The factors of 6[tex]x^{2}[/tex]+ 37x - 60 are 2(x - 2) and 3(x + 5), which is answer c.
To factor the polynomial 6[tex]x^{2}[/tex] + 37x - 60, we need to find two numbers whose product is -360 (the product of the leading coefficient and the constant term) and whose sum is 37 (the coefficient of the linear term).
One way to do this is to list all the possible factor pairs of -360 and look for a pair that adds up to 37. Some of the factor pairs are:
1, -360
2, -180
3, -120
4, -90
5, -72
6, -60
8, -45
9, -40
10, -36
12, -30
15, -24
18, -20
We can see that 15 and -24 add up to 37, so we can use them as the coefficients of the linear term. To get the correct sign, we need to use -24 and 15 instead of 15 and -24.
So we have:
6[tex]x^{2}[/tex] + 37x - 60 = 6[tex]x^{2}[/tex] + 15x - 24x - 60
= 3x(2x + 5) - 12(2x + 5)
= (3x - 12)(2x + 5)
= 6(x - 2)(x + 5)
Therefore, the factors of 6[tex]x^{2}[/tex] + 37x - 60 are 2(x - 2) and 3(x + 5), which is answer c.
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2. The table below shows the lengths of four earthworms found by the lake. Earthworm A B C D Length (cm) 10.2 3 9- 4 9.23 9/²/2 2 Write the lengths in order from shortest to longest.
From shortest to longest, the earthworms measure the following lengths: B (3 cm), D (4.5 cm), C (9.23 cm) and A (10.2 cm)
how can we describe length ?A physical concept known as length measures the gap between two points or the expanse of an object in one dimension.
Common units used to measure it include metres (m), feet (ft), millimetres (in), centimetres (cm), etc. In several disciplines, including mathematics, engineering, physics, and engineering, length is a crucial concept.
given
From shortest to longest, the earthworms measure the following lengths:
B (3 cm), D (4.5 cm), C (9.23 cm) and A (10.2 cm)
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3
Find the perimeter of a square that is 3 Inches on a side.
30 inches
0 12
3
4
inches
15 inches
07/1/20 inches
The perimeter of a square that is 3 inches on a side include the following: B. 12 inches.
How to calculate the perimeter of a square?In Mathematics and Geometry, the perimeter of a square can be calculated by using the following formula;
P = 4x
Where:
P is the perimeter of a square.x is the side length of a square.By substituting the given side lengths into the formula for the perimeter of a square, we have the following;
Perimeter of a square, P = 4x
Perimeter of a square, P = 4(3)
Perimeter of a square, P = 12 inches.
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The perimeter of a square with 3 inches on a side is B. 12 inches.
What is the perimeter?The perimeter refers to the distance that encompasses or surrounds an object or drawing.
The formula for computing the perimeter is 2L + 2W. But for a square, the perimeter formula is 4L.
The length of each square side = 3 inches
The perimeter = 12 inches (4 x 3)
Thus, the perimeter of the square can be concluded to be 12 inches.
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R=[(a,1),(b,2),(c,3)] is it function or not
Answer:
Yes The set R = [(a,1),(b,2),(c,3)] is a Function.
Step-by-step explanation:
A function ia a relation between two sets ,where each element in domain is associated with only one range.
Some examples of function -
1- x2 (squaring) is a function
2- x3+1 is also a function
3- Sine, Cosine and Tangent are function
in the case the domain {a,b,c} and the range is {1,2,3}
IN R each domain is associated with only one element in range,So R SATISFIES the definiton of Function
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or
The copy machine at the library made a copy of Leslie's 3-page essay in just
1
10
of a minute. What is the speed of the copy machine?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
The speed of the copy machine is 30 pages per minute.
What is Fraction ?
A fraction is a way of representing a part of a whole or a division of a quantity into equal parts. It consists of two numbers, one written above the other and separated by a horizontal or diagonal line called a fraction bar. The number written above the fraction bar is called the numerator, and the number written below the fraction bar is called the denominator.
If the copy machine made a copy of Leslie's 3-page essay in just 1/10 of a minute, then it made a copy of one page in 1/10 ÷ 3 = 1/30 of a minute.
To find the speed of the copy machine, we can take the reciprocal of the time it takes to make one copy, which is:
1 ÷ (1/30) = 30
Therefore, the speed of the copy machine is 30 pages per minute.
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This
distance-time graph shows the journey of a hot-air balloon.
For how long during the journey was the balloon more than 600 m from the
ground?
Give your answer in minutes.
< Back to task
1200
Distance from ground (m)
1000
800-
600
400
200-
04
13:30 13:40 13:50 14:00 14:10 14:20 14:30 14:40 14:50
Time
Watch video
Answer >
Answer:
its 1000 because if you count the blue line thing up it will show you do you have a profile picher i need one you can be my freind pleas i have only two my name is Isabella
what is the length of the missing leg? If necessary, round to the nearest tenth.
Answer:
48 yards
Step-by-step explanation:
Use the Pythagorean theorem:
[tex] {a}^{2} = {52}^{2} - {20}^{2} = 2704 - 400 = 2304[/tex]
[tex]a > 0[/tex]
[tex]a = \sqrt{2304} = 48 \: yd[/tex]
Help please! No silly answers. Need this as soon as possible thank you.
Step-by-step explanation:
Every ten minutes the car travels eleven miles
11 miles / 10 min = 1.1 mile / min <=====unit rate
after 18 minutes : 1.1 mile/min * 18 min = 19.8 miles
A quarter is about I Inch In
diameter. The word "Liberty"
makes about a 100° angle. How
long is the word in inches?
According to the question the word "Liberty" on the quarter is about 0.872 inches long.
what is diameter?In geometry, a circle's diameter is any straight segment whose endpoint is on the circle and which passes through its centre. Another name for it is the circle's longest chord. Either idea can be used to determine a sphere's diameter. The diameter is indeed the length of both the line perpendicular to the two points at each end of the circle. If you think of length as the distance between two points, then diameter is length. The diameter of a circle is the separation between its two farthest points.
Since the quarter has a diameter of about 1 inch, we can use its diameter as a reference to estimate the length of the word "Liberty" on the quarter.
If the word "Liberty" makes about a 100° angle, that means it takes up about 100/360 or 5/18 of the circumference of the quarter. The circumference of a circle is given by:
C = 2πr
where C is indeed the circumference, pi (roughly 3.14), is a mathematical constant, and r is the circle's radius. The quarter's approximate 1 inch diameter means that the radius equals 1/2 inch, approximately 0.5 inches.
The circumference of the quarter is therefore:
C = 2π(0.5 inches) = π inches
The length of the word "Liberty" on the quarter is approximately 5/18 of this circumference, which is:
(5/18) × π inches ≈ 0.872 inches
So the word "Liberty" on the quarter is about 0.872 inches long.
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Describe the transformation of the graph of f(x) to g(x). f(x) = x^2 g(x) = (x - 2)^2 + 5
The transformation of the graph of f(x) to g(x) is defined as: 2 units shift on the left side and 5 units shift upward.
Explain about the transformation:Think about the function f (x). We measure the movement using the x- and y-axes on a coordinate grid. The following are guidelines for function transformations that could be used with function graphs. All algebraic and graph of transformations are possible.
Transformations can be divided into four categories: translation, rotation, reflection, plus dilation.
Given :
Transformation of the graph of f(x) ---> g(x)
f(x) = x² g(x) = (x - 2)² + 5
There is a shift of 2 units on the left. Subtract 2 from x to get the value (x - 2)
There is a shift of 5 units upward. Add 5 on the function f(x) to get the function g(x).
Thus, the transformation of the graph of f(x) to g(x) is defined as: 2 units shift on the left side and 5 units shift upward.
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The area of a rectangular field is 80 square meters. If its length is 20 m, how far would you have travelled if you walked the whole way around the field?
Answer: We can start by finding the width of the rectangular field using the formula for area of a rectangle:
Area = length x width
80 = 20 x width
width = 4 meters
Now we can use the formula for perimeter of a rectangle:
Perimeter = 2 x length + 2 x width
Perimeter = 2 x 20 + 2 x 4
Perimeter = 40 + 8
Perimeter = 48 meters
So, you would have traveled 48 meters if you walked the whole way around the field.
Step-by-step explanation:
art 2: 10 Points each. Show all work for full credit.
11. Ryan bought three bags of mixed tulip bulbs at a local garden store. The first bag contained 7 yellow
bulbs, 8 red bulbs, and 5 white bulbs. The second bag contained 3 yellow bulbs, 11 red bulbs, and 6
white bulbs. The third bag contained 13 yellow bulbs, 2 red bulbs, and 5 white bulbs. Ryan combined
the contents of these three bags into a single container. He randomly selected one bulb, planted it, and
then randomly selected another and planted that one. Determine if it is more likely that Ryan planted a
red bulb and then another red bulb, or planted a yellow bulb and then a white bulb. Justify your answer.
It is more likely that Ryan planted a yellow bulb and then a white bulb than planted a red bulb and then another red bulb. The probability of planting a yellow bulb and then a white bulb is 0.3905, which is higher than the probability of planting two red bulbs in a row, which is 0.345.
How to solve probability?
To determine which scenario is more likely, we need to calculate the probability of each outcome. Let's start by calculating the probability of planting two red bulbs in a row.
The probability of selecting a red bulb from the first bag is 8/20, from the second bag is 11/20, and from the third bag is 2/20. Thus, the probability of selecting two red bulbs in a row is:
(8/20) * (11/20) + (8/20) * (2/20) + (11/20) * (2/20) = 0.345
Now, let's calculate the probability of planting a yellow bulb and then a white bulb.
The probability of selecting a yellow bulb from the first bag is 7/20, from the second bag is 3/20, and from the third bag is 13/20. The probability of selecting a white bulb from the first bag is 5/20, from the second bag is 6/20, and from the third bag is 5/20. Thus, the probability of selecting a yellow bulb and then a white bulb is:
(7/20) * (5/20) + (7/20) * (6/20) + (3/20) * (5/20) + (3/20) * (6/20) + (13/20) * (5/20) + (13/20) * (6/20) = 0.3905
Therefore, it is more likely that Ryan planted a yellow bulb and then a white bulb than planted a red bulb and then another red bulb. The probability of planting a yellow bulb and then a white bulb is 0.3905, which is higher than the probability of planting two red bulbs in a row, which is 0.345.
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The surface area of this square pyramid is 741 ft². Can the value of x be 24? Explain.
(the pyramid's length and base are 13, and x is the height.)
Therefore , the solution of the given problem of surface area comes out to be x cannot equal 24.
What does an area actually mean?By calculating how much space would be needed to fully enclose its exterior, its overall size can be calculated. The surrounding region is considered when selecting a comparable product in the rectangular design. The surface area of something determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal forms determines how much water it can hold.
Here,
The calculation for a square pyramid's surface area is:
=> S = l² + 2lh
where S is the surface area, h is the height of the pyramid, and l is the length of one edge of the square base.
=> l² = 13² = 169
We also know that the pyramid's surface area is 741 square feet, so we can construct the following equation:
=> 741 = 169 + 2(13)(x)
When we condense the right half, we obtain:
=> 741 = 169 + 26x
169 from both parts are subtracted, giving us:
=> 572 = 26x
When we multiply both parts by 26, we get:
=> x = 22
As a result, rather than 24 feet, the pyramid's height is 22 feet.
Thus, x cannot equal 24.
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a researcher is conducting a test to determine if a test prep program increases the pass rate for a certification program. what assumptions must be met in order to use the large sample z-test for a difference in two proportions?
To use the large sample z-test for a difference in two proportions, assumptions that must be met include having independent samples, a large sample size, and success-failure conditions must be met.
In order to use the large sample z-test for a difference in two proportions, the following assumptions must be met:
The sample is random and each observation is independent. The sample size for each group is large enough such that both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the proportion of success.
The two groups being compared are independent of each other. The data is binomially distributed, meaning each observation is either a success or a failure. The populations from which the samples are drawn have similar variances.
If these assumptions are met, the large sample z-test can be used to test the null hypothesis that there is no difference between the two proportions.
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The leneght of four insects are 0.02 cm ,1/8cm,0.1cm and 2/3cm. Arrange the leneght in descending order
The descending order of the length of the four insects is as follows: 2/3 cm, 0.1 cm, 0.02 cm, 1/8 cm.
The length of four insects are 0.02 cm, 1/8 cm, 0.1 cm, and 2/3 cm.
Arrange the length in descending orderIn order to arrange the lengths of the four insects in descending order, we need to convert the fractions to decimals so that we can compare all the values.
1/8 cm = 0.125 cm
2/3 cm = 0.6667 cm
Now we have the values in decimal form, we can proceed to arrange them in descending order from the highest to the lowest value:
2/3 cm = 0.6667 cm
0.1 cm
0.02 cm
1/8 cm = 0.125 cm.
In conclusion, the lengths of four insects were arranged in descending order by first converting the fractions to decimals before comparing them.
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QUICK!!!!
If a universal set is {1, 2, 3, 4, 5, 6, 7} and set C equals {1, 2, 3}, What is the complement of the complement of C?
A) {1, 2, 3}
B) {1, 2, 3, 4, 5, 6, 7}
C) {4, 5, 6, 7}
D) Ø
The concept of a complement of a set is the set of all elements in the universal set that are not in the original set. The answer is B) {1, 2, 3, 4, 5, 6, 7}.
What is a universal set?It is denoted by U. Universal sets are used to define the scope of an expression or equation, as well as to denote sets of all objects, such as the set of real numbers or the set of natural numbers.
The complement of a set is also referred to as its opposite set. In this case, the universal set is {1, 2, 3, 4, 5, 6, 7}, and the set C is {1, 2, 3}.
The complement of C is {4, 5, 6, 7}.
The complement of the complement of C is the set of all elements that are not in the complement of C.
Since the complement of C is {4, 5, 6, 7}, the complement of the complement of C is the set of all elements in the universal set that are not in the complement of C, which is {1, 2, 3, 4, 5, 6, 7}.
Therefore, the answer is B) {1, 2, 3, 4, 5, 6, 7}.
To summarize, the complement of the complement of C is the set of all elements in the universal set that are not in the complement of C.
In this case, the complement of C is {4, 5, 6, 7}, so the complement of the complement of C is {1, 2, 3, 4, 5, 6, 7}.
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Amanda Bryan purchased a used car for $12,875 with a 25% down payment. What amount did she finance?
Answer: If Amanda Bryan purchased a used car for $12,875 and made a 25% down payment, then she paid:
25% of $12,875 = 0.25 * $12,875 = $3,218.75
This means that the amount she financed (i.e. borrowed) to purchase the car is the difference between the total cost of the car and the down payment:
Amount financed = Total cost - Down payment
Amount financed = $12,875 - $3,218.75
Amount financed = $9,656.25
Therefore, Amanda Bryan financed $9,656.25 to purchase the used car.
Step-by-step explanation:
PLS HELP ASAP !!! What does this mean
Answer:
2 Nd is in order from least to grater
Find an angle in each quadrant with a common reference angle with 332°
Answer:
Step-by-step explanation:
In first quadrent, reference angle is equal to 332
in secodn quadrent, 332-180
angle - 180 so 332-180
fouth Quadrent, 360-332
Answer is equal to 28
Answer:
Quadrant 1: 152°
Quadrant 2: 28°
Quadrant 3 (Given): 332°
Quadrant 4: 208°
Step-by-step explanation:
A 332° angle in standard position has its terminal side in quadrant 3 since 332° is between 180° and 360°.
332° - 180° = 152°
The reference angle for 332° is 152°
Quadrant 1: 152°
Quadrant 2: 180° - 152° = 28°
Quadrant 3 (Given): 332°
Quadrant 4: 360° - 152° = 208°
Please help me with this I have no idea
Answer:
x = 8
Step-by-step explanation:
The two sides equal each other
5x - 13 = x + 19 Subtract x from both sides
5x - x - 13 = x - x + 19
4x - 13 = 19 Add 13 to both sides
4x - 13 + 13 = 19 + 13
4x = 32 Divide both sides by 4
x = 8
Helping in the name of Jesus.
Find x of the problem
There is no real solution for X. This means that the given measurements do not form a valid right triangle.
What is the value of X?
Triangle KJL forms a right triangle, with length KL (hypothenuse side) = 10 and JL = X and KL = 24.
We can use the Pythagorean theorem to solve for the missing side, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Therefore, we have:
KL² = KJ² + JL²
Substituting the given values, we get:
10² = 24² + X²
Simplifying and solving for X, we get:
100 = 576 + X²
X² = 100 - 576
X² = -476
Since X² is negative, there is no real solution for X. This means that the given measurements do not form a valid right triangle.
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How many four letter code words can be formed from the letters in the word "MIRAGE" if no letter is repeated, and the second-to-last letter must be a vowel?
Required number of four letters are 120.
What are letters?
Letters are symbols that represent sounds or phonemes in a language. They are used to form words and written communication. The letters of the alphabet are the basic units of written language, and each language has its own set of letters that represent its sounds. In many languages, the letters are organized into an alphabet, which is a standardized order of the letters used for writing. The letters can be written in uppercase or lowercase form, and they may have different shapes or styles depending on the font used. In addition to the letters of the alphabet, there are also other types of symbols used in written communication, such as punctuation marks, numerals, and special characters.
The given word "MIRAGE" has six letters, and we need to form a four-letter code word using these letters such that the second-to-last letter is a vowel and no letter is repeated.
There are two vowels in "MIRAGE" - "I" and "A". We can choose one of these two vowels to be the second-to-last letter in the four-letter code word. Once we have chosen the vowel, we can choose any one of the remaining five letters for the last letter in the code word, since no letter can be repeated.
After choosing the second-to-last and last letters, we have two letters left to choose for the first two positions in the code word. Since no letter can be repeated, we have four choices for the first letter, and three choices for the second letter.
Thus, the total number of four-letter code words that can be formed from the letters in the word "MIRAGE" if no letter is repeated, and the second-to-last letter must be a vowel is 2 (choices for the second-to-last letter) x 5 (choices for the last letter) x 4 (choices for the first letter) x 3 (choices for the second letter)
= 2 x 5 x 4 x 3
= 120
Therefore, there are 120 four-letter code words that can be formed from the letters in the word "MIRAGE" if no letter is repeated, and the second-to-last letter must be a vowel.
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pls solve thisss......
The height of the cone is 15cm.
How to find the radius of the object?From the question;
Height of cylinder = 28cm
Let the radius of the solid object = Rcm
The slant height of the cone = 17cm
Cost of painting = Rs. 140 per 100 sq cm
Cost of painting 1 cm² = 140/100 = RS1.4
The total cost of painting = Rs. 2851.2
Total area of the object = total cost of painting/Cost of painting per sq cm
Total area of the object = 2851.2/1.4 = 2036.57143 cm²
Total surface area of object = CSA of Cylinder + CSA of cone + area of the circle at the bottom
Total surface area of the object = [tex]\pi rh + \pi rl + \pi r^2[/tex]
So, [tex]\frac{2851.2}{1.4}[/tex] = [tex]\pi rh + \pi rl + \pi r^2[/tex]
[tex]\frac{2851.2}{1.4}[/tex] = [tex]2\pi r * 28 + \pi r * 17 + \pi r^2[/tex]
[tex]\frac{2851}{1.4}[/tex] = [tex]\frac{1232}{7}r =+\frac{374}{7} r + \frac{22}{7} r^2[/tex]
[tex]\frac{2851}{1.4}[/tex] = [tex]\frac{1606}{7} r + \frac{22}{7} r^2[/tex]
[tex]\frac{2851}{2}[/tex]= [tex]1606r + 22r^2[/tex]
[tex]14256 = 1606r + 22r^2[/tex]
[tex]22r^2 + 1606r - 14256 =0[/tex]
Solving the quadratic equation, the possible value of radius are:
r = 8cm
r = -81cm
r = -81cm will be neglected because radius can not be negative.
Therefore, the radius of the object is 8cm
To find the height of the cone, we should know that the relation between radius, height and slant height of the cone is:
[tex]l^2 = r^2 + h^2[/tex]
[tex]h=\sqrt{l^2 - r^2}[/tex]
[tex]h=\sqrt{17^2 - 8^2}[/tex]
[tex]h=\sqrt{225}[/tex]
[tex]h=15cm[/tex]
Therefore, height of cone in the solid object is 15cm
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What is the solution to x2 + 4x>12?
The sοlutiοn tο the inequality [tex]x^2 + 4x > 12[/tex] is: x < -6 οr x > 2
In interval nοtatiοn, this can be written as: (-∞, -6) ∪ (2, ∞)
What is Algebraic expressiοn ?An algebraic expressiοn is a mathematical phrase that can cοntain variables, cοnstants, and οperatοrs (such as additiοn, subtractiοn, multiplicatiοn, and divisiοn) that are used tο represent quantities and their relatiοnships.
Tο sοlve this inequality, we need tο find the values οf x that satisfy the inequality [tex]x^2 + 4x > 12.[/tex]
First, we can mοve all the terms tο οne side οf the inequality tο get:
[tex]x^2 + 4x - 12 > 0[/tex]
Next, we can factοr the left-hand side οf the inequality tο get:
(x + 6)(x - 2) > 0
Nοw we need tο find the values οf x that make the inequality true. We can dο this by analyzing the signs οf the expressiοns οn each side οf the inequality fοr different ranges οf x.
When x < -6, bοth factοrs (x + 6) and (x - 2) are negative, sο their prοduct is pοsitive.
When -6 < x < 2, the factοr (x + 6) is pοsitive and the factοr (x - 2) is negative, sο their prοduct is negative.
When x > 2, bοth factοrs are pοsitive, sο their prοduct is pοsitive.
Therefοre, the sοlutiοn tο the inequality [tex]x^2 + 4x > 12[/tex] is: x < -6 οr x > 2
In interval nοtatiοn, this can be written as: (-∞, -6) ∪ (2, ∞)
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which type of sampling assumes all the members of a population have an equal chance of being selected for participation in the study?
The type of sampling that assumes all members of a population have an equal chance of being selected for participation in the study is called Simple Random Sampling.
In Simple Random Sampling, each individual in the population has an equal probability of being chosen as a participant, and the selection process is unbiased. This method ensures that the sample is representative of the entire population, thus allowing for valid conclusions to be drawn about the population as a whole.
Here is a step-by-step explanation of how Simple Random Sampling is conducted:
1. Define the population: First, clearly identify the population you want to study.
2. Assign a unique number to each member: To ensure equal chances of selection, assign a unique number to every individual in the population.
3. Determine the sample size: Decide how many participants you need in your study based on factors like required level of accuracy and available resources.
4. Use a random selection method: Use a random selection method such as a random number generator, a lottery system, or a random number table to pick the required number of participants.
5. Collect data from the selected individuals: Once the participants are chosen, collect data from them using appropriate research methods like surveys, interviews, or experiments.
By using Simple Random Sampling, you can obtain a sample that is unbiased and representative of the entire population, which is essential for accurate and reliable research findings.
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Tonya worked 42.5 hours this week at a rate of 9.75 what is her overtime pay ?
Since overtime is paid at one and one-half, Tonya's overtime pay for this week is $36.56.
What is overtime pay?The overtime pay is the product of the overtime pay rate and the number of overtime hours.
The normal work week is 40 hours. The overtime hours, in this situation, are 2.5 hours.
The total number of hours Tonya worked this week = 42.5 hours
The hourly pay rate = $9.75
Overtime pay rate = $14.625 ($9.75 x 1.5)
Overtime hours worked = 2.5 hours (42.5 - 40)
Overtime pay = $36.56 ($14.625 x 2.5)
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due tomorrow , please help!!
The surface areas are 756.87 km², 2567.6 in², 853.91 yd², 749.72 cm² and the area to paint is 3268.60 in²
Calculating the surface areasFigure 9
This is calculated as
Area = Base area + 1/2 * Perimeter * Slant height
So, we have
Surface area = (1/4 * 14² * √3) + 1/2 * (14 + 14 + 14) * 32
Surface area = 756.87 km²
Figure 10
This is calculated as
Area = Sum of side areas
So, we have
Surface area = 2 * 1/2 * (35 + 10) * 20.3 + 32 * 17 + 10 * 17 + 20.3 * 17 + 35 * 17
Surface area = 2567.6 in²
Figure 11
Start by calculating the radius using
(2r)² = 19.4² - 14.4²
2r = 13
So, we have
r = 6.5
This area is then calculated as
Area = 2πr(h + r)
So, we have
Area = 2 * 22/7 * 6.5(14.4 + 6.5)
Surface area = 853.91 yd²
Figure 12
This area is calculated as
Area = lw + l√[(w/2)² + h²] + w√[(l/2)² + h²]
So, we have
Area = 15 * 18 + 18√[(15/2)² + 12²] + 15√[(18/2)² + 12²]
Surface area = 749.72 cm²
Area to paintWithout painting the bottom, the area is
Area = 2 * 1/2 * 34 + 42.8 + 36 * √(34² + 42.8²) + 34 * 36
Evaluate
Area = 3268.60 in²
Volume of the coneUnclear dimensions
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Giving brainliest, please help!
Answer:
[tex]54in^{3}[/tex]
Step-by-step explanation:
The formula for the volume of a rectangular prism is:
A= lwh
So we just plug in those values.
A= 3*3*6
A= 9*6
A= 54in^3
The table shows the number of goals made by two hockey players.
Player A Player B
2, 3, 1, 3, 2, 2, 1, 3, 6 1, 4, 5, 1, 2, 4, 5, 5, 11
Find the best measure of variability for the data and determine which player was more consistent.
Player B is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with a range of 10.
Player A is the most consistent, with an IQR of 1.5.
Player A is the most consistent, with a range of 5
Player B is the most consistent, with an IQR of 2. This means that 50% of their scores fell within the range of 3 to 5.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen
To determine which player was more consistent, we need to find the best measure of variability for the data. The two common measures of variability are range and interquartile range (IQR).
The range is the difference between the highest and lowest values in the data set. For Player A, the range is 6 - 1 = 5, and for Player B, the range is 11 - 1 = 10.
The interquartile range (IQR) is a measure of dispersion based on dividing the data into quartiles. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
To find the IQR for each player, we first need to find the quartiles.
For Player A:
Arrange the data in order: 1, 1, 2, 2, 2, 3, 3, 3, 6
Find Q1: (2 + 2) / 2 = 2
Find Q3: (3 + 3) / 2 = 3
Calculate IQR: Q3 - Q1 = 3 - 2 = 1
For Player B:
Arrange the data in order: 1, 1, 2, 4, 4, 5, 5, 5, 11
Find Q1: (2 + 4) / 2 = 3
Find Q3: (5 + 5) / 2 = 5
Calculate IQR: Q3 - Q1 = 5 - 3 = 2
Therefore, Player B is the most consistent, with an IQR of 2. This means that 50% of their scores fell within the range of 3 to 5. In contrast, Player A has an IQR of 1, indicating that 50% of their scores fell within the range of 2 to 3.
Therefore, we can conclude that Player B was more consistent than Player A.
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the production of a certain polymer fiber follows a normal distribution with a true mean diameter of 20 mm and a standard deviation of 30 mm. compute the probability of a measured value greater than 80 mm. compute the probability of a measured value between 50 and 80 mm.
The probability of a measured value greater than 80 mm in a normal distribution with mean 20 mm and standard deviation 30 mm is (0.0228). The probability of a measured value between 50 and 80 mm is 0.1359.
Probability of a measured value greater than 80 mm:
We can use the standard normal distribution to find this probability, by standardizing the value of 80 mm:
z = (80 - 20) / 30 = 2
Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being greater than 2 is approximately 0.0228. Therefore, the probability of a measured value of the polymer fiber being greater than 80 mm is approximately 0.0228.
Probability of a measured value between 50 and 80 mm:
Again, we can standardize the values of 50 mm and 80 mm:
z1 = (50 - 20) / 30 = 1
z2 = (80 - 20) / 30 = 2
Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being between 1 and 2 is approximately 0.1359. Therefore, the probability of a measured value of the polymer fiber being between 50 and 80 mm is approximately 0.1359.
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Help please in need this asap
For the given values, the standard deviation for this data set is approximately 3.67 minutes.
What is standard deviation?
In statistics, standard deviation is a measure used to quantify the amount of spread or dispersion of a set of numerical data around the mean. This measure indicates how much the data values vary from the average value of the dataset.
To find the standard deviation, you can follow these steps:
Find the mean (average) of the data set:
mean = (11 + 7 + 14 + 2 + 8 + 13 + 3 + 6 + 10 + 3 + 8 + 4 + 8 + 4 + 7) / 15 = 7.2
Subtract the mean from each data point:
(11 - 7.2), (7 - 7.2), (14 - 7.2), (2 - 7.2), (8 - 7.2), (13 - 7.2), (3 - 7.2), (6 - 7.2), (10 - 7.2), (3 - 7.2), (8 - 7.2), (4 - 7.2), (8 - 7.2), (4 - 7.2), (7 - 7.2)
Simplifying, we get:
3.8, -0.2, 6.8, -5.2, 0.8, 5.8, -4.2, -1.2, 2.8, -4.2, 0.8, -3.2, 0.8, -3.2, -0.2
Square each result:
13.44, 0.04, 46.24, 27.04, 0.64, 33.64, 17.64, 1.44, 7.84, 17.64, 0.64, 10.24, 0.64, 10.24, 0.04
Find the mean (average) of the squared results:
(13.44, 0.04, 46.24, 27.04, 0.64, 33.64, 17.64, 1.44, 7.84, 17.64, 0.64, 10.24, 0.64, 10.24, 0.04) / 15 = 12.49
Take the square root of the mean:
[tex]\sqrt{(12.49)[/tex] ≈ 3.67
Therefore, the standard deviation for this data set is approximately 3.67 minutes.
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