function is a rule that associates each input value (also known as the independent variable) with a unique output value (also known as the dependent variable). It is a mathematical object that takes one or more input values and produces an output value.
The input values are usually taken from a set called the domain, and the output values are taken from a set called the range.
We can use the given formula to find the value of f(3) as follows:
f(2) = f(1) + 0.25f(1) = 4.0 billion + 0.25(4.0 billion) = 5.0 billion
f(3) = f(2) + 0.25f(2) = 5.0 billion + 0.25(5.0 billion) = 6.25 billion
Therefore, the value of f(3) is 6.25 billion, which is option B.
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Given that the square root of 225 is 15 and the square root of 256 is 16, which number is closest to the square root of 240?
Responses
15.1
15.1
15.5
15.5
15.8
15.8
15.9
15.9
We can approach this problem by first finding the two perfect squares that 240 lies between:
15^2 = 225 and 16^2 = 256.
Since the square root of 240 must lie between the square root of 225 and 256, we can choose the number that is closest between 15 and 16.
To do this, we can calculate the distance between the square root of 240 and each of the two numbers:
The distance between 15 and the square root of 240 is |15 - sqrt(240)| = 1.18
The distance between 16 and the square root of 240 is |16 - sqrt(240)| = 0.34
Therefore, 16 is closest to the square root of 240.
A chocolate bar takes up an area of 30 cm2. What are the dimensions of the bar, if the length and width have a sum of 13?