Answer:
163 and 164
Step-by-step explanation:
n being defined as an integer
n+(n+1) = 327
2n+1=327
2n=326
n=163
verify answer
163 + (163+1)=327
163+164=327
Answer:
108 + 109 + 110 = 327
I think this is the correct answer
Given the polynomial P(x) = 2x3+ 9x2 + 7x – 6, if (x+ 3) is one of its factors, then what are the other two factors of P(x)?
The other two factors of given polynomial are (x+2) and (2x-1).
What is polynomial?A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.
Sums of terms with the pattern kxn—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction Using the sum of powers in one or more variables multiplied by coefficients, a polynomial is a type of mathematical expression.
Given that x+3 is a factor of polynomial 2x³ + 9x² + 7x - 6. So that
2x³ + 9x² + 7x - 6
⇒ 2x³ + 6x² + + 3x² + 7x - 6
⇒ 2x²(x+3) + 3x² + 7x - 6
⇒ 2x²(x+3) + 3x² + 9x - 2x - 6
⇒ 2x²(x+3) + 3x(x+3) - 2(x+3)
⇒ (x+3)(2x² + 3x - 2)
⇒ (x+3)(2x² + 4x - x - 2)
⇒ (x+3)[2x(x+2) -1(x+2)]
⇒ (x+3)(x+2)(2x-1)
Hence, Factors of given expression are (x+3)(x+2)(2x-1)
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what is the maximum capacity of a cdma system with a chip rate of 3.84 mchips/s at a data rate of 3.84 kbps and an eb/no = 20 (decimal) and beta of .0
The maximum capacity of a CDMA system with a chip rate of 3.84 Mcps at a data rate of 3.84 kbps and an Eb/No = 20 dB and 0 spreading factor (beta) is 20,000 users.
The maximum capacity of a CDMA system depends on several factors, including the chip rate, data rate, Eb/No (energy per bit to noise power spectral density ratio) and the spreading factor (beta).
Given that the chip rate is 3.84 Mcps, the data rate is 3.84 kbps, the Eb/No is 20 dB and the spreading factor (beta) is 0, the maximum capacity of the CDMA system can be calculated using the formula:
Capacity (in users) = (Chip rate / Data rate) x (Eb/No / (2 x beta²))
Capacity (in users) = (3.84 Mcps / 3.84 kbps) x (20 dB / (2 x 0²))
Capacity (in users) = 1,000 x 20
Capacity (in users) = 20,000
Therefore, the maximum capacity of the CDMA system is 20,000 users.
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What is 25 pounds in kilograms?
Kilograms and pounds are two different units of measurements used to measure mass or weight. 25 pounds is equal to 11.34 kilograms. This is because 1 kilogram is equal to 2.2 pounds. To convert pounds to kilograms, you divide the value by 2.2. In this case, 25 divided by 2.2 is equal to 11.34 kilograms.
The Kilogram is a metric unit of mass, while the Pound is a unit of mass used in the imperial system of measurement. The difference between the two can be easily seen when comparing different objects. For example, a pound of apples will weigh much more than a kilogram of apples.
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please hep me asap!!!
a sample of 25 days of operation shows a sample mean of 290 rooms occupied per day and a sample standard deviation of 20 rooms.
The sample mean and sample standard deviation provide valuable information about a set of data, but they should be used with caution when making inferences about the population. It is important to use statistical methods to determine the reliability of these estimates and to account for sources of variability in the data.
Firstly, the sample mean is a measure of central tendency that represents the average value of a set of data. In this case, the sample mean of 290 rooms occupied per day is the sum of the number of rooms occupied each day over the 25-day period divided by the total number of days. It is important to note that the sample mean is only representative of the specific sample of 25 days and may not accurately reflect the population mean.
Secondly, the sample standard deviation is a measure of dispersion that indicates how spread out the data is from the mean. A smaller standard deviation means that the data points are closer to the mean, while a larger standard deviation means that the data points are more spread out. In this case, the sample standard deviation of 20 rooms indicates that there is some variability in the number of rooms occupied each day.
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Step by step explanation pls for 30 points!
Answer:
For (iv) the answer is 26587199959
Step-by-step explanation:
Answer:
(i) - 3 x 49 x 88 = 12,936 21 x 11 = 231
7 x 7 = 49. 11 x 8 = 88
(iv) - 8 x 81 x 4 = 2,592
(vii) - 2 x 3 x 4 = 24
a political scientist investigated the effect of political advertisements on the way that people voted in the presidential election. they want to do a hypothesis test to determine if political advertisements influenced the vote of less than 31% of all voters. the political scientist randomly surveyed 2509 voters and asked if political advertisements influenced the way the person voted. 709 said the advertisements did influence their vote. calculate the test statistic. round your final answer to two decimal places.
The probability of the influenced voters, if The political scientist randomly surveyed 2509 voters, 709 said the advertisements did influence their vote, is 0.283.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a value between 0 and 1.
Given:
The political scientist randomly surveyed 2509 voters, n = 2509,
709 said the advertisements did influence their vote, S = 709,
Calculate the probability of influenced voter as shown below,
\(Probability = S / n\)
Probability = 709 / 2509
Probability = 0.283
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Simplify the expression. (t −2)6 t12
Answer:
6t^13-12t^12
Step-by-step explanation:
6t^12(t-2)
6t^12t+6t^12*-2
6t^12+1 +6t^12*-2
6t^13+6t^12*-2
6t^13-12t^12
6 identical toys weigh 1.8kg. a) convert 1.8kg to grams. b) what is the weight of one toy? Give your answer in grams. c) how much would 4 toys weigh? Give your answer in kilograms
Answer: a) 1800g b) 300g c) 1200g
Step-by-step explanation:
a) 1.8 x 1000 = 1800g
b) 1800g / 6 toys= 300g > the weight of one toy
c) 300g x 4 toys = 1200g / 1000 = 1.2 kg
Answer:
a. 1.8kg to grams
1000g =1kg
x =1.8kg
cross multiply
x = 1.8 x 1000
x= 1800g
b. weight of one toy
6 toys = 1800g
1 toy = 1800÷6
1 toy = 300g
c. 1kg = 300g
4toys = x
x = 4 x 300
x = 1200g
1200g to kilogram
1000g = 1kg
1200g = x
cross multiply
1000x = 1200
x = 1200÷1000
x = 1.2kg
guys plz help will mark brainlyest
Answer:
To Little
Step-by-step explanation:
this problem has too little information because it does not state the weight small rocks and big rocks. Plz give brainily, Thx!
Solve the following initial value problem:
dy/dt=t^2+1, t ≥ 0, y = 6 when t=0
The solution of the initial value problem is \(y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}\)
A differential equation is a mathematical equation that relates a function and its derivatives to some independent variables.
In this case, the differential equation is given by:
dy/dt = t² + 1, t ≥ 0
with the initial value y = 6 when t = 0.
To solve this initial value problem, we can use the method of integrating factor.
We can find the integrating factor for this differential equation by using the formula:
\(= > e^{\intP(t)dt,\)
where P(t) = t² + 1
So,
\(= > e^{\int P(t)dt} = e^{t^3/3 + t}\)
By the product rule, we have:
\(= > d/dt(e^{t^3/3 + t)y} = d/dt(e^{t^3/3 + t)(t^2 + 1)})\)
We can evaluate the integral on the right side using standard integration techniques, and we get:
\(= > e^{t^3/3 + t}y = e^{(t^3/3 + t)(t^3/3 + t^2 + t + C)\)
Finally, we can isolate y by dividing both sides of the equation by e^(t^3/3 + t):
\(= > y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}\)
To find the value of C, we can use the initial value y = 6 when t = 0:
6 = Ce⁰
So, C = 6.
Therefore, the solution to the initial value problem is:
\(y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}\)
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The following are the ages of 13 mathematics teachers in a school district.
29, 32, 33, 33, 35, 41, 42, 43, 44, 51, 53, 56, 58
Notice that the ages are ordered from least to greatest.
Give the median, lower quartile, and upper quartile for the data set.
Answer:
Median = 42
LQ = 33
UQ = 52
Step-by-step explanation:
median is given by the term that divides the groups in two equally quantities. In this case is (n+1)/2 = (13+1)/2 = 14/2 = 7
the 7th term is: 42
(notice this means 6 values are below 42 and 6 values are above 42, the definition of a median)
the first (lower) quartile is given then by the (n+1)/4 value
(13+1)/4=3.5, this is the half between 3th and 4th terms.
since the term is the same (3th value is 33 and 4th value is 33)
LQ=33
(25% of the values are below 33)
for the upper quartile the value represents the top 75%, this is given by
3(13+1)/4 = 10.5
this is the half between 10th and 11th terms
(51+53)/2=52
(25% of the values are above 52)
If JH is the perpendicular bisector of GI, what is JI ?
Length of segment JI is: C. 21.
Recall:
A perpendicular bisector is a segment that divides a segment into equal halves.
Thus:
JH divides GI into GH and HI
Therefore:
\(GH = HI = 15\)
Also, since JH in right triangle JHG = JH in right triangle JHI, therefore:
the third side, GJ in right triangle JHG, will equal the third side, JI in right triangle JHI.
GJ = JI = 21
Therefore, JI is 21.
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Answer:
C. 21
Step-by-step explanation:
I got it right one the test, also on the other side it says 21, and they're the same length, soo
11) A local school board wants to randomly select five teachers from their population of 354 teacher to
get their opinions on a new proposed salary schedule. The school board wants to ensure that the sample reflects
their population of interest. From the population, the average teaching salary is $43,000 with a standard
deviation of $5,600. If the five teachers have an average salary of $49,000, should we be concerned that the
sample does not accurately reflect the population?
(A) Yes we should be concerned; the probability that we get a sample of 5 with a mean salary of $49,000 or
greater is 0.1420.
(B) Yes we should be concerned; the probability that we get a sample of 5 with a mean salary of $49,000 or
greater is 0.0083.
(C) Yes we should be concerned; the probability that a randomly selected teacher has a salary of $49,000 is
0.0083.
(D) No we should not be concerned; the probability that a randomly selected teacher has a salary of $49,000 is
0.1420.
(E) No we should not be concerned; the probability that a randomly selected teacher has a salary of $49,000 is
0.0083.
Yes we should be concerned; the probability that we get a sample of 5 with a mean salary of $49,000 or greater is 0.0083.
How to determine if a sample accurately reflects a population using sample means and standard deviation ?
We can use a t-test to determine if the sample accurately reflects the population. The null hypothesis is that the sample mean is equal to the population mean, and the alternative hypothesis is that the sample mean is greater than the population mean.
t = (sample mean - population mean) / (standard deviation / square root of sample size)
Determine if a sample accurately reflects a population :
Plugging the given values in the above formula, we get:
\(t = (49000 - 43000) / (5600 / \sqrt{5}) = 2.60\)
Using a t-distribution table with 4 degrees of freedom (sample size - 1), we can find the probability of getting a t-value of 2.60 or greater. The probability is 0.0083, which is less than the usual significance level of 0.05.
Therefore, we can reject the null hypothesis and conclude that the sample mean of $49,000 is significantly different from the population mean of $43,000.
This suggests that the sample may not accurately reflect the population, and we should be concerned about the validity of our sample.
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let x stand for the number of minutes spent at the mall. 100 people are sampled at a time. for the sampling distribution, the mean is 46 minutes and the standard deviation is 0.4 minutes. what is the mean and standard deviation of the population? a.) mean
The mean of the population is 46 and standard deviation of the population is 4.
The mean of the sampling distribution of the sample mean will always be the same as the mean of the original non-normal distribution. In other words, the sample mean is equal to the population mean. Based on the information provided, the population mean is 46 minutes same as the mean of sample.
The standard deviation of the sampling distribution of means is equal to the standard deviation of the population divided by the square root of the sample size. Hence, standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the same size. Standard deviation 0.4 minutes and sample size is 100, hence standard deviation = 0.4/√100 = 0.4/10 = 4.
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which of these af3 molecules will have a nonzero dipole moment? choose all that apply. which of these molecules will have a nonzero dipole moment?choose all that apply. request answer
The first molecule will have a ZERO dipole moment since all the F atoms are at 120 degree making the net dipole zero.
What exactly is a molecule?A molecule is a group of two or more atoms held together by chemical bonds; depending on the context, the term may or may not include ions that meet this criterion.
A molecule is a particle composed of two or more atoms that are chemically bonded together; the number of atomic nuclei constituting a molecule is fixed. HCl(g), for example, is a molecule composed of one hydrogen atom bonded to one chlorine atom. It is a diatomic molecule because it is composed of two atoms.
The second molecule will have a NON ZERO dipole moment. The net dipole moment will be downwards. The third molecule will have a NON ZERO dipole moment.
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Is (3, 28) a solution to 4x-y=-16
Answer:
Yes
Step-by-step explanation:
4(3) - 28 = -16
12= -16 + 28
12 = 12
Hope that helps!
Factor completely, than place the factors in the proper location on the grid
Y^2x -y^x-20
Answer: Cannot be factored
Step-by-step explanation:
= Factor Y^2x -y^x-20
= Cannot be factored
Can anyone tell me if my answer to this problem is correct? I'm stuck, but have a guess at an answer. y = 2^x ?
Your guess is
\(y=2^x\)If all the tabular values satisfy the equation, this is the right answer. Let's check:
If x = 0
y = 2^0 = 1
If x = 1,
y = 2^1 = 2
If x = 2,
y = 2^2 = 4
If x = 3
y = 2^3 = 8
All the values from the table area satisfied via the equations y = 2^x.
Thus, the equation representing the table is:
\(y=2^x\)3x - 5(x -5) = - 3 + 5x + 7
Answer:
x=3
Step-by-step explanation:
3x-5x+25= 5x+4
-2x+25=5x+4
+2x. +2x
25=7x+4
-4. -4
21=7x
/7. /7
3=x
Hopes this helps please mark brainliest
Answer:
x = 3Step-by-step explanation:
3x - 5(x -5) = - 3 + 5x + 7
3x - 5x + 25 = 4 + 5x
3x - 5x -5x = 4 - 25
-7x = -21
x = -21 : (-7)
x = 3
Worth 60 points for a rapid reply- find the area of each regular polygon. Answers are rounded to the nearest whole number.
The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
How to calculate for the area of the polygonArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of octagon × (n)number of side.
apothem = s/[2tan(180/n)].
11 = s/[2tan(180/12)]
s = 11 × 2tan15
s = 5.8949
perimeter = 5.8949 × 12 = 70.7388
Area of dodecagon = 1/2 × 11 × 70.7388
Area of dodecagon = 389.0634 in²
Area of pentagon = 1/2 × 5.23 × 7.6
Area of pentagon = 19.874 in²
Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.
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A famous golfer tees off on a straight 380 yard par 4 and slices his drive to the right. The drive goes 270 yards from the tee. Using a 7-iron on his second shot, he hits the ball 170 yards and it lands inches from the hole. How many degrees (to the nearest degree) to the right of the line from the tee to the hole did he slice his drive?
The golfer sliced his drive approximately \(40\) degrees to the right of the line from the tee to the hole, according to the trigonometry used.
To determine the angle to the right of the line from the tee to the hole at which the golfer sliced his drive, we can use trigonometry.
The golfer's slice forms a right triangle, where the adjacent side is the distance the drive went (\(270\) yards) and the hypotenuse is the distance of the par 4 (\(380\) yards). Using the inverse trigonometric function, we can calculate the angle.
To calculate the angle at which the golfer sliced his drive, we can use the inverse tangent function:
\(\[\theta = \arctan\left(\frac{{\text{{adjacent side}}}}{{\text{{hypotenuse}}}}\right)\]\)
Substituting the values, we have:
\(\[\theta = \arctan\left(\frac{{270}}{{380}}\right)\]\)
Calculating this in degrees, we find:
\(\[\theta \approx 40^\circ\]\)
Therefore, the golfer sliced his drive approximately \(40\)degrees to the right of the line from the tee to the hole.
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O No; there are y-values that have more than one x-value.
• No; the graph fails the vertical line test.
• Yes; the graph passes the vertical line test.
Yes; there are no y-values that have more than one x-value.
The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.
How do functions work?According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.
Please refer to the image instead of the graph, which is related to it.
The graphic displays a graph.
A parabola is seen on the graph.
The vertical line test determines if a graph can be a function, as is common knowledge.
The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.
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Describe how the graph of the function is a transformation of the graph of the original function f(x)?
Answer:
This is how
Step-by-step explanation:
A function transformation takes whatever is the basic function f (x) and then "transforms" it (or "translates" it), which is a fancy way of saying that you change the formula a bit and thereby move the graph around. ... Moving the function down works the same way; f (x) – b is f (x) moved down b units.
Answer:
reflected over the x-axiscompressed horizontally by a factor of 3Step-by-step explanation:
Multiplying a function by -1 reflects its graph over the x-axis. Multiplying x by a factor compresses the graph horizontally by that factor.
The graph of g(x) is the graph of f(x) ...
reflected over the x-axiscompressed horizontally by a factor of 3an airplane is flying at an elevation of 1500 feet. what is the airplane's angle of elevation (exact and decimal) from the runway when it is 5000 feet from the runway?
The airplane's angle of elevation from the runway is approximately 17.36 degrees, and the distance between the plane and the ground is 4772.79 ft.
Here are the main answers to the question:
First, we will find the distance between the plane and the ground:5000² = 25000000+ 1500² = 2250000d² = 22750000d = 4772.79 ft.
To find the angle of elevation, we will use the tangent ratio:tan A = opposite/hypotenuse = 1500/4772.79A = tan⁻¹(1500/4772.79)A = 17.36°.
The airplane's angle of elevation from the runway is approximately 17.36 degrees.
In conclusion, the airplane's angle of elevation from the runway is approximately 17.36 degrees, and the distance between the plane and the ground is 4772.79 ft.
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Find The Point On The Plane 4x - Y + 4z = 40 Nearest The Origin. (X, Y, Z) =
To find the point on the plane nearest to the origin, we need to minimize the distance between the origin and any point on the plane. We can use the formula for the distance between a point and a plane. The point on the plane nearest to the origin is (2, 12, 2).
distance = |ax + by + cz + d| / sqrt(a^2 + b^2 + c^2)
where (x, y, z) is any point on the plane, and a, b, c, and d are the coefficients of the plane equation.
In our case, the plane equation is 4x - y + 4z = 40, so a = 4, b = -1, c = 4, and d = -40. The distance between the origin and any point on the plane is:
distance = |4x - y + 4z - 40| / sqrt(4^2 + (-1)^2 + 4^2)
We want to minimize this distance, so we need to find the point on the plane that makes the distance as small as possible. To do this, we can use Lagrange multipliers:
Let f(x, y, z) = (x^2 + y^2 + z^2) be the function we want to minimize subject to the constraint 4x - y + 4z = 40. We can write this as:
grad(f) = λ grad(g)
where grad(f) = <2x, 2y, 2z> and grad(g) = <4, -1, 4>. Solving for x, y, z, and λ, we get:
x = 2, y = 12, z = 2, λ = 8 / sqrt(33)
Therefore, the point on the plane nearest to the origin is (2, 12, 2).
To find the point on the plane 4x - y + 4z = 40 nearest to the origin, we can use the formula for the distance between a point and a plane: D = |Ax + By + Cz + D| / √(A² + B² + C²).
In this case, A = 4, B = -1, C = 4, and D = -40. Let's plug in the origin (0, 0, 0) for (x, y, z):
D = |(4*0) - (1*0) + (4*0) - 40| / √(4² + (-1)² + 4²)
D = |-40| / √(16 + 1 + 16)
D = 40 / √33
Now, we use the normal vector (4, -1, 4) and multiply it by the distance D to find the nearest point (x, y, z):
x = (4 * 40) / √33
y = (-1 * 40) / √33
z = (4 * 40) / √33
The nearest point (x, y, z) on the plane 4x - y + 4z = 40 to the origin is approximately (4.94, -1.24, 4.94).
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(4/5)^(- 2)I need to rewrite this without an exponent.
ANSWER
\(\frac{25}{16}\)EXPLANATION
We have the fraction:
\((\frac{4}{5})^{-2}\)To simplify this, we can apply a law of indices.
One of laws of indices states that if a fraction is raised to a negative power, we can simplify it by swapping the numerator and denominator and making the power positive.
In other words:
\((\frac{4}{5})^{-2}\text{ becomes (}\frac{5}{4})^2\)Simplifying that we have:
\(\begin{gathered} (\frac{5}{4})^2\text{ = }\frac{5^2}{4^2} \\ =\text{ }\frac{25}{16} \end{gathered}\)That is the answer.
A bridge, PR, across a river is 400 m long. Gabe is launching a canoe at point Q.
He will paddle in a diagonal line across the river to point P. He plans to return along a route beside the bridge from P to R, and then along the shore from R back to Q. How far will this be altogether?
Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.
To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.
First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.
The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.
Using the Pythagorean theorem, we have:
x^2 + (width of the river)^2 = PR^2
Since the width of the river is not given, we'll represent it as w. Therefore:
x^2 + w^2 = 400^2
Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.
Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.
To find the total distance, we add up the distances:
Total distance = QP + PR + RQ
= x + 400 + x
= 2x + 400
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To make a batch of four dozen cookies, Denis needs 1 3/4 cups of four, 1 cup of sugar, and 1/3 cup of milk. Calculate the amount of each ingredient that Denis needs to make 12 dozen cookies
Answer:
Flour = 5 1/4 Cups
Sugar = 3 Cups
Milk = 1 Cup
Step-by-step explanation:
4 Dozens = Respectively 1 3/4, 1, and 1/3 Cups -->
4(3) = 12 Dozens --> Otherwise A Gross
--> Multiply the formula by 3
7/4 x 3 = 21/4
1 x 3 = 3
1/3 x 3 = 1
Convert to a mixed number
Thus You have your answers
Hope this helps!
Mark
the absolute maximum point of the graph.
Answer:
6
Step-by-step explanation:
Answer:
Point (0,6)
Step-by-step explanation:
Point (0,6) is the highest point plotted on the graph.