Answer:
There are 5 quarters and 1 nickel
Step-by-step explanation:
Let Q and N be the numbers of Quarters and Nickels that Senor Pena found, respectively.
The value of each coin is $0.25 for quarters and $0.05 for each nickel
The total of $1.30 would be the result of:
1) Quarters: $0.25*Q, and
2) Nickels: $0.05*N
So we can write: $0.25*Q + $0.05*N = $1.30
We also know he found 6 coins, so:
Q + N = 6
We have two equations and two unknowns. We can use substitution to find the answer.
Rearrange the second equation to isolate one of the two variables. lets isolate Q:
Q = 6-N
We can use this definition of Q in the first equation by substitution:
$0.25*Q + $0.05*N = $1.30
$0.25*(6-N) + $0.05*N = $1.30
Leaving off the $ signs for clarity:
0.25(6-N) + 0.05N = 1.30
1.5 - 0.25N + 0.05N = 1.30
-0.2N = -0.20
N = 1
There is 1 nickel
Since Q = 6-N, Q = 5
There are 5 quarters and 1 nickel
CHECK
Do 5 quarters and 1 nickel add to $1.30?
5*($0.25) + 1*($0.05) = $1.30?
$1.25 + $0.05 = $1.30 YES
a student in stat 121 wants to estimate the average score on the stat 121 final exam from last semester. they asked 200 students who took the class last semester what their final exam score was and recorded it. what is the sample?
If a student in stat 121 wants to estimate the average score on the stat 121 final exam from last semester. The sample is: The 200 students interviewed.
What is sample?Sample can be defined as the data or information that are randomly collected from a group of population so as to reach or drawn a conclusion.
Based on the scenario the sample will be the 200 students who took the class last semester as the 200 students were randomly selected from a larger population so as to reach a conclusion.
Therefore we can conclude that the sample is the 200 students interviewed.
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The graph of a sinusoidal function intersects its midline at (0,-6) and then has a minimum point at (2.5,-9)
The sine function that intersects its midline at (0,-6) and then has a minimum point at (2.5,-9) is given as follows:
y = 3sin(0.6πx) - 6.
How to define the sinusoidal function?The standard definition of the sine function is given as follows:
y = Asin(Bx) + C.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.The midline is at y = -6, while the minimum point is at y = -9, hence the amplitude of the function is given as follows:
A = -6 - (-9)
A = 3.
A sinusoidal function with amplitude 3 should oscillate between -3 and 3, while it oscillates between -3 and -9, hence the vertical shift is given as follows:
C = -6.
The distance from the midline to the minimum value is of 3/4 of the period, hence the period is of:
3/4P = 2.5
P = 4 x 2.5/3
P = 10/3.
This means that the parameter b is obtained as follows:
2π/B = 10/3
10B = 6π
B = 0.6π
This means that the function is defined as follows:
y = 3sin(0.6πx) - 6.
The graph of the sinusoidal function is given by the image presented at the end of the answer, and the labeled points show that the desired features are present.
Missing InformationThe complete problem is given as follows:
The graph of a sinusoidal function intersects its midline at (0,-6)(0,−6)left parenthesis, 0, comma, minus, 6, right parenthesis and then has a minimum point at (2.5,-9).
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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,
Please Help Soon
Simplify each of 10−8 and 8−10 to determine if the commutative property applies to subtraction. State your findings
Answer:
The communicative property does not apply to subtraction.
10 - 8 = 2
8 - 10 = -2
We do not get the same answer. 2 and -2 are not the same number.
Step-by-step explanation:
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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factorize 9( x - 1 ) ^ { 2 } - 16 ( x + 2 ) ^ { 2 }
Answer:
(7x + 5)(- x - 11)
Step-by-step explanation:
9(x - 1)² - 16(x + 2)² ← is a difference of squares and factors in general as
a² - b² = (a + b)(a - b)
9(x - 1)² - 16(x + 2)²
= [ 3(x - 1) ]² - [4(x + 2) ]² with a = 3(x - 1) and b = 4(x + 2)
= [ 3(x - 1) + 4(x + 2) ] [ 3(x - 1) - 4(x + 2) ] ← distribute parenthesis
= [ 3x - 3 + 4x + 8 ] [ 3x - 3 - 4x - 8 ]
= (7x + 5)(- x - 11 )
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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10
Velocity (m/s)
8-
6-
4
2-
of
0-
0 2 4 6 8 10
10 12 14 16 18 20
Time (seconds)
a) Work out the total distance travelled on the cycle.
b) Work out the acceleration in the last 8 seconds.
The total distance travelled on the cycle is 30.46m and the acceleration is the last 8 seconds is 0.85 m/s².
What is acceleration?"Acceleration is the measure of the speed at which velocity changes."
OR "Acceleration depends upon the velocity if the velocity continously increases or decreases the acceleration will be produced."
Positive acceleration results from continuously increasing velocity.
Negative acceleration will be negative if the velocity is continuously decreasing.
FORMULA
Acceleration is defined as a change in velocity divided by time, or a = (Vf-Vi)/t UNIT.
Meter/second+square, or m/S², is the SI unit of velocity in the MKS system.
a. Total distance = Hypotenuse₁ + mid distance + Hypotenuse₂
Hypotenuse₁ = [tex]$ \sqrt{10^2 + 6^2} $[/tex]
Hypotenuse₁ = 11.66m
mid distance = 12 - 6
= 6m
Hypotenuse₂ = [tex]$ \sqrt{10^2 + (20-12)^2} $[/tex]
Hypotenuse₂ = [tex]$ \sqrt{10^2 + (8)^2} $[/tex]
Hypotenuse₂ = 12.80m
Total distance = 11.66m + 6m + 12.80m
Total distance = 30.46m
b. Acceleration [tex]{\displaystyle ={\frac { \text{v - u} }{t}}[/tex]
[tex]\displaystyle = {\frac { \text{12.80 - 6} }{8}[/tex]
[tex]\displaystyle = {\frac { 6.80 }{8}[/tex]
0.85 m/s²
Thus, the total distance travelled on the cycle is 30.46m and the acceleration is the last 8 seconds is 0.85 m/s².
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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]
: Given the following P(A)-0.3 P(B) = 0.2 PA and B) 0.06 A and B are disjoint and independent. A and B are disjoint. A and B are independent A and B are neither disjoint nor independent.
Given the following P(A) = 0.3, P(B) = 0.2, P(A) and P(B) 0.06. So, A and B are independent. This can be solved using probability concept.
What is probability?The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Given that,
P(A) = 0.3
P(B) = 0.2
P(A and B) = 0.06
Now, P(A and B) = P(A) × P(B)
or, 0.06 = 0.3 × 0.2
So, A and B are independent.
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2.3.2: Excel: Linear Regression.
The provided statement indicates that the regression line's equation is[tex]\hat{Y}[/tex] = -0.06392X + 3.42231. Hence the formula for predicting the anticipated sepal size of a floral with panicle length 6.39 is [tex]\hat{Y}[/tex] = 3.01
We employ linear regression because:More specifically, the nature and degree of the correlation between a variable y and a number of different independent variables are assessed using linear regression. It aids in the creation of models for making predictions, such as projecting the stock price of a corporation.
Let X represent the sepal's length, and Y represent its breadth. Next, we have the information below:
Cov (X, Y) = -0.0438254
[tex]$$\begin{aligned}& \bar{Y}=3.04966 \\& \sigma_Y=0.445429 \\& \bar{X}=5.829932 \\& \sigma_X=0.828054\end{aligned}$$[/tex]
The following provides the least squares estimates of the intercept and regression coefficient:
[tex]\hat{\beta_0}=\bar{Y}-\hat{\beta_1} \bar{X}[/tex]
[tex]$\hat{\beta_1}$[/tex] = Cov (X, Y)/[tex]$\sigma_X^2$[/tex]
[tex]\begin{aligned}& \hat{\beta}_1=\frac{-0.0438254}{0.828054^2} \\& \hat{\beta}_1=-0.06392\end{aligned}[/tex]
and,
[tex]$$\begin{aligned}& \hat{\beta_0}=3.04966-(-0.06392) *(5.829932) \\& \Rightarrow \hat{\beta}_0=3.42231\end{aligned}$$[/tex]
Thus, the regression line's equation is as follows:
[tex]\hat{Y}[/tex] = -0.06392X + 3.42231
With a sepal length of 6.39, the following formula predicts the sepal breadth of a flower:
[tex]$$\begin{aligned}\hat{Y} & =-0.06392 * 6.39+3.42231 \\\Rightarrow \hat{Y} & =3.0138612 \simeq 3.01\end{aligned}$$[/tex]
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The complete question is-
The famous iris dataset (the first sheet of the spreadsheet linked above) Was first published in 1936 by Ronald Fisher. The dataset contains 50 samples from 3 iris species. setosa, virgiria, and versicolor. Four features are measured, all in cm sepal length, sepal with, petal length, and petal width.
What is the equation tor the least,square regressian line where the independen; or predictor variabie is pelat Iength and the dependent of response variable is petal width for iris versicolar?
What is the predicted petal width for iris versicolor for a flower with a pelal length of 4.1?
****************
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°
jon gets to work in 20 min when he drives his car. riding his bike (by the same route) takes him 45 min. his average driving speed is 14.5 mph greater than his average speed on the bike. how far does he travel to work?
The distance Jon travels to work is 472.5 miles.
Let d be the distance Jon travels to work.
The time it takes to drive is 20 minutes and the time it takes to bike is 45 minutes.
The difference in speed between driving and biking is 14.5 mph.
We can set up the following equation:
20min * (14.5mph + x) = 45min * x
Solving for x gives us the average speed of Jon on the bike, which is 10.5 mph.
Now we can use the distance formula to solve for d:
d = rate * time
d = 10.5mph * 45min
d = 472.5 miles
Therefore, the distance Jon travels to work is 472.5 miles.
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Assume that the linear function f(x) contains the points f(1) = 5 and f(9) = 37. What is the value of f(f(6))?
Answer:
101
Step-by-step explanation:
f(1) = 5 = 4*1 +1
f(9) = 37 = 4*9+1
f(6) = 4*6+1 = 25
f(f(6)) = f(25) = 4*25+1 =101
Answer:
101
Step-by-step explanation:
Given the values of a linear function f(1) = 5 and f(9) = 37, you want the value of f(f(6)).
Linear functionThe given ordered pairs are (1, 5) and (9, 37). Using these, we can find the slope of the function to be ...
m = (y2 -y1)/(x2 -x1)
m = (37 -5)/(9 -1) = 32/8 = 4
The y-intercept is ...
b = y -mx
b = 5 -4(1) = 1
So the function in slope-intercept form is ...
y = mx +b
f(x) = 4x +1
ApplicationThe value of f(6) is ...
f(6) = 4·6 +1 = 25
The value of f(f(6)) is ...
f(f(6)) = f(25) = 4·25 +1 = 101
The value of f(f(6)) is 101.
A triangle has two sides of length 14 and 6. What is the smallest possible whole-number length for the third side?
The smallest possible whole-number length for the third side is 12
How to determine the valueFollowing the Pythagorean theorem which states that the hypotenuse square is equal to the sum of the squares of the other two sides in a triangle.
This is represented as;
a² = b² + c²
Given that;
a is the hypotenuse sideb is the opposite sidec is the adjacent side of the triangleFrom the information given, we have that;
14² = 6² + c²
Find the square values
196 = 36 + c²
collect like terms
c² = 196 - 36
subtract the values
c² = 160
Find the square root of both sides
c = √160
c = 12. 65
Thus, the value is 12
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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
Look at where the diver started and where she is heading. She started at –5 and descended to –75. That means she dropped 70 feet more.
These two points on the number line describe that she descended by 70 units.
What is a number line?A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.
Here,
She started at –5 and descended to –75.
On the number line, the difference between -75 and -5 is given as
= -5 - (-75)
= 70
Thus, these two points on the number line describe that she descended by 70 units.
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Evaluate the function.
g(x)=-3x² - x; Find g(5)
Answer:
[tex]g(5)=-75[/tex]
Step-by-step explanation:
[tex]g(x)=-3x^{2} \\g(5)=-3(5)^{2} \\g(5)=-75[/tex]
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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!
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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Ms. Carlson is planning a dance recital for her students. The maximum duration for the recital is 76 minutes. Group dance numbers last 6 minutes and a solo performance lasts 2 minutes.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
The inequality that describes this situation will be 6x + 2s ≤ 76
How to compute the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
x = number of group dance numbers
s = number of solo performances
The inequality will be 6x + 2s ≤ 76
This inequality can be read as "the total duration of the group dance numbers (6 minutes per group dance number) plus the total duration of the solo performances (2 minutes per solo performance) is less than or equal to 76 minutes."
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find the area of the part of the plane 5x + 3y + z = 15 that lies in the first octant.
The area of the part of the plane 5x + 3y + z = 15 that lies in the first octant is 15x^3/6 + 45x^2y/2.
What is area?Area is a measure of the size of a surface or the amount of space it takes up. It can be measured in square units such as square feet, square meters, or acres. Area is used to describe the size of a two-dimensional object or shape, and is often used when discussing the size of a plot of land, a room, or other geographical area.
The first octant is defined as the area in the three-dimensional Cartesian coordinate system where all the coordinates are positive. In this case, the equation 5x + 3y + z = 15 can be rearranged to solve for z: z = 15 - 5x - 3y. This new equation can then be used to find the area of the plane that lies in the first octant by integrating the equation over the area of the octant.
To solve for the area, we must first find the boundaries of the octant. Since all coordinates must be positive, the boundaries of the octant are x = 0, y = 0, and z = 0. The area of the plane that lies in the first octant is then computed using the triple integral:
Area = ∫∫∫ 0 0 0 15-5x-3y dzdydx
= ∫∫ 0 0 (15x + 45y)dydx
= ∫ 0 (15x^2/2 + 45xy)dx
= 15x^3/6 + 45x^2y/2
Therefore, the area of the part of the plane 5x + 3y + z = 15 that lies in the first octant is 15x^3/6 + 45x^2y/2.
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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
4. explain why there are two high tides and two low tides each day. strictly speaking, should the period during which there are two high tides be 24 hours? if not, what should the interval be?
The interval should be 12 hours and 25 minutes for the two high tides and two low tides.
What is interval ?
An interval refers to the amount of time it takes for a tide to go from high to low or low to high
The reason for two high tides and two low tides each day is due to the gravitational pull of the moon and the sun on Earth's oceans. These gravitational forces cause the water in the oceans to bulge, creating high tides. The gravitational pull of the moon is stronger than that of the sun, so the moon has a greater impact on tides.
The time it takes for the tide to go from high to low and back to high is called the tidal period, which is about 12 hours and 25 minutes. This is not exactly 24 hours because the Earth is also rotating on its axis, so the position of the Moon and the Sun relative to a specific location on the Earth's surface is constantly changing.
So, the interval should be 12 hours and 25 minutes for the two high tides and two low tides.
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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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amy sells beaded necklaces. each large necklace sells for $4.10 and each small necklace sells for $3.80. how much will she earn from selling 7 large necklaces and 1 small necklace?
Amy will earn $28.70 + $3.80 = $32.50.
Profit and loss:
A profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year. These records provide information about a company’s ability or inability to generate profit by increasing revenue, reducing costs, or both. P&L statements are often presented on a cash or accrual basis. Company managers and investors use P&L statements to analyze the financial health of a company.
Amy will earn $28.70 from selling 7 large necklaces (7 x $4.10 = $28.70) and $3.80 from selling 1 small necklace, so in total, she will earn $28.70 + $3.80 = $32.50.
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gasoline costs $3.58 per gallon. if karl paid $30.43 for gasoline, how many gallons did he buy? responses
If the Gasoline costs $3.58 per gallon and Karl paid $30.43 , the number of gallons Karl purchased is 8.5 gallons .
The Per unit cost of Gasoline is = $3.58 ;
the amount paid by Karl for gasoline is = $30.43 ;
we have to calculate the number of gallons of gasoline purchased by Karl,
the number of gallons can be calculated by the formula :
Number Of Gallons purchased = [tex]\frac{Total \; Amount }{Cost \; per \; Gallon}[/tex] ;
Substituting the values of amount and cost per gallon in the formula ,
we get ;
Number of gallons = [tex]\frac{30.43}{3.58}[/tex] ;
we get ; ⇒ 8.5 .
Therefore , Karl purchased 8.5 gallons of gasoline .
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Find the area of the region enclosed by the inner loop of the curve.r = 6 + 12 sin θ
The area of the region enclosed by the inner loop of the curve can be calculated by integrating the function r = 6 + 12 sin θ over the interval of θ.
The area of the inner loop is given by Area = 1/2 ∫r^2 dθ = 1/2 ∫(6 + 12 sin θ)^2 dθ
We can solve this integral by breaking it into two parts: Area = 1/2 (∫(6 + 12 sin θ)^2 dθ) = 1/2(∫36 + 72sin θ + 144sin^2 θ dθ)
The first integral is simple and equals to 36*θ and the second one is equal to 48θ - 48cos(2θ)
The limits of integration are [0, 2π]
So the area of the inner loop is 1/2(36*2π + 48(2π) - 48(2)) = 72π
So the area of the region enclosed by the inner loop of the curve is 72π square units.
Which table shows a linear function?
O
X
-5
-3
-1
1
2
X
-4
-3
-2
1
2
X
-5
-3
-1
0
2
y
-4
-3
-2
265 35.
-1
-3
-5
-2
0
9236
5
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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