The different ways in which 6 candles be chosen 84 ways.
What is a combination?
The combination is a method of choosing things from a collection where the order of the choices is irrelevant.
Given, When we have 'n' types of elements and choose 'r' elements from them, then we have C(n+r-1, r) combinations.
n=4(4 types of candles), r=6(no of candles to pick)
Choose 6 different candles, then
=C(4+6-1,6)
=C(9,6)
= 9! / (9-6)! (6!)
= 9!/ 6! 3!
=84
The different ways in which 6 candles can be chosen are 84 ways.
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An icicle that is 12 mm long melts at a constant rate of 1.2 mm per minute. Let t represent the number of minutes since the icicle started melthing and suppose R is a function such that R(t) represents the remaining length of the icicle (in mm) t minutes after it started melting.
A.Write a function formula for R in terms of t.
b.What is the domain of R relative to this context? Enter your answer as an interval.
c.What is the range of R relative to this context? Enter your answer as an interval.
d.What is the domain of R−1 relative to this context? Enter your answer as an interval.
e.What is the range of R−1 relative to this context? Enter your answer as an interval.
f.Solve R(t)=6.6 for t.
t= g.What does your solution in part (f) represent in this context? Select all that apply.
How long it takes for the icicle to melt completely.
How many minutes since the icicle started melting when it is 6.6 mm long.
The length of the icicle (in mm) 6.6 minutes after it started melting.
R(t)=6.6 for t, 5 minutes, the domain of R relative to this context [0, 65 ÷ 6], the range of R related to this context, the domain of R relative to this context, [0, 12], and the range of R relative to this context.
The values of variables, domain, and range:
a) 12 - 1.2t, Using the build equation.
b) Least length = 0 mm.
max time = 12 - 1.2t = 0
t = 65 ÷ 6 minutes.
domain t ∈ [0, 65 ÷ 6]
c) range, R ∈ [0, 12]
d) domain of [tex]R^{-1}[/tex] [0, 12]
e) domain of [tex]R^{-1}[/tex] [0, 65 ÷ 6]
f) 12 - 1.2t = 7
1.2t = 7
t = 5
R(t)=6.6 for t, 5 minutes.
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find a parametric representation using spherical-like coordinates for the upper half of the ellipsoid 4x2 8x 9 y2 36(z 1)2
A parametric representation using spherical-like coordinates for the upper half of the ellipsoid is given by x2 = 9 + -2.25y2 + 0.25z2.
What is ellipsoid?
A sphere can be deformed into an ellipsoid by applying directional scalings, or more generally, an affine transformation, to it.
A quadric surface, or surface that can be described as the zero set of a polynomial of degree two in three variables, is an ellipsoid. An ellipsoid among quadric surfaces has one of the two characteristics listed below. Every cross section of a flat surface is either an ellipse, empty, or reduced to a single point (this explains the name, meaning "ellipse-like"). It can be contained in a sphere that is big enough because it is bounded.
Three pairwise perpendicular axes of symmetry intersect at an ellipsoid's center of symmetry, or the
According to our question-
To each side of the equation, add "-9y2".
4x2 + 9y2 + -9y2 + -1z2 = 36 + -9y2
combining similar terms 9y2 + -9y2 = 0
4x2 + 0 + -1z2 = 36 + -9y2
4x2 + -1z2 = 36 + -9y2
To either side of the equation, add "z2".
4x2 + -1z2 + z2 = 36 + -9y2 + z2
Hence, A parametric representation using spherical-like coordinates for the upper half of the ellipsoid is given by x2 = 9 + -2.25y2 + 0.25z2.
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lapeer flour mills purchased new equipment and made the following expenditures: purchase price $ 64,000 sales tax 5,450 shipment of equipment 890 insurance on the equipment for the first year 590 installation of equipment 1,780
Orion Flour Mills will initially report the $590 insurance amount as prepaid insurance and expense over the first year of coverage is $72120.
Given that,
Lapeer Flour Mills spent money on the following items in addition to buying new machinery: $64,00 in purchase price, plus sales tax 5,450 equipment shipments, 890 equipment insurance for the first year, and 590 equipment installations 1,780
We have to find the above expenditures for the new machines.
We know that,
Total cost of new machine = Purchase price + Sales tax+ Shipment of machine+ Installation of machine
= $64000+$5450+$890+$1780
= $72120
Therefore, Orion Flour Mills will initially report the $590 insurance amount as prepaid insurance and expense over the first year of coverage is $72120.
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a super happy fun ball is dropped from a height of 6 feet and rebounds 10 11 of the distance from which it fell.
The ball will need to travel 126 feet since it will be dropped from a height of 6 feet and then bounce 10/11 feet.
What is division?A number is split in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of things being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
Here,
2*{6/(1-10/11)}-6
2*(6/1/11)-6
2*6*11-6
required distance=126 feet
The required distance will be 126 feet as the ball is dropped from 6 feet and rebounds 10/11 of the distance.
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What is the slope of a line perpendicular to the line whose equation is 3x+18y=1083x+18y=108.
The slope of a line perpendicular to the given equation of line is 6.
Explain the term slope of the line?A line's slope is how steeply it slopes from LEFT toward RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations here on line you choose, the slope of this line will always be constant (it never varies).For the stated question, the equation of the line is given as;
3x + 18y = 10
This can be written as;
y = -3/18 x + 10/18
y = -1/6 x + 5/9
Comparing with general equation of line in slope intercept form.
y = mx + c
slope m = -1/6
The relation of slope for the two perpendicular lines are-
m x m1 = -1
m1 = -1/(-1/6)
m1 = 6
Thus, the slope of a line perpendicular to the given equation of line is 6.
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a newsletter publisher believes that less than 46% of their readers own a rolls royce. is there sufficient evidence at the 0.01 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
the null and alternative hypotheses for the above scenario This is a left failed test.
What is confidence interval?
In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. Although 95% is the most common confidence level, confidence intervals can also be calculated at other levels, such 90% or 99%. The confidence level is the proportion of linked CIs over the long run which really contain the true value of the parameter. The breadth of the CI may be influenced by a number of variables, including sample size, sample variability, and degree of confidence. If all other factors were same, a larger sample would lead to a narrower confidence interval. A sample with greater variability would result in a broader confidence interval and a higher level of confidence.
a newsletter publisher believes that less than 46% of their readers own a rolls Royce.
there is sufficient evidence at the 0.01 level to substantiate the publisher's claim
The null hypothesis (Mo) in this case has a P value of 0.46. P 0.46 Alternative Hypothesis (Ha) (claim)
The left test failed here.
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joan, compliance officer at xyz hospital, explains to the hospital board that in 2003 a provision was added to emtala that stated that there is a yard zone that continues to apply when defining the hospital campus. how many yards are included in this zone? a. 500 b. 100 c. 200 d. 250
The stated zone in EMTALA in 2003 when defining a hospital campus is d. 250 yards
What is EMTALA?
EMTALA stands for Emergency Medical Treatment & Labor Act. It is passed by the US Congress in 1986 to ensure public access to emergency services regardless of ability to pay.
2003 revision of EMTALA provides that the 250-yard zone will continue to apply when defining the "hospital campus". However, that sphere does not include non-medical businesses (shops and restaurants located close to the hospital), nor does it include physicians' offices or other medical entities that have a separate Medicare identity.
Hence, the correct answer is d. 250 yards.
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What is the mean for this set of data? {3, 5, 8, 11, 11, 12} question 4 options:
a. 8
b. 8.33
c. 11
d. 9.5
Answer:
b. 8.33
Step-by-step explanation:
"mean" is the math word for what non-math people call average. This is where you add up all the numbers and divide by however many there are.
3+5+8+11+11+12 is 50
There are 6 numbers in the data set. So 50/6 is 8.3333...
b. 8.33 is the correct answer.
Mean means add and divide.
find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius cm. what is the maximum volume?
The dimensions of a right circular cylinder of maximum volume are
[tex]5\sqrt{6}[/tex] and [tex]10\sqrt{3}[/tex].
Given the radius of sphere is 15 cm.
Let's assume radius of right circular cylinder = r
height of right circular cylinder = h.
Since the cylinder is inscribed in the sphere, their centers will coincide. As a result, the height is divided into two equal portions from the sphere's center. Therefore, we can apply Pythagoras' Theorem to get the cylinder's half-height in terms of radius.
[tex]R^2 = r^2 + (h/2)^2[/tex].
[tex]r^2=R^2-h^2/4[/tex]
Volume of cylinder = [tex]\pi r^2h[/tex]
Now we can substitute value of [tex]r^2[/tex] in volume of cylinder.
V = π*([tex]R^2[/tex] - [tex]h^2[/tex]/4)*h
taking R = 15 .
V = π*(225 - [tex]h^2[/tex]/4)*h
V = π*225*h - π*[tex]h^3[/tex]/4
For maximum volume we have to do derivative of volume = 0
derivative with respect to h.
V' = π*225 - 3*π[tex]h^2[/tex]/4
V' = 0
π*225 - 3*π[tex]h^2[/tex]/4 = 0
3*[tex]h^2[/tex]/4 = 225
[tex]h^2[/tex] = 75*4
h = [tex]10\sqrt{3}[/tex]
put the value of h in [tex]r^2=R^2-h^2/4[/tex]
[tex]r^2[/tex] = 225 - (300/4)
[tex]r^2[/tex] = 150
r = [tex]5\sqrt{6}[/tex]
Given Question is incomplete, Complete Question here
find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 15 cm. what is the maximum volume?
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if measurements are made on four different days, find the level ll such that there is probability only 0.03 that the mean glucose level of four test results falls above all for sheila's glucose level distribution. what is the value of ll?
The probability of having L greater than Shelia's mean glucose level is 0.03 for L = 144.48.
Sheila's glucose level is shown to have a normal distribution, with a mean of 128 mg/dl and a standard deviation of 8 mg/dl.
L represents the patient's blood test level.
The probability that the mean glucose level, 128 mg/dl, is greater than L is given as 0.03.
To find L,
P(128>L) = 0.03
= 1 - P(128 ≤ L) = 0.03
=P(128 ≤ L) = 0.98
We know that we can find the probability of any normal distribution by converting it to standard form and then checking the p-value.
P(X < x) = Φ[(x - μ)/σ]
μ = mean
σ = standard deviation
=Φ[(L - 128)/8] = 0.98
Therefore ,
(L - 128)/8 = 2.06
= L - 128 = 16.48
= L = 128 + 16.48
= 144.48
= L
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A compound is made up of various elements totaling 120 ounces. If the total amount of copper in the
compound weighs 6 ounces, what percent of the compound is made up of copper?
Answer: 5%
Step-by-step explanation:
To find the percentage you put the part over the whole so in this case it would be 6/120 or 6÷120
pop that into a calculator and you get 0.05 or [tex]\frac{5}{100}[/tex] or 5%
Hope that helps
A charity bingo game costs $2 per round and has a $13 entry fee for an adult. It costs $3 per round and a $10 entry fee for a child. For how many rounds of bingo are the costs the same for an adult and a child?
2
3
4
5
Answer:
it is 5 you don't add the 3 in it
when you hand in your test do you think you will get a higher score than you actually do? a professor collected data
After solving, the observed statistic for this study is 2.5.
In the given question, a professor collected data.
After fishing a test, the 27 students in the class wrote their pedicted scores on their tests and these were compared with the actual scores after they were graded.
The mean predicted score was 83.7. So SD = 83.7.
The mean actual score was 81.2. So SD = 15.6
the aen of the difference was 2.5. So SD = 8.6
Null: The average difference in test score (predicted-actual) is 0. μ = 0
Alternative: The average difference in test score (predicted-actual) is greater than 0. μ > 0
We have to find the observed statistic for this study.
predict mean = 83.7 S.D = 8.6
actual mean = 81.2 S.D = 15.6
n = 27
x = (predict mean - actual mean )
x = 83.7 - 81.2
x = 2.5
Hence, the observed statistic for this study is 2.5.
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The right question is given below:
the price for bananas was 75 cents per pound over last month. today, we see that it's been marked up to 81 cents per pound. what is the increase in percent
When bananas cost 75 cents per pound over the previous month, the increase was 8%. Today, we notice that the price per pound has increased to 81 cents.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Here,
The solution is attached in image.
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true/false: transformations are mathematical operations that map 3d space to 2d space and so mathematics has standard ways to represent them.
The statement: transformations are mathematical operations that map 3d space to 2d space and so mathematics has standard ways to represent them is false.
What is 3D to 2D projection?
A three-dimensional (3D) object is displayed on a two-dimensional (2D) surface using a 3D projection, also known as a graphic projection. In order to project a complex object for viewing capability on a simpler plane, these projections rely on visual perspective and aspect analysis.
The fundamental method is: u = x / z; v = y / z; if you're converting from world-space (x, y, z) coordinates to screen-space (u, v) coordinates. Before applying the projection matrix, transform (x, y, z) by the view matrix if the camera is not positioned at the origin.
Hence, the statement transformations are mathematical operations that map 3d space to 2d space and so mathematics has standard ways to represent them is false.
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help me please and thank you:)))
Answer:
c
Step-by-step explanatio
Sam and ben are grading english tests. Sam grades 6 tests in 24 minutes and ben grades 5 tests in 20 minutes. At these rates, what is the total number of tests they can grade in 3 hours? enter the answer in the box.
The total number of tests they can grade in 3 hours are 90.
What is graded test?
Your grade in an exam or written assignment is the letter or number you receive as a mark that represents your level of proficiency.
A graded exercise test (GXT) is a screening tool for determining a person's level of fitness. The test measures the cardiovascular response to exercise in order to assess the participant's capacity for exercise.
Since, the number of minutes in 3 hours is:
= 3 x 60 minutes per hour
= 3 x 60
= 180 minutes
The number of tests that Sam can grade in these 3 hours is therefore:
= ( Number of total minutes / Minutes taken by Sam for 6 tests) x 6 tests
= ( 180 / 24) x 6
= 45 tests
The number of tests that Ben can grade are:
= ( Number of total minutes / Minutes taken by Ben for 5 tests) x 5 tests
= ( 180 / 20 ) x 5
= 45 tests
So, the total number of tests they can grade in 3 hours is:
= 45 + 45
= 90 tests
Hence, the total number of tests they can grade in 3 hours are 90.
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need help on 11 and 12! or you can solve one instead of both if u want?
Answer:
Step-by-step explanation:
mr. goodman sets a goal to outscore these numbers. at the end of the year he takes a random sample of his evaluations and finds 10 1's, 13 2's, 48 3's, and 52 4's. at the 0.05 level of significance, can mr. goodman claim that his evaluations are significantly different than the history department's?
No as their no difference in Mr. Goodman's evaluation and the History department
What is Statistics ?
The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.
descriptive statistics types in mathematics The data in this type of statistics is summarized using the provided observations. Statistics that are inferential. To interpret the meaning of descriptive statistics, this kind of statistics is employed. Example of Statistics.
Seeing the data we can conclude that their no difference in Mr. Goodman's evaluation and the History department
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Students filled 6 rows in Level 1 of Section A and 3 rows in Level 3 of Section B.
How many students were seated in the auditorium?
Number of Seats Per Row in the Auditorium
Section Level 1 Level 2 Level 3
A 9 12 14
B 12 16 18
Which steps are used to solve this problem? Select all that apply.
A.
Find how many seats are in each of the rows where the students are sitting.
B.
Add 6 and 3 to find the number of rows that are filled in all.
C.
Add 9 and 18 to find the number of seats that are filled in each row.
D.
Multiply 6 and 9 to find the number of students seated in Section A.
E.
Multiply 3 and 18 to find the number of students seated in Section B.
F.
Multiply 9 and 27 to find the number of students seated in the auditorium
As per the unitary method, the number of students in the auditorium is 108
Unitary method.
In algebra, the process of finding the value of a single unit, and based on this value is known as unitary method.
Given,
Students filled 6 rows in Level 1 of Section A and 3 rows in Level 3 of Section B.
Here we need to find the number of students were seated in the auditorium.
As per the given table, in level 1, the total number of rows in A section is 9.
So, the number of students is
=> 9 x 6
=> 54
Similarly, there are 3 rows in Level 3 of Section B.
So, the number of students in the level 2,
=> 3 x 18
=> 54
Therefore, the total number of students is,
=> 54 + 54 = 108
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The graph shows the relationship between x and y-values. Find the value of m.
The line has a slope with a measure of 8 / 5.
How to determine the slope of a line
According to Euclidean geometry, lines can be constructed by knowing the location of two distinct points on a plane. By analytic geometry we can determined the slope of the line by knowing these two points and using the secant line formula:
m = Δy / Δx
Where:
m - Slope of the lineΔx - Change in the horizontal axis.Δy - Change in the vertical axis.If we know that (x₁, y₁) = (- 2, - 5) and (x₂, y₂) = (2, 3), then the slope of the line shown in the picture is:
m = [3 - (- 5)] / [3 - (- 2)]
m = 8 / 5
The slope of the line is equal of 8 / 5.
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2x-10
factor out........
Answer:
2 x-5
Step-by-step explanation:
The inequality -4x + 1 > y describes which of the following graphs?
the measures of a pair of supplementary angles are in the ratio of $7:2$. how many degrees are in the measure of their positive difference?
Answer:
100°
Step-by-step explanation:
You have two supplementary angles in the ratio 7:2, and you want the measure of their positive difference.
Ratio unitsThe sum of supplementary angles is 180°. The sum of the ratio units in the ratio 7:2 is 7+2 = 9, so each ratio unit must stand for 180°/9 = 20°.
The difference in ratio units is 7 -2 = 5, so the difference in the angles will be 5·20° = 100°.
The measure of their difference is 100°.
__
Additional comment
The two angles are 7·20° = 140°, and 2·20° = 40°. The difference is 140° -40° = 100°.
the area of trapezoid $abcd$ is $60$. one base is $4$ units longer than the other, and the height of the trapezoid is $5$. find the length of the median of the trapezoid.
The length of the median of the trapezoid is 12 units.
What is trapezoid?
Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides. This article provides formulas for the area of the trapezium as well as its types, attributes, and other trapezoids.Let the parallel sides be x and x+4
The area of a trapezium is the average or the parallel sides multiplied by the height
Area = [(x + x+ 4)/2 ] *h
= [ (2x+4)/2] * 5
= [2(x+2)/2] * 5
Area = 5(x+2)
60 = 5(x+2)
60/5 = x+2
12 = x+2
x = 12 - 2
x = 10
The parallel sides are 10 and 14 units.
Now the median length is the average of the parallel side lengths
Length of median = (10+14)/2
Length of median = 12 units
Hence, the length of the median of the trapezoid is 12 units.
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ANSWER QUICK
This scatter plot shows the height of 8 children and their age.
Based on the information in the scatter plot, what is the best prediction for the height of a 5 year old child?
Responses
25 inches
25 inches
35 inches
35 inches
45 inches
45 inches
55 inches
Answer:
it is actually 35
Step-by-step explanation:
This is because the plot is accelerating not decreasing also like if you think peter griffin is in! EPIC
Consider the quadratic equation x2 + 10x + 27 = 0. Completing the square leads to the equivalent equation (x + )2 =.
The completing the square leads to the equivalent equation of (x +5)² = -2.
Explain the term completing square?When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. This square formula is employed to factorize quadratic polynomials when we want to express a quadratic polynomial and equation as a perfect square with an additional constant.The given quadratic equation is-
x² + 10x = -27
Now, add a square of 1/2 of coefficient of 'x':
x² + 10x + 5² = -27 + 5²
x² + 10x + 5² = -27 + 25
Write this equation in the form of perfect square as;
(x +5)² = -2
Thus, the completing square leads to the equivalent equation of (x +5)² = -2.
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How many solution does the equation have 3=|y+7|
Please answer the question in the picture
In a Survey of a group of students, it was found that 35% of the student likes mathematics, 30% of student Like account and 600 student like both of them and 5%. Like none of them.
Answer:
Explanation: The idea is to draw a Venn Diagram and find the intersection. We have one circle of 70 and another with 40. When we add the two circles plus the 10 students who joined neither, we should get 100 students.
Step-by-step explanation: