The area of the triangle is (a-6, b-12) square units 6 sq unit.
What is the triangle?A triangle is described as a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees.
This means that the sum of the interior angles of a triangle is equal to 180°
Now that we have the points they make a 3-4-5 triangle.
The two legs are 3 and 4, so the hypotenuse has to be 5.
We could also use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5
We then calculate the area
Area =1/2 b*h
Area = 1/2(3*4)
Area = 6 sq unit
The area of the triangle is (a-6, b-12) square units 6 sq unit.
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What is the image of (5,−4) after a dilation by a scale factor of 4 centered at the origin?
The image of (5,−4) after a dilation by a scale factor of 4 centered at the origin is (20,−16)
What is the image after a dilation centered at the origin?From the question, we have the following parameters that can be used in our computation:
Point = (5,−4)
Scale factor of 4 centered at the origin
The image after a dilation centered at the origin is
Image = Point * Scale factor
Substitute the known values in the above equation, so, we have the following representation
image = (5,−4) * 4
Evaluate
image = (20,−16)
Hence, the image after a dilation centered at the origin is (20,−16)
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Find the x- and y-intercepts of the graph of 4x+8y=20. State each answer as an integer or an improper fraction in simplest form
The cordinate points with x- and y-intercepts of the graph of a linear equation, 4x+ 8y = 20, are equals to the (5,0) and (0, 5/2).
We have an equation, 4x + 8y = 20 --(1) which is linear equation with two variables. We have to determine the the x- and y-intercepts of the graph of equation (1). The graph of line (1) is present in above figure. Slope intercept form of equation (1) is written as [tex]y = - \frac{1}{2}x + \frac{5}{2}[/tex],
The x-intercept is point where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. As we know, two points determine any line, we can graph lines using the x- and y-intercepts. To determine the x-intercept, we substitute y=0 and solve for x. So, when y = 0 then 4x + 0 = 20
=> x = 5
similarly to determine the y-intercept, set x=0 and solve for y. When x = 0
=> 8y = 20
=> y = 5/2.
Hence, required value are (5,0) and (0,5/2).
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Write an exponential regression function to model the situation.
The exponential regression function to model the situation above is: y = 400,000(0.841)^x
What is the explanation for the above response?The exponential regression function to model the situation is:
y = ab^x
where,
y = flour in grams
x = number of weeks since the bakery opened
a = initial amount of flour (Y-intercept) = 400,000 grams
b = growth factor
To find the value of b, we can use any two points from the table. Let's use the first and second points.
When x = 0, y = 400,000
When x = 1, y = 336,400
Substituting these values in the equation, we get:
400,000 = ab^0
336,400 = ab^1
Simplifying these equations, we get:
a = 400,000
b = 0.841
Therefore, the exponential regression function is:
y = 400,000(0.841)^x
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Select the correct answer. team goal scored in first five minutes p 2.34% q 3.56% r 1.24% s 4.01% t 3.88% total 2.86% the probabilities of a particular soccer team scoring a goal within the first five minutes of the game are given in the table. what is the probability of a goal being scored in the first five minutes of the game, given that the team is team q? a. 1.24% b. 2.86% c. 3.56% d. insufficient data
The probability of a goal being scored in the first five minutes of the game, given that the team is team q is 1.24%. The correct option is a.
The probability of a goal being scored in the first five minutes of the game, given that the team is team q, is given by the conditional probability:
P(goal scored in first 5 min | team is q) = P(goal scored in first 5 min and team is q) / P(team is q)
From the table, we have:
P(goal scored in first 5 min and team is q) = 3.56%
P(team is q) = 3.56%
Therefore:
P(goal scored in first 5 min | team is q) = 3.56% / 3.56% = 1
This means that if we know the team is team q, the probability of a goal being scored in the first five minutes of the game is 100% (or certain). So the correct answer is (a) 1.24%.
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Susan got a prepaid debit card with 20 on it.For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 16 cents per yard. If after that purchase there was 14.88 left on the card, how many yards of ribbon did Susan buy?
Answer:
32 yards
Step-by-step explanation:
Let's see, the card started out with $20 on it, and ended up with $14.88.
To find how much she spent on ribbon, we can first subtract the 2 amounts:
20-14.88
=5.12
So, Susan spent $5.12 on ribbon. We also know that each yard of ribbon was $0.16, so we can divide the spent amount ($5.12) by $0.16 to find out how many yards she bought:
5.12/0.16
=32
So, Susan bought 32 yards of ribbon.
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if an airplane travels around the world, flying just above the equator it would travel 1.25 x 10^4 miles. How many miles would a plane travel if it flew around the world just above the equator 3 1/2 times?
(in standard form)
A plane flying just above the equator around the world 3 1/2 times would cover a distance of 4.375 x 10⁴ miles.
If an airplane travels around the world just above the equator once, it covers a distance of 1.25 x 10⁴ miles. To find how many miles it would cover if it flew around the world 3 1/2 times, we need to multiply this distance by 3.5:
1.25 x 10⁴ miles x 3.5 = 4.375 x 10⁴ miles
To understand this calculation, we need to know that 3 1/2 times means 3.5 times. So, we multiply the distance covered in one round of the world by 3.5 to find the total distance covered in 3 1/2 times around the world.
We use standard form to express the answer in a more compact and convenient way, where 4.375 x 10⁴ represents the number 43,750 in scientific notation.
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What is the value of B? Bº 58° 61°
Answer:
61 degrees
Step-by-step explanation:
Triangle interior measures add up to 180 degrees.
61 + 58 + x = 180
119 + x = 180
x = 61
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One medical procedure used today allows parents to select the gender of their future baby. The procedure has been found to be effective 75% of the time, meaning that 75% of the time parents get a baby of the preferred gender. Suppose this method is used by 5 couples at one particular clinic. For #6 and 7, write the numeric value and write in words what it represents
6. The probability that all 5 couples will have a baby of the preferred gender is 0.2373.
7. The probability that at least 4 of the 5 couples will have a baby of the preferred gender is 1 - 0.3672 = 0.6328.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to predict with absolute certainty.
6. What is the probability that all 5 couples will have a baby of the preferred gender?Answer: The probability that one couple will have a baby of the preferred gender is 0.75. Assuming the gender of each baby is independent of the others, the probability that all 5 couples will have a baby of the preferred gender is 0.75⁵ = 0.2373.
Numeric value: 0.2373
In words: The probability that all 5 couples will have a baby of the preferred gender is 0.2373.
7. What is the probability that at least 4 of the 5 couples will have a baby of the preferred gender?Answer: There are two ways to approach this problem. One way is to calculate the probability of each possible outcome (0 to 5 couples having a baby of the preferred gender) and then add up the probabilities for the outcomes where at least 4 couples have a baby of the preferred gender. Another way is to use the complement rule and subtract the probability that fewer than 4 couples have a baby of the preferred gender from 1.
Using the first method, we can calculate the probabilities as follows:
- 0 couples: 0.25⁵ = 0.0009766
- 1 couple: 5 x 0.75 x 0.25⁴ = 0.01465
- 2 couples: 10 x 0.75² x 0.25³ = 0.08789
- 3 couples: 10 x 0.75³ x 0.25² = 0.2637
- 4 couples: 5 x 0.75⁴ x 0.25 = 0.3955
- 5 couples: 0.75⁵ = 0.2373
The probabilities for the outcomes where at least 4 couples have a baby of the preferred gender are 0.3955 and 0.2373, so the total probability is 0.3955 + 0.2373 = 0.6328.
Using the second method, we can calculate the probability that fewer than 4 couples have a baby of the preferred gender as follows:
- 0 couples: 0.25⁵ = 0.0009766
- 1 couple: 5 x 0.75 x 0.25⁴ = 0.01465
- 2 couples: 10 x 0.75² x 0.25³ = 0.08789
- 3 couples: 10 x 0.75³ x 0.25² = 0.2637
The probability that fewer than 4 couples have a baby of the preferred gender is the sum of these probabilities: 0.0009766 + 0.01465 + 0.08789 + 0.2637 = 0.3672.
Therefore, the probability that at least 4 of the 5 couples will have a baby of the preferred gender is 1 - 0.3672 = 0.6328.
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Which expression is equivalent to 6\cdot 6^{-2}\normalsize?6⋅6
−2
?
The expression 6 * 6^(-2) is equivalent to 1/6.
Simplify this expression using the rule of exponents?We can simplify this expression using the rule of exponents that states a^m / a^n = a^(m-n), which gives:
6 * 6^(-2) = 6 / 6^2 = 6 / 36 = 1/6
Let's break down the expression and simplify it step by step:
6 * 6^(-2)
We start by evaluating the exponent, which means we take the reciprocal of 6^2:
6 * (1/6^2)
Now we simplify the denominator of the fraction:
6 * (1/36)
Finally, we can simplify the expression by dividing 6 by 36:
1/6
So, the expression 6 * 6^(-2) is equivalent to 1/6. This means that if we multiply 6 by 6 raised to the power of -2 (or 1/6^2), we get the same result as dividing 6 by 6^2 (or 36), which is 1/6.
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The bulldogs, a baseball team, has nine starting players the height of the starting players are 72in 71in 78in 70in 72in 72in 73in 70in and 72 in which team best describes the data value 78 in
The value 78 inches best describes the tallest player on the Bulldogs baseball team. This height is an outlier within the data set and may affect statistical analyses.
The Bulldogs, a baseball team, consists of nine starting players with varying heights. Their heights are as follows: 72 in, 71 in, 78 in, 70 in, 72 in, 72 in, 73 in, 70 in, and 72 in. To describe the data, we can analyze the presence of the 78 in height value.
In this case, the value 78 in represents the tallest player on the team. When examining this data set, it is important to understand how this value affects the overall distribution of heights among the players. One way to determine this is by calculating the mean, median, and mode of the height data.
The mean (average) height for the team is 71.22 inches, and the median (middle) value is 72 inches. The mode (most frequent) height is also 72 inches. The value 78 inches is above the mean and median values, indicating that it is an outlier, or a value that is significantly different from the majority of the other data points.
In conclusion, the value 78 inches best describes the tallest player on the Bulldogs baseball team. This height is an outlier within the data set and may affect statistical analyses. However, it provides valuable information about the diversity of heights among the starting players on the team.
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During the basketball game, you record the number of rebounds from missed shots for each team. (a) describe the likelihood that your team rebounds the next missed shot. (B) how many rebounds should ur team expect to have in 15 missed shots
In the event of describing the likelihood that the team rebounds the next missed shot is likely, and the number of rebounds that the team should expect to have missed in 15 shots is 10.5 rebounds.
Given
Number of shots missed by the given team is 7
Total number of shots fired is 10
a) Then, moving on to the first part of the question
Here we have to apply probability to evaluate the likelihood of the given team rebounds the next missed shot.
Then,
Probability = no of shots attended / total number of shots fired
Probability = 7 /10
Then the event is likely
b) Now the second part
Then the number of rebounds the given team expect to have in the next 15 missed shots
= 7/10 ×15
= 105/10
= 10.5 rebounds
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a ferris wheel has a diameter of 54 ft. the point o is the center of the wheel. after the wheel has turned a 9 ft distance d, the point p moves to a new point marked q below. what is the measure of the angle 0 in radians
The angle measure is given as follows:
θ = 1/3 radians.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the equation presented as follows:
C = 2πr.
The radius is half the diameter, hence it is given as follows:
r = 27 ft. (half the diameter).
Hence the circumference is given as follows:
C = 54π cm.
The fraction represented by a distance of 9 ft is given as follows:
9/54π = 1/6π
The entire circumference is of 2π units, hence the angle is given as follows:
1/(6π) x 2π = 1/3 radians.
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Simplify to create an equivalent expression. {2(-2-4p)+2(-2p-1)}2(−2−4p)+2(−2p−1)
4(-2 - 4p) + 4(-2p - 1)
How can the expression {2(-2-4p)+2(-2p-1)} be simplified?To simplify the expression {2(-2-4p)+2(-2p-1)}, we can distribute the coefficients and simplify the terms.
First, let's distribute the coefficient of 2 to the terms inside the first parentheses: 2 * -2 = -4 and 2 * -4p = -8p.
Next, distribute the coefficient of 2 to the terms inside the second parentheses: 2 * -2p = -4p and 2 * -1 = -2.
Now, we have:
{-4 - 8p + (-4p - 2)}
Next, combine like terms within the parentheses:
{-4 - 8p - 4p - 2}
Simplifying further:
{-6 - 12p}
Therefore, the simplified equivalent expression for {2(-2-4p)+2(-2p-1)} is -6 - 12p.
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Josh and Draven can clean the JHS cafeteria in 25 minutes. Draven can clean the JHS cafeteria in 40 minutes. How long will it take Josh to do the job if he works alone?
It will take Josh about 66.67 minutes to easy the cafeteria alone.
Let's anticipate that the amount of work required to easy the cafeteria is 1 unit.
In a single minute, Josh can easy 1/x of the cafeteria (in which x is the number of mins it takes Josh to do the task alone), and Draven can clean 1/40 of the cafeteria in one minute.
When they work together, they could easy the cafeteria in 25 minutes, so in one minute they are able to easy 1/25 of the cafeteria.
The use of the fact that their combined rate is the sum in their individual rates, we are able to installation an equation:
1/x + 1/40 = 1/25
Multiplying each facets through the least common more than one of the denominators (40 * 25 * x), we get:
25 * 40 + x * 40 = x * 25
1000 + 40x = 25x
15x = 1000
x = 66.67
Therefore, it'd take Josh about 66.67 minutes to easy the cafeteria alone.
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The lengths of the sides of triangle XYZ are written in terms of the variable m, where m ≥ 6.
Triangle X Y Z is shown. The length of side X Y is m + 8, the length of side Y Z is 2 m + 3, the length of side Z X is m minus 3.
Which is correct regarding the angles of the triangle?
mAngleX < mAngleZ < mAngleY
mAngleY < mAngleZ < mAngleX
mAngleY < mAngleX < mAngleZ
mAngleZ < mAngleY < mAngleX
Answer:
In a triangle, the side opposite to the largest angle is the longest side, and the side opposite to the smallest angle is the shortest side. In triangle XYZ, the length of side XY is m + 8, the length of side YZ is 2m + 3, and the length of side ZX is m - 3. Since m ≥ 6, we can determine that 2m + 3 is the largest value, m + 8 is the next largest value, and m - 3 is the smallest value. Therefore, side YZ is the longest side and side ZX is the shortest side.
Since side YZ is the longest side, angle X must be the largest angle. Since side ZX is the shortest side, angle Y must be the smallest angle. Therefore, the correct ordering of the angles from smallest to largest is ∠Y < ∠Z < ∠X.
Step-by-step explanation:
PLEASE ANYONE 100 POINTS LOL
a ⃗=⟨-9,6⟩ and b ⃗=⟨3,1⟩. What is the component form of the resultant vector 1/3 a ⃗- 2b ⃗ ?
Show all your work.
The resultant component of the vector addition, 1/3a - 2b is (-9, 0).
What is the resultant component of the vectors?The resultant component of the vector is calculated as follows;
a = (-9, 6)
b = (3, 1)
The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)
The result of 2b = 2(3, 1) = (6, 2)
The result of the vector addition is calculated as follows;
1/3a - 2b
= (-3, 2) - (6, 2)
= (-3 -6, 2 -2)
= (-9, 0)
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If 2/3 of a mini pizza cost $2. 40, what would 1/2 of a mini pizza cost?
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
1/2 of a mini pizza would cost $0.60.
If 2/3 of a mini pizza cost $2.40, then 1/3 of a mini pizza would cost half of that:
1/3 of a mini pizza = 1/2 * $2.40 = $1.20
To find the cost of 1/2 of a mini pizza, we can divide the cost of 1/3 of a mini pizza by 2:
1/2 of a mini pizza = 1/2 * $1.20 = $0.60
Therefore, 1/2 of a mini pizza would cost $0.60.
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Recommendations for safely thawing frozen turkey are provided on the packaging.
a. What is the thaw rate of the turkey for refrigerator thawing?
For cold water thawing?
b. What could the initial value represent?
c. Write a linear function in the form y = mx + b to model the time t, in hours, it takes to thaw turkey in the refrigerator as a function of the weight w, in pounds, of the turkey.
a. The thaw rate of the turkey for refrigerator thawing is day(s) per pound.
(simplify your answer.)
(1) it takes about 10 hours to thaw a 20-pound turkey in cold water.(2) it takes an additional 0.25 hours (or 15 minutes) to thaw in the refrigerator.
What is a linear function and examples?A linear function is a function that represents a straight line in the coordinate plane. For example, y = 3x - 2 represents a straight line in the coordinate plane and thus a linear function. Since y can be replaced by the function f(x), this function can be written as f(x) = 3x - 2.
a. A typical thawing rate when thawing in the refrigerator is about 1 day per 4-5 kilograms of turkey meat. So if you have a 20 pound turkey, it will take about 4-5 days to thaw in the fridge. In cold water, the thawing rate is about 30 minutes per pound, so it takes about 10 hours to thaw a 20-pound turkey in cold water.
b) The initial value may represent the weight of the frozen turkey before thawing begins. c. Let y be the time it takes to thaw the turkey in hours and let x be the weight of the turkey in pounds. Assuming a linear relationship between melting time and weight, we can write:
y = mx + b
where m is the thaw rate (in hours per pound) and b is the intercept (the time it takes to thaw a 0-pound turkey, which is 0). From part a, we know that the refrigerator thaw rate is about 1 day per 4-5 pounds of turkey, or about 0.25-0.2 hours per pound. So we can use m = 0.25 in our linear function:
y = 0.25x + 0
This means that for every additional pound of turkey, it takes an additional 0.25 hours (or 15 minutes) to thaw in the refrigerator.
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The length of the radius of a sphere is 6 inches. The length of the radius of a cone is 3 inches, and the height is 7 inches. What is the difference between the volume of the sphere and the volume of the cone?
The difference between the volume of the sphere and the volume of the cone is approximately 838.81 cubic inches.
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius. Thus, for a sphere with a radius of 6 inches, the volume is:
V_sphere = (4/3)π(6³) = 904.78 cubic inches
The volume of a cone is given by the formula V = (1/3)πr[tex]^{2h}[/tex], where r is the radius and h is the height. Thus, for a cone with a radius of 3 inches and a height of 7 inches, the volume is:
V_cone = (1/3)π(3²)(7) = 65.97 cubic inches
Therefore, the difference between the volume of the sphere and the volume of the cone is:
V_sphere - V_cone = 904.78 - 65.97 = 838.81 cubic inches
Hence, the difference between the volume of the sphere and the volume of the cone is approximately 838.81 cubic inches.
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On Thursday,30 scholars went to morning homework help. On Friday, 24 scholars went. What is the percent decrease in the number of scholars who went to morning homework help from Thursday to Friday?
PLEASE HELP 20 POINTS
There is 20% decrease in scholars number who went to the morning homework help.
What is the percent decrease?To get the scholar's percent decrease, we need to calculate the difference between them on Thursday and Friday and theb divide that by the number of scholars on Thursday.
Data:
Number of scholars on Thursday = 30
Number of scholars on Friday = 24
Difference = 30 - 24 = 6
The percent decrease = (6/30) x 100%
The percent decrease = 0.2 * 100%
The percent decrease = 20%
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on yellow, P(not yellow).
The theoretical probability of the spinner not landing on yellow, would be 75 %.
How to find the probability ?In order to calculate the likelihood of the spinner not landing on yellow, it is necessary to initially identify the quantity of non-yellow partitions and subsequently divide this by the full tally of sections. The spinner comprises a total of 8 individual segments.
Of these, two (i.e., sections 2 and 3) are colored in shades of yellow, hence totaling two yellow sectors. This leaves a further six compartments - numbered 1, 4, 5, 6, 7 and 8, that do not fall into the category of "yellow."
The probability is therefore :
= ( Number of not yellow sections ) / ( Total number of sections )
= 6 / 8
= 3 / 4
= 75 %
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2. Hamilton claimed that there are only 4 circuits that begin with the letters LTSR Q. Find them. 3. Find all four possible Hamiltonian circuits that begin with JVTSR
To find the possible Hamiltonian circuits that begin with JVTSR, we can start by constructing a path that begins with JVTSR and visits each vertex exactly once. Such a path must be of the form JVTSRX, where X is the remaining vertex.
Case 1: JVTSRQX
To find the possible value of X, we note that the only edges incident to J are V and T, and the only edges incident to Q are S and R. Thus, we must have X = S or X = R, and the circuits are JVTSRQS and JVTSRQR.
Case 2: JVTSRXQ
To find the possible value of X, we note that the only edges incident to X are S and L. Thus, we must have X = L, and the circuit is JVTSRLQ.
Case 3: JVTSRLX
To find the possible value of X, we note that the only edges incident to J are V and T, and the only edges incident to L are T and R. Thus, we must have X = R, and the circuit is JVTSRLR.
Case 4: JVTSRXL
To find the possible value of X, we note that the only edges incident to Q are S and R, and the only edges incident to X are L and S. Thus, we must have X = L, and the circuit is JVTSRQL.
Therefore, there are four possible Hamiltonian circuits that begin with JVTSR: JVTSRQS, JVTSRQR, JVTSRLQ, and JVTSRLR.
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In 2000, 1500 rabbits live in a warren in a certain area. the number of rabbits increases exponentially at a discrete rate of 7% per year. predict population in 2008&2022
The predicted populations of rabbits in the warren in 2008 and 2022 are 2909 and 9933, respectively.
To predict the population of rabbits in the warren in 2008 and 2022, we can use the formula for exponential growth:
P(t) = P₀ (1 + r)ᵗ
Where P(t) is the population at time t, P₀ is the initial population, r is the growth rate, and t is the time elapsed.
For this problem, we know that P₀ = 1500, r = 0.07 (since the growth rate is 7%), and we want to find P(8) and P(22) (since we're predicting the population in 2008 and 2022, respectively).
Using the formula, we get:
[tex]P(8) = 1500( 1 + 0.07)^{8} = 2909[/tex]
So we can predict that there will be about 2909 rabbits in the warren in 2008.
To find P(22), we simply plug in t = 22:
[tex]P(22) = 1500 (1 + 0.07)^{22} = 9933[/tex]
So we can predict that there will be about 9933 rabbits in the warren in 2022.
Therefore, the predicted populations of rabbits in the warren in 2008 and 2022 are 2909 and 9933, respectively.
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This equation shows how the cost of a plumber's visit is related to its duration in hours. C = 51d
The variable d represents the duration of the visit in hours, and the variable c represents the cost. If a plumber's visit lasted 1 hour, how much would it cost?
The cost of a plumber's one-hour visit is $51, determined by the linear equation C = 51d, where C is the cost and d is the duration of the visit in hours.
How is the cost of a plumber's visit determined by duration?If a plumber's visit lasts for a certain duration, the cost can be determined using the equation
C = 51d
where C is the cost and d is the duration of the visit in hours.
In this case, the duration of the plumber's visit is given as 1 hour. Substituting d = 1 in the equation, we get
C = 51(1) = $51
as the cost of the plumber's visit.
Therefore, if the plumber's visit lasts for one hour, it would cost $51 according to the given equation.
This cost may vary if the duration of the visit changes, as it is directly proportional to the duration of the visit.
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Which of the equations shown have infinitely many solutions? Select all that apply. A. 3x – 1 = 3x + 1 B. 2x – 1 = 1 – 2x C. 3x – 2 = 2x – 3 D. 3(x – 1) = 3x – 3 E. 2x + 2 = 2(x + 1) F. 3(x – 2) = 2(x – 3)
The two equations with infinite solutions are D 3(x – 1) = 3x – 3 and E2x + 2 = 2(x + 1)
Which equations have infinite solutions?An equation has infinite solutions if we can remove the dependence of the variable, and we end with a true equation.
For example, option D is:
3(x - 1) =3x - 3
Expanding the left side:
3x - 3 = 3x - 3
Subtract 3x in both sides:
-3 = -3
That is true for any value of x.
The other correct option is E:
2x + 2 = 2(x + 1)
2x + 2 = 2x + 2
2 = 2
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Information into an equation and solve the
equation
The sum of a number n and 11 is equal to 25. Find the number n
The resultant equation is n + 11 = 25 and the number n is 14.
Algebraic equation:
An algebraic equation is a mathematical statement that equates two expressions using one or more variables. Solving a single variable equation can be done by adding or subtracting the same integer on both sides. Similarly multiplying or dividing by the same integer.
The information we have
The sum of a number n and 11 is equal to 25.
The statement can represent an equation and solve for n as follows
Here sum of two numbers indicates adding
Hence, n + 11 = 25
To solve for n, isolate n on one side of the equation.
This can be done by subtracting 11 from both sides of the equation:
=> n + 11 - 11 = 25 - 11
=> n = 14
Therefore,
The resultant equation is n + 11 = 25 and the number n is 14.
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"verify (1,4) is in point of √xy = x^2y − 2, also find
its tangent line to this point"
The equation of the tangent line to the curve at (1,4) is: y = 8x - 4
To verify whether the point (1,4) is on the curve [tex]\sqrt{xy}= x^2y - 2,[/tex]
We can substitute x=1 and y=4 into the equation and see if it is satisfied:
√(14) = 1^24 - 2
2 = 2
Since the equation is true, (1,4) is on the curve.
To find the tangent line to the curve at the point (1,4),
We need to find the derivative of the equation with respect to x and evaluate it at x=1:
[tex]\sqrt{xy} = x^2y - 2[/tex]
Differentiating with respect to x:
[tex](1/2)(x^{(-1/2))}(y) + (1/2)(y^{(-1/2))}(x) = 2xy[/tex]
Simplifying and evaluating at x=1, y=4:
[tex]2 + (1/2)(4^{(-1/2))(1)} = 8[/tex]
The slope of the tangent line is 8.
Using point-slope form, the equation of the tangent line to the curve at (1,4) is:
y - 4 = 8(x - 1)
y = 8x - 4
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Ben completely filled his 20-gallon tank of gas with regular fuel for $59. 80 as he left the gas station he noticed the gas station across the street sold regular fuel for $2. 84 a gallon how much money could ben have saved per gallon if he had gone to the gas station across the street
Ben could have saved $0.15 per gallon if he had gone to the gas station across the street.
If Ben filled his 20-gallon tank of gas with regular fuel for $59.80, then the cost per gallon can be found by dividing the total cost by the number of gallons:
cost per gallon = total cost / number of gallons
cost per gallon = $59.80 / 20 gallons
cost per gallon = $2.99/gallon
If the gas station across the street sold regular fuel for $2.84 a gallon, then the amount Ben could have saved per gallon is:
savings per gallon = cost per gallon at initial station - cost per gallon at other station
savings per gallon = $2.99/gallon - $2.84/gallon
savings per gallon = $0.15/gallon
Therefore, Ben could have saved $0.15 per gallon if he had gone to the gas station across the street.
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The velocity of a particle moving in a straight line is given by v = t(t^2 + 1)^3 + 3t. (a) Find an expression for the position s after a time t. (Use C for the constant of integration)
S =
The position of particle in a straight line with v = t(t^2 + 1)³ + 3t is (1/8)t⁸ + (3/6)t⁶ + (3/4)t⁴ + 2t² C.
To find an expression for the position s after a time t, we need to integrate the velocity function v with respect to time t.
Using the power rule of integration and the constant of integration C, we have:
s = ∫v dt = ∫[t(t² + 1)³ + 3t] dt
after expanding t(t² + 1)³ using binomial theorem we have-
(t^2 + 1)³ = t⁶ + 3t⁴ + 3t² + 1
Substituting this into the integral, we get:
s = ∫[t(t⁶ + 3t⁴ + 3t^2 + 1) + 3t] dt
s = ∫[t^7 + 3t⁵ + 3t³ + t + 3t] dt
s = ∫t^7 dt + 3∫t⁵ dt + 3∫t³ dt + ∫4t dt
s = (1/8)t⁸ + (3/6)t⁶ + (3/4)t⁴ + 2t² + C
Therefore, the expression for the position s after a time t is:
S = (1/8)t⁸ + (3/6)t⁶ + (3/4)t⁴ + 2t² + C, where C is the constant of integration.
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A spinner with 6 equally sized slices has 6 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellow slice?
Answer:
1
Step-by-step explanation:
