A quadratic function with leading coefficient 1 and roots of p can be expressed as f(x) = (x - p)(x - p), which simplifies to f(x) = x^2 - 2px + p^2.
To construct a quadratic function with leading coefficient 1 and roots of p, we utilize the relationship between the roots and the factors of a quadratic equation. Since p is a root, the factors of the quadratic function would be (x - p) and (x - p). By multiplying these factors together, we obtain the quadratic function f(x) = (x - p)(x - p). Simplifying further, we can expand the expression:
f(x) = (x - p)(x - p) = x^2 - px - px + p^2 = x^2 - 2px + p^2
Hence, the quadratic function with leading coefficient 1 and roots of p is given by f(x) = x^2 - 2px + p^2. This form allows for easy identification of the coefficients and reveals that the constant term of the quadratic is p^2.
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For the function given, state the starting point for a sample period:
ƒ(t) = −100sin (50t − 20).
plz help
Use the form a sin ( b x − c ) + d to find the amplitude, period, phase shift, and vertical shift.
Amplitude: 100
Period: π / 25
Phase Shift: 2 /5 ( 2 /5 to the right)
Vertical Shift: 0
Which shape must have opposite sides that are parallel and congruent, and diagonals that are perpendicular bisectors of each other? A.Parallelogram B.Rectangle C.Rhombus D.Trapezoid
Answer:
C. Rhombus.
Step-by-step explanation:
A rhombus is quadrilateral who each pair of opposite side are parallel and congruent and whose each diagonal is perpendicular to the other diagonal, which bisectors it.
In the cases of rectangle, parallelogram and trapezoid, diagonals are not perpendicular to each other. In the case of the trapezoid, only one pair of sides are parallel.
In consequence, right answer is C.
A car can go 35 1/2 miles in 1 1/2 miles gallons. How many gallons does a car need to go 639 miles?
Need work please!!
Answer: 27 gallons
Step-by-step explanation:
Since the car can go 35½ miles in 1½ miles gallons, we need to first calculate the number of miles that the car can go in 1 gallon. This will be:
= 35½ / 1½
= 71/2 / 3/2
= 71/2 × 2/3
= 23⅔ miles per gallon.
Therefore, the amount of gallons that the car need to go 639 miles will be:
= 639 / 23⅔
= 639 ÷ 71/3
= 639 × 3/71
= 27
The car will need 27 gallons.
What is the surface area of the right prism below?
A. 360 sq. units
B. 384 sq. units
C. 432 sq. units
D. 336 sq. units
The surface area of the right prism cone is,
⇒ 1960 units²
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A right prism shown in image.
Now, We get;
Base area of cone = 14 x 10
= 140
And, Height of cone = 6
And, Perimeter of the base = 2 (10 + 14)
= 280
Thus, WE know that;
The surface area of the right prism cone is,
⇒ 2B + hP
⇒ 2 × 140 + 6 × 280
⇒ 280 + 6 × 280
⇒ 280 + 1680
⇒ 1960 units²
Thus, The surface area of the right prism cone is,
⇒ 1960 units²
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Lily likes to collect records. Last year she had 10 records in her collection. Now she has 11 records,
What is the percent increase of her collection?
The percent increase of her collection is %.
Answer:7
Step-by-step explanation:
Students in an Introductory Statistics class at BYU-Idaho were studying prices of cold cereal at grocery stores in Rexburg. To get a sample of cold cereal prices, they went to Albertson's and rolled a die to decide which box from the left of the top shelf they would start on. They then recorded every 6th cereal after the first, moving from left to right down the shelves, recording the name, size, and price of each cereal in their sample. Is this study an experiment or an observational study, and why
Answer: Observational study
Step-by-step explanation:
The study illustrated in the question is an observational study. It is referred to as an observational study, because in this case, the price of the individual cereals us not being controlled by the students. They've no control over it.
If it was an experiment, there'll have been a control group and the students will have control over the price. Also, the sampling methods used here is a systematic random sampling.
Write the Recursive form and next of the following sequence
8,10,12,14,16...
Answer:
Step-by-step explanation:
The recursive form is a(n + 1) = a(n) + 2, with a(1) = 8.
The next term is a(6) = a(5) + 2, which heere is a(6) = 16 + 2 = 18
A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 1100 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions? The maximum area of the rectangular plot is?
The largest area that can be enclosed with 1100 m of wire is 151,250 square meters, and its dimensions are 275 meters by 550 meters.
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
To find the largest area that can be enclosed with 1100 m of wire, we need to determine the dimensions of the rectangular plot.
Let's denote the length of the rectangular plot as L and the width as W. Since the river forms one side of the plot, we have two equal sides of length L and two sides of length W.
The perimeter of the plot is given by:
Perimeter = 2L + W = 1100 m
We can solve this equation for one variable in terms of the other. Let's solve it for W:
W = 1100 m - 2L
Now, we can express the area A of the rectangular plot in terms of L:
A = L * W
A = L * (1100 m - 2L)
To find the maximum area, we need to find the critical points of the area function A(L) and determine which one corresponds to the maximum. We can do this by finding the derivative of A(L) with respect to L and setting it equal to zero:
dA/dL = 1100 - 4L
Setting dA/dL = 0 and solving for L:
1100 - 4L = 0
4L = 1100
L = 275 m
Substituting this value of L back into the equation for W:
W = 1100 m - 2(275 m)
W = 550 m
So, the dimensions of the rectangular plot that maximize the area are L = 275 m and W = 550 m.
To calculate the maximum area, we substitute these values into the area formula:
A = L * W
A = 275 m * 550 m
A = 151,250 m^2
Therefore, the largest area that can be enclosed with 1100 m of wire is 151,250 square meters, and its dimensions are 275 meters by 550 meters.
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What is the volume, in cubic in, of a rectangular prism with a height of 16in, a width
of 10in, and a length of 17in?
Answer:
45 inches
Step-by-step explanation:
got it right on edg
Answer:
2720
Step-by-step explanation:
Suppose we have a ring R and ideals I and J of R. (a) Denote the set {a+b:a e I and b E J} by I + J. Show that I + J is an ideal of R. (b) Let IJ denote the set of of all sums of the form n Laibi i=1 where ai e I and bi E J and neNt. Show that I J is an ideal of R. (c) Show that I n J is an ideal of R. (d) Show that IJ CINJ (e) The ideals I and J of R are called coprime if there exist a eI and b E J such that a+b = 1. You should check that if in the PID,Z we have ideals I = (m) and J = (v) then the ideals I and J are coprime if and only if m and n are coprime, that is relatively prime. Let I and J be coprime ideals of R. Show that INJ CIJ and thus by the preceding problem I J = I UJ ?
I + J is an ideal of R because it satisfies closure under addition and absorption of elements from R.
To show that I + J is an ideal of R, we need to verify two conditions: closure under addition and absorption of elements from R.
1. Closure under addition:Let x, y ∈ I + J. This means that x = a + b and y = c + d, where a ∈ I, b ∈ J, c ∈ I, and d ∈ J. We have:
x + y = (a + b) + (c + d) = (a + c) + (b + d)
Since a + c ∈ I and b + d ∈ J (as I and J are ideals), (a + c) + (b + d) ∈ I + J. Therefore, I + J is closed under addition.
2. Absorption of elements from R:Let r ∈ R and x ∈ I + J. This means that x = a + b, where a ∈ I and b ∈ J. We have:
rx = r(a + b) = ra + rb
Since ra ∈ I (as I is an ideal) and rb ∈ J (as J is an ideal), ra + rb ∈ I + J. Therefore, I + J absorbs elements from R.
Hence, we have shown that I + J satisfies the conditions of being an ideal of R.
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Determine the domain of the following graph:
12
11
10
8
6
5
2
-12-11-10 -2 -8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8 9 10 11 12
-4
-9
-10
-11
-12
Answer: am not sure i know that one.
Step-by-step explanation:
In a simultaneous inspection of 10 units, the probabilities of getting a defective unit and non-defective unit are equal.
(a) Find the probability of getting at least 7 non-defective units. [5] [BTL-4] [CO02]
(b) Find the probability of getting at most 6 defective units. [5] [BTL-4] [CO02]
The probability of getting at least 7 non-defective units is 0.1718 and the probability of getting at most 6 defective units is 0.8282.In a simultaneous inspection of 10 units, the probabilities of getting a defective unit and non-defective unit are equal.
(a) Probability of getting a defective unit = P(D)Probability of getting a non-defective unit = P(N)P(D)
= P(N) (equal probabilities)P(D)
= 1/2P(N)
= 1/2Total number of units inspected
= 10(a)
Find the probability of getting at least 7 non-defective units
P(X = x) = nCx * P^x * q^(n-x)
Where nCx is the binomial coefficient
P is the probability of successq is the probability of failuren is the total number of trialsx is the number of successes
(a) The probability of getting at least 7 non-defective units
= P(X ≥ 7)P(X ≥ 7)
= P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)P(X = x)
[tex]= nCx * P^x * q^{(n-x)}P(X = 7)[/tex]
= 10C7 * (1/2)^7 * (1/2)^3 = 0.1172P(X = 8)
= 10C8 * (1/2)^8 * (1/2)^2 = 0.0439P(X = 9)
= 10C9 * (1/2)^9 * (1/2)^1 = 0.0098P(X = 10)
= 10C10 * (1/2)^10 * (1/2)^0 = 0.00098P(X ≥ 7)
= 0.1172 + 0.0439 + 0.0098 + 0.00098
= 0.1718
(b) Find the probability of getting at most 6 defective units
P(X = x) = [tex]nCx * P^x * q^{(n-x)}[/tex]
Where nCx is the binomial coefficient P is the probability of success
q is the probability of failuren is the total number of trialsx is the number of successes
(b) The probability of getting at most 6 defective units
= P(X ≤ 6)P(X ≤ 6)
= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)P(X = x)
= [tex]nCx * P^x * q^{(n-x) }\times P(X = 0)[/tex]
= 10C0 * (1/2)^0 * (1/2)^10
= 0.00098P(X = 1)
= 10C1 * (1/2)^1 * (1/2)^9 = 0.0098P(X = 2) = 10C2 * (1/2)^2 * (1/2)^8 = 0.044P(X = 3)
= 10C3 * (1/2)^3 * (1/2)^7 = 0.1172P(X = 4)
= 10C4 * (1/2)^4 * (1/2)^6 = 0.2051P(X = 5)
= 10C5 * (1/2)^5 * (1/2)^5 = 0.2461P(X = 6)
= 10C6 * (1/2)^6 * (1/2)^4 = 0.2051P(X ≤ 6)
= 0.00098 + 0.0098 + 0.044 + 0.1172 + 0.2051 + 0.2461 + 0.2051
= 1- P(X ≥ 7) = 1 - 0.1718= 0.8282
The probability of getting at least 7 non-defective units is 0.1718 and the probability of getting at most 6 defective units is 0.8282.
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How many events are in the sample space if you choose 3 letters from the alphabet (without replacement)? O 17576 O 15600 2600 None of the above
There will be 2600 events are in the sample space if you choose 3 letters from the alphabet (without replacement).
To calculate the number of events in the sample space, we need to consider the number of ways to choose 3 letters from the alphabet without replacement.
The total number of letters in the alphabet is 26. When choosing 3 letters without replacement, the order of selection does not matter. We can use the concept of combinations to calculate the number of events.
The number of combinations of 26 letters taken 3 at a time is given by the formula:
C(26, 3) = 26! / (3!(26-3)!) = 26! / (3!23!) = (26 * 25 * 24) / (3 * 2 * 1) = 2600
Therefore, the correct answer is 2600.
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Can you please help me?
Answer:
-3, -4, -4, 0, 16, 64, 192.
Step-by-step explanation:
I don't know for sure if this is correct, but when i did it theses are the answers i got. You do y=8*2^x. Meaning you substitute the x for the x values such as -3, -2, and -1.
Also if you have one there's a setting you can go to on an actual calculator and type in this on a Y/X chart. I didn't use one this time because i don't have one, but thought you'd find that information useful.
Describe the translation in each function as it relates to the graph of f(x) = x.
g(x)=x-5
Answer:
f(x) was translated to the left by 5 units to form g(x)
Step-by-step explanation:
Given the function f(x) = x to g(x)=x-5, if you look at the g(x) function, you will see that 5 was subtracted from the abscissa x that is;
g(x) = f(x) - 5
This shows' that the function f(x) was translated to the left by 5 units to form g(x). This described the required translation
Examine the two distinct lines defined by the following two equations in slope-intercept form:
Line ℓ: y = 34x + 6
Line k: y = 34x - 7
Are lines ℓ and k parallel?
a) Yes
b) No
We need to check if lines ℓ and k are parallel. For two lines to be parallel, they must have the same slope and different y-intercepts.Let's compare the given lines:Line ℓ: y = 34x + 6Slope of line ℓ = 34Line k: y = 34x - 7Slope of line k = 34We see that the slope of lines ℓ and k is the same (34), which means that they could be parallel.
However, we still need to check if they have different y-intercepts. Line ℓ: y = 34x + 6 has a y-intercept of 6.Line k: y = 34x - 7 has a y-intercept of -7.So, lines ℓ and k have different y-intercepts, which means they are not parallel. Therefore, the correct answer is b) No.In slope-intercept form, the equation of a line is y = mx + b, where m is the slope of the line and b is its y-intercept. In this case, both lines have the same slope of 34 (the coefficient of x). The y-intercepts are different (+6 for line l and -7 for line k). Thus, the lines are not parallel.
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The answer is option a) Yes. Lines ℓ and k are parallel to each other.
The two distinct lines defined by the following two equations in slope-intercept form are:
Line ℓ: y = 34x + 6
Line k: y = 34x - 7
To determine if the lines are parallel, we need to compare their slopes since two non-vertical lines are parallel if and only if their slopes are equal.
Both lines are in slope-intercept form, so we can immediately read off their slopes:
Line ℓ has a slope of 34, and line k has a slope of 34.
Both the lines ℓ and k have the same slope of 34.
Hence, the answer is option a) Yes. Lines ℓ and k are parallel to each other.
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PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
Function 1 has the greatest rate of change.
Step-by-step explanation:
The rate of change is also known as the slope.
Slope is rise over run: change in y over change in x.
Function 1's slope: 3 / 2
Function 2's slope: (0 - (-4)) / (5 - (-5)) = 4/10 = 2/5
3/2 > 2/5
Function 1 has the greatest rate of change.
Please help me with the answer!!!
5x = 7x - 8
7x - 5x = 8
2x = 8
x = 8 ÷ 2
x = 4
3 1/2 X 1 2/3 =
what is it?????
Answer:
[tex]5 \frac{5}{6} [/tex]
Step-by-step explanation:
[tex]3 \frac{1}{2} \times 1 \frac{2}{3} \\ = 5 \ \frac{5}{6} [/tex]
Convert the fractions to improper fractions.
3 1/2 = 7/2
1 2/3 = 5/3
7x5=35
2x3=6
35/6 or 5 5/6
---
hope it helps
PLEASE ANSWER THIS ASAP I WILL MARK YOU THE BRAINLIEST
SHOW YOUR WORK!!!
Calculate the volume of the following three-dimensional object
a child who is 44.39 inches tall is one standaer deviation above the mean. what percent of children are between 41.25 aand 44.29 inches tall?
A child who is 44.39 inches tall is one standard deviation above the mean. Approximately 50.58% of children are between 41.25 and 44.29 inches tall.
To find the percentage of children between 41.25 and 44.29 inches tall, we need to calculate the area under the normal distribution curve within this range.
Given that the child's height of 44.39 inches is one standard deviation above the mean, we can infer that the mean height is 44.39 - 1 = 43.39 inches.
Next, we need to determine the standard deviation. Since the child's height of 44.39 inches is one standard deviation above the mean, we know that the difference between the mean and 41.25 inches is also one standard deviation.
Let's denote the standard deviation as σ. We have:
43.39 - 41.25 = σ
Simplifying the equation:
σ = 2.14
Now, we can calculate the percentage of children between 41.25 and 44.29 inches tall using the z-scores.
The z-score formula is given by:
z = (x - μ) / σ
For the lower bound, x = 41.25 inches:
z₁ = (41.25 - 43.39) / 2.14 = -0.997
For the upper bound, x = 44.29 inches:
z₂ = (44.29 - 43.39) / 2.14 = 0.421
We need to find the area under the normal distribution curve between z₁ and z₂. Using a standard normal distribution table or a calculator, we can find the corresponding probabilities.
Let P₁ be the probability associated with z₁, and P₂ be the probability associated with z₂. Then, the percentage of children between 41.25 and 44.29 inches tall is given by:
Percentage = (P₂ - P₁) * 100
Using the z-score table or a calculator, we find that P₁ ≈ 0.1587 and P₂ ≈ 0.6645.
Substituting these values into the formula:
Percentage = (0.6645 - 0.1587) * 100 ≈ 50.58%
Therefore, approximately 50.58% of children are between 41.25 and 44.29 inches tall.
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Increasingly, developers are using tools that can quickly create screen mockups, referred to as element. A) Protoypes B) Wireframes C) Forms D) Reports
Increasingly, developers are using tools that can quickly create screen mockups, referred to as element Wireframes
Wireframes:Wireframes is a type of tool which is allow designers to quickly and effectively mock up an outline of a design as easily as possible. Designers easily drag the images and drop to placeholder images , header and content also.
There are three types of wireframes, which is very useful :
Low-fidelity wireframes.Mid-fidelity wireframes.High-fidelity wireframes.Wireframes generally is used for visual designer, developer, business analysts, user experience designers and information architecture and user research.
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Find all entire functions f where f(0) = 7, f'(2) = 4, and |ƒ"(2)| ≤ π for all z € C.
All entire functions f where f(0) = 7, f'(2) = 4, and |ƒ"(2)| ≤ π for all z € C are given by f(z) = 2z + 7.
Given that f is an entire function, which means that it is holomorphic on the entire complex plane C. Let us write the Taylor series for f(z) centered at z = 0. Since f is an entire function, its Taylor series has an infinite radius of convergence. Thus, we can write:
f(z) = a0 + a1z + a2z² + · · ·
Differentiating both sides of the above equation with respect to z, we get:
f′(z) = a1 + 2a2z + · · ·
Given that f(0) = 7 and f'(2) = 4, we get the following equations:
a0 = 7
a1 + 4 = f′(2)
Subtracting the second equation from the first, we get:
a1 = −3
Differentiating both sides of the above equation with respect to z, we get:
f″(z) = 2a2 + · · ·
Using the inequality |ƒ"(2)| ≤ π, we get the following inequality:
|2a2| ≤ π
Thus, we get the inequality:
|a2| ≤ π/2
Therefore, the Taylor series for f(z) is given by:
f(z) = 7 − 3z + a2z² + · · ·
where |a2| ≤ π/2.
However, we can further simplify the expression by observing that f(z) = 2z + 7 is an entire function that satisfies the given conditions. Therefore, by the identity theorem for holomorphic functions, we conclude that f(z) = 2z + 7 is the unique entire function that satisfies the given conditions.
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let . explain how to find a set of one or more homogenous equations for which the corresponding solution set is w
The homogeneous equation corresponding to W = Span(2, 1, -3) is 0.
To discover a set of one or more homogeneous equations for which the corresponding answer set is W = Span(2, 1, -three), we will use the idea of linear independence.
The set of vectors v1, v2, ..., vn is linearly unbiased if the only strategy to the equation a1v1 + a2v2 + ... + anvn = 0 (wherein a1, a2, ..., an are scalars) is a1 = a2 = ... = an = 0.
Since W = Span(2, 1, -3), any vector in W may be represented as a linear aggregate of (2, 1, -three). Let's name this vector v.
Now, to find a homogeneous equation corresponding to W, we need to discover a vector u such that u • v = 0, in which • represents the dot product.
Let's bear in mind the vector u = (1, -1, 2). To check if u • v = 0, we compute the dot product:
(1)(2) + (-1)(1) + (2)(-3) = 2 - 1 - 6 = -5.
Since u • v = -five ≠ zero, the vector u = (1, -1, 2) is not orthogonal to v = (2, 1, -3).
To discover a vector that is orthogonal to v, we can take the go product of v with any other vector. Let's pick the vector u = (1, -2, 1).
Calculating the cross product u × v, we get:
(1)(-3) - (-2)(1), (-1)(-3) - (1)(2), (2)(1) - (1)(1) = -3 + 2, 3 - 2, 2 - 1 = -1, 1, 1.
So, the vector u = (-1, 1, 1) is orthogonal to v = (2, 1, -3).
Therefore, the homogeneous equation corresponding to W = Span(2, 1, -3) is:
(-1)x + y + z = 0.
Note that this equation represents an entire answer set, now not only an unmarried solution. Any scalar more than one of the vectors (-1, 1, 1) will satisfy the equation and belong to W.
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The correct question is:
a rectangular window dimensions areX by X +2 and window has a 3 inch frame all the way around the total area of the window and frame is 195 in
Answer:
Length of window = 9 inch
Width of window = 7 inch
Step-by-step explanation:
Given;
Area of window and frame = 195 inch²
Frame width = 3 inch
Length of window = x + 2
Width of window = x
Find:
Value of x
Computation:
Length of window and frame = x + 2 + 3 + 3
Length of window and frame = x + 8
Width of window and frame = x + 3 + 3
Width of window and frame = x + 6
Area of window and frame = (l)(b)
(x + 8)(x + 6) = 195
x² + 6x + 8x + (8)(6) = 195
x² + 14x + 48 = 195
x² + 14x - 147 = 0
x² + 21x - 7x - 147 = 0
x(x + 21) - 7(x + 21) = 0
So,
x + 21 = 0 and x - 7 = 0
So,
X = 7
Value of x = 7
Length of window = 9 inch
Width of window = 7 inch
a transformation of δstv results in δutv. which transformation maps the pre-image to the image? dilation reflection rotation translation
The transformation that maps the pre-image δSTV to the image δUTV is a translation.
A translation is a transformation that shifts each point in a figure by the same distance and in the same direction. In this case, the pre-image δSTV undergoes a transformation resulting in the image δUTV. This indicates that the figure has been moved or shifted.
Unlike other transformations like dilation, reflection, or rotation which involve changing the size, orientation, or mirroring of the figure, a translation specifically involves a shift in position. By applying a translation, each point in the pre-image is moved a certain distance and direction, resulting in the corresponding points of the image. Therefore, the given information suggests that the transformation from δSTV to δUTV is best described as a translation.
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Given the data 4, y, 9, 5, 2, 7. Find y if the mean is 5
Answer:
3
Step-by-step explanation:
(4+y+9+5+2+7)/6=5
(27+y)/6=5
Y=3
a hot dog stand sells two type of hot dogs: plain hot dogs and chili-cheese dogs. plain hot dogs code $3 and chili-cheese dogs cost $5. every hot dog (both kinds) comes with a wrapper. The hot dog salesman notices at the end of the dat he has made $145 and used 38 wrappers
Answer:
i love hotdogs
Step-by-step explanation:
Help ASAP 20 Points
Answer:
volume of hemisphere = 452.16 ft³
volume of cylinder = 2260.8 ft³
total volume = 2712.96 ft³
1/3 full = 904.32 ft³
Step-by-step explanation:
volume of hemisphere = 1/2(4/3)(3.14)(6³) = 452.16 ft³
volume of cylinder = (3.14)(6²)(20) = 2260.8 ft³
total volume = 452.16 + 2260.8 = 2712.96 ft³
1/3 full = 2712.96/3 = 904.32 ft³
Anyone know how to solve?
Answer:
was there more
Step-by-step explanation:
(i will edit answer)