Therefore , the solution of the given problem of equation comes out to be y" = -1/4 *√x * ln(x) + 1/2√x -1/2 * √x .
What is the equation?A mathematical equation looks to be a formula that joins two statements and indicates equality when it uses the equals symbol (=). In algebra, an equation is a statement of fact that demonstrates the equality of different mathematical variables . For instance, the result obd + 6 = 12 has an equal sign between quantities ptdc + 6 and 12. There is a mathematical formula that describes the connection between the syllables on either side of each letter. The emblem and the statement are frequently the same.
Here,
y = √x ln(x)
To find the y'
=> dy/dx = d(√x ln(x)) /dx
=> dy/dx = 1/2√x * ln(x) + 1/x *√x
=> dy/dx = 1/2√x * ln(x) + 1/√x
To find the value of y ''
=> dy'/dx = d(1/2√x * ln(x) + 1/√x ) / dx
=> dy'/dx = 1/2 * (-1/2* √x * ln(x) + 1/√x ) -1/2 * √x
=>dy'/dx = -1/4 *√x * ln(x) + 1/2√x -1/2 * √x
Therefore , the solution of the given problem of equation comes out to be y" = -1/4 *√x * ln(x) + 1/2√x -1/2 * √x .
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how many places can you put the lens to form a well-focused image of the candle flame on the wall?
The number of places you put the lens to form a well-focused image of the candle flame on the wall is either we have to move the screen towards the lens or the lens towards the screen.
Here we have given that the lens to form a well-focused image of the candle flame on the wall.
As we all know that if the candle is further from the wall than the focal length of the lens, then there are two places which will result in an image. Here we have know that one of them is just beyond the focal length from the wall.
Here we have given the other is that same distance from the candle.
Then the position near the wall will yield a small image.
Here the position near the candle will produce a large image.
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Line AD is parallel to line HE. Identify one pair of alternate interior angles.
[tex]\angle 3[/tex] and [tex]\angle 6[/tex]
A,B AND C form a triangle where BAC=90 AB=15MM and BC=18.1
find the length of AC giving your answer rounded to 1 decimal place
The measurement of side AC in the given right triangle is 10.12 units.
What is right triangle?A triangle having at least one angle measuring 90° is called a right triangle.
Given that, a triangle ABC, right-angled at A,
AB = 15 and BC = 18.1, we need to find AC,
Please refer to the figure attached,
Using Pythagoras theorem,
BC² = AB² + AC²
AC² = BC² - AB²
AC² = (18.1)² - 15²
AC² = 327.61 - 225
AC² = 102.61
AC = 10.12
Hence, the value of AC = 10.12
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a 5-card hand is drawn from a deck of standard playing cards. (a) how many 5-card hands have at least one club? (b) how many 5-card hands have at least two cards with the same rank?
5-card hands have at least one club 2023203
5-card hands have at least two cards with the same rank 916,272
N[at least one club] = N[total ways] - N'[at least one club]
= N[total ways] - N[no clubs]
There are 39 cards without a club. So there are 39 choose 5 = 575757 ways to not get a club.
There are 2598960 possible hands, leaving us with 2598960-575757 ways.
Which is 2023203 hands.
How many 5 card hands will have (at least) two of the same number?
This is a standard deck. Take 2–10 to be what I mean by numbers.
N=∑k=24(91)(4k)⋅(125−k)(41)5−k+[(92)+(91)(41)](42)2⋅(111)(41)
+(91)(42)⋅(121)(43)+(91)(43)⋅(41)(42)
=(760,320+38,016+432)+114,048+2,592+864
=916,272
A standard deck of playing cards contains 13 unique ranks, each with 4 distinct suits. Since we are interested in only pairs from ranks 2 to 10, we shall define A be the collection of the 9 relevant ranks and B be the collection of the 4 ranks (ace, jack, queen, king) where pairs are not a consideration. Collection C is the union of A and B, which contains all 13 ranks.
When computing probabilities we need to select the ranks(s) from a collection and then choose a number of suits (cards). When ranks are chosen from either A or B they are also chosen from C. This is important since we might choose twice from the same collection. For example, we might choose a rank from A for a pair (9 choose 1) and later choose 3 ranks from C for singletons (12 choose 3).
To hopefully make understanding the logic easier, I have first chosen the ranks either from A, B, or C, and immediately following I have chosen the number of cards, which is always choosing from 4 suits. I have inserted a dot between different card selections.
We begin by computing the number of combinations with exactly 2, 3, and 4 of a kind from A. The singletons come from C.
N1=∑k=24(91)(4k)⋅(125−k)(41)5−k=760,320+38,016+432=798,768
We add the case of either two pairs from A or a pair from each of A and B. The singleton comes from C.
N2=[(92)+(91)(41)](42)2⋅(111)(41)=114,048
We add the case of a pair from A and 3 of a kind from C.
N3=(91)(42)⋅(121)(43)=2,592
Finally, we add the case of 3 of a kind from A and a pair from B. Note that the case of both 3 of a kind and a pair from A is the same as the case of both a pair and 3 of a kind from A, which has already been included.
N4=(91)(43)⋅(41)(42)=864
N=N1+N2+N3+N4=916,272
5-card hands have at least one club 2023203
5-card hands have at least two cards with the same rank 916,272
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what is the correct answer
By using the given relationship the values of k are 2.5 , 2.5,2.5,2.5 respectively.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given,
table shows the relation y = kx .
so the given x values = 2,3,5,8 .
and the y values = 5,7.5,12.5,20
From the relation y = kx .
By substituting the given values
we get,
y = kx
y=5 x = 2
5 = k * 2
k = 2.5
y=7.5 x = 3
7.5 = k*3
k = 7.5/3
k = 2.5
y = 12.5 x = 5
12.5 = 5*k
k= 12.5 / 5
k = 2.5
y=20 x = 8
20 = k*8
k = 20/8
k = 5/2
k = 2.5
Hence, By using the given relationship the values of k are 2.5 , 2.5,2.5,2.5 respectively.
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The length of a rectangle is 7 more than twice the width. Which equation could represent the area of the rectangle in terms of the width
Answer:
Step-by-step explanation:
Need this done asap please help
The proof of the vertical angle theorem as required is explained in the answer below:
What are vertical angles?
Vertical angles are two angles that have the same properties and measure of their angles. Majorly these angles are opposite to each other and formed by the same extended lines.
So that, the required proof of the vertical angle theorem is;
STATEMENT REASON
1. AC intersect BD at E Given
2. m<AEB m<DEA = 180^o Linear pair theorem
3. m<DEC + m<DEA = m<AEB + m<DEA Substitution property
4. m<DEC = 180^o - m<BEC Subtraction property
5. m<DEC = m<AEB Vertical angle theorem
Therefore it can be deduced in the diagram that;
m<DEC = m<AEB (vertical angle theorem)
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Which of the following number is divisible by 3 but not by 9 Mcq?
(i) 221
(ii) 543
(iii) 28492
(iv) 92349
Therefore , the solution to the given problem of number line comes out to be option 2 543 is correct.
What is the number line?An introduction to mathematics tool is the number line, which is a visual integer depiction of real numbers. It is a representation of an intensity line. Each actual figure is taken to symbolize a point on the real number, or each precise figure is taken to symbolize a position. On a number line, distances between increments are equal. A line's numbers can only be answered in the way that is specified by those numbers. The question that corresponds with the number will define how it is used. B: Speak your mind.
Here,
Given :
Number are as follows : 221 ,543,28492 and 92349
Thus,
To find that the number is divisible by 3 but not 9.
So , as we know that sum of individual number of that number is divisible by 3 .
Then thw hole number is divisible by 3 .
So , we see 543 is divisible by 3 but not 9 .
Therefore , the solution to the given problem of number line comes out to be option 2 543 is correct.
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a number is divisible by 3 if the sum of its digits is divisible by 3.
a number is divisible by 9 if the sum of its digits is divisible by 3.
the number divisible by 3 but not by 9 is 543,
what is the maximum possible value of a sine ratio? in two or more complete sentences, explain your answer
The Sine Ratio is written as [tex]\frac{Perpendicular }{Hypoynuse}[/tex] , then the maximum possible value of a Sine Ratio is 1 .
What is Sine Ratio ?
In a Right Triangle , the Sine of angle is defined as the ratio of length of the opposite side divided by the length of the hypotenuse .
we know that the domain for the Sine function is ⇒ all real numbers ;
and the range of Sine function is ⇒ [-1,1] ;
so , from the range we can conclude that , the maximum value is 1 .
Therefore , the maximum value of Sine ratio is = 1 .
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Timothy purchased a computer for $1,000. the value of the computer depreciates by 20% every year.
this situation represents
the rate of growth or decay, r, is equal to
year.
so the value of the computer each year is
% of the value in the previous
it will take
years for the value of the computer to reach $512.
Answer: It takes 3 years
Step-by-step explanation:
20 percent of 1000 is 200 so 1000-200=800. Year 1
20 percent of 800 is 160 so 800-160=640. Year 2
20 percent of 640 is 128 so 640-128=512. Year 3
So in total in takes 3 years
Answer:
See photo
Step-by-step explanation:
Edmentum/Plato
You put $300 at the end of each month in an investment plan that pays an apr of 7%. how much will you have after 18 years? compare this amount to the total deposits made over the time period. a. $129,201.10; $64,800 c. $129,216.31; $64,800 b. $129,211.25; $64,775 d. $129,218.51; $64,775
We have to pay $129,216.31; $64,800.
Option (c) is correct.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is the interest on interest, and it is the mechanism that causes an investment to grow at an exponential rate.
To calculate the amount of money you will have in the investment plan after 18 years, we can use the formula for compound interest:
A = P(1 + r)^n
Where:
A is the final amount (the future value)
P is the principal, or the initial deposit, in this case $300
r is the annual interest rate, in this case 7% (expressed as 0.07)
n is the number of years, in this case 18
m is the number of times the interest is compounded per year. in this case 12 (monthly)
By using this formula, the final amount will be:
A = 300(1 + 0.07/12)^(12*18)
A = $129,218.51
To compare this amount to the total deposits made over the time period, we can calculate the total amount of money deposited by multiplying the deposit amount ($300) by the number of deposits made per month (12) by the number of years (18).
Total deposit = 3001218 = $64,800
Hence, we have to pay $129,216.31; $64,800.
Option (c) is correct.
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I WILL CHOOSE YOUR ANSWER BRAINLIEST HELPP
Answer:
see explanation
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 )
y = [tex]\frac{3}{4}[/tex] x - 1 ← is in slope- intercept form
with slope m = [tex]\frac{3}{4}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line
to find c substitute (8, 4 ) into the partial equation
4 = [tex]\frac{3}{4}[/tex] (8) + c = 6 + c ( subtract 6 from both sides )
- 2 = c
y = [tex]\frac{3}{4}[/tex] x - 2 ← equation of parallel line
---------------------------------------------------------------
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] , then
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (8, 4 ) into the partial equation
4 = - [tex]\frac{4}{3}[/tex] (8) + c = - [tex]\frac{32}{3}[/tex] + c ( add [tex]\frac{32}{3}[/tex] to both sides )
4 + [tex]\frac{32}{3}[/tex] = c , then
c = [tex]\frac{44}{3}[/tex]
y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{44}{3}[/tex] ← equation of perpendicular line
When Mike graduated college, his dad bought him a new truck worth $22,000. One year later, the truck had dropped 15% in value. If the truck's value continued to drop by 15% each year, what is the trucks value after 3 years? Round your answer to the nearest dollar.
When Mike graduated college, his dad bought him a new truck worth $22,000. One year later, the truck had dropped 15% in value. If the truck's value continued to drop by 15% each year, what is the trucks value after 3 years? Round your answer to the nearest dollar.
need this asap
Answer:
If the truck's value dropped 15% each year, after one year the value of the truck is 22000*(1-0.15) = $18700
After the second year, the value of the truck would be 18700*(1-0.15) = $15995
After the third year, the value of the truck would be 15995*(1-0.15) = $13596.75
Rounding the answer to the nearest dollar, the value of the truck after 3 years is $13597
Help me please thanu you sm
Step-by-step explanation:
now you should be able to dive these things yourself.
A no
(1/4)v = 4
4×(1/4)v = 4×4
v = 16
this is not v = 4
B no
n + 4 = 25
n + 4 - 4 = 25 - 4
n = 21
this is not n = 17
C yes
2z = 28
2z/2 = 28/2
z = 14
****************
The ratio of the three angles in a triangle are 1:2:6. Work out the size of each angle.
***********
Answer:
20° , 40° , 120°
Step-by-step explanation:
sum the parts of the ratio, 1 + 2 + 6 = 9 parts
divide the sum of the angles in a Δ , 180° by 9 to find the value of one part of the ratio.
180° ÷ 9 = 20° ← value of 1 part of the ratio, then
2 parts = 2 × 20° = 40°
6 parts = 6 × 20° = 120°
the 3 angles are 20° , 40° and 120°
Lucia is comparing monthly cell phone plans. Each plan will include a total of 6. 5% fees and taxes on the subtotal.
Features Plan A Plan B Plan C
Unlimited talk, text, regular data $52. 00 $50. 00 $48. 00
Unlimited high speed data Included in base price $10. 00 $12. 00
Hotspot $8. 00 Included in base price Not offered
Using the information provided, determine which plan is the least expensive
Answer:
Step-by-step explanation:
Plan C is the least expensive plan, as it has the lowest subtotal of $48.00 plus 6.5% fees and taxes.
Emmy took a math quiz lat week. There were 75 problem on the quiz and Emmy anwered 60% of them correctly. How many problem did Emmy get correct?
Emmy answered average of 60 out of 75 math problems correctly on the quiz she took last week, meaning she answered a total of 60 problems correctly.
60/75 = 0.8
0.8 x 75 = 60
Emmy took a math quiz last week and answered 60% of the 75 problems correctly. To calculate how many problems Emmy got correct, we need to divide 60 by 75, which gives us 0.8. Then, we multiply 0.8 by 75, which gives us 60. This means that Emmy correctly answered 60 out of 75 math problems on the quiz. This is equivalent to 60%, which is the percentage of problems she got correct. It is important to note that if Emmy had answered any more or any less problems correctly, the percentage of correct answers would have been different. Therefore, it is important to understand the relationship between percentages and total number of problems answered correctly in order to accurately calculate the number of correct answers.
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The word "and" in probability implies that we use the ____ rule.
A. Subtraction
B. Division
C. Addition
D. Multiplication
The word "and" in probability implies that we use the Multiplication rule.
The correct option is Option D.
What is the Multiplication Rule of Probability?The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.
The relationship between two events is explained by the probability multiplication rule.
Set A∩B represents the events in which both events A and B have occurred for two events A and B related to a sample space S. Consequently, (A∩B) indicates that occurrences A and B happened at the same time. You can write the event A∩B as AB. Using the characteristics of conditional probability, the likelihood of event AB is calculated.
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Find the circumcenter of the triangle ABC.
A(8,-8), B(-4, 4), C(8.4).
The circumcenter is
(Type an ordered pair.)
Answer:
Circumcenter (x) = 2
Circumcenter (y) = -2
Answer:
(2, -2)
Step-by-step explanation:
Midpoint of BC: ([-4 + 8]/2, (4 + 4)/2) = (2, 4)
Perpendicular bisector of BC has equation: x = 2
Midpoint of AC: ([8 + 8]/2, (-8 + 4)/2) = (8, -2)
Perpendicular bisector of AC has equation y = -2
Point of intersection of the two perpendicular bisectors:
(2, -2)
Answer: (2, -2)
The plot line shows the number of miles the individual members in a group of runners run each day How many runners run at most 2 miles per day?13963
13 number of runners run at most 2 miles per day .
calculation is explained below as
at 2 miles = 6 runners run
at 3 miles = 4 runners run
at 4 miles = 2 runners run
at 5 miles = 1runners run
on adding to calculate how many number of members run at most 2 miles per day is = 6 + 4 + 2 + 1 = 13 .
hence 13 number of members run at most 2 miles per day .
A number line plot is a simple way of visual representation of data patterns at the coordinate axis. on comparing the height of the specific columns, the least frequently of occurring number can be calculated. The number line of plot becomes a bar graph when the box is drawn around the Xs or dots in each and every column. A horizontal line, also called as x-axis, with equal intervals which are labelled with values which makes a number line plot. Xs or dots can be used to describe or evaluate the frequency in which a number, or a set a defined numbers, occurs on number line . Stacks of such producing Xs or dots that are used to represent data on the axis is known as plot number. .
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Neftali is filling up a pool with water. The depth of water in the pool can be represented by the function d(t)=0.25t+30, where t is the time in minutes and d(t) is the depth, in inches, of water in the pool.
How deep is the water in the pool when Neftali starts filling the pool with water?
Answer: The answer is 0.25 inches every minute
Step-by-step explanation: The equation tells you that the pool started at 30 inches (0.25t+30). It says that the pool's depth rises 0.25 inches every minute. So the answer is that the pool started out as 30 inches (which is the y-intercept) and rose 0.25 inches every minute.
Hope this helped
100 POINTS: can someone convert these to vertex form? shown work is appreciated
The vertex form of the parabolae equations are, respectively:
y + 36 = (x - 3)² y - 3 = (x - 2)² y + 25 = (x + 5)² y - 1 = (x + 7)² y + 9 / 4 = (x - 3 / 2)² y - 7 / 4 = (x - 5 / 2)² y + 8 = 2 · (x + 2)² y - 7 = 3 · (x + 1)² y + 86 = 5 · (x + 4)² y + 49 = (x - 2)² y + 49 = (x + 3)² y + 16 = (x + 6)² y + 4 = (x + 4)² y + 9 / 4 = (x + 5 / 2)² y + 81 / 4 = (x - 1 / 2)² y + 2 = 2 · (x + 3)² y + 9 = (x + 3)² y + 108 = 3 · (x - 2)²How to find the vertex form of the parabola equation
Parabolae are described by quadratic equations, whose standard and factor form are shown below:
Standard form
y = a · x² + b · x + c
Factor form
y = a · (x - r₁) · (x - r₂)
Where:
a - Lead coefficientb, c - Other coefficientsr₁, r₂ - Roots of the quadratic equationThis equation can be modified into vertex form:
y - k = C · (x - h)²
Where:
C - Vertex constanth, k - Coordinates of the vertexThe complete procedure to find vertex form is described below:
Expand the polynomial to standard form.Complete the square.Factor the perfect square trinomial.Use algebra properties until vertex form is found.Now we proceed to find the vertex form of each expression:
Case 1
y = x² - 6 · x - 27
y = (x² - 6 · x + 9) - 36
y + 36 = (x - 3)²
Case 2
y = x² - 2 · x + 7
y = (x² - 2 · x + 4) + 3
y = (x - 2)² + 3
y - 3 = (x - 2)²
Case 3
y = x² + 10 · x
y + 25 = x² + 10 · x + 25
y + 25 = (x + 5)²
Case 4
y = x² + 14 · x + 50
y = (x² + 14 · x + 49) + 1
y = (x + 7)² + 1
y - 1 = (x + 7)²
Case 5
y = x² - 3 · x
y + 9 / 4 = x² - 3 · x + 9 / 4
y + 9 / 4 = (x - 3 / 2)²
Case 6
y = x² - 5 · x + 8
y = (x² - 5 · x + 25 / 4) + 7 / 4
y - 7 / 4 = (x - 5 / 2)²
Case 7
y = 2 · x² + 8 · x
y = 2 · (x² + 4 · x)
y + 2 · 4 = 2 · (x² + 4 · x + 4)
y + 8 = 2 · (x + 2)²
Case 8
y = 3 · x² + 6 · x + 10
y = 3 · (x² + 2 · x + 10 / 3)
y = 3 · (x² + 2 · x + 1) + 7
y - 7 = 3 · (x + 1)²
Case 9
y = 5 · x² + 40 · x - 6
y = 5 · (x² + 8 · x - 6 / 5)
y + 5 · 16 = 5 · (x² + 8 · x + 16) - 6
y + 86 = 5 · (x + 4)²
Case 10
y = (x + 5) · (x - 9)
y = x² - 4 · x - 45
y + 4 = (x² - 4 · x + 4) - 45
y + 49 = (x - 2)²
Case 11
y = (x - 4) · (x + 10)
y = x² + 6 · x - 40
y + 9 = (x² + 6 · x + 9) - 40
y + 49 = (x + 3)²
Case 12
y = (x + 2) · (x + 10)
y = x² + 12 · x + 20
y + 16 = x² + 12 · x + 36
y + 16 = (x + 6)²
Case 13
y = (x - 2) · (x - 6)
y = x² - 8 · x + 12
y + 4 = x² - 8 · x + 16
y + 4 = (x + 4)²
Case 14
y = (x + 1) · (x + 4)
y = x² + 5 · x + 4
y + 9 / 4 = x² + 5 · x + 25 / 4
y + 9 / 4 = (x + 5 / 2)²
Case 15
y = (x + 4) · (x - 5)
y = x² - x - 20
y + 1 / 4 = (x² - x + 1 / 4) - 20
y + 81 / 4 = (x - 1 / 2)²
Case 16
y = 2 · (x + 2) · (x + 4)
y = 2 · (x² + 6 · x + 8)
y + 2 · 1 = 2 · (x² + 6 · x + 9)
y + 2 = 2 · (x + 3)²
Case 17
y = x · (x + 6)
y = x² + 6 · x
y + 9 = x² + 6 · x + 9
y + 9 = (x + 3)²
Case 18
y = 3 · (x + 4) · (x - 8)
y = 3 · (x² - 4 · x - 32)
y + 3 · 4 = 3 · (x² - 4 · x + 4) - 3 · 32
y + 12 = 3 · (x - 2)² - 96
y + 108 = 3 · (x - 2)²
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part 1.b. now consider a problem this equation might solve. a local restaurant owner is considering the purchase of a pier, whose walkway is 50 cm above the high-water mark, for use in outdoor events. the owner has been advised that piers with walkways less than 30 cm above the high-water mark should be avoided because they can be flooded by storms and very high tides. if submergence continues at the rate you calculated, how many years will pass before the high-water mark is less than 30 cm from the base of the walkway?
Using the equation, the restaurant owner can determine how long it will take before the high-water mark is less than 30 cm from the base of the walkway. In this case, the answer is 40 years.
1. Subtract the desired end point from the current height of the walkway:
50 cm - 30 cm
= 20 cm
2. Divide the difference by the rate of submergence:
20 cm / 0.5 cm/yr
= 40 years
The restaurant owner can use the equation to calculate the number of years it will take for the high-water mark to be less than 30 cm from the base of the pier’s walkway. By subtracting the desired end point from the current height of the walkway, the owner can determine the difference in height. Then, by dividing this difference by the rate of submergence, the owner can calculate the number of years it will take before it is necessary to take action to protect the pier from flooding. In this case, the answer is 40 years.
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suzanne receives a t-score of -3.6 in her bone mineral density (bmd) test results. what does this score indicate to her doctor?
A T-score of -3.6 indicates that the individual has a severe case of osteoporosis
A T-score is a standard score used to compare an individual's bone mineral density (BMD) to that of a healthy young adult population. A T-score of -3.6 on a BMD test indicates that the individual's BMD is significantly lower than that of a healthy young adult. Specifically, it means that the individual's BMD is 3.6 standard deviations below the average BMD of a healthy young adult.
A T-score of -2.5 or lower is considered to indicate osteoporosis, which is a condition characterized by low bone density and an increased risk of fractures. Therefore, a T-score of -3.6 indicates that the individual has a severe case of osteoporosis, and the doctor will likely recommend treatment such as medication and lifestyle changes to help increase bone density and reduce the risk of fractures.
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Which measure of central tendency would the store owner use if she wanted to argue that the employees are paid well?
A. the mean
B. the median
C. the mode
D. the range
If the business owner wanted to make the case that the workers are paid well, she would use the range of central tendency.
The range, D
How can I find the central tendency?You are undoubtedly most familiar with the mean, which is the arithmetic average and a measure of central tendency. It is extremely easy to calculate the mean. Simple addition and division by the dataset's observation count are all that are required to calculate the values. All data values are included in the mean calculation.
Finding a variable's maximum observed value (also known as the range) and deducting its least observed value will yield the range (the minimum).
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Which is the approximate measure of angle jgh? 18.4° 19.5° 70.5° 71.6°
The approximate measure of angle JGH is 70.5°.
According to this question, we have a right triangle in which lengths of its hypotenuse (GH), in centimeters, and one leg (JH) are known and we must determine the measure of an angle (∠JGH), in degrees. A representation of this triangle is included in the image attached below.
By trigonometry we have the following expression for the required angle:
cos∠GJH = HJ/GH .......(1)
Given, HJ = 2, GH = 6
cos∠GJH = 2/6
∠GJH = [tex]cos^{-1}\frac{2}{6}[/tex]
≈ 70.529
The approximate measure of angle JGH is 70.5°.
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Which of the following is a polynomial with roots 4, 2i, and −2i?
a. f(x)= x^3-4x^2+8-4
b. f(x)=^3-8^2+16-4
c. f(x)= x^3-4x^2+4x-16
d. f(x)= x^3-4x^2+8x-16
The polynomial with roots 4, 2i, and −2i is f(x)= x^3-4x^2+4x-16, which can be found by using the factor theorem.
c. f(x)= x^3-4x^2+4x-16
The polynomial with the given roots is a cubic polynomial. To get the coefficients of the polynomial, we can use the factor theorem. The factor theorem states that if a polynomial has a factor (x - a), then a is a root of the polynomial.
Therefore, the polynomial with roots 4, 2i, and -2i is f(x) = (x - 4)(x - 2i)(x +2i)
Expanding this polynomial, we get f(x) = x^3-4x^2+4x-16
The polynomial with roots 4, 2i, and −2i is f(x)= x^3-4x^2+4x-16, which can be found by using the factor theorem.
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your statistics class has 15 juniors out of 30 total students. you put the names of all the students in your statistics class on slips of paper into a hat. you mix up the names, and draw 4 of them without looking. what is the probability that you pick exactly 2 juniors?
The probability that you pick exactly 2 juniors is 15/30 x 14/29 x 13/28 x 12/27, or 0.081.
1. Probability of picking the first junior: 15/30
2. Probability of picking the second junior: 14/29 (14 remaining juniors out of 29 total students after the first pick)
3. Probability of picking the third non-junior: 13/28 (13 remaining non-juniors out of 28 total students after the second pick)
4. Probability of picking the fourth non-junior: 12/27 (12 remaining non-juniors out of 27 total students after the third pick)
Therefore, the probability of picking exactly 2 juniors is
15/30 x 14/29 x 13/28 x 12/27
= 0.081.
The probability of picking exactly 2 juniors out of 4 slips of paper from a hat with the names of all 30 students in your statistics class is 0.081. This is calculated by taking the probability of picking the first junior (15/30) and multiplying it by the probability of picking the second junior (14/29, since there are 14 remaining juniors out of 29 total students after the first pick), the probability of picking the third non-junior (13/28, since there are 13 remaining non-juniors out of 28 total students after the second pick), and the probability of picking the fourth non-junior (12/27, since there are 12 remaining non-juniors out of 27 total students after the third pick).
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Two bowling alleys have different prices.
• Bowl More charges $4.50per game plus $5.00for shoe rental.
Bowling Pinz charges $4.75per game plus $3.00for shoe rental.
For what number of games will the cost to bowl be the same at both places?
.
games
Answer:
x (number of games) = 8
Step-by-step explanation:
We want these two to be equal, which means we want:
4.50x + 5 = 4.75x + 3
We will minus 4.50x and 3 from both sides, giving us:
2 = .25x
Then, multiply by 4 to get a whole number of x, which gives us:
x = 8
Now, we will check our answer. We have:
4.50 * 8 + 5 = 4.75 * 8 + 3
36 + 5 = 38 + 3
41 = 41
So this proves x = 8.
So, the amount of games where the price would be the same is 8, x = 8.
Hope this helped!
The total amount of garbage y is proportional to the number of days x, as shown in the graph.
Write an equation to represent this relationship.
The equation that represent the relationship between pounds of garbage y and of days x is y = 4.5x
What direct variation?Direct variation describes a simple relationship between two variables . We say y varies directly with x , then y=kx. for some constant k , called the constant of variation or constant of proportionality .
From the graph when y = 4.5 , x = 1 and when y = 9 , x = 2. we can take any of these values to find K
y = kx
9 = 2k
therefore K = 9/2 = 4.5
representing K for 4.5 in y = kx
then, y = 4.5x
therefore the equation of the relationship between y and x is y = 4.5x
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