The number of square inches or area of gift wrap that the makeup artist will need is 10.8π square inches.
Given that,
A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap.
Radius of each lipstick = 0.6 inch
Height of the lipstick = 2.4 inches
Now,
Area of the each lipstick = 2πrh + 2πr², where r is the radius and h is the height.
Area = 2π (0.6) (2.4) + 2π (0.6)²
= 2.88π + 0.72π
= 3.6π
Area of the wrap for 3 lipsticks = 3 × 3.6π = 10.8π square inches.
Hence the area is 10.8π square inches.
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Carson and his children went into a restaurant where they sell hamburgers for $6 each and tacos for $2.50 each. Carson has $65 to spend and must buy a minimum of 12 hamburgers and tacos altogether. If Carson decided to buy 8 tacos, determine the maximum number of hamburger that he could buy.
A wolf leaps out of the bushes and takes a hunter by surprise. Its trajectory can be mapped by the equation f(x) = −x2 + 11x − 18. Write f(x) in intercept form and find how far the wolf leaped using the zeros of the function. (1 point)
y = (x − 3)(x + 6); the wolf leaped a distance of 9 feet using zeros −6 and 3
y = −(x − 3)(x − 6); the wolf leaped a distance of 3 feet using zeros 3 and 6
y = −(x − 2)(x − 9); the wolf leaped a distance of 7 feet using zeros 2 and 9
y = (x + 2)(x − 9); the wolf leaped a distance of 11 feet using zeros −2 and 9
y = −(x − 2)(x − 9); the wolf leaped a distance of 7 feet using zeros 2 and 9. Therefore, option B is the correct answer.
Given that, trajectory can be mapped by the equation f(x) = -x² + 11x - 18.
Here, -x² + 11x - 18=0
-x² + 9x+2x - 18=0
-x(x-9)+2(x-9)=0
(x-9)(-x+2)=0
x-9=0 and -x+2=0
x=9 and x=2
Therefore, option B is the correct answer.
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When you order a salad from Nelly's Deli, you can choose from 5 different base salads, 3 different proteins, and 6 different dressings. How many different combinations for a salad are possible?
Answer:
90
Step-by-step explanation:
This type of problem is an example of combinations. In this case, in one salad, it states that you can chose between 5 bases, 3 proteins, and 6 dressings.
In this problem, you would have to multiply all numbers together.
In this case, 5(bases)x3(protiens)x6(dressings)=90
I hope this helps you!
can my a value be negative in a exponential function
Yes, the coefficient of a value can be negative in an exponential function.
How is this possible?A coefficient in mathematics is a multiplicative factor in some term of a polynomial, series, or expression; it is generally a number, although it can be any expression.
Recall that the general form of an exponential function is f(x) = a^(bx + c), where a is the base.
This can be negative or positive. But cannot be equal to zero. A negative exponential function can model the decay of a radioactive substance or, in accounting, depreciation of an asset.
Thus, it is correct to state that , the coefficient a value can be negative in an exponential function.
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QUESTIONS 1. Explain and illustrate the difference between and (4) 2. Explain and illustrate the difference between ratio and proportional reasoning. Do not copy definitions from any source but use your own understanding. (4) 3. Illustrate with a drawing or diagram what "fifth" means in each of the following instances: ● ordinal number ● unit fraction 4. Show with a diagram 3, using the following: 1.1 the area model 1.2 set mode 1.3 the length model (3) 2. A rectangular piece of paper has a perimeter of 54 cm. Its length is 1 of its width. Find its dimensions. (3) 3. If the given regular hexagon represents one whole: 3.1 Show three sixths. 3.2 Write the equivalence 6.1 above. 3 Represent+ in the figure given to prove that a set of two halves 6 make a whole. (4) 6.3.1 Draw a number line showing a whole made of six equal parts. Show the sum of two halves on the same number line. (1) (1) (2) (3)
The difference between 1/5 and 2/10 is that they are different representations of the same value.
The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.
"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.
The diagram can be used to illustrate fraction concepts.
How to solve1/5 is simple, but 2/10 can be reduced to 1/5 by dividing both numbers by 2. They are both 0.2 or 20%. 1/5 and 2/10 are different fractions with different purposes.
Use 1/5 for 5 parts and 1/5 (simplified from 2/10) for 10 parts. 1/5 and 2/10 = 0.2, ratio reasoning emphasizes ratios between quantities. A 2:3 boys-to-girls ratio compares the constant ratio between changing quantities.
Proportional reasoning maintains constant ratios between quantities, while ratio reasoning uses fractions or ratios to compare relationships. For instance, if distance doubles, so does speed.
Step 3/5: "Fifth" is the ordinal number for the object five places away in a sequence. See diagram. The fifth circle is 1/5 of a whole in unit fraction sequence. Imagine a rectangle divided into five equal parts, each shaded to show 1/5. Shaded part = 1/5 of whole.
To show 25/7 with area model, make 7x25 rectangle and split into 7 equal parts. 25/7 per part.
1.2 The set model:
To represent 25/7, divide 25 objects into 7 equal sets, resulting in 3 objects per set with 1 left over. This represents the fraction of 25/7.
Step 5/5
Let's assume the width of the rectangular piece of paper as x cm. Then the length of the paper would be:
Now we know that the perimeter of the rectangle is given by the formula:
So, for this rectangle:
54 = 2(5x + x)
Simplifying and solving for x, we get:
54 = 2(6x)
27 = 6x
x = 4.5 cm
Therefore, the width of the paper is 4.5 cm and the length is 5 times the width which is 22.5 cm
The difference between 1/5 and 2/10 is that they are different representations of the same value.
The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.
"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.
The diagram can be used to illustrate fraction concepts.
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Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse.
-10
The graph of the inverse function is given by the image presented at the end of the answer, and the correct option is given by option 3.
How to obtain the inverse function?The parent function for this problem is the cube function translated up two units, hence it is defined as follows:
y = x³ + 2.
To obtain the inverse function, first we must exchange the variables x and y on the definition of the function, as follows:
x = y³ + 2.
Then we must isolate the variable y, as follows:
[tex]y^3 = x + 2[/tex]
[tex]y = \sqrt[3]{x + 2}[/tex]
Which has the correct dashed graph given by option 3 on the image given.
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Give the domain and range. On a coordinate plane, points are at (negative 2, negative 1), (0, 1), (2, 3). a. domain: {2, 0, 2}, range: {1, 1, 3} b. domain: {–1, 1, 3}, range: {–2, 0, 2} c. domain: {–2, 0, 2}, range: {–1, 1, 3} d. domain: {1, 1, 3}, range: {2, 0, 2} Please select the best answer from the choices provided A B C D
Answer:
c. domain: {-2, 0, 2}, range: {-1, 1, 3}
Step-by-step explanation:
From the given points (negative 2, negative 1), (0, 1), (2, 3), we can determine the domain and range.
The domain represents the set of all possible x-values of the points, and the range represents the set of all possible y-values of the points.
In this case, we can see that the x-values are -2, 0, and 2, and the corresponding y-values are -1, 1, and 3.
Therefore, the correct answer is:
c. domain: {-2, 0, 2}, range: {-1, 1, 3}
Find the equation of the line.
Use exact numbers.
Answer:
y = - 3x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line
m = [tex]\frac{1-7}{2-0}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3
the line crosses the y- axis at (0, 7 ) ⇒ c = 7
y = - 3x + 7 ← equation of line
The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7
Writing the equation of the line in slope-intercept form.The linear graph represents the given parameter
For the graph, we have the points
(0, 7) and (25, 0)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 7
Using the point (2.5, 0) on y = mx + 7, we have
m(2.5) + 7 = 0
2.5m + 7 = 0
Evaluate
m = -2.8
So, we have
y = -2.8x + 7
Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7
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answer the following steps to find the volume of the composite figure. what is the volume the 3 mm tall cone? what is the volume of the cylinder? what is the volume of the 1 mm tall cone? what is the volume of the composite figure?
We are unable to determine the volumes of the individual components and the composite figure due to missing data on the radii and precise component configurations.
We must determine the volumes of the three separate parts—a cylinder, a 1 mm tall cone—in order to get the volume of the composite figure.
The 3 mm tall cone's volume is:
The formula [tex]V = (1/3)r^{2} h,[/tex] where r is the radius of the base and h is the height, determines the volume of a cone.
We must determine the radius because the cone's height is 3 mm. We are unable to determine the volume of the 3 mm tall cone without additional information.
Dimensions of the cylinder:
The formula V = r2h, where r is the radius of the base and h is the height, determines the volume of a cylinder.
We are unable to determine the volume of the cylinder without precise measurements for its height and radius.
Volume of the 1 mm tall cone: Once more, in order to calculate the volume of the 1 mm tall cone, we need to know the radius of the base. Without this additional information, we are unable to do so.
The composite figure's volume:
We would need to know the sizes and configurations of the different parts (cones and cylinder) within the composite figure in order to determine its volume.
We are unable to determine the volume of the composite figure without this information.
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The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 7.4% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. (a) Explain why this is a binomial experiment.
(b) Assuming his suspicion that 7.4% of his customers buy a magazine is correct, what is the probability that exactly 3 out of the first 14 customers buy a magazine? Give your answer as a decimal number rounded to two digits.
(c) What is the expected number of customers from this sample that will buy a magazine?
The experiment is binomial , probability that 3 out of 14 customers buy a magazine is 0.06 and the expected value is 1.036.
Part AThe experiment described is binomial because it satisfies the following conditions:
There are a fixed number of trials, which is 14 in this case.Each trial has two possible outcomes: The outcome of each trial is whether or not a customer buys a magazine. The probability of success is constant. 7.4%The trials are independent: Each customer's behavior is independent of others.Part BThe probability that exactly 3 out of the first 14 customers buy a magazine. Using the binomial probability formula:
[tex]P(X = k) = (nCk) \times (p^k) \times {q}^{n - k} [/tex]
Where:
n = number of trials (14 in this case)
k = number of successful trials (3 in this case)
p = probability of success (7.4% or 0.074)
q = 1-p
Plugging in the values:
P(X = 3) = (14C3) × (0.074³) × 0.926¹¹
P(X= 3) = 0.0633
Part CThe expected number of customers from this sample that will buy a magazine can be calculated using the formula:
E(X) = n × p
Where:
- n is the number of trials
- p is the probability of success
Plugging in the values:
E(X) = 14 × 0.074 = 1.036
Therefore, the experiment is binomial and the expected value is 1.036.
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Solve the system using substitution. Show all work.
-12x + 5y = 9
y = 2x - 5
Solution of the given system is,
x = 8
y = 11
The given system of equation
-12x + 5y = 9 ....(i)
y = 2x - 5 ...(ii)
Now we have to solve it by using substitution method.
So put value of y from equation (ii) into equation (i)
Therefore,
⇒ -12x + 5y = 9
⇒ -12x + 5(2x - 5) = 9
⇒ -12x + 10x - 25 = 9
⇒ -2x = 16
⇒ x = 8
Now put the values of x into (ii) we get,
⇒ y = 2x8 - 5
⇒ y = 11
Hence,
solutions be ,
x = 8
y = 11
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Solve for x.
-3
X=
X
= -48
Answer:x = {-4, 4}
explanation:
7. A scuba diver's depth in yards as a function of time in minutes (x) is
represented by the equation d(x) = 12x² - 144x.
a. What was the deepest the diver went?
b. How long did it take the diver to return to the surface?
c. How deep was the diver after one minute?
a) The deepest that the diver went is of: 432 yards deep.
b) It took 12 minutes for the diver to return to the surface.
c) After one minute, the diver was 132 yards deep.
How to obtain the features?The quadratic function modeling the diver's height after x seconds is given as follows:
d(x) = 12x² - 144x.
The coefficients are given as follows:
a = 12, b = -144, c = 0.
The x-coordinate of the vertex is given as follows:
x = -b/2a
x = 144/24
x = 6.
Item a:
As a > 0, in item a, the minimum height is given as follows:
d(6) = 12(6)² - 144(6)
d(6) = -432 feet.
Item b:
The roots of the function, in item b, are obtained as follows:
12x² - 144x = 0
12x(x - 12) = 0
Hence:
12x = 0 -> x = 0.x - 12 = 0 -> x = 12.12 - 0 = 12, hence it took 12 minutes for the diver to return to the surface.
Item c:
After one minute, the depth of the diver, in item c, is given as follows:
d(1) = 12(1)² - 144
d(1) = -132 yards.
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The following figure is made of 2 triangles. Figure Triangle A Triangle B A Whole figure 9 Find the area of each part of the figure and the whole figure. 7 B 3 Area (square units)
Area of triangle A = 13.5 square units
Area of triangle B = 10.5 square units
Total area of figure = 24 square units
In the given figure,
It consist of two triangles
Now for triangle A :
Height = 3
Base = 9
Since we know that,
Area of triangle = (1/2) x base x height
= 0.5 x 9 x 3
= 13.5 square units
Now for triangle B :
Height = 3
Base = 7
Since we know that,
Area of triangle = (1/2) x base x height
= 0.5 x 7 x 3
= 10.5 square units
Now the total are of figure is sum of are of both triangles,
Therefore,
total area of figure,
⇒ 13.5 + 10.5
⇒ 24 square units
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The missing figure of question is attached below:
100 points! A list of rational numbers is given.
one and four fifths, negative seven fourths, forty-one percent, negative 1.3
Part A: Rewrite all the values into an equivalent form as fractions. (3 points)
Part B: Rewrite all the values into an equivalent form as decimal numbers. (3 points)
Part C: List the given rational numbers from greatest to least. (3 points)
Part D: How did you determine their order? Please explain your answer. (3 point)
The ascending order of the rational numbers are -1.75 < -1.3 < 0.41 < 1.8
Given are the list of the rational numbers, so,
1 4/5, -7/4, 41% and -1.3
So,
1) The fraction form :-
a) 1 4/5 = 9/5
b) -7/4
c) 41% = 41/100
d) -1.3 = 13/10
2) The decimal form :-
a) 1 4/5 = 9/5 = 1.8
b) -7/4 = -1.75
c) 41% = 41/100 = 0.41
d) -1.3 = 13/10 = -1.3
3) The ascending order of the rational numbers =
You can arrange them by seeing the value and sign,
-1.75 < -1.3 < 0.41 < 1.8
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Finding missing sides with trig rations
-Solve for x. Round to the nearest tenth.
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
hello
the answer is:
1)
Sin 28° = x/19 ----> x = 8.91 or 9
2)
tan 41° = x/32 ----> x = 27.8 or 28
3)
Cos 21° = x/26 ----> x = 24.2 or 24
4)
Cos 55° = 8/x ----> x = 13.9 or 14
5)
Sin 33° = 15/x ----> 27.57 or 28
6)
Cos 43° = 36/x ----> x = 49.2 or 49
7)
tan 72° = 25/x ----> x = 8.12 or 8
8)
Cos 64° = x/11 ----> x = 4.81 or 5
Help me figure this out
Answer:
35
Step-by-step explanation:
perimeter = sum of the lengths of the sides
In a parallelogram, opposite sides are congruent.
Two sides have length 7.5 cm.
We need the length of the top and bottom sides.
area = base × height
62 cm² = base × 6.2 cm
base = (62 cm²)/(6.2 cm)
base = 10 cm
Two sides have length 10 cm.
perimeter = 7.5 cm + 7.5 cm + 10 cm + 10 cm
perimeter = 35 cm
Type the correct answer in the box. Use numerals instead of words.
For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.
Simplify the numerical expression.
2
3
÷
2
4
+
(
3
4
+
1
6
)
÷
1
3
The expression has a value equal to
Answer:67/24
hope it helps bye
The expression equivalent to the given numerical expression is 67/24.
The given numerical expression is 2/3 ÷ 2⁴+(3/4 +1/6)÷1/3.
Here, 2/3 ÷ 2⁴+(3/4 +1/6)÷1/3
= 2/3 ÷ 16+(9/12 +2/12)÷1/3
= 2/3 × 1/16 +11/12 ×3/1
= 2/48 + 33/12
= 1/24 + 33/12
= 1/24 + 66/24
= 67/24
Therefore, the expression equivalent to the given numerical expression is 67/24.
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Algebra 2 Unit 4 Standards Tasks Shannon Barker S.CP.B.6: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. In the East Orange School District, students are only allowed to enroll in AP Calculus if they have already taken pre-calculus or general calculus. Out of 825 incoming seniors: * 465 took pre-calculus *166 took general calculus *133 took both. Part A (3 points): Given this information, determine the probability a randomly selected incoming Senior is allowed to enroll in AP Calculus. AN In another district an additional prerequisite course is math analysis. In that district there are 550 incoming seniors. . 345 took pre-calculus, 125 took general calculus, 40 took math analysis • 35 took pre-calculus and general calculus • 20 took math analysis and general calculus . 0 took both pre-calculus and math analysis Part B (2 points): In this school district, How many seniors were not able to take AP calculus? Submit
The given fractions representing the conditional probability is P(A | B) = P(AnB)/P(B)
We know that,
Conditional Probability is:
This is the probability that an event has happened given another event. If the two events are A and B, hence;
The conditional probability of A given B is expressed as:
P(A | B) = P(AnB)/P(B)
This given the fractions representing the conditional probability
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9. A plant seed may get carried very far on a windy day, and sprout in another field full of the same type of
plant. What mechanism of evolution is this an example of? Explain.
As a result of the seed growing in a field with a different population of plants, we can witness how gene flow works in action.
It will have introduced its alleles into that population once this plant reproduces there. Any movement of people from one group to another—also known as migration—and/or the genetic material they carry is referred to as gene flow. Pollen being carried to a new location by the wind or individuals relocating to new cities or nations are just a few examples of the many different types of events that contribute to gene flow.
Vertical and horizontal gene flow are two different types of gene transfer. Gene flow describes the transfer of genetic material between groups.
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given f (x) = 4x^2+6x+9 find (-7)
The value of f(-7) is 172.
To find the value of f(-7) for the given function f(x) = 4x^2 + 6x + 9, we substitute -7 for x in the function and evaluate it.
f(-7) = 4(-7)^2 + 6(-7) + 9
Simplifying the equation:
f(-7) = 4(49) - 42 + 9
= 196 - 42 + 9
= 163 + 9
= 172
Therefore, f(-7) = 172.
By substituting -7 into the function, we obtained the value of 172. This means that when x is equal to -7, the corresponding value of the function f(x) is 172.
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The graph shows the cube root parent function.
-5
5
Which statement best describes the function?
A
The statement of the function is (b) when x > 0, the graph is positive
Describing the transformation of the function f(x)From the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
In the graph, we can see that
The graph of the function passes through (0, 0)
This means that
When x > 0, the graph is positive
When x < 0, the graph is negative
Hence, the statement of the function is (b)
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find the difference between points (3,5) and (-1,5)
b'
Let the given points be A(3,-5) and B(5,-1).
AB= sqrt of (5−3) ² +(−1+5)²
= sqrt of 4+16
= sqrt of 20
=2 sqrt of 5 units
add or subtract (3x^2-7x-4)-(6x^2-6x+1)
pls help
answers
–3x^2 – x –5
–3x^2 –13x + 5
9x^2 – x + 5
3x^2 – 13x – 5
Answer:
-3x² - x - 5
Step-by-step explanation:
(3x² - 7x - 4) - (6x² - 6x + 1) =
= -3x² - x - 5
I NEED THE ANSWER ASAP
I WILL MAKE THE FIRST PERSON TO ANSWER MY QUESTION BRAINLY!
ALSO YOU WILL GET 100 POINTS
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
Answer:
3) 50 in²
4) 85 cm²
Step-by-step explanation:
Question 3The given figure is composed of 2 triangles, each with a base of 10 inches and a height of 5 inches.
The area of a triangle is half the product of its base and height.
Therefore, the area of the composite figure can be calculated as follows:
[tex]\begin{aligned}\textsf{Area of compositie figure}&=\sf Area_{Triangle\;1}+Area_{Triangle\;2}\\\\&=\dfrac{1}{2} \cdot 10 \cdot 5 + \dfrac{1}{2} \cdot 10 \cdot 5\\\\&=5\cdot 5+5\cdot 5\\\\&=25+25\\\\&=50\; \sf square\;inches\end{aligned}[/tex]
Therefore, the area of the composite figure is 50 square inches.
[tex]\hrulefill[/tex]
Question 4The given figure is composed of a rectangle with width of 6 cm and length of 10 cm, and a triangle with base of 10 cm and height of 5 cm.
The area of a rectangle is the product of its width and length.
The area of a triangle is half the product of its base and height.
Therefore, the area of the composite figure can be calculated as follows:
[tex]\begin{aligned}\textsf{Area of compositie figure}&=\sf Area_{Rectangle} + Area_{Triangle}\\\\&=6 \cdot 10+\dfrac{1}{2} \cdot 10 \cdot 5\\\\&=60+5 \cdot 5\\\\&=60+25\\\\&=85\; \sf square\;centimeters\end{aligned}[/tex]
Therefore, the area of the composite figure is 85 square centimeters.
what type of data would best be displayed in a box plot
Answer:(2x+7)+(2x+7)
Step-by-step explanation:
what you do is put 2x on the top and on the side and then seven on the top and on the side and then you got your answer
Which of the following will have a smaller standard deviation, if nine observations are randomly drawn from a population?
The distribution of the individual observations, X
The distribution of the sample means,
x
¯
This cannot be determined from the information given.
The distribution of the sample means will have a smaller standard deviation
Identifying which will have a smaller standard deviationFrom the question, we have the following parameters that can be used in our computation:
Observations = 9
The population is not given
However by the theorem of the central limit; we understand that
The distribution of the sample means will always have a smaller standard deviation
This is because the sample mean selected from the population might not totally represent the whole population, but would have smaller standard deviation
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100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!
A. The distributions of the periods is that using the five number summary is that
The 7th Period has higher minimum and lower maximumThe 3rd period is more spread (from the quartiles)The 7th Period has higher medianB. The box and whisker plot of the periods is attached
A. Comparing the distributions of the periodsFrom the question, we have the following parameters that can be used in our computation:
7th Period
66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96
3rd Period
52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97
The distributions of the periods will be compared using the five-number summaries
Using a graphing tool, the five-number summaries are:
7th Period
Minimum: 66Lower Quartile Q1: 79.5Median: 88Upper Quartile Q3: 92.25Maximum: 963rd Period
Minimum: 52Lower Quartile Q1: 64.75Median: 75.5Upper Quartile Q3: 85.75Maximum: 97B. Creating a box and whisker plot of the periodsThe box and whisker plot of the periods is added as an attachment
From the box and whisker plot attached, we can see the five-number summaries of the periods
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Please help as soon as possible, thank you in advance
The logo that fits the requirement is the circle logo i.e. logo 1
Calculating the area and the width in metersFrom the question, we have the following parameters that can be used in our computation:
The figures that represent the logos
For the circle logo, we have
Area = 22/7 * 1/2 * 1/2
Convert units to feet using the scale
Area = 22/7 * 1/2 * 7 * 1/2 * 7
Evaluate
Area = 38.5 square feet
Also, we have
Width = 2 * 1/2 * 7 feet
Width = 7 feet
For the plus-shaped logo, we have
Area = 5 * 1/2 * 1/2
Convert units to feet using the scale
Area = 5 * 1/2 * 7 * 1/2 * 7
Evaluate
Area = 61.25 square feet
Also, we have
Width = 3 * 1/2 feet * 7
Width = 10.5 feet
Hence, the logo that fits the requirement is the circle logo i.e. logo 1
This is because its area is not up to the maximum area (40 square feet) and the width is greater than the minimum width (4 feet)
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What is the equation of the circle with center at (9,5) that passes through (13,7)? Write your answer in standard form.
The equation of circle with a center at (9, 5) that passes through (13, 7) is (x - 9)² + (y - 5)² = 20.
we have Center at (9, 5) and passes thorough (13, 7).
To find the equation of a circle with center (h, k) and a point (x, y) on the circle, we can use the standard form equation of a circle:
(x-h)² + (y-k)² = r²
So, (x - 9)² + (y - 5)² = r
Since the circle passes through (13, 7), then
(13 - 9)² + (7 - 5)² = r²
²4 + (2)² = r²
16 + 4 = r²
20 = r²
So, the equation of circle is
(x - 9)² + (y - 5)² = 20
Therefore, the equation of circle with a center at (9, 5) that passes through (13, 7) is (x - 9)² + (y - 5)² = 20.
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